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Name __________________
Chemical Kinetics Unit 5 (sev e n c l ass per io ds )
Unit 51 Collision Theory amp Potential Energy Diagrams
1) Collision theory -- Reactions only occur if reactants collide with enough
energy amp in the correct orientation
a) Reactions that produce products are known as fruitful collision
b) The energy they need to have when they collide is known as the
activation energy It an amount of energy needed to overcome
their intramolecular attraction to convert shift those attractions to
another atom or groups of atoms
2) The rate of fruitful can be seen if we graph the concentration of each species of a reaction
a) The rate of a reaction is how quickly the molarity (119898119900119897119871frasl ) of reactants or
products changes over time Therefore its units are 119872 119904119890119888frasl or 119898119900119897
119871lowast119904119890119888
b) The rate of a reaction can only be determined experimentally and in second year
chemistry (AP Chemistry) we will do just that For now just know that it is
possible to change the rate of a reaction a couple of ways
3) How to speed up a chemical reaction
a) Increase the concentration of the particles ndash the more particles you have in the reaction container the more
likely they are to collide with sufficient energy and in the correct orientation to produce a product
b) Increase the amount of particles ndash the more particles you have in the reaction container the more likely they
are to collide with sufficient energy and in the correct orientation to produce a product
c) Speed up the particles of the reaction ndash by increasing the speed of the particles you increase the number of
them that have sufficient energy when they collide to overcome their activation energy
i) Heat lsquoem up speed lsquoem up
ii) Generally every 10oC increase in temperature doubles the rate of the reactions
d) Break up clumps to increase surface area ndash when particles are clumped together they insulate particles on the
inside from colliding By breaking solids up you allow more locations for collisions to occur
e) Add a catalyst ndash catalysts lower the activation energy of a reaction thus allowing more collisions to overcome
this obstacle
4) Enthalpy (H)
a) The potential energy stored in a substances bonds we sometimes refer to it as heat
b) However it is always a massive number therefore we focus on the change in this value
c) For a reaction to occur the bonds holding the reactants together must
be broken before the bonds of a product can form
i) When bonds break energy must be absorbed
ii) When bonds are formed energy is released
d) The change in enthalpy between your reactants and products is known
as the heat or enthalpy of the reaction
e) When energy is absorbed the reaction is said to be endothermic
f) When energy is released the reaction is said to be exothermic
Products Because they are appearing
Reactants Because they are being used up
5) Potential energy diagrams
a) Graphical representation of the enthalpy of a reaction as it proceeds
b) Shows the enthalpy of the reaction (Hrxn) and can be calculated as products ndash reactants
c) Reactants are always on the left and products are always on the left
d) A catalyst lowers the activation energy by either providing an additional lower energy pathway or by orienting
the reactants
6) Maxwell-Boltzmann Distributions
a) You can mark the position of activation energy Ea on a Maxwell-
Boltzmann distribution to get a diagram like the one shown right If
the temperature is increased the molecules speed up and collide
more frequently with more energetic collisions
b) Only those particles represented by the area to the right of the
activation energy mark will react when they collide The great
majority dont have enough energy and will simply bounce apart
c) If we increase the temperature from T1 to T2 more molecules are
energetic enough to achieve the Ea thus more molecules react and
the overall reaction rate increases Notice how many more molecules
are to the right of the activation energy and thus will react when they
collide
d) A general rule of thumb is that reaction rate doubles for each 10 1048689C rise in temperature
7) Chemical Reaction Rates
a) The speed of a reaction is expressed in terms of its ldquoraterdquo which is equal to some measurable quantity that is
changing with time
b) The rate of a chemical reaction is measured by the decrease in concentration of a reactant or an increase in
concentration of a product in a unit of time
c) Concentration can be abbreviated as [x] where x is the substance in question
119929119938119957119942 = minus∆[119955119951119957]
∆119957 119952119955
∆[119953119955119952119941]
∆119957
d) Rate is not constant it changes
with time Graphing the data of an
experiment will show an average
rate of reaction
e) Calculating the rate of a reaction
can be done a number of ways
i) Instanteous rate law ndash the rate
at a given moment
ii) Relative reaction rate ndash the rate of one species vs another
iii) Differential rate law ndash experimentally determined rate based on the
rate at the instant of mixing
iv) Integrated rate law ndash experimentally determined rate based on
mathematical manipulation of concentrations of
ONE substance over the course of time
8) Instataneous Reaction Rate
a) The rate at a given time
b) The slope (y=mx+b) of the tangent line is the reaction
rate
i) (+) for reactants
ii) (-) for products
9) Relative Reaction Rate
a) Rate relate to each other in the context of a given chemical system based on their stoichiometric values
Consider the reaction 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892)
b) reveals that oxygen gas can appear only half as rapidly as the nitrogen dioxide gas disappears while NO gas
appears twice as fast as oxygen appears
c) The simplest way to obtain relative rate expressions
i) place a one over each coefficient in the balanced equation
ii) make reactants negative (-) as they will be used up
iii) make products positive (+) as they will be produced
Exercise 1 Determine the rate of the species at the given
time
Reactant
10s
20s
Product
10s
20s
Co
mm
on
mu
ltip
le
cho
ice
que
stio
ns
Co
mm
on
FR
Q
qu
est
ion
s
d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor
to eliminate the fractions
For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121
52 Rate Law Expression
1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at
what exactly that means but for now it means we will need to look at the rate of reactions at the moment of
mixing
2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data
is obtained by
a Count number of bubbles of gas produce (capture volume by water displacement)
b Mass of precipitate formed
c spectrophotometry
3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense
tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is
some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is
k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B
Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio
4 1198751198673 rarr 1198754 + 6 1198672
Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of
nitrosyl chloride NOCl
2 119873119874119862119897 rarr 2 119873119874 + 1198621198972
119886119860 + 119887119861 rarr 119909119883
Rate Law written as
119929119938119957119942 = 119948[119912]119950[119913]119951
Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION
a Rate constant (k)
i A lower case k we will use the upper case for another constant later
ii Varies wildly with temperature
iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897
119871 119905119894119898119890 or
119872
119905119894119898119890)
b Orders of reaction with respect for each reagent
i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe
reaction is zero order with respect to Ardquo
ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)
Say ldquoThe reaction is 1st order with respect to Ardquo
iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe
reaction is 2nd order with respect to Ardquo
THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS
4 Differential Rate law
a Examining Concentration vs rate data Allows you to determine the rate expression
b Two methods
i Table logic
1 look at the data find two experiments where one reactant is static and the other makes
a measureable change see how the rate reacts Which order is that
2 Pros Fast Good for MC
3 Cons requires you recognize the math on FRQs requires exact explanations
YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while
reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the
reaction is ltordergt with respect to ltBgtrdquo
ii Dirty quick math
1 Since any value divided by itself is 1 we could set two
experimental data sets us a fraction and they should
cancel out
I suggest you put the experiment with the larger values as the numerator
2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with
respect to ltBgtrdquo
3 Cons MUCH slower
c Determining K
i Value ndash simply plug any experiment into the rate law you determined and solve for k
ii Units
1 Since rate MUST be 119898119900119897
119871 119905119894119898119890 k must have units that cancel out the concentrations and
provides that time unit
2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1
119871(119874119860119874minus1)
119898119900119897(119874119860119874minus1) 119905119894119898119890 or
1
119872(119874119860119874minus1) 119905119894119898119890
On the next two pages please take notes on BOTH ways to do the same problem
1199031198861199051198902 = 1198962[119860]2119898[119861]2
119899
1199031198861199051198901 = 1198961[119860]1119898[119861]1
119899
Exercise 4a Table logic
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
5) Potential energy diagrams
a) Graphical representation of the enthalpy of a reaction as it proceeds
b) Shows the enthalpy of the reaction (Hrxn) and can be calculated as products ndash reactants
c) Reactants are always on the left and products are always on the left
d) A catalyst lowers the activation energy by either providing an additional lower energy pathway or by orienting
the reactants
6) Maxwell-Boltzmann Distributions
a) You can mark the position of activation energy Ea on a Maxwell-
Boltzmann distribution to get a diagram like the one shown right If
the temperature is increased the molecules speed up and collide
more frequently with more energetic collisions
b) Only those particles represented by the area to the right of the
activation energy mark will react when they collide The great
majority dont have enough energy and will simply bounce apart
c) If we increase the temperature from T1 to T2 more molecules are
energetic enough to achieve the Ea thus more molecules react and
the overall reaction rate increases Notice how many more molecules
are to the right of the activation energy and thus will react when they
collide
d) A general rule of thumb is that reaction rate doubles for each 10 1048689C rise in temperature
7) Chemical Reaction Rates
a) The speed of a reaction is expressed in terms of its ldquoraterdquo which is equal to some measurable quantity that is
changing with time
b) The rate of a chemical reaction is measured by the decrease in concentration of a reactant or an increase in
concentration of a product in a unit of time
c) Concentration can be abbreviated as [x] where x is the substance in question
119929119938119957119942 = minus∆[119955119951119957]
∆119957 119952119955
∆[119953119955119952119941]
∆119957
d) Rate is not constant it changes
with time Graphing the data of an
experiment will show an average
rate of reaction
e) Calculating the rate of a reaction
can be done a number of ways
i) Instanteous rate law ndash the rate
at a given moment
ii) Relative reaction rate ndash the rate of one species vs another
iii) Differential rate law ndash experimentally determined rate based on the
rate at the instant of mixing
iv) Integrated rate law ndash experimentally determined rate based on
mathematical manipulation of concentrations of
ONE substance over the course of time
8) Instataneous Reaction Rate
a) The rate at a given time
b) The slope (y=mx+b) of the tangent line is the reaction
rate
i) (+) for reactants
ii) (-) for products
9) Relative Reaction Rate
a) Rate relate to each other in the context of a given chemical system based on their stoichiometric values
Consider the reaction 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892)
b) reveals that oxygen gas can appear only half as rapidly as the nitrogen dioxide gas disappears while NO gas
appears twice as fast as oxygen appears
c) The simplest way to obtain relative rate expressions
i) place a one over each coefficient in the balanced equation
ii) make reactants negative (-) as they will be used up
iii) make products positive (+) as they will be produced
Exercise 1 Determine the rate of the species at the given
time
Reactant
10s
20s
Product
10s
20s
Co
mm
on
mu
ltip
le
cho
ice
que
stio
ns
Co
mm
on
FR
Q
qu
est
ion
s
d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor
to eliminate the fractions
For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121
52 Rate Law Expression
1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at
what exactly that means but for now it means we will need to look at the rate of reactions at the moment of
mixing
2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data
is obtained by
a Count number of bubbles of gas produce (capture volume by water displacement)
b Mass of precipitate formed
c spectrophotometry
3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense
tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is
some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is
k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B
Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio
4 1198751198673 rarr 1198754 + 6 1198672
Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of
nitrosyl chloride NOCl
2 119873119874119862119897 rarr 2 119873119874 + 1198621198972
119886119860 + 119887119861 rarr 119909119883
Rate Law written as
119929119938119957119942 = 119948[119912]119950[119913]119951
Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION
a Rate constant (k)
i A lower case k we will use the upper case for another constant later
ii Varies wildly with temperature
iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897
119871 119905119894119898119890 or
119872
119905119894119898119890)
b Orders of reaction with respect for each reagent
i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe
reaction is zero order with respect to Ardquo
ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)
Say ldquoThe reaction is 1st order with respect to Ardquo
iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe
reaction is 2nd order with respect to Ardquo
THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS
4 Differential Rate law
a Examining Concentration vs rate data Allows you to determine the rate expression
b Two methods
i Table logic
1 look at the data find two experiments where one reactant is static and the other makes
a measureable change see how the rate reacts Which order is that
2 Pros Fast Good for MC
3 Cons requires you recognize the math on FRQs requires exact explanations
YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while
reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the
reaction is ltordergt with respect to ltBgtrdquo
ii Dirty quick math
1 Since any value divided by itself is 1 we could set two
experimental data sets us a fraction and they should
cancel out
I suggest you put the experiment with the larger values as the numerator
2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with
respect to ltBgtrdquo
3 Cons MUCH slower
c Determining K
i Value ndash simply plug any experiment into the rate law you determined and solve for k
ii Units
1 Since rate MUST be 119898119900119897
119871 119905119894119898119890 k must have units that cancel out the concentrations and
provides that time unit
2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1
119871(119874119860119874minus1)
119898119900119897(119874119860119874minus1) 119905119894119898119890 or
1
119872(119874119860119874minus1) 119905119894119898119890
On the next two pages please take notes on BOTH ways to do the same problem
1199031198861199051198902 = 1198962[119860]2119898[119861]2
119899
1199031198861199051198901 = 1198961[119860]1119898[119861]1
119899
Exercise 4a Table logic
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
d) Rate is not constant it changes
with time Graphing the data of an
experiment will show an average
rate of reaction
e) Calculating the rate of a reaction
can be done a number of ways
i) Instanteous rate law ndash the rate
at a given moment
ii) Relative reaction rate ndash the rate of one species vs another
iii) Differential rate law ndash experimentally determined rate based on the
rate at the instant of mixing
iv) Integrated rate law ndash experimentally determined rate based on
mathematical manipulation of concentrations of
ONE substance over the course of time
8) Instataneous Reaction Rate
a) The rate at a given time
b) The slope (y=mx+b) of the tangent line is the reaction
rate
i) (+) for reactants
ii) (-) for products
9) Relative Reaction Rate
a) Rate relate to each other in the context of a given chemical system based on their stoichiometric values
Consider the reaction 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892)
b) reveals that oxygen gas can appear only half as rapidly as the nitrogen dioxide gas disappears while NO gas
appears twice as fast as oxygen appears
c) The simplest way to obtain relative rate expressions
i) place a one over each coefficient in the balanced equation
ii) make reactants negative (-) as they will be used up
iii) make products positive (+) as they will be produced
Exercise 1 Determine the rate of the species at the given
time
Reactant
10s
20s
Product
10s
20s
Co
mm
on
mu
ltip
le
cho
ice
que
stio
ns
Co
mm
on
FR
Q
qu
est
ion
s
d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor
to eliminate the fractions
For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121
52 Rate Law Expression
1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at
what exactly that means but for now it means we will need to look at the rate of reactions at the moment of
mixing
2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data
is obtained by
a Count number of bubbles of gas produce (capture volume by water displacement)
b Mass of precipitate formed
c spectrophotometry
3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense
tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is
some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is
k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B
Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio
4 1198751198673 rarr 1198754 + 6 1198672
Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of
nitrosyl chloride NOCl
2 119873119874119862119897 rarr 2 119873119874 + 1198621198972
119886119860 + 119887119861 rarr 119909119883
Rate Law written as
119929119938119957119942 = 119948[119912]119950[119913]119951
Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION
a Rate constant (k)
i A lower case k we will use the upper case for another constant later
ii Varies wildly with temperature
iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897
119871 119905119894119898119890 or
119872
119905119894119898119890)
b Orders of reaction with respect for each reagent
i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe
reaction is zero order with respect to Ardquo
ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)
Say ldquoThe reaction is 1st order with respect to Ardquo
iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe
reaction is 2nd order with respect to Ardquo
THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS
4 Differential Rate law
a Examining Concentration vs rate data Allows you to determine the rate expression
b Two methods
i Table logic
1 look at the data find two experiments where one reactant is static and the other makes
a measureable change see how the rate reacts Which order is that
2 Pros Fast Good for MC
3 Cons requires you recognize the math on FRQs requires exact explanations
YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while
reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the
reaction is ltordergt with respect to ltBgtrdquo
ii Dirty quick math
1 Since any value divided by itself is 1 we could set two
experimental data sets us a fraction and they should
cancel out
I suggest you put the experiment with the larger values as the numerator
2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with
respect to ltBgtrdquo
3 Cons MUCH slower
c Determining K
i Value ndash simply plug any experiment into the rate law you determined and solve for k
ii Units
1 Since rate MUST be 119898119900119897
119871 119905119894119898119890 k must have units that cancel out the concentrations and
provides that time unit
2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1
119871(119874119860119874minus1)
119898119900119897(119874119860119874minus1) 119905119894119898119890 or
1
119872(119874119860119874minus1) 119905119894119898119890
On the next two pages please take notes on BOTH ways to do the same problem
1199031198861199051198902 = 1198962[119860]2119898[119861]2
119899
1199031198861199051198901 = 1198961[119860]1119898[119861]1
119899
Exercise 4a Table logic
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
d) You will OFTEN be asked to express this as a ratio To do that Simply multiply ALL the terms by the same factor
to eliminate the fractions
For 2 1198731198742(119892) rarr 2 119873119874(119892) + 1 1198742(119892) the ratio would be -121
52 Rate Law Expression
1 Most reactions are reversible meaning that products can combine to form reactants In unit 7 we will look at
what exactly that means but for now it means we will need to look at the rate of reactions at the moment of
mixing
2 The rate of the reaction is determined experimentally (I will give you data which you have to analyze) This data
is obtained by
a Count number of bubbles of gas produce (capture volume by water displacement)
b Mass of precipitate formed
c spectrophotometry
3 we will look only at reactants since at the moment of mixing there shouldnrsquot be any products Common sense
tells us that ratereaction [reactants] mathematically a proportion () can be replaced with ldquo= krdquo where k is
some constant This is how we got all those gas laws in unit 3 thus a rate expressions general format is
k = rate constant [A] = concentration of reactant A [B] = concentration of reactant B m = order of reaction for reactant A n = order of reaction for reactant B
Exercise 2 What is the relative reaction rate for the reaction below What is the whole number ratio
4 1198751198673 rarr 1198754 + 6 1198672
Exercise 3 Write the relative rates of change in concentration of the products and reactant in the decomposition of
nitrosyl chloride NOCl
2 119873119874119862119897 rarr 2 119873119874 + 1198621198972
119886119860 + 119887119861 rarr 119909119883
Rate Law written as
119929119938119957119942 = 119948[119912]119950[119913]119951
Can be zero whole numbers or fractions CAN ONLY BE DETERMINED BY EXPERIMENTATION
a Rate constant (k)
i A lower case k we will use the upper case for another constant later
ii Varies wildly with temperature
iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897
119871 119905119894119898119890 or
119872
119905119894119898119890)
b Orders of reaction with respect for each reagent
i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe
reaction is zero order with respect to Ardquo
ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)
Say ldquoThe reaction is 1st order with respect to Ardquo
iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe
reaction is 2nd order with respect to Ardquo
THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS
4 Differential Rate law
a Examining Concentration vs rate data Allows you to determine the rate expression
b Two methods
i Table logic
1 look at the data find two experiments where one reactant is static and the other makes
a measureable change see how the rate reacts Which order is that
2 Pros Fast Good for MC
3 Cons requires you recognize the math on FRQs requires exact explanations
YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while
reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the
reaction is ltordergt with respect to ltBgtrdquo
ii Dirty quick math
1 Since any value divided by itself is 1 we could set two
experimental data sets us a fraction and they should
cancel out
I suggest you put the experiment with the larger values as the numerator
2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with
respect to ltBgtrdquo
3 Cons MUCH slower
c Determining K
i Value ndash simply plug any experiment into the rate law you determined and solve for k
ii Units
1 Since rate MUST be 119898119900119897
119871 119905119894119898119890 k must have units that cancel out the concentrations and
provides that time unit
2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1
119871(119874119860119874minus1)
119898119900119897(119874119860119874minus1) 119905119894119898119890 or
1
119872(119874119860119874minus1) 119905119894119898119890
On the next two pages please take notes on BOTH ways to do the same problem
1199031198861199051198902 = 1198962[119860]2119898[119861]2
119899
1199031198861199051198901 = 1198961[119860]1119898[119861]1
119899
Exercise 4a Table logic
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
a Rate constant (k)
i A lower case k we will use the upper case for another constant later
ii Varies wildly with temperature
iii Units are required so that rate is measured in concentration for each unit of time (119898119900119897
119871 119905119894119898119890 or
119872
119905119894119898119890)
b Orders of reaction with respect for each reagent
i Zero order ndash changing the concentration of this reactant has no effect on the rate Say ldquoThe
reaction is zero order with respect to Ardquo
ii First order ndash doubling the concentration doubles the rate of the reaction (all nuclear decay is 1st order)
Say ldquoThe reaction is 1st order with respect to Ardquo
iii Second order ndash doubling the concentration quadruples the rate of the reaction Say ldquoThe
reaction is 2nd order with respect to Ardquo
THE OVER ALL ORDER IS THE SUM OF ALL THE REACTION ORDERS
4 Differential Rate law
a Examining Concentration vs rate data Allows you to determine the rate expression
b Two methods
i Table logic
1 look at the data find two experiments where one reactant is static and the other makes
a measureable change see how the rate reacts Which order is that
2 Pros Fast Good for MC
3 Cons requires you recognize the math on FRQs requires exact explanations
YOU MUST explain it as ldquoIn experiments ltXgt amp ltYgt reactant ltAgt is constant while
reactant ltBgt ltmakes changegt and the rate ltmakes changegt This shows the
reaction is ltordergt with respect to ltBgtrdquo
ii Dirty quick math
1 Since any value divided by itself is 1 we could set two
experimental data sets us a fraction and they should
cancel out
I suggest you put the experiment with the larger values as the numerator
2 Pros never fails is its own explaination you only need to say ldquoreaction is ltordergt with
respect to ltBgtrdquo
3 Cons MUCH slower
c Determining K
i Value ndash simply plug any experiment into the rate law you determined and solve for k
ii Units
1 Since rate MUST be 119898119900119897
119871 119905119894119898119890 k must have units that cancel out the concentrations and
provides that time unit
2 Therefore the units of k are always 1M to the -OAO (overall order of the reaction)-1
119871(119874119860119874minus1)
119898119900119897(119874119860119874minus1) 119905119894119898119890 or
1
119872(119874119860119874minus1) 119905119894119898119890
On the next two pages please take notes on BOTH ways to do the same problem
1199031198861199051198902 = 1198962[119860]2119898[119861]2
119899
1199031198861199051198901 = 1198961[119860]1119898[119861]1
119899
Exercise 4a Table logic
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Exercise 4a Table logic
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Exercise 4b dirty math
a) What is the order of the reaction with respect to A
b) What is the order of the reaction with respect to B
c) What is the value of the rate constant including units
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Exercise 5
Exercise 6
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
5) Reaction mechanisms
a) the sequence of bond-making and bond-breaking steps that occurs during the conversion of reactants to
products
i) Must be experimentally determined
ii) Must agree with the overall stoichiometry
iii) Must agree with the experimentally determined rate law
b) The vocabulary of mechanisms involves elementary steps amp molecularity which describes the number of
molecules that participate in an atomic rearrangement Add these terms into your explanations
i) unimolecular involves one reactant molecule that collides with a solvent or background molecule thereby
becoming collisionally activated In this state the reactant molecule is thermodynamically favorable for
converting into product
ii) bimolecular involves a collision between two reactant molecules
iii) termolecular simultaneous collision between three reactant molecules [very rare]
c) the rate expression cannot be predicted from overall stoichiometry The rate expression of an elementary step is
predicted from the stoichiometry of the elementary step as per the table below
d) Catalysts ndash species that are reactants in an elementary step but in subsequent steps is a product They LOWER
the activation energy amp donrsquot change H
i) Homogeneous catalyst ndash exist in the same phase as the reactants
ii) Heterogeneous catalyst ndash exist in a different phase than the reactants
e) Intermediaries ndashspecies that are products in an elementary step but in subsequent steps are reactants amp
consumed
i) Neither catalysts or intermediaries appear in the overall reaction or rate law
Exercise 7
Label the intermediaries amp catalysts
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
f) the slowest step is the rate determining step -- the rate of the overall reaction is limited by and is exactly equal
to the combined rates of all elementary steps up to and including the slowest step in the mechanism
Exercise 8
Exercise 9
In the reaction 2X+Y rarr Z
For a particular reaction the rate is found to be rate=k[Y]
Which of the below purposed mechanisms is a valid mechanism for this reaction
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
53 Rate Law Expression pt 2
1 Differential rate law
a Concentration vs rate data
b Use table logic or ugly algebra to find rate law amp value of K
2 Integrated rate law
a Concentration vs time data
b Must choose the straightest line graph and know what it means
c ONLY one reactant
d Done to determine how long a reaction must run to reach a certain concentration of reactant
e The value of the rate constant k is equal to the absolute value of the slope of the best fit line which is
decided by examining 3 linear regressions and analyzing the regression correlation coefficient (r)
i Graphs WILL be provided (except for the lab)
ii Time is ALWAYS X
iii The Y axi are
1 concentration of the reactant
2 natural log of the concentration (ln[A] NOT log[A])
3 reciprocal of the concentration on the y-axis of the third graph
iv If you remember them in this order with the y-axes being ldquoconcentrationrdquo ldquonatural log of
concentrationrdquo and ldquoreciprocal concentrationrdquo the alphabetical order of the y-axis variable
leads to 0 1 2 orders respectively for that reactant
REMEMBER what each variable is
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Exercise 10
y = -00002x + 00831Rsup2 = 08871
-005
0
005
01
015
0 200 400 600
[N2O5]
y = -00069x - 23026Rsup2 = 1
-6
-4
-2
0
0 200 400 600
Ln [N2O5] y = 03535x - 78441
Rsup2 = 08841
-100
0
100
200
0 200 400 600
1[N2O5]
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
$$
amp(
)$$+amp(
$ampamp()+$-$+++-amp
amp$$$
($$$$
(amp$$$
-$$$$
-amp$$$
0$$$$
0amp$$$
$ amp$ ($$ (amp$ -$$ -amp$ 0$$ 0amp$ $$
$amp
()amp
$+amp-amp()amp
1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
-amp0+
$0amp+
$0amp
$)amp
$)amp1
$)amp)
$)amp+
$)amp
+ ) 0 1 2
$$
amp(
)$$+amp(
$$amp()+(-
$+
0$$$
1$$$
2$$$
$$$
amp$$$$
ampamp$$$
amp($$$
amp-$$$
amp$$$
amp+$$$
$ amp$$$ ($$$ -$$$ $$$ +$$$ 0$$$ 1$$$
$amp
()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
$amp
()amp
$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
$$
amp(
)$$+amp(
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Unit 54 Kinetics Clean up
1 Half Life
a the time required for one half of one of the
reactants to disappear
b focus on the half-life for first order reactions only
i Discuss order (what order is it NOT)
ii Determine half life
iii What is the concentration after a set
number of half lives
iv What time would a set concentration be
found
2 In lab we will determine the order of a reaction by ldquoswampingrdquo We maximize one reactants concentration so
that ANY change is negligible
Exercise 11
a) What order is it NOT
b) Determine half life
c) What is the concentration after the second half life
d) When would 75 of the sample have decayed
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
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$0amp-
$0amp
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1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
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amp$
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amp$
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2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
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+amp)))-
$amp
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3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
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Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
For the generic reaction A + B C
1 The reaction below was studied at 25frac14C and the following data was obtained
NH4+ + NO2
N2 + 2H2O(L)
a What is the rate law
b What is the rate constant Be sure and include units
2 The reaction below was studied at 10frac14C and the following data was obtained
2NO(g) + Cl2(g) 2NOCl(g)
a What is the rate law
b What is the rate constant Be sure and include units
3 The reaction below was studied and the following data were obtained
2ClO2 + 2OH ClO3 + ClO2
+ H2O
a What is the rate law
b What is the rate constant Be sure and include units
4 The reaction below was studied and the following data were obtained
I + OCl IO + Cl
a What is the rate law
b What is the rate constant Be sure and include units
5 The reaction below was studied and the following data were obtained
BrO3 + 5 Br + 6 H+ 3 Br2 + 3 H2O
a What is the rate law
b What is the rate constant Be sure and include units
P E1 (pg 1 of 3) Using Initial Rates to Determine Order Name_____________________Per___
[NO]0
(molL)[Cl2]0
(molL)Initial Rate
(moleL min)
010 010 018
010 020 035
020 020 145
[I]0
(molL)[OCl]0
(molL)Initial Rate
(molL s)
012 018 791 102
006 018 395 102
003 009 988 103
024 009 791 102
[ClO2]0
(molL)[OH]0
(molL)Initial Rate
(molL s)
0050 0100 0057
0100 0100 023
0100 0050 0115
[NH4+]0
(molL)[NO2
]0
(molL)Initial Rate(moleL sec)
0100 0005 135 107
0100 0010 270 107
0200 0010 540 107
[BrO3]0
(molL)[Br]0
(molL)[H+]0
(molL)Initial Rate
(molL s)
0100 0100 0100 80 104
0200 0100 0100 16 103
0200 0200 0100 32 103
0100 0100 0200 32 103
trial[A]0
(molL)[B]0
(molL)Initial Rate
(moleL hour)
1 4 6 20
2 4 3 10
3 2 6 5
rate1
rate2=k
k
[A]ox
[A]ox
[B]oy
[B]oy
20
10=k
k
[4]ox
[4]ox
[6]oy
[3]oy
2 = [2]y
y = 1
20
5=k
k
[4]o
x
[2]o
x
[6]o
1
[6]o
1
4 = [2]x
x = 2 rate = k[A]2[B]
While it is most likely that any rate laws on the AP exam will only be first or second order it is possible that other orders will show up and are indeed possible When the order is not so obvious it is useful to know a useful log rule
RateRatio = [ConcRatio]x
log[RateRatio] = x log[ConcRatio] thus it is quite simple to solve for the order x log[RateRatio]
log[ConcRatio]= x
6 Given the hypothetical data below determine the order of the reaction A + B + C D + E
[A] (M) [B] (M) [C] (M) Rate (Msec)
10 10 10 00076
20 10 10 00304
10 10 20 00107
10 20 10 00152
7 Given the hypothetical data below determine the order of the reaction H + I + J K
[H] (M) [I] (M) [J] (M) Rate (Msec)
10 10 10 17
23 10 10 391
10 10 40 27
10 18 20 694
8 Given the hypothetical data below determine the order of the reaction P + Q + R S + T
[P] (M) [Q] (M) [R] (M) Rate (Msec)
10 10 10 00365
10 635 10 147
10 10 075 00274
19 47 23 185
9 Given the hypothetical data below determine the order of the reaction V + W + X Y + Z
[V] (M) [W] (M) [X] (M) Rate (Msec)
001 001 001 280 106
001 004 001 448 105
001 002 006 672 105
005 0025 0036 141 104
P E1 (pg 2 of 3) Using Initial Rates to Determine Order
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
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1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
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2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
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()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
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amp$$
$$
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Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Nitrogen dioxide will decompose into nitrogen oxide and oxygen gas as indicated in the equation below
2 NO2(g) 2 NO(g) + O2(g)
A graph of the concentration of each constituent at various times during the course of the reaction at 300frac14C is presented below Use this graph to understand that the loss of reactant and formation of products is stoichiometrically related
Decomposition of nitrogen dioxide
0
0002
0004
0006
0008
001
0012
0 100 200 300 400 500
time
co
nc
Next you can use the concentration of the reactant vs time data presented in the data table above and manipulate the concentration
values to ln[NO2] and 1
[NO2]
and then graph ln[NO2] vs time and also graph 1
[NO2]
vs time You can use these two graphs to
look for which of the graphs presented will give a straight line in order to determine the order of the reaction These two graphs are shown below
The r2 value which is the coefficient of determination you will learn more about r and r2 when you take a statistics course but for now you can think of it as a Ogravegoodness-of-fitOacute indicator The closer the r2 is to 1 the better the data fits to a straight line Thus
you can see that the r2 value is best for 1
[NO2]
vs time indicating this reaction is second order
P E2 (pg 1 of 6) Rate Laws Using data amp graphs Name_____________________Per____
Decomposition of Nitrogen Dioxide
time (sec) [NO2] [NO] [O2]
0 001 0 0
50 00079 00021 00011
100 00065 00035 00018
150 00055 00045 00023
200 00048 00052 00026
250 00043 00057 00029
300 00038 00062 00031
350 00034 00066 00033
400 00031 00069 00035
$amp()$amp+-
amp++
$-amp
$0amp(
$0amp-
$0amp
$0amp
$0amp
$amp(
$amp-
0 1 10 0 2 20 0
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1 The dimerization of butadiene is studied at 500 K and the following reaction and experimental data is presented below
2 C4H6(g) C8H12(g)
a Determine the rate law for this reaction
b Determine the rate constant
c Calculate the half-life for this reaction (If it is not 1st order calculate the half-life at the initial concentration)
P E2 (pg 2 of 6) Rate Law for Dimerization of Butadiene
Time (s) [C4H6(g)] (M)
0 00167
195 00160
604 00150
1246 00130
2180 00110
6210 00068
$
$
amp$
amp$
amp($
amp$
amp$
$ amp$ $ )$ ($ $ $ +$
$
amp$
()$+$amp$
$amp($)amp)+
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$0amp+
$0amp
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amp$$$
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()amp
$+amp-amp()amp
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
$amp($amp)
+amp)))-
$amp
$amp
$amp-
$amp
$amp0
$amp
amp
1 1
$$
amp(
)$$+amp(
$$$ampamp($))
+$-$
$0$
amp$$
amp0$
$$
0$
1$$
10$
$ 0$$ amp$$$ amp0$$ $$$
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$+amp-amp()amp
$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
$$$amp()$amp+
-$++
)$$
$$$
$$
amp$$
$$
$$
$$$
$$
amp$$
$$
$$
$$$
$$
$ 0$$ $$$ 0$$ $$$ 0$$ 1$$$ 10$$ amp$$$
$amp
()amp
$+amp-amp()amp
$amp($amp)
+amp-
$amp
$amp
$0amp
$0amp
$1amp
$1amp
$amp
amp
1 1 0 0 )
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amp(
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$
$
amp$
$
($
)$
$
+$
$
$
$ $ amp$ ($ $ $ $ amp$ ($ $ $
$
amp$
()$+$amp$
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
2 Dinitrogen pentoxide can be decomposed according to the reaction below
2 N2O5(soln) 4 NO2(soln) + O2(g) All Trials are performed at 45frac14C
Data for this reaction can be collected in different ways It is presented in two different ways below instantaneous rates for various concentrations and concentration at various time The concentration vs time data is graphed
Concentration and Initial Rates
a What are a few methods by which you could determine the reaction order
b What are several different methods by which you could determine the rate constant k
c What are a few different methods by which you could determine the half-life
P E2 (pg 3 of 6) Decomposition of Dinitrogen Pentoxide
[N2O5(solOtilden)] (molesL)
Instantaneous rate Msec
10 000060
050 000030
025 000015
Concentration vs Time DataConcentration vs Time Data
Time (s)[N2O5(solOtilden)] (molesL)
0 100
200 088
400 078
600 069
800 061
1000 054
1200 048
1400 043
1600 038
1800 034
2000 030
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3 The decomposition of hydrogen peroxide was studied at a particular temperature and experimental data is presented in the table to the right
2 H2O2(g) 2H2O(g) + O2(g)
a What are the two methods that you could use to determine the rate law for this reaction with the data that has been given
b Write out the rate law for this decomposition reaction
c What are the three methods that you could use to determine the rate constant
i Use the easiest of these two methods to determine a value for k
ii What are the units on k
d Now that you know the order of the reaction calculate the half-life for this reaction (if it is not 1st order calculate the half-life at the initial concentration)
yen Show how the conc vs time graph confirms the value that you calculated
P E3 (pg 4 of 6) Decomposition of H2O2
Time (s) [H2O2(g)] (moleL)
0 10
120 091
300 078
600 059
1200 037
1800 022
2400 013
3000 0082
3600 0050
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Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____
Please work in PENCIL Please put some work on the page that indicates HOW you did the problem
1 If a 84 g sample of thorium decays with a 10 minute half life how much would the sample weigh in a half hour
2 A sample of radioactive iodine (half life = 3 days) originally weighed 10 g but now weighs 0625 g How old is this sample
You can estimate the half life quickly and easily but youOtildell need a calculator to use the integrated rate equation and half life equations
3 A sample of radioactive calcium originally weighed 24 g and in 12 hours it weighs 125 g What is the half-life
4 If a 500 g sample of barium decays with a 45 day half life how much would the sample weigh in a 18 days
5 A sample of an ancient grass mat containing radioactive carbon (half life = 5730 years) seems to be emitting on 625 of the radiation that a sample of a grass mat woven last year would have How old is this ancient grass mat
6 A sample of radioactive calcium originally weighed 32 kg and in 2 days it weighs 05 kg What is the half-life in hours
7 If a 96 g sample of tin decays with a 25 minute half life how much would the sample weigh in 15 minutes
8 A sample of radioactive magnesium (half life = 183 days) originally weighed 80 g but now weighs 25 g How many years old is this sample
9 A sample of radioactive radium originally weighed 56 g and in three days it weighs just less than a gram What is the half life in hours
P E3 (pg 1 of 2) Half Life ETH The Rate of Radioactive Decay Name________________________Per____