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Chapter 12
Chemical Kinetics
Kinetics
• Study of Speed at which reactions take place
– Effect of each reactant
– Effect of concentration
– Mechanisms
– Reaction process
– Energy requirements for reactions
Reaction Rate• Change in concentration of reactant or
product per unit of time
Rate = Δ[A]/ Δt
• Rates decrease as time increases
• Rates are given positive values
• If you know the rate of one species in a reaction you can calculate the others
2NO2 2NO + O2 Page 558
Based on the graph
What do you notice?
Calculate the rate of
• NO2 0s to 50.s
• NO2 50.s to 100.s
• O2 0s to 50.s
Rate Laws
• Only depends on the forward reaction
• An expression that shows how the rate depends on the concentrations of reactants
• A way of determining rate or concentration – Depends on what you know.
Form of the Rate Law
• Assuming the reaction A B + C
Rate = k[A]n
• k and n are both experimentally determined
• k is a constant called the rate constant– Units vary depending on n
• n is the order– Does NOT depend on balanced equation– Whole numbers including zero and fractions
Units of k
• Depends on what number n is
• k has units that gives the rate units of mol/L*s
• Consider - Rate = k[A]n
• What are the units of k if n is 1? 2? 0?
Multiple Reactants
• Consider the reaction A + B C
• What is the rate law?
• Rate = k[A]n[B]m
• What are the units for k when n is 1 & m is 1
Specifically
• These types of rate laws are differential rate laws– Just called rate laws
• There are also integrated rate laws
• The form you use depends on the data you have
Homework
• P. 598 #’s 17,18,19,20
Method of Initial Rates
Integrated Rate Laws
• A way of determining the order and rate constant of a reaction when time and concentration data is known.
• Must be for a single reactant.– Or have one in excess
• Equations for 0th, 1st, and 2nd order
• Use equations as tests for order
1st Order
ln[A] = -kt + ln[A]o
• [A] concentration of reactant at time t
• [A]o concentration of reactant at time t=0
• k is the rate constant
• This is the equation of a ________?– LINE– Y axis is ln[A], X axis is t– The slope is the rate constant
1st Order
• If a graph of ln[A] vs t is a straight line then the reaction is 1st order
• A straight line is the check for all of these
2N2O5 4NO2 + O2
• Example
1. Use the data to determine the rate law.
2. Determine the rate constant.
3. Determine the [N2O5] at 2000.s
Time (s) [N2O5]
0 .100
100. .0614
300. .0233
600. .00541
900. .00126
1st Order Half Life
• The half life is the time required for a reactant to reach half of its previous concentration
• Meaning [A] = [A]o/2
• Derive Half Life Equation
• t1/2=ln2/k
• Half life is always the same for first order kinetics
2N2O5 4NO2 + O2
• Example
1. Use the data to determine the rate law.
2. Determine the rate constant.
3. Determine the [N2O5] at 2000.s
4. Determine the half life
Time (s) [N2O5]
0 .100
100. .0614
300. .0233
600. .00541
900. .00126
2nd Order
• Integrated Rate Law 1/[A] = kt + 1/[A]o
• This is the equation of a ________?– LINE– Y axis is 1/[A], X axis is t– The slope is the rate constant
• Half Life
• t1/2 = 1/(k[A]o)
• Each half life is double the previous
2C4H6 C8H8
Example #33 p. 600
1. Determine the rate law
2. Determine the rate constant.
3. Determine the half-life
Time (s) [C4H8]
0 .017
195 .016
604 .015
1246 .013
2180 .011
6210 .0068
0th Order
• Integrated Rate Law [A] = -kt + [A]o
• This is the equation of a ________?– LINE– Y axis is [A], X axis is t– The slope is the rate constant
• Half Life
• t1/2 = [A]o/2k
• Each half life is the same
2N2O 2N2 + O2
1. Determine the rate law.
2. Determine the rate constant.
3. Determine the half-life
Time (s) [C4H8]
0 .44
10. .33
20. .22
30. .11
40. 0
Page 578
Homework
• Page 599 #’s 27,29,30,32
Reaction Mechanism
• A series of elementary steps that must satisfy two requirements
1. The sum of the steps must equal the overall balanced equation
2. Must agree with the rate law
• Elementary Step – Steps in the mechanism. (Think back to organic)
Cont.
• Intermediates – Species that are produced in one elementary step and consumed in another– Not part of the overall balanced equation
• Rate-determining step – Slowest step in a reaction that determines the rate
• Molecularity – Number of species that must collide to produce an elementary step
Molecularity Table
Elementary Step Molecularity Rate Law
A Products Unimolecular Rate=k[A]
2 A Products Bimolecular Rate=k[A]2
A + B Products Bimolecular Rate=k[A][B]2
2A + B Products Termolecular Rate=k[A]2[B]
A+B+C Products Termolecular Rate=k[A][B][C]
NO2 + CO NO + CO2
The reaction above has an experimentally determined rate law of
Rate=k[NO2]2
Is the proposed mechanism possible? Explain
Step 1 = NO2 + NO2 NO3 + NO
Step 2 = NO3 + CO NO2 + CO2
Collision Model for Kinetics
• For a reaction to occur particles must collide to react.
– Must collide in the proper orientation
– Must collide with enough energy
• Activation Energy
Proper Orientation
+
Images from: http://www.sparknotes.com/chemistry/kinetics/mechanisms/section1.rhtml
Improper Orientation
+
Images from: http://www.sparknotes.com/chemistry/kinetics/mechanisms/section1.rhtml
Activation Energy (Ea)
• The energy required to convert atoms or molecules into their transition state– Minimum energy required for effective
collisions
• Can be found by running the same reaction at different temps.
• Use Arrhenius Equation
Arrhenius Equation
• K = rate constant• Ea = Activation Energy• R = Energy Gas Constant 8.314 J/mol*K• T = Temp in K• A = Frequency Factor• Equation of a line Y is ln k X is 1/T• Slope is –Ea/R
ATR
Ek a ln
1ln
• Find the activation energy
2N2O5 4NO2 + O2
Rate Constant
Temp (ºC)
2.0x10-5 20
7.3x10-5 30
2.7x10-4 40
9.1x10-4 50
2.9x10-3 60
2 Temp. Ea Equation
• You can manipulate the Arrhenius Equ if you only have to temps and rate constants by subtracting the lower temp equation from the higher temp equation
211
2 11ln
TTR
Ea
k
k
Catalysts
• Chemical that speeds up a chemical reaction but is not consumed in the reaction
• Do this by
– Lowering activation energy
– Provide alternate reaction pathways
– Increase effective collisions
Cont.
Below are two steps in the destruction of ozone. What is the overall rxn? What is the catalyst? What is the intermediate?
Cl + O3 ClO + O2
O + ClO Cl + O2
Homework
• Page 602 #’s 45,48,49,54
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