Upload
letitia-heath
View
227
Download
1
Tags:
Embed Size (px)
Citation preview
Kinetics
Chemical kinetics is the study of the time dependence of chemical reactions.
Objectives Understand rates of reaction and the
conditions affecting rates Derive the rate equation, rate constant and
reaction order from experimental data Use integrated rate laws Understand the collision theory of reaction
rates and the role of activation energy Relate reaction mechanisms and rate laws
Kinetics
Reaction rate The change in concentration of a
reactant or product per unit time
timeinchange
ionconcentratinchangereactionofRate
t
ARate
][
Rate of Reaction Rate of reaction may be described based on
either the increase in concentration of a product or the decrease in concentration of a reactant per unit time Rates decrease with time Minus sign is required because the concentration
of A decreases with time, and the rate is always expressed as a positive quantity.
Instantaneous rate can be determined by finding the slope of a line tangent to a point representing a particular time.
Rate of Reaction
Decomposition of N2O5
2N2O5 4 NO2 + O2
Rate can be expressed as
t
ONRate
][ 52
Rate of Reaction
Rate could also be expressed in terms of the formation of NO2 or the rate of formation of O2. Rates expressed in these terms will have positive signs.
Formation of NO2 is 2x rate of decomposition of N2O5
Formation of O2 is one half of the rate of decomposition of N2O5
Rate of Reaction
Example Assume the disappearance of N2O5
between 40 min and 55 min is
min15
/12.0
min40min55
)/22.1()/10.1(][ 52 LmolLmolLmol
t
ON
min0080.0 52
L
consumedONmol
Rate of Reaction
Rate in terms of the appearance of NO2
consumedONmol
formedNOmol
L
consumedONmol
t
NORate
52
2522
2
4
min
0080.0][
min016.0 2
L
formedNOmol
Rate of Reaction
Rate in terms of the rate at which O2 is formed
consumedONmol
formedOmol
L
consumedONmol
t
ORate
52
2522
2
1
min
0080.0][
min0040.0 2
L
formedOmol
Rate of Reaction This procedure gives the average rate Graphing concentration vs. time does not
give a straight line because the rate of the reaction changes during the course of the reaction.
The instantaneous rate is given at a single point by drawing a line tangent to the concentration-time curve at a particular time and obtaining the slope of this line.
Rate of Reaction
Rate of Reaction
For this reaction, if the rate is measured at a range of instantaneous concentration during the experiment, a Rate vs. Concentration graph can be plotted. The resulting graph is given below:
Rate of Reaction
Rate of Reaction This graph shows that the rate of reaction is
directly proportional to the concentration of [N2O5]:
Rate = constant x [N2O5]
Rate = k[N2O5]
This expression is called a rate equation, where k is called the rate constant
Rate of Reaction
Summarizing the rate expressions
To equate rates of disappearance or appearance, divide [reagent]/t by the stoichiometric coefficient in the balanced chemical equation
t
O
t
NO
t
ON
][][
4
1][
2
1 2252
Rate of Reaction
PROBLEMGive the relative rates for the disappearance of reactants and formation of products for the following reaction:
4 PH3(g) P4(g) + 6 H2(g)
Rate of Reaction
PROBLEMData collected on the concentration of dye as a function of time are given in the graph below. What is the average rate of change of the dye concentration over the first 2 minutes? What is the average rate of change during the fifth minute (from t = 4 to t = 5)? Estimate the instantaneous rate at 4 minutes.
Rate of Reaction
Rate Laws
Reversibility of Reactions For the reaction 2N2O5 4 NO2 + O2
the reverse reaction may also take place The reverse reaction effects the rate of
change in concentration [N2O5] depends on the difference in the
rates of the forward, kf, and the reverse, kb, reactions
Reaction Conditions and Rate
Molecular collisions required for reaction to take place. Atoms and molecules are mobile (mixture of gases or using solutions of reactants)
Under these conditions several factors affect the rate of reaction
Reaction Conditions and Rate
Concentration Temperature Catalyst Surface area (if reactant is a solid)
Effect of Concentration
Rate Equation Relationship between reactant
concentration and reaction rate is expressed by the rate equation or rate law. For our example, N2O5
Rate of Reaction = k[N2O5]
Effect of Concentration
k = proportionality constant = rate constant at a given temperature
Rate equation indicates reaction rate is proportional to the concentration of the reactant
[N2O5] doubles as the rate doubles
Effect of Concentration
In general,aA + bB xX
Rate equation formRate = k[A]m[B]n
m and n are not necessarily the stoichiometric coeffcients (a and b). The exponents must be determined by experiment. m and n may be positive, negative, fractions or zero
Order of Reaction
Order of a reaction is with respect to a particular reactant is the exponent of its concentration in the rate expression
Total reaction order is the sum of the exponents
Order of Reaction
Example Decomposition of H2O2 in the
presence of iodide ion (clock reaction) Reaction rate = k[H2O2][I-] Reaction is first order with respect to
H2O2 and I-; second order overall.
Order of Reaction
So, what does it mean? Rate doubles if either H2O2 or I- is
doubled and rate increases by a factor of 4 if both concentrations are doubled.
Order of Reaction
Let’s consider the following rate law
Rate = k[NO]2[Cl2]
Reaction rate is second order in NO Reaction rate is first order in Cl2 Overall third order
Order of Reaction
Let’s look at some data
Exp [NO] M [Cl2] M Rate M∙s-1
1 0.250 0.250 1.43 x 10-6
2 0.500 0.250 5.72 x 10-6
3 0.250 0.500 2.86 x 10-6
4 0.500 0.500 11.4 x 10-6
Order of Reaction
Exp 1 & 2 – [Cl2] held constant; [NO] is 2x; reaction rate increases by factor of 4
Exp 1, 3, 4 – Compare 1 & 3; [NO] held constant, [Cl2] 2x; rate doubles compare 1& 4; [NO] and [Cl2] 2x; rate 8x original value
1
4
/1043.1
/1072.5
1
26
6
sLmolx
sLmolx
ExpRate
ExpRate
Rate Constant k
Reaction rates ([A]/t) have units of mol/L∙time when [ ] are given as moles/L
Rate constants must have units consistent with the units for the other terms in the rate equation
Rate Constant k
1st order reactions: units of k are time-
1
2nd order reactions: units of k are L/mol∙time
zero order reactions: units of k are mol/L∙time
Determining a Rate Equation
“Method of Initial Rates” Initial rate (instantaneous reaction
rate at start of reaction (rate at t = 0) Mix reactants then determine
[products]/t or -[reactants]/t after 1% or 2% of limiting reactant has been used up.
Determining a Rate Equation
ExampleCH3CO2CH3(aq) + OH-(aq) CH3CO2
-(aq) + CH3OH(aq)
Initial Concentrations Initial Rxn Rate
Exp [CH3CO2CH3 ] M
[OH-] M M∙s-1
1 0.050 0.050 0.00034
no change x 2 x 2
2 0.050 0.10 0.00069
x 2 no change x 2
4 0.10 0.10 0.00137
Determining a Rate Equation
When initial [reactant] is 2x while other [reactant] held constant, initial rxn rate 2x
Reaction is directly proportional to the concentrations of both reactants
Reaction is first order in each reactantRate = k[CH3CO2CH3][OH-]
Determining a Rate Equation
If rate equation is known, the value of k can be found by substituting values for the rate and concentration into rate equation
Determining a Rate Equation
Using our example Substitute data from one of the
experiments into the rate equation
L
mol
L
molk
sL
molRate
050.0050.000034.0
smolLLmolLmol
sLmolk
/14.0
/050.0/050.0
/00034.0
Integrated Rate Laws
What are they? Equations that describe
concentration-time curvesWhy use them? Calculate a concentration at any
given time Find length of time needed for a given
amount of reactant to react
First Order Reactions
If reaction ‘A products’ is first order, the reaction rate is directly proportional to [A]1
A little calculus…
][][
Akt
A
First Order Reactions
Integrated rate equation
Where [A]0 and [A]t are concentrations of reactants at time t = 0 and at a later time, t
This ratio is the fraction of reactant that remains after a given time has elapsed.
ktA
A t 0][
][ln
First Order Reactions
Negative sign (-) means ratio is less than 1 because [A]t is always less than [A]0.
Logarithm of ratio is negative therefore other side of equation must be negative
First Order Reactions
Equation is useful in three ways: If [A]t/[A]0 is measured after some amount
of time has elapsed then k can be calculated
2. If [A]0 and k are known than [A]t can be calculated (amount remaining after a given amount of time
3. If k is known, then time elapsed until a specific fraction ([A]t/[A]0) remains can be calculated
First Order Reactions
Note k for 1st order reactions is
independent of concentration; k has units of time-1
Therefore any unit for [A]t and [A]0 can be chosen (M, mol, g, atoms, molecules, pressure)
First Order ReactionsPROBLEM
When heated cyclopropane rearranges to propene in a first order process
Rate = k[cyclopropane] k = 5.4 x 10-2 h-1
If the initial concentration of cyclopropane is 0.050 mol/L, how much time (in hours) must elapse for its concentration to drop to 0.010 mol/L
First Order Reactions
SOLUTION
ktnecyclopropa
necyclopropa t 0][
][ln
thx )104.5(]050.0[
]010.0[ln 12
hhxhx
t .30104.5
)61.1(
104.5
)20.0ln(1212
Second Order Reactions
If reaction ‘A products’ is second order, the reaction rate equation is
A little calculus again…
2][][
Akt
A
Second Order Reactions
Integrated rate equation
In this case k is the second-order rate constant (L/mol ∙ time)
ktAA t
0][
1
][
1
Second Order ReactionsPROBLEM
The gas-phase decomposition of HIHI(g) ½ H2(g) + ½ I2(g)
has the rate equation
Where k = 30. L/mol ∙ min at 443C. How much time does it take for the concentration of HI to drop from
0.010 mol/L to 0.0050 mol/L at 443C?
2][][
HIkt
HI
Second Order Reactions
SOLUTION
tmolLLmolLmol
min/.30/010.0
1
/0050.0
1
tmolLmolLxmolLx min/.30/100.1/100.2 22
min3.3t
Zero Order Reactions
If reaction ‘A products’ is zero order, the reaction rate equation is
A little calculus again…
0][][
Akt
A
Zero Order Reactions
Integrated rate equation
Where k has the units mol/L ∙ s
ktAA t ][][ 0
Graphical Methods for Determining Reaction Order and the Rate Constant
First Order
[A]t = - kt + [A]0
y mx b
Graphical Methods for Determining Reaction Order and the Rate Constant
Second Order
1/[A]t = + kt + 1/[A]0
y mx b
Half-Life and First Order Reactions
Half-life t1/2
Time required for the concentration of a reaction to decrease to one-half its initial value; reactant R remaining is ½
Used primarily when dealing with 1st order reactions
Indicates the rate at which a reactant is consumed – is reaction fast or slow?
Longer the half-life – slower the reaction
Half-Life and First Order Reactions
Where:[R]0 = initial concentration
[R]t = concentration after the reaction is half complete
2
1
2
1
00
R
RorRR t
t
Half-Life and First Order Reactions
Let’s evaluate t1/2 for 1st order reaction
Substitute [R]t/[R]0 = ½ and t = t1/2 in integrated rate equation
ktR
R t 0
ln
2/12
1ln kt
Half-Life and First Order Reactions
Rearrange equation (ln 2 = 0.693)
Equations relates half-life to 1st order rate constant
t1/2 is independent of concentration
kt
693.02/1
Half-Life, Zero Order & Second Order Reactions
Zero order reaction
Second order reaction
k
Rt
20
2/1
02/1
1
Rkt
Half-LifePROBLEM Sucrose, C12H22O11, decomposes to fructose
and glucose in acid solution with the rate law
Rate =k[sucrose]k = 0.208 h-1 at 25C
What amount of time is required for 87.5% of the initial concentration of sucrose to decompose?
Half-Life
SOLUTION After 87.5% of sucrose has decomposed,
12.5% remains (fraction remaining = 0.125). This will require 2 half-lives to reach this point.
Time elapsed = 3 x 3.33 h = 9.99 h
hh
t 33.3208.0
693.012/1
Half-LifeYOUR TURN
The following reaction is first order with respect to [NH2NO2]. The rate constant, k, is 9.3 x 10-5 s-1. What is the half-life of this reaction?
NH2NO2(aq) N2O(g) + H2O(l)
The following reaction at 400K is second order with respect to [CF3] and the value of the rate constant, k, is 2.51 x 1010 M-1s-1. If the initial [CF3] = 2.0M, what is the half-life of the reaction?
2 CF3(g) C2F6(g)
Collision Theory of Reaction Rates
Theory states that for any reaction to occur 3 conditions must be met The reacting molecules must collide with
one another The reacting molecules must collide with
sufficient energy to break bonds The molecules must collide in an
orientation that can lead to rearrangement of the atoms
Collision Theory of Reaction Rates
So, molecules must collide with one another.
The rate of their reaction is primarily related to the number of collisions, which is in turn related to their concentration
The number of collisions between the two reactant molecules is directly proportional to the concentration of each reactant, and the rate of the reaction shows a first order dependence on each reactant
Collision Theory of Reaction Rates
Temperature, Reaction Rate, & Activation Energy
How and why does temperature affect reaction rates?
In any sample of gas or liquid some molecules have very low energies, others have high energies, most have intermediate energies.
As temperature increases average energy of the molecules in a sample increases as does the fraction having higher energies
Activation Energy Molecules require some minimum energy to
react; ‘energy barrier’ Energy required to surmount the barrier is
called the activation energy, Ea
Barrier low, energy requirement (Ea) is low, a high proportion of molecules in a sample have sufficient energy to react – reaction is fast
Barrier high, energy requirement (Ea) is high and only a few reactant molecules in a sample have sufficient energy to react – reaction is slow
Activation Energy
Reaction Coordinate Diagram
Consider HI H2 + I2
Reaction can not occur without input of energy
Energy reaches maximum at transition state; sufficient energy has been concentrated in bonds, bonds can break, reaction can move forward.
Activation Energy
Effects of Temperature Increase
Raising the temperature always increases the reaction rate by increasing the fraction of molecules with enough energy to surmount the activation energy barrier
Effects of Molecular Orientation on Reaction Rate
The lower the probability of achieving alignment, the smaller the value of k, the slower the reaction
The Arrhenius Equation Reaction rates depend on energy, frequency of
collision between reactants, temperature, and correct geometry. Arrhenius equation summarizes these factors:
R = gas constant 8.314 x 10-3 kJ/K∙mol A = frequency factor L/mol∙s (related to number of
collision and fraction of collisions w/correct geometry. A is specific to each reaction and temperature dependent
Fraction of molecules having the minimum energy required for reaction. Value is always <1
RTEaAeconstratek /
RTEae /
The Arrhenius Equation
Use to calculate: Value of Ea
Rate constant for a given temperature if Ea and A are known
RT
EAk alnln
The Arrhenius Equation
A little rearrangement…
ATR
Ek a ln
1ln
y mx + b
The Arrhenius Equation
PROBLEM Calculate Ea for the reaction
2N2O (a) 2N2 (g) + O2 (g)
Exp T (K) K (L/mols)
1 1125 11.59
2 1053 1.67
3 1001 0.380
4 838 0.0011
The Arrhenius Equation
Kinetics problems that deal with changing rates, or rate constants (k), and temperature changes require use of the Arrhenius equation
121
212
11lnlnln
TTR
E
k
kkk a
The Arrhenius Equation
PROBLEM What is the activation energy of a
reaction that has a rate constant of 2.50 x 102 kJ/mol at 325K and a rate constant of 5.00 z 102 kJ/mol at 375K?
One - step, irreversible, unimolecular reactions One - step, irreversible, bimolecular reactions One - step, reversible reactions
Catalysis Catalyst increases
the rate of a reaction without being consumed by it.
Catalyst lowers the activation energy required thus speeding up the reaction
Heterogeneous & Homogeneous Catalysis Heterogeneous – catalyst is in a different phase from
the reaction mixture; generally a solid that increases the rate of a gas phase or liquid phase reaction
Au
N2O(g) N2(g) + ½ O2(g)
N2O is chemically absorbed on the surface of the solid catalyst.
A bond is formed between the N2O molecule and Au (covalent bonds) thus weakening the bond between nitrogen and oxygen making it easier for N2O to break apart.
Heterogeneous & Homogeneous Catalysis
N N – O(g) + Au(s) N N --- O --- Au(s) N N(g) + O2(g) + Au(s)
Heterogeneous catalyst generally used in industrial processes: Preparation of
ammonia sulfuric acid methanol
Pt catalyst used to reduce automobile emissions
Heterogeneous & Homogeneous Catalysis
Homogeneous – catalyst that is present in the same phase as the reactants.
Speeds up reaction by forming a reactive intermediate that decomposes to give products thus providing an alternative path of lower activation energy for the reaction
Heterogeneous & Homogeneous Catalysis
Clock reaction (decomposition of hydrogen peroxide)
Uncatalyzed2H2O2 (aq) 2H2O + O2 (g)
CatalyzedStep 1:H2O2 (aq) + I- (aq) H2O + IO- (aq)
Step 2:H2O2 (aq) + IO- (aq) H2O + O2 (g) + I- (aq)
2H2O2 (aq) 2H2O + O2(g)
Reaction Mechanisms
Sequence of bond-making and bond-breaking steps during a reaction
A ‘guess’ to help better understand the chemistry
Nano level (atoms and molecules) Use rate equation to understand
mechanisms
Reaction Mechanisms
Most reactions occur in a sequence of steps
Br2(g) + 2 NO(g) 2 BrNO(g) Written as a single step, this reaction
would require the 3 reactants to collide simultaneously with the right velocity and orientation to react.
Low probability of this happening
Reaction Mechanisms
Using a sequence of steps involving only one or two molecules increases the probability of a collision (production of an intermediate)
Step 1 Br2(g) + NO(g) Br2NO(g)
Step 2 Br2NO(g) + NO(g) 2 BrNO(g)
Br2(g) + 2 NO(g) 2 BrNO(g)
Reaction Mechanisms
Each step of mechanism is referred to as an elementary step Describes a single molecular event Each step has its own Ea and k Steps must add up to give overall
balance chemical equation
Molecularity
Classification of elementary steps based on # of reactant molecules colliding Unimolecular – one molecule in an
elementary step O2(g) O2(g) + O(g) Bimolecular – two molecules (same or
different) O2(g) + O(g) 2 O2(g)
Molecularity
Termolecular – three molecules (same or different)
O(g) + O2(g) + N2(g) O3(g) + energetic N2(g)
Molecularity
Elementary Step Molecularity Rate Equation
A product Unimolecular Rate = k[A]
A + A product Bimolecular Rate = k[A]2
A + B product Bimolecular Rate = k[A][B]
2 A + B product Termolecular Rate = k[A]2[B]
Molecularity
The rate equation of an elementary step is defined by the reaction stoichiometry. The rate equation of an elementary step is given by the product of the rate constant and the concentrations of the reactants in that step.
The molecularity of an elementary step and its order are the same. This is not true for the overall reaction.
Rate Equations & Mechanisms
Products of a reaction can never be produced at a rate faster than the rate of the slowest step
Slowest step = Rate-determining step
Rate Equations & Mechanisms
For the slowest step Rate = k1[A][B] Note: the rate law must be written with respect
to the reactants only
MXBAk
elEaSlow
1
arg,
YAMk
smallEaFast
2
,
YXBA 2