Chemical Kinetics
Kinetics
Kinetics in chemistry is concerned with how
quickly a reaction proceeds
Factors that affect rate
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Physical state of the reactants
Concentration of the reactants
Temperature at which the reaction occurs
The presence of a catalyst
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Reaction Rates
Reaction rates depend on
the frequency of collisions
between molecules
Reaction rate = speed of a
reaction (M/s)
A B
[B]/t = -[A]/t
Average Rate
Change of Rates with Time
C4H9Cl(aq) + H2O(l) C4H9OH(aq) + HCl(aq)
What is happening to
the rate as the
reaction proceeds?
Graphs of the data
allow you to find the
instantaneous rate
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Reaction Rates and Stoichiometry
Stoichiometry will affect the rates of
disappearance and formation
2HI(g) H2(g) + I2(g)
Practice
-1/2[HI]/t = [H2]/t = [I2]/t
For any general reaction
How is the rate of disappearance of ozone related to
the rate of appearance of oxygen in the following
equation: 2O3(g) 3O2(g)? If the rate of appearance
of oxygen is 6.0x10-5 M/s at a particular instant what
is the value of the rate of disappearance of ozone at
this same time?
aA + bB cC + dD
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Answer: 4.0x10-5 M/s
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Practice
Beer's Law
The decompostion of N2O5 proceeds according to the
following equation:
2N 2O5(g) 4NO2(g) + O2(g)
If the rate of decomposition of dinitrogen pentoxide at a
particular instant in a reaction vessel is 4.2x10- 7 M/s,
what is the rate of appearance of NO2 and O2?
Spectroscopic methods
are useful in seeing how
concentration changes
with time
2HI(g) H2(g) + I2(g)
A = abc
Answer: 8.4x10-7 M/s, 2.1x10-7 M/s
A : absorbance
a : molar absorptivity
b : path length
c : concentration
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Concentration and Rate
To determine the effect
of concentration of rate,
you can vary the
concentration of
reactants and monitor
the change in initial rate
Rate Law
NH4+(aq) + NO2-(aq) N2(g) + 2H2O(l)
Rate law shows the rate of a reaction is related to
the concentrations of the reactants
What happens to the
initial rate when the
concentrations are
changed?
For a general reaction: aA + bB cC + dD
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Rate = k[A]m[B]n
k = rate constant
Rate = k[NH4+][NO2-]
The magnitude of k is affected by changes in temp.
If we know the rate law we can calculate k
From exp. 1: r = 5.4x10-7 M/s = k(0.0100M)(0.200M)
k = 2.7x10-4 M-1 ·s-1
Reaction Orders
m and n are reaction orders
Rate = k[NH4+][NO2-]
Units of Rate Constants
Rate = k[A]m[B]n
Each compound is 1st order but the overall order is 2nd
(just add the exponents)
Reaction orders must be determined
experimentally
2N2O5(g) 4NO2(g) + O2(g)
:
Rate = k[N2O5]
2HI(g) H2(g) + I2(g)
:
Rate = k[H2][I2]
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Units of the rate constant depend on the overall order
of the rate law
What are the overall reaction orders and units of the
rate constant for the following reactions?
2N2O5(g) 4NO2(g) + O2(g)
2HI(g) H2(g) + I2(g)
CHCl3(g) + Cl2(g) CCl4(g) + Hcl(g)
–
–
–
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Rate = k[N2O5]
Rate = k[H2][I2]
Rate = k[CHCl3][Cl]1/2
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Using Initial Rates
Observing the effect of changing the initial
concentrations of the reactants on the initial
rate allows us to determine reaction orders
Exponents will commonly be 0, 1, 2
Practice
What effect will a reactant with a reaction order of 0
have on the reaction? 1? 2?
The following data were measured for the reaction of nitric oxide
with hydrogen:
Determine the rate law for this reaction, the value of the rate
constant and the rate when [NO] = 0.050M and [H2] = 0.150M
Experiment
Number
1
2
3
[NO] (M)
0. 100
0. 100
0. 200
[B] (M)
0.100
0.200
0.100
Initial Rate
(M/s)
1.23E-03
2.46E-03
4.92E-03
Answer: r = k[NO]2[H2], k = 1.2 M -2 s-1 , r = 4.5x10- 4 M/s
Rate laws can be converted to tell us what the
concentration of a substance is at any time
during a reaction.
There are two special cases and you must be
able to use them.
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Practice
Rate = -[A]/t = k[A]
ln[A]t – ln[A]0 = -kt
With some rearrangement we get
something similar to y = mx + b
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Rate laws tell us how the rate of a reaction
changes at a given temperature as
concentration changes.
After some math magic (involving
integration)
Answer: r = k [A]2, 4.0x10-3 M- 1 s-1 ,
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For a first order reaction that
proceeds A products the rate
law is
Initial Rate
(M/s)
4.00E-05
4.00E-05
1.60E-04
First Order Reactions
[B] (M)
0.100
0.200
0.100
Changing Concentration with Time
2NO(g) + 2H2(g) N2(g) + 2H2O(g)
[A] (M)
0.100
0.100
0.200
r = 1.0x10-5 M/s
Practice
Experiment
Number
1
2
3
Remember only the rate depends on
concentration
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The initial rate of a reaction A + B C was measured for several
different starting concentrations of A
and B. Using this data determine the
rate law for the reaction; the
magnitude of the rate constant; and
the rate when [A] = 0.050M and [B]
= 0.100M
The first order rate constant for the decomposition
of a certain insecticide in water at 12°C is 1.45 yr 1
. A quantity of the insecticide is washed into a
lake on June 1, leading to a concentration of
5.0x10- 7 g/mL. What is the concentration of
insecticide after 1 year? How long will it take for
the concentration to drop to 3.0x10- 7 g/mL?
ln[A]t = -kt + ln[A]0
What would you graph to see if
the reaction was first order?
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Answer: 1.2x10-7 g/mL, 0.35 years
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Practice
Second Order Reactions
The decomposition of dimethyl ether, (CH3)2O, at 510°C is a
first order process with a rate constant of 6.8x10 -4 s-1 :
(CH3)2O(g) CH4(g) + H2(g) + CO(g)
If the initial pressure of dimethyl ether is 135 torr, what is the
partial pressure after 1420s?
For a reaction that
proceeds A products or
A+B products that are
second order in just one
reactant A:
After some calculus magic
this becomes:
Answer: 51 torr
Rate = - [A]/t = k[A]2
1/[A]t = kt + 1/[A]0
If plotting 1/[A]t creates a
straight line the reaction is
second order
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Practice
The following data were obtained for the
gas phase decomposition of nitrogen
dioxide at 300°C, NO2(g) NO(g) + ½
O2(g):
Time (s)
0.0
50.0
100.0
200.0
300.0
Half Life
[NO2] (M)
0.01000
0.00787
0.00649
0.00481
0.00380
Is the reaction first or second order in
NO2? What is k? If the initial
concentration of NO2 is 0.0500M, what
is the concentration after 0.500hr?
Half life (t½) is the time it takes for the
concentration of a reactant to drop to one half of
its initial value
Using algebra you can find the half life of a 1st
order reaction
Answer: 2nd order r = k[NO2]2, k = 0.543
M-1 s- 1 , 1.00x10-3 M
t½ = 0.693/k
Half life for a second order reaction depends on
concetration
t½ = 1/k[A]0
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Temperature and Rate
Rate of most chemical reactions increase as
temperature increases
Increasing temperature increases the rate
constant and thus the rate
Collision Model
Glow stick fun
Molecule must collide
with enough energy
to react
What effect did the ice and hot water have on the
reaction?
What does increasing
temperature do?
Collision Theory
Orientation Factor
Activation Energy
–
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Ea
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Activation Energy
Arrhenius Equation
Higher activation
energy the lower the
rate
Rates depend on
Fraction of molecules with an energy of Ea or greater
Collisions per second
Fraction of collision with proper orientation
Only a fraction of
molecules have
energy to generate
products upon
collision
Arrhenius used these ideas to relate k and Ea
k = Ae-Ea/ RT
Taking the natural log of both sides
ln k = (-Ea/R)T + ln A
So we can graph ln k versus 1/T to find Ea
f = e-Ea/RT
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We can relate the rate constants of a reaction at different
temperatures
ln(k1/k2) = Ea/R (1/T2 - 1/T1)
Practice
The following table shows the rate
constants for the rearrangement of
methyl isonitrile at various
temperatures. From these data,
calculate the activation energy for
the reaction. What is the value of the
rate constant at 430.0K?
Reaction Mechanisms
Temperature (°C) k (s-1)
189.7
0.0000252
198.9
0.0000525
230.3
0.0006300
251.2
0.0031500
Reaction mechanisms show how a reaction
occurs
Elementary Steps
NO(g) + O3(g) NO2(g) + O2(g)
Molecularity
–
–
–
Answer: Ea = 160 kJ/mol, k = 1.0x106 -1
s
Unimolecular
Bimolecular
Termolecular
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Multistep Mechanisms
Many reactions do not happen in just one step
NO2(g) + CO(g) NO(g) + CO2(g)
NO2(g) + NO2(g) NO3(g) + NO(g)
NO3(g) + CO(g) NO2(g) + CO2(g)
Practice
It has been proposed that the conversion of ozone into O2 proceeds via two
elementary steps:
–
O3(g) O2(g) + O(g)
–
O3(g) O(g) + 2O2(g)
Describe the molecularity if each step in this mechanism. Write the equation for
the overall reaction. Identify any intermediates.
Elementary steps must add up to give the
overall reaction
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For the reaction Mo(CO)6 + P(CH3)3 Mo(CO)5P(CH3)3 + CO
The proposed mechanism is
Mo(CO)6 Mo(CO)5 + CO
Intermediate
Mo(CO)5 + P(CH3)3 Mo(CO)5P(CH3)3
Is the proposed mechanism consistent with the equation for the overall reaction?
Identify any intermediates.
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Rate Laws for Elementary Steps
Practice
Rate laws cannot
normally be predicted
from the coefficients of
balanced equations.
Why?
H2(g) + Br2(g) 2HBr(g)
For elementary steps
the equation tells you
the rate law.
If the following reaction occurs in a single elementary step,
predict the rate law:
Rate law is determined
by its molecularity
Consider the following reaction: 2NO(g) + Br2(g) 2NOBr(g). Write the rate law for the reaction assuming it
involves a single elementary step. Is a single elementary
step likely for this reactipon?
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Rate Laws for Multistep
Mechanisms
In multistep systems the rate laws is set by the
slowest step
Mechanisms with Initial Fast Step
2NO(g) + Br2(g) 2NOBr(g)
Rate determining step
Mechanisms with slow first step
Step 1: NO2(g) + NO2(g) NO3(g) + NO(g) (slow)
Step 2: NO3(g) + CO(g) NO2(g) + CO2(g) (fast)
Overall: NO2(g) + CO(g) NO(g) + CO2(g)
You need to derive the rate law for a mechanism in
which there is an intermediate.
Rate = k[NO]2[Br2]
Possible Mechanism
NO(g) + Br2(g) NOBr2(g)
NOBr2(g) + NO(g) 2NOBr(g) (slow)
(fast)
Algebra fun
When a fast step precedes a slow one we can solve for
the concentration of an intermediate by assuming that
an equilibrium is established in the fast step.
Rate = k1[NO2]2
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Practice
Catalysis
Show that the following mechanism for the reaction producing NOBr also
produces a rate law consistent with the experimentally observed one:
Step 1: NO(g) + NO(g) N2O2(g)
(fast)
What does a catalyst do?
Types of catalysts
Step 2: N2O2(g) + Br2(g) 2NOBr(g) (slow)
The first step of a mechanism involving the reaction of bromine is: Br2(g)
2Br(g) (fast). What is the expression relating the concentration of Br(g)
to that of Br2(g)
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Homogeneous – same
phase as the reactants
Heterogeneous – different
phase from the reactants
–
Adsorption happens first
Enzymes
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