Chemical Kinetics
The Study of Reaction Rates
Chemical Kinetics
Kinetics involves the study of several factors
that affect the rates of chemical reactions. The
final goal is to use all of the data to develop a
step-by-step reaction mechanism.
The mechanism is a possible path by which
reactants become products.
Factors Affecting Reaction Rates
Scientists typically examine how each of the
following factors affect the rate of a particular
reaction.
 Concentration of Reactants
 Temperature
 Solvent (if applicable)
 Catalysts (if applicable)
Reaction Rates
The rate of reaction is typically expressed in
the rate of disappearance of reactants, or the rate
of formation of products. Since the
stoichiometry of the reaction is known, the
concentration of only one component of the
reaction needs to be measured.
Reaction Rates
Note that the
concentration
of NO
increases by
the same
amount that
[NO2]
decreases.
Reaction Rates
[O2] = ½[NO]
So only one
component of
the reaction
need be
measured.
Reaction Rates
For the reaction: 2NO2(g)  2NO(g) + O2(g)
rate of loss of NO2 = rate of formation of NO
= 2 (rate of formation of O2)
Reaction Rates
For the reaction: 2NO2(g)  2NO(g) + O2(g)
rate of loss of NO2 = rate of formation of NO
= 2 (rate of formation of O2)
-Δ[NO2] = Δ[NO] = 2(Δ[O2])
Δt
Δt
Δt
Note the negative sign for the rate of loss of
reactant.
Reaction Rates
-Δ[NO2] = Δ[NO] = 2(Δ[O2])
Δt
Δt
Δt
This relationship can also be seen in a
graphical presentation of concentration versus
time.
2NO2(g)  2NO(g) + O2(g)
Note that the
rate of reaction
varies as the
reaction
proceeds.
Reaction Rates: 2NO2(g)  2NO(g) +O2(g)
The rate of reaction
of NO2 is most rapid at
the beginning of the
reaction. It slows
considerably as the
reaction proceeds.
Reaction Rates
Reaction rates vary with time, and also
depend upon the temperature and stoichiometry
of the reaction. As a result, we must be very
specific in what we mean by a reaction rate.
Initial rates are often used. This is the rate
of reaction just after the reaction begins. The
tangent to the curve during the initial moments
of the reaction provides the rate.
Reaction Rates
This graph for the
decomposition of N2O5
to form NO2 and O2
shows an initial rate of
5.4 x 10-4 mol/L-s
Reaction Rates
The convention for dealing with the
stoichiometry of the reaction is that for a general
reaction:
aA + bB  cC + dD
Rate =
- 1 Δ[A] = - 1 Δ[B] = 1 (Δ[C]) = 1(Δ[D])
a Δt b Δt
c Δt
d Δt
Rate Laws
One of the goals of kinetics is to determine
the rate law for a reaction. The rate law is the
mathematical relationship that shows how the
reaction rate depends upon the concentration of
reactants.
Rate = k[A]x[B]y
k is the rate constant, and is highly temperature
dependent
Rate Laws
For a decomposition reaction such as
A  products
the rate law will be
Rate = k[A]n
n is the reaction order, and is usually equal to 0,
1 or 2. The value of n must be determined
experimentally.
Rate Laws
The value of n can be
obtained by graphing
concentration versus
time.
Rate Laws
The relationship
between reaction rate
and concentration
also illustrated the
effect of reaction
order.
Rate Laws
Note that the reaction
rate doesn’t depend
upon concentration
of reactant for a zero
order rate law.
Rate Laws
Rate = k[A]x[B]y
x and y are called the order of the reaction with
respect to reactant A and B respectively. They
will usually have the value of 0, 1 or 2, though
other values are possible.
Rate laws must be determined experimentally.
Rate Laws
The exponents in the rate law provide
information on which reactants may be involved
in critical steps of the reaction mechanism.
The mechanism is the step-by-step process
by which reactants become products.
Rate laws must be determined experimentally.
Rate Laws
The rate law of a reaction, along with
information about temperature effects and
solvent effects can be used to develop a possible
reaction mechanism.
The goal of kinetics is often to determine a
possible reaction mechanism for a known
reaction.
Determination of Rate Laws
All rate laws are experimentally determined.
There are two basic methods used:
1. The Method of Initial Rates
2. Graphical Techniques using the
Integrated Rate Law
The Method of Initial Rates
The reaction rate is measured for several
different experiments. In each trial, on reactant
concentration is changed (usually doubled) while
the others are held constant. The change in rate
will depend only upon the reactant with the
changed concentration.
The Method of Initial Rates
The Method of Initial Rates
O
[NO2-] doubles
The Method of Initial Rates
O
[NO2-] doubles
Rate doubles
The Method of Initial Rates
O
[NO2-] doubles
Rate α [NO2-] 1
Rate doubles
The Method of Initial Rates
O
[NH4+] doubles
Rate α [NH4+] 1
Rate doubles
The Method of Initial Rates
rate α [NH4+][NO2-]
or
rate = k [NH4+][NO2-]
The reaction is first-order in ammonium ion,
first-order in nitrite ion, and second-order
overall.
The Method of Initial Rates
The Method of Initial Rates
[BrO3-] doubles
rate doubles
rate α [BrO3-]1
The Method of Initial Rates
[H+] doubles rate quadruples
rate α [H+]2
The Method of Initial Rates
[Br-] doubles
rate α [Br-]1
rate doubles
Method of Initial Rates
rate α [BrO3-][Br-][H+]2
The rate law is usually written with the rate
constant, k, included:
rate =k[BrO3-][Br-][H+]2
The reaction is first order in bromate, first
order in bromide, and second order in
hydronium ion.
Method of Initial Rates
rate =k[BrO3-][Br-][H+]2
The data for any reaction trial can be used to
calculate the value of k, the rate constant. The
reaction rate has the units mol/liter-time, so the
units of k depend upon the exponents in the
rate law. Usually the value of k for several trials
is averaged.
Graphical Techniques
The Integrated Rate Laws
The Integrated Rate Law
In general, rate laws will be first or second
order. In either case, the rate law can be
integrated to provide a linear equation of the
form: y=mx + b. This permits graphical
presentation of the data and determination of
the value of the rate constant.
The Integrated Rate Law
Once concentration versus time data have
been collected, the scientist constructs one or
more graphs to determine both the order of the
reaction and the value of the rate constant.
The Integrated Rate Law
We need not measure concentration. Any
property that is proportional to concentration
(intensity of color, pressure or volume of gases,
pH, etc.) may be graphed.
HCO2H(aq) + Br2(aq)  2Br1-(aq) + CO2(g)
The Integrated Rate Law- First
Order Reactions
rate = - d[A] = k[A]1
dt
Rearranging, we obtain:
-d[A] = kdt
[A]
When this expression is integrated from time =0
to time t, we obtain:
ln[A] = -kt + ln[A]o
The Integrated Rate Law- First
Order Reactions
ln[A] = -kt + ln[A]o
This is the integrated rate law for first-order
reactions. It has the linear form y=mx+b. If the
reaction is first-order, a graph of ln[A] versus
time will be linear with a slope equal to –k.
The Integrated Rate Law- First
Order Reactions
The linearity indicates that the reaction is
first-order with respect to N2O5. The rate
constant (- slope) has the units of (time)-1.
The Integrated Rate Law- First
Order Reactions
ln[A] = -kt + ln[A]o
If a graph isn’t linear, a second-order plot
must be prepared.
The Integrated Rate Law- First
Order Reactions
The curvature
of the graph
of ln[A] vs
time indicates
that this
reaction is not
first order.
The Integrated Rate Law – 2nd Order
Reactions
rate = - d[A] = k[A]2
dt
Rearranging, we obtain:
- d[A] = kdt
[A]2
When this expression is integrated from time
=0 to time t, we obtain:
1 = kt + 1_
[A]
[A]o
The Integrated Rate Law – 2nd Order
Reactions
1 = kt + 1_
[A]
[A]o
This equation has a linear (y=mx +b) form.
If a reaction is second-order, a plot of 1/[A]
versus time is linear, with the slope equal to the
rate constant.
The rate constant has the units (M)-1(time)-1.
The Integrated Rate Law – 2nd Order
Reactions
The linearity of the graph of [A]-1 indicates that
the reaction is second-order with respect to NO2.
The Integrated Rate Law- 2nd Order
Reactions
The linearity
of the graph
of 1/[A]
versus time
indicates that
the reaction is
second-order
with respect to
C4H6.
Zero-Order Rate Laws
Most reactions involving a single reactant
exhibit first or second-order kinetics. Rarely, a
reaction will have zero-order kinetics.
In this case,
Rate = k[A]0 = k(1) = k
Zero-Order Rate Laws
Rate = k[A]0 = k(1) = k
The integrated rate law is:
[A] = -kt + [A]o
and a graph of [A] versus time is linear.
Zero-Order Rate Laws
Unlike the rate
laws for other
reactions, for a zeroorder reaction, a
graph of [A] versus
time is linear.
The slope = -k.
Graphical Techniques
Half-life and
st
1
Order Reactions
The half-life is the time it takes for the
concentration of a reactant to halve. It is
represented by the symbol t½.
The half-life for a 1st-order reaction doesn’t
depend upon concentration. First-order
reactions have a constant half-life. That is, it
takes the same length of time for the
concentration to halve throughout the reaction.
Half-life and
st
1
Order Reactions
Half-life and
st
1
Order Reactions
First order
reactions have
a constant
half-life
throughout
the course of
the reaction.
First-Order Half-Life
Half-life and
st
1
Order Reactions
The first order rate law can be rearranged:
ln[A] = -kt + ln[A]o
ln [A]o = kt
[A]
Since [A] = ½[A]o at the half-life,
ln ([A]o/.5[A]o ) = kt½
ln(2.00) = kt½
0.693 = kt½
Half-life and
st
1
Order Reactions
0.693 = kt½
or
t½=0.693
k
The half-life is constant throughout a first
order reaction. All radioactive decay exhibits
first-order kinetics.
Half-life Problem

A mummy’s shroud has a 14C activity of 8.9
dis/min/gC. Living things have a 14C activity of
15.2 dis/min/gC. The half-life of 14C is 5, 730
years. Estimate the age of the shroud.
Half-life and
nd
2
Order Reactions
For a 2nd order
reaction, each
successive halflife is twice the
previous one.
Half-life and
nd
2
Order Reactions
The half-life of second-order reactions
depends upon the concentration of reactant. As
the concentration decreases, the half-life
increases.
Half-life and
nd
2
Order Reactions
The integrated rate law for a 2nd order
reaction is:
1 = kt + 1_
[A]
[A]o
At the half life, [A]= ½ [A]o, and t = t½.
1 = k t½ + 1_
.5[A]o
[A]o
Half-life and
nd
2
Order Reactions
1 = k t½ + 1_
.5[A]o
[A]o
1 = k t½
[A]o
t½ = 1/k [A]o
The half-life changes with concentration of
reactant for a second-order reaction.
Summary
Rate Laws for Multiple Reactants
For reactions with two or more reactants,
the reaction order for each reactant can be
determined graphically by monitoring the
concentration of one reactant while ensuring
that all other reactants are in very large (at least
ten-fold) excess.
In this way, the rate will depend only upon
the reactant studied. The concentrations of
other reactants will not change much during the
reaction.
Energy & Reaction Rates
Collisions with the proper orientation also
need sufficient energy to form products. For all
reactions, exothermic or endothermic, a
minimum amount of energy is required for the
reactants to form products. This minimum
amount of energy is called the activation energy.
Energy & Reaction Rates
The activation energy, Ea, is used to help
weaken the bonds of reactants and help form the
bonds in products.
Energy & Reaction Rates
Energy & Reaction Rates
Since the
kinetic energy of
the collisions
influences the
reaction rate, there
is a relationship
between
temperature and
the value of the
rate constant.
Energy & Reaction Rates
The experimentally based Arrhenius
equation relates temperature and activation
energy to the rate constant.
k = Ae-Ea/RT
where k is the rate constant; Ea is the activation
energy (J/mol); R = 8.314 J/K-mol; T is
temperature in Kelvins; and A is the frequency
factor.
Energy & Reaction Rates
k = Ae-Ea/RT
A, the frequency factor, (or pre-exponential
factor) takes into account the frequency of
collisions and the fraction with proper
orientation to form products.
Energy & Reaction Rates
k = Ae-Ea/RT
The Arrhenius equation is best used in
logarithmic form:
E
1
a
ln(k) = - R T + ln(A)
This equations has the linear form y = mx +b.
A graph of ln k versus 1/T has a slope of -Ea/R.
Energy and Chemical Reactions
Reaction rates depend upon concentrations
of reactants because molecules need to collide
with each other in order to form products.
Not all molecular collisions lead to product
formation. The collisions must have sufficient
energy to weaken existing bonds and also the
proper orientation to produce product(s).
Determination of Ea
Chemists usually
determine the value
of the rate constant
for a reaction at
several temperatures.
A graph of ln(k)
versus 1/T will be
linear, with the slope
equal to – Ea/R.
Temperature and Reaction Rate
Chemical reactions always go faster when the
temperature is increased. However, increasing
the temperature of a reaction may be costly, or
cause unwanted side reactions to occur.
Collision Theory
Reaction Mechanisms
The goal of kinetics is to determine the series
of steps by which reactants become products.
This series of steps is called a reaction mechanism.
The reaction mechanism is a series of
elementary steps that represent single chemical
events such as a collision, decomposition, etc.
Reaction Mechanisms
Because each elementary step represents a
single event, we can write rate laws for each of
the steps.
For example, if an elementary step involves
the collision of molecule A with molecule B,
than the rate will depend upon both the
concentration of A and the concentration of B.
Rate = k[A][B]
Reaction Mechanisms
Rate laws can only be written for elementary
steps. They cannot be written for chemical
reactions unless experiments are performed to
determine the relationship between rate and
concentration.
Elementary Steps and their Rate
Laws
Reaction Mechanisms
Scientists study a particular reaction and
experimentally determine the rate law. Using
other experimental information, they propose
a reaction mechanism.
The reaction mechanism is a series of
elementary steps that represent single chemical
events such as a collision, decomposition, etc.
Reaction Mechanisms
The proposed reaction mechanism must
meet two criteria:
1. The proposed mechanism for the reaction must
be consistent with the observed rate law.
2. The sum of the elementary steps must give the
overall balanced equation for the chemical
reaction.
Reaction Mechanisms
Consider the reaction between NO2(g) and
CO(g). The balanced equation is:
NO2(g) + CO(g)  NO(g) + CO2(g)
The experimentally determined rate law for
the reaction is:
Rate = k[NO2]2
Reaction Mechanisms
The proposed mechanism for the reaction is:
k1
NO2(g) + NO2(g)  NO3(g) + NO(g)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g)
Reaction Mechanisms
The sum of the steps must add up to the
overall balanced equation:
k1
NO2(g) + NO2(g)  NO3(g) + NO(g)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g)
Reaction Mechanisms
The sum of the steps must add up to the
overall balanced equation:
k1
NO2(g) + NO2(g)  NO3(g) + NO(g)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g)
NO2(g) + CO(g)  NO(g) + CO2(g)
Reaction Intermediates
This is a species that is neither a reactant nor
a product. It is produced during the course of
the reaction and consumed in a later step.
k1
NO2(g) + NO2(g)  NO3(g) + NO(g)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g)
NO2(g) + CO(g)  NO(g) + CO2(g)
Reaction Mechanisms
NO2(g) + NO2(g)  NO3(g) + NO(g)
NO3(g) + CO(g)  NO2(g) + CO2(g)
Reaction Mechanisms
NO3 is a reaction intermediate. It is formed
and consumed during the course of the
reaction.
Reaction Mechanisms
NO2(g) + CO(g)  NO(g) + CO2(g)
The proposed two-step mechanism provided
the overall balanced equation for the reaction.
For the mechanism to be valid, the
experimental or observed rate law must match
the rate law derived from the proposed reaction
mechanism.
Reaction Mechanisms
NO2(g) + CO(g)  NO(g) + CO2(g)
The experimentally determined rate law for
the reaction is:
Rate = k[NO2]2
Reaction Mechanisms
The proposed mechanism for the reaction is:
k1
NO2(g) + NO2(g)  NO3(g) + NO(g)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g)
k1 and k2 are the rate constants for the two
steps of the mechanism. Many reaction
mechanisms contain a rate determining step.
Reaction Mechanisms
If a multi-step process has one step which is
much slower than all of the other steps, the slow
step will determine the overall rate. The slow
step is called the rate determining step.
The overall reaction can be no faster than its
slowest step.
Reaction Mechanisms
The proposed mechanism for the reaction is:
k1
NO2(g) + NO2(g)  NO3(g) + NO(g) (slow)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g) (fast)
For this mechanism, the researcher has
proposed that first step is slow compared to
the second, and is the rate determining step.
Reaction Mechanisms
The proposed mechanism for the reaction is:
k1
NO2(g) + NO2(g)  NO3(g) + NO(g) (slow)
k2
NO3(g) + CO(g)  NO2(g) + CO2(g) (fast)
The rate of the reaction will be the rate of
the first step.
Rate = k1[NO2]2
This is the derived rate law.
Reaction Mechanisms
The derived rate law is:
Rate = k1[NO2]2
The observed rate law is:
Rate = k[NO2]2
Since the rate laws match, the proposed
mechanism may be the correct mechanism.
Reaction Mechanisms
Further experimentation and research into
related reaction mechanisms would be needed to
help confirm the proposed reaction mechanism.
In general, reaction mechanisms cannot be
proven absolutely.
Mechanisms with a rapid preequilibrium
2 NO + 2 H2  N2 + 2 H2O
Observed rate law: rate = k [NO]2[H2]
Proposed Mechanism:
2 NO  N2O2 (fast, k1 and k-1)
N2O2 + H2  N2O + H2O (slow, k2)
N2O + H2  N2 + H2O (fast, k3)
Mechanisms with a rapid preequilibrium
2 NO + 2 H2  N2 + 2 H2O
Observed rate law: rate = k [NO]2[H2]
Proposed Mechanism:
2 NO  N2O2 (fast, k1 and k-1)
N2O2 + H2  N2O + H2O (slow, k2)
N2O + H2  N2 + H2O (fast, k3)
2 NO + 2 H2  N2 + 2 H2O
Catalysts
A catalyst is a substance which provides a
lower energy pathway for the reaction. Catalysts
alter the reaction mechanism of the reaction.
Catalysts allow the reaction to proceed more
rapidly at lower temperatures.
Catalysis
The reaction
will go faster
with a catalyst,
or proceed at a
comparable
rate at lower
temperatures.
Catalysis
The reaction goes faster because a greater
percentage of molecules have sufficient
energy to form products when the activation
energy is lower.
Catalysts
Catalysts are present at the beginning of the
reaction. Although they are involved in the
reaction, they are regenerated. The net result is
that the catalyst speeds up the reaction without
being consumed.
Biological catalysts are called enzymes.
Enzymes allow many complex chemical
reactions to occur at body temperature (37oC).
Catalysis
Catalysis and the Ozone Layer
Freons, or chloroflurocarbons, have been
linked to destruction of the ozone layer of the
earth. Freons, when exposed to high energy
light in the upper atmosphere, form highly
reactive chorine atoms. These chlorine atoms
convert ozone to oxygen and are regenerated in
the process.
Catalysis and the Ozone Layer
CFCl3 + hν  •CFCl2 + •Cl
•Cl + O3  •ClO + O2
•ClO + O  •Cl + O2
_____________________
O3 + O 2 O2
Ozone is depleted, and the chlorine radical is
regenerated.
Heterogeneous Catalysis
Heterogeneous catalysis usually involves
gaseous reactants that react on the surface of a
solid catalyst. An example is the reaction of
ethylene with hydrogen.
H2C=CH2(g) + H2(g)  H3CCH3(g)
Heterogeneous Catalysis
H2C=CH2(g) + H2(g)  H3CCH3(g)
The reaction proceeds slowly due to the
strength of the bond in hydrogen. The gaseous
reactants are collected on the surface of catalysts
such as platinum, palladium or nickel, where the
reaction occurs.
Heterogeneous Catalysis
The metal catalyst
interacts with the
hydrogen molecules and
weakens the H-H bond.
Heterogeneous Catalysis