Chemical Kinetics
Chapter 13
1
Chemical Kinetics
• Kinetics is the study of how fast chemical reactions
occur and how they occur.
• There are 4 important factors which affect rates of
reactions:
–
–
–
–
reactant concentration
temperature
catalyst
surface area
• Goal: to understand chemical reactions at the
molecular level.
2
Reaction Rates
• Speed of a reaction (rxn) is measured by the change in
concentration with time.
• For a rxn A → B
change in the number of moles of B
Average rate 
change in time
 moles of B final mol B - initial mol B

=
t
t
• Suppose A reacts to form B. Let us begin with 1.00
mol A (and no B).
3
Reaction Rates
– At t = 0 (time zero) there is 1.00 mol A (100
red spheres) and no B present.
– At t = 20 min, there is 0.54 mol A and 0.46
mol B.
– At t = 40 min, there is 0.30 mol A and 0.70
mol B.
– Eventually, there will be no more A left, and
only B will be present.
4
Reaction Rates
5
Reaction Rates
6
Reaction Rates
• We can use this data to find the average
rate:
 moles of B 
Average rate 
t

moles of B at t  10  moles of B at t  0 

10 min - 0 min
0.26 mol - 0 mol

 0.026 mol/min
10 min - 0 min
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Chemical Kinetics
Reaction Rates
• For the rxn A →B there are two ways of measuring
rate:
– the speed at which the products appear (i.e. change in
moles of B per unit time), or
– the speed at which the reactants disappear (i.e. the
change in moles of A per unit time).
-(mol A)
Ave rate =
t
– Note the minus sign! This reminds us that the rate is
being expressed as the disappearance of a reactant.
8
Rates in Terms of Concentrations
• Most of the time, we will determine the rate of a rxn
by monitoring a change in concentration of a reactant
or product.
• Molarity is the most useful unit for rxn rates although
pressure is used for gases. Since volume is usually
constant, molarity (or pressure) and moles are
directly proportional.
9
Rates in Terms of Concentrations
• Consider:
C4H9Cl(aq) + H2O(l) →C4H9OH(aq) + HCl(aq)
• We can calculate the average rate in terms of the
disappearance of C4H9Cl.
• The units for average rate are mol/L•s or M/s.
• The average rate decreases with time as C4H9Cl
disappears.
10
Rates in Terms of Concentrations
C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
11
Rates in Terms of Concentrations
• We now plot [C4H9Cl] versus time.
• The rate at any instant in time is called the
instantaneous rate.
• The instantaneous rate is the slope of the straight line
tangent to the curve at that instant.
• Instantaneous rate is different from average rate.
• Note: The instantaneous rate is usually just called the
rate, unless otherwise specified.
12
Rates in Terms of Concentrations
13
Reaction Rates and Stoichiometry
• For the rxn
C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
we know
C4H 9Cl  C4H 9OH 
Rate  

t
t
• What if the stoichiometric relationships aren’t 1:1?
2HI(g) → H2(g) + I2(g)
• The HI:H2 ratio and the HI:I2 ratio are both 2:1!
14
Reaction Rates and Stoichiometry
2HI(g) →H2(g) + I2(g)
• It should be clear that as HI is consumed (or
disappears), only half as much H2 (and I2) is produced
or appears.
• So the rate of disappearance of HI is twice the rate of
appearance of H2 (and I2).
rateHI = 2rateH2 OR
rateH2 = 0.5rateHI
15
Reaction Rates and Stoichiometry
• We now have 2 different rates for the same rxn.
• These rates are related by the balanced equation
stoichiometry.
• We commonly talk in terms of the rxn rate, or the rate
of the rxn, not just in terms of the rate of appearance
of a product or the rate of disappearance of a product.
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Reaction Rates and Stoichiometry
• The rxn rate, or called just the rate, may be expressed
as:
-1  HI  H 2   I2 
rate =
=
=
2 t
t
t
• Or we can write it more generally as:
raterxn = rateH2 = rateI2 = 0.5rateHI
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Reaction Rates and Stoichiometry
• In general for the rxn:
aA + bB → cC + dD
• The overall rxn rate may be expressed as:
1 A
1 B 1 C 1 D
Rate  



a t
b t
c t
d t
• Or in nonmathematical terms:
1
1
1
1
rate = rateA = rateB = rateC = rateD
a
b
c
d
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Reaction Rates and Stoichiometry
• Be careful!
• Experiments are conducted in terms of the rates of
appearance/disappearance of a product/reactant.
• These rates may then be converted to rxn rates using
the balanced equation.
• Read problems carefully so you know what you are
given!
• If it is not specified, it is by default a rxn rate.
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The Dependence of Rate on Concentration
• In general, rates:
– Increase when reactant [ ] are increased.
– Decrease when product [ ] are increased.
• We often examine the effects of concentration on a
rxn rate by measuring how the rxn rate at the
beginning of a rxn depends on concentration.
• The instantaneous rxn rate at the start of a rxn is
called the initial rate.
20
The Dependence of Rate on Concentration
• Let’s look at the following rxn:
NH4+(aq) + NO2-(aq) →N2(g) + 2H2O(l)
• The initial rate is the instantaneous rate at t = 0.
(You get the initial rate from a graph.)
• We find the initial rate for various initial
concentrations of each reactant; for this rxn, NH4+
and NO2-.
21
Finding Initial Rate
22
The Dependence of Rate on Concentration
23
The Dependence of Rate on Concentration
• As [NH4+] doubles, with [NO2-] constant, the
rate doubles.
• So the rate is proportional to [NH4+]
• As [NO2-] doubles, with [NH4+] constant, the
rate doubles.
• So the rate is proportional to [NO2-]
• We conclude that the rate ∝ [NH4+] and to
[NO2-].
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The Dependence of Rate on Concentration
• The overall concentration dependence of the
rxn rate is given in a rate law or rate
expression.
• For this example, the rate law is:
Rate = k[NH4+][ NO2-]
• k is the rate constant and is constant except
for a change in temperature.
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The Dependence of Rate on Concentration
• So what is a rate law?
• It is a mathematical description of how the
concentration of a reactant affects the rate of
the rxn.
• After we determine the rate law and k for a
rxn, we can then use this info to calculate
initial rates or concentrations for any initial
reactant concentrations.
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Reaction Order
• For a general reaction with rate law
Rate = k[reactant 1]m[reactant 2]n,
we say the reaction is mth order in reactant 1 and
nth order in reactant 2.
• The overall rxn order is m + n + ….
• The rxn orders (values of the exponents) must be
determined experimentally. They are not necessarily
related to stoichiometry.
• Rxn orders of 0, 1, and 2 are common (0th, 1st, and
2nd orders).
• But negative and fractional rxn orders are possible.
27
Reaction Order
• For the rxn:
NH4+(aq) + NO2-(aq) → N2(g) + 2H2O(l)
• The rxn has been experimentally found to be
1st order in NH4+ and 1st in NO2-.
• The overall rxn order is 2.
• So, the rate law is:
Rate = k[NH4+][ NO2-].
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Units of k, the Rate Constant
• The units of the rate constant, k, depend on
the overall rxn order.
• For example, for a rxn with a rxn order of 2,
the k units are:
Units of rate = (units of rate constant)(units of concentration)2
• Or:
rate constant units =
units of rate
units of concentration 2
M
1
rate constant units =
= M -1s-1
M
Ms
The time unit s could be any other time unit, depends on rxn
s =
2
29
Using Initial Rates to Determine Rate Laws
• To determine the rate law, we observe the
effect of changing initial concentrations.
• For the general rxn:
aA + bB → cC + dD
• The rate law is:
Rate = k[A]m[B]n
30
Using Initial Rates to Determine Rate Laws
• Mathematically, we compare the rates of 2 or more
experiments, which are conducted at different
reactant concentrations.
k A 2 B2
A 2 B2  A 2   B 2 
rate2

=
m
n =
m
n = 
  B 
rate1
A


k A 1 B1
A
B
 1  1  1    1 
m
n
m
n
m
n
• Solving this gives us the exponents, which gives us
the rxn order.
• Once the exponents are known, k may be calculated.
• We then know the complete rate law!
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Using Initial Rates to Determine Rate Laws
• A rxn is zero order in a reactant if the change in
concentration of that reactant produces no effect.
• A rxn is first order if doubling the concentration
causes the rate to double.
• A rxn is second order if doubling the concentration
results in a 22 increase in rate.
• A rxn is nth order if doubling the concentration
causes an 2n increase in rate.
• Note that the rate, not the rate constant, depends on
concentration.
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• Example for rxn A + B → C:
Exp #
[A]
[B]
Initial rate
(M/s)
1
0.100
0.100
4.0x10-5
2
0.100
0.200
4.0x10-5
3
0.200
0.100
16.0x10-5
4
0.400
0.400
5
0.100
2.0x10-5
• Find a) rate law; b) k; and c) fill in the blanks.
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