NCERT Textbook: Chemical Kinetics | Chemistry Class 12 - NEET PDF Download

 Page 1


Chemistry, by its very nature, is concerned with change.
Substances with well defined properties are converted
by chemical reactions into other substances with
different properties. For any chemical reaction, chemists
try to find out
(a) the feasibility of a chemical reaction which can be
predicted by thermodynamics ( as you know that a
reaction with DG < 0, at constant temperature and
pressure is feasible);
(b) extent to which a reaction will proceed can be
determined from chemical equilibrium;
(c) speed of a reaction i.e. time taken by a reaction to
reach equilibrium.
Along with feasibility and extent, it is equally
important to know the rate and the factors controlling
the rate of a chemical reaction for its complete
understanding. For example, which parameters
determine as to how rapidly food gets spoiled? How
to design a rapidly setting material for dental filling?
Or what controls the rate at which fuel burns in an
auto engine? All these questions can be answered by
the branch of chemistry, which deals with the study
of reaction rates and their mechanisms, called
chemical kinetics. The word kinetics is derived from
the Greek word ‘kinesis’ meaning movement.
Thermodynamics tells only about the feasibility of a
reaction whereas chemical kinetics tells about the rate
of a reaction.  For example, thermodynamic data
indicate that diamond shall convert to graphite but
in reality the conversion rate is so slow that the change
is not perceptible at all. Therefore, most people think
After studying this Unit, you will be
able to
· define the average and
instantaneous rate of a reaction;
· express the rate of a reaction in
terms of change in concentration
of either of the reactants or
products with time;
· distinguish between elementary
and complex reactions;
· differentiate between the
molecularity and order of a
reaction;
· define rate constant;
· discuss the dependence of rate of
reactions on concentration,
temperature and catalyst;
· derive integrated rate equations
for the zero and first order
reactions;
· determine the rate constants for
zeroth and first order reactions;
· describe collision theory.
Objectives
Chemical Kinetics helps us to understand how chemical reactions
occur.
3
Chemical Kinetics
Unit Unit Unit Unit Unit
3
Chemical Kinetics
Reprint 2024-25
Page 2


Chemistry, by its very nature, is concerned with change.
Substances with well defined properties are converted
by chemical reactions into other substances with
different properties. For any chemical reaction, chemists
try to find out
(a) the feasibility of a chemical reaction which can be
predicted by thermodynamics ( as you know that a
reaction with DG < 0, at constant temperature and
pressure is feasible);
(b) extent to which a reaction will proceed can be
determined from chemical equilibrium;
(c) speed of a reaction i.e. time taken by a reaction to
reach equilibrium.
Along with feasibility and extent, it is equally
important to know the rate and the factors controlling
the rate of a chemical reaction for its complete
understanding. For example, which parameters
determine as to how rapidly food gets spoiled? How
to design a rapidly setting material for dental filling?
Or what controls the rate at which fuel burns in an
auto engine? All these questions can be answered by
the branch of chemistry, which deals with the study
of reaction rates and their mechanisms, called
chemical kinetics. The word kinetics is derived from
the Greek word ‘kinesis’ meaning movement.
Thermodynamics tells only about the feasibility of a
reaction whereas chemical kinetics tells about the rate
of a reaction.  For example, thermodynamic data
indicate that diamond shall convert to graphite but
in reality the conversion rate is so slow that the change
is not perceptible at all. Therefore, most people think
After studying this Unit, you will be
able to
· define the average and
instantaneous rate of a reaction;
· express the rate of a reaction in
terms of change in concentration
of either of the reactants or
products with time;
· distinguish between elementary
and complex reactions;
· differentiate between the
molecularity and order of a
reaction;
· define rate constant;
· discuss the dependence of rate of
reactions on concentration,
temperature and catalyst;
· derive integrated rate equations
for the zero and first order
reactions;
· determine the rate constants for
zeroth and first order reactions;
· describe collision theory.
Objectives
Chemical Kinetics helps us to understand how chemical reactions
occur.
3
Chemical Kinetics
Unit Unit Unit Unit Unit
3
Chemical Kinetics
Reprint 2024-25
62 Chemistry
that diamond is forever. Kinetic studies not only help us to determine
the speed or rate of a chemical reaction but also describe the
conditions by which the reaction rates can be altered. The factors
such as concentration, temperature, pressure and catalyst affect the
rate of a reaction. At the macroscopic level, we are interested in
amounts reacted or formed and the rates of their consumption or
formation. At the molecular level, the reaction mechanisms involving
orientation and energy of molecules undergoing collisions,
are discussed.
In this Unit, we shall be dealing with average and instantaneous
rate of reaction and the factors affecting these. Some elementary
ideas about the collision theory of reaction rates are also given.
However, in order to understand all these, let us first learn about the
reaction rate.
Some reactions such as ionic reactions occur very fast, for example,
precipitation of silver chloride occurs instantaneously by mixing of
aqueous solutions of silver nitrate and sodium chloride. On the other
hand, some reactions are very slow, for example, rusting of iron in
the presence of air and moisture. Also there are reactions like inversion
of cane sugar and hydrolysis of starch, which proceed with a moderate
speed. Can you think of more examples from each category?
You must be knowing that speed of an automobile is expressed in
terms of change in the position or distance covered by it in a certain
period of time. Similarly, the speed of  a reaction or  the rate of a
reaction can be defined as the change in concentration of  a reactant
or product in unit time. To be more specific, it can be expressed in
terms of:
(i) the rate of decrease in concentration of any one of the
reactants,or
(ii) the rate of increase in concentration of any one of the products.
Consider a hypothetical reaction, assuming that the volume of the
system remains constant.
R ® P
One mole of the reactant R produces one mole of the product P. If
[R]
1
  and [P]
1
 are the concentrations of R and P respectively at time t
1
and [R]
2
 and [P]
2
 are their concentrations at time  t
2
 then,
Dt = t
2
 – t
1
D[R] = [R]
2 
– [R]
1
D [P] = [P]
2
 – [P]
1
The square brackets in the above expressions are used to express
molar concentration.
Rate of disappearance of R
[ ] Decrease in concentration of R
R
=
Time taken t
?
= - ?
(3.1)
3.1 3.1 3.1 3.1 3.1 Rate of a Rate of a Rate of a Rate of a Rate of a
Chemical Chemical Chemical Chemical Chemical
Reaction Reaction Reaction Reaction Reaction
Reprint 2024-25
Page 3


Chemistry, by its very nature, is concerned with change.
Substances with well defined properties are converted
by chemical reactions into other substances with
different properties. For any chemical reaction, chemists
try to find out
(a) the feasibility of a chemical reaction which can be
predicted by thermodynamics ( as you know that a
reaction with DG < 0, at constant temperature and
pressure is feasible);
(b) extent to which a reaction will proceed can be
determined from chemical equilibrium;
(c) speed of a reaction i.e. time taken by a reaction to
reach equilibrium.
Along with feasibility and extent, it is equally
important to know the rate and the factors controlling
the rate of a chemical reaction for its complete
understanding. For example, which parameters
determine as to how rapidly food gets spoiled? How
to design a rapidly setting material for dental filling?
Or what controls the rate at which fuel burns in an
auto engine? All these questions can be answered by
the branch of chemistry, which deals with the study
of reaction rates and their mechanisms, called
chemical kinetics. The word kinetics is derived from
the Greek word ‘kinesis’ meaning movement.
Thermodynamics tells only about the feasibility of a
reaction whereas chemical kinetics tells about the rate
of a reaction.  For example, thermodynamic data
indicate that diamond shall convert to graphite but
in reality the conversion rate is so slow that the change
is not perceptible at all. Therefore, most people think
After studying this Unit, you will be
able to
· define the average and
instantaneous rate of a reaction;
· express the rate of a reaction in
terms of change in concentration
of either of the reactants or
products with time;
· distinguish between elementary
and complex reactions;
· differentiate between the
molecularity and order of a
reaction;
· define rate constant;
· discuss the dependence of rate of
reactions on concentration,
temperature and catalyst;
· derive integrated rate equations
for the zero and first order
reactions;
· determine the rate constants for
zeroth and first order reactions;
· describe collision theory.
Objectives
Chemical Kinetics helps us to understand how chemical reactions
occur.
3
Chemical Kinetics
Unit Unit Unit Unit Unit
3
Chemical Kinetics
Reprint 2024-25
62 Chemistry
that diamond is forever. Kinetic studies not only help us to determine
the speed or rate of a chemical reaction but also describe the
conditions by which the reaction rates can be altered. The factors
such as concentration, temperature, pressure and catalyst affect the
rate of a reaction. At the macroscopic level, we are interested in
amounts reacted or formed and the rates of their consumption or
formation. At the molecular level, the reaction mechanisms involving
orientation and energy of molecules undergoing collisions,
are discussed.
In this Unit, we shall be dealing with average and instantaneous
rate of reaction and the factors affecting these. Some elementary
ideas about the collision theory of reaction rates are also given.
However, in order to understand all these, let us first learn about the
reaction rate.
Some reactions such as ionic reactions occur very fast, for example,
precipitation of silver chloride occurs instantaneously by mixing of
aqueous solutions of silver nitrate and sodium chloride. On the other
hand, some reactions are very slow, for example, rusting of iron in
the presence of air and moisture. Also there are reactions like inversion
of cane sugar and hydrolysis of starch, which proceed with a moderate
speed. Can you think of more examples from each category?
You must be knowing that speed of an automobile is expressed in
terms of change in the position or distance covered by it in a certain
period of time. Similarly, the speed of  a reaction or  the rate of a
reaction can be defined as the change in concentration of  a reactant
or product in unit time. To be more specific, it can be expressed in
terms of:
(i) the rate of decrease in concentration of any one of the
reactants,or
(ii) the rate of increase in concentration of any one of the products.
Consider a hypothetical reaction, assuming that the volume of the
system remains constant.
R ® P
One mole of the reactant R produces one mole of the product P. If
[R]
1
  and [P]
1
 are the concentrations of R and P respectively at time t
1
and [R]
2
 and [P]
2
 are their concentrations at time  t
2
 then,
Dt = t
2
 – t
1
D[R] = [R]
2 
– [R]
1
D [P] = [P]
2
 – [P]
1
The square brackets in the above expressions are used to express
molar concentration.
Rate of disappearance of R
[ ] Decrease in concentration of R
R
=
Time taken t
?
= - ?
(3.1)
3.1 3.1 3.1 3.1 3.1 Rate of a Rate of a Rate of a Rate of a Rate of a
Chemical Chemical Chemical Chemical Chemical
Reaction Reaction Reaction Reaction Reaction
Reprint 2024-25
63 Chemical Kinetics
Rate of appearance of P
[ ] Increase in concentration of P
P
=
Time taken t
?
= +
?
(3.2)
Since, D[R] is a negative quantity (as concentration of reactants is
decreasing), it is multiplied with –1 to make the rate of the reaction a
positive quantity.
Equations (3.1) and (3.2) given above represent the average rate of
a reaction, r
av
.
Average rate depends upon the change in concentration of reactants
or products and the time taken for that change to occur (Fig. 3.1).
Fig. 3.1:  Instantaneous and average rate of a reaction
Units of rate of a reaction
From equations (3.1) and (3.2), it is clear that units of rate are
concentration time
–1
. For example, if concentration is in  mol L
–1
  and
time is in seconds then the units will be mol L
-1
s
–1
. However, in gaseous
reactions, when the concentration of gases is expressed in terms of their
partial pressures, then the units of the rate equation will be atm s
–1
.
From the concentrations of C
4
H
9
Cl (butyl chloride) at different times given
below, calculate the average rate of the reaction:
C
4
H
9
Cl  +  H
2
O  ®  C
4
H
9
OH + HCl
during different intervals of time.
t/s 0 50 100 150 200 300 400 700 800
 [C
4
H
9
Cl]/mol L
–1
0.100 0.0905 0.0820 0.0741 0.0671 0.0549 0.0439 0.0210 0.017
We can determine the difference in concentration over different intervals
of time and thus determine the average rate by dividing D[R] by Dt
(Table 3.1).
{         }
Example 3.1 Example 3.1 Example 3.1 Example 3.1 Example 3.1
Solution Solution Solution Solution Solution
Reprint 2024-25
Page 4


Chemistry, by its very nature, is concerned with change.
Substances with well defined properties are converted
by chemical reactions into other substances with
different properties. For any chemical reaction, chemists
try to find out
(a) the feasibility of a chemical reaction which can be
predicted by thermodynamics ( as you know that a
reaction with DG < 0, at constant temperature and
pressure is feasible);
(b) extent to which a reaction will proceed can be
determined from chemical equilibrium;
(c) speed of a reaction i.e. time taken by a reaction to
reach equilibrium.
Along with feasibility and extent, it is equally
important to know the rate and the factors controlling
the rate of a chemical reaction for its complete
understanding. For example, which parameters
determine as to how rapidly food gets spoiled? How
to design a rapidly setting material for dental filling?
Or what controls the rate at which fuel burns in an
auto engine? All these questions can be answered by
the branch of chemistry, which deals with the study
of reaction rates and their mechanisms, called
chemical kinetics. The word kinetics is derived from
the Greek word ‘kinesis’ meaning movement.
Thermodynamics tells only about the feasibility of a
reaction whereas chemical kinetics tells about the rate
of a reaction.  For example, thermodynamic data
indicate that diamond shall convert to graphite but
in reality the conversion rate is so slow that the change
is not perceptible at all. Therefore, most people think
After studying this Unit, you will be
able to
· define the average and
instantaneous rate of a reaction;
· express the rate of a reaction in
terms of change in concentration
of either of the reactants or
products with time;
· distinguish between elementary
and complex reactions;
· differentiate between the
molecularity and order of a
reaction;
· define rate constant;
· discuss the dependence of rate of
reactions on concentration,
temperature and catalyst;
· derive integrated rate equations
for the zero and first order
reactions;
· determine the rate constants for
zeroth and first order reactions;
· describe collision theory.
Objectives
Chemical Kinetics helps us to understand how chemical reactions
occur.
3
Chemical Kinetics
Unit Unit Unit Unit Unit
3
Chemical Kinetics
Reprint 2024-25
62 Chemistry
that diamond is forever. Kinetic studies not only help us to determine
the speed or rate of a chemical reaction but also describe the
conditions by which the reaction rates can be altered. The factors
such as concentration, temperature, pressure and catalyst affect the
rate of a reaction. At the macroscopic level, we are interested in
amounts reacted or formed and the rates of their consumption or
formation. At the molecular level, the reaction mechanisms involving
orientation and energy of molecules undergoing collisions,
are discussed.
In this Unit, we shall be dealing with average and instantaneous
rate of reaction and the factors affecting these. Some elementary
ideas about the collision theory of reaction rates are also given.
However, in order to understand all these, let us first learn about the
reaction rate.
Some reactions such as ionic reactions occur very fast, for example,
precipitation of silver chloride occurs instantaneously by mixing of
aqueous solutions of silver nitrate and sodium chloride. On the other
hand, some reactions are very slow, for example, rusting of iron in
the presence of air and moisture. Also there are reactions like inversion
of cane sugar and hydrolysis of starch, which proceed with a moderate
speed. Can you think of more examples from each category?
You must be knowing that speed of an automobile is expressed in
terms of change in the position or distance covered by it in a certain
period of time. Similarly, the speed of  a reaction or  the rate of a
reaction can be defined as the change in concentration of  a reactant
or product in unit time. To be more specific, it can be expressed in
terms of:
(i) the rate of decrease in concentration of any one of the
reactants,or
(ii) the rate of increase in concentration of any one of the products.
Consider a hypothetical reaction, assuming that the volume of the
system remains constant.
R ® P
One mole of the reactant R produces one mole of the product P. If
[R]
1
  and [P]
1
 are the concentrations of R and P respectively at time t
1
and [R]
2
 and [P]
2
 are their concentrations at time  t
2
 then,
Dt = t
2
 – t
1
D[R] = [R]
2 
– [R]
1
D [P] = [P]
2
 – [P]
1
The square brackets in the above expressions are used to express
molar concentration.
Rate of disappearance of R
[ ] Decrease in concentration of R
R
=
Time taken t
?
= - ?
(3.1)
3.1 3.1 3.1 3.1 3.1 Rate of a Rate of a Rate of a Rate of a Rate of a
Chemical Chemical Chemical Chemical Chemical
Reaction Reaction Reaction Reaction Reaction
Reprint 2024-25
63 Chemical Kinetics
Rate of appearance of P
[ ] Increase in concentration of P
P
=
Time taken t
?
= +
?
(3.2)
Since, D[R] is a negative quantity (as concentration of reactants is
decreasing), it is multiplied with –1 to make the rate of the reaction a
positive quantity.
Equations (3.1) and (3.2) given above represent the average rate of
a reaction, r
av
.
Average rate depends upon the change in concentration of reactants
or products and the time taken for that change to occur (Fig. 3.1).
Fig. 3.1:  Instantaneous and average rate of a reaction
Units of rate of a reaction
From equations (3.1) and (3.2), it is clear that units of rate are
concentration time
–1
. For example, if concentration is in  mol L
–1
  and
time is in seconds then the units will be mol L
-1
s
–1
. However, in gaseous
reactions, when the concentration of gases is expressed in terms of their
partial pressures, then the units of the rate equation will be atm s
–1
.
From the concentrations of C
4
H
9
Cl (butyl chloride) at different times given
below, calculate the average rate of the reaction:
C
4
H
9
Cl  +  H
2
O  ®  C
4
H
9
OH + HCl
during different intervals of time.
t/s 0 50 100 150 200 300 400 700 800
 [C
4
H
9
Cl]/mol L
–1
0.100 0.0905 0.0820 0.0741 0.0671 0.0549 0.0439 0.0210 0.017
We can determine the difference in concentration over different intervals
of time and thus determine the average rate by dividing D[R] by Dt
(Table 3.1).
{         }
Example 3.1 Example 3.1 Example 3.1 Example 3.1 Example 3.1
Solution Solution Solution Solution Solution
Reprint 2024-25
64 Chemistry
It can be seen (Table 3.1) that the average rate falls from 1.90× 0
-4
 mol L
-1
s
-1
 to
0.4 × 10
-4
 mol L
-1
s
-1
. However, average rate cannot be used to predict the
rate of a reaction at a particular instant as it would be constant for the
time interval for which it is calculated. So, to express the rate at a particular
moment of time we determine the instantaneous rate. It is obtained
when we consider the average rate at the smallest time interval say dt ( i.e.
when Dt approaches zero). Hence, mathematically for an infinitesimally
small dt instantaneous rate is given by
[ ] [ ] -? ?
= =
? ?
av
R P
r
t t
(3.3)
As  Dt ® 0 or
? ? ? ?
inst
d d
R P
d d
r
t t
?
? ?
Table 3.1: Average rates of hydrolysis of butyl chloride
[C
4
H
9
CI]
t
1
 / [C
4
H
9
CI]
t
2
 / t
1
/s t
2
/s r
av
 × 10
4
/mol L
–1
s
–1
 mol L
–1
mol L
–1
[ ] [ ] ( )
{ }
= – - ×
2 1
4
4 9 4 9 2 1
t t
C H Cl – C H Cl / t t 10
0.100 0.0905 0 50 1.90
0.0905 0.0820 50 100 1.70
0.0820 0.0741 100 150 1.58
0.0741 0.0671 150 200 1.40
0.0671 0.0549 200 300 1.22
0.0549 0.0439 300 400 1.10
0.0439 0.0335 400 500 1.04
0.0210 0.017 700 800 0.4
Fig 3.2
Instantaneous rate
of hydrolysis of butyl
chloride(C
4
H
9
Cl)
Reprint 2024-25
Page 5


Chemistry, by its very nature, is concerned with change.
Substances with well defined properties are converted
by chemical reactions into other substances with
different properties. For any chemical reaction, chemists
try to find out
(a) the feasibility of a chemical reaction which can be
predicted by thermodynamics ( as you know that a
reaction with DG < 0, at constant temperature and
pressure is feasible);
(b) extent to which a reaction will proceed can be
determined from chemical equilibrium;
(c) speed of a reaction i.e. time taken by a reaction to
reach equilibrium.
Along with feasibility and extent, it is equally
important to know the rate and the factors controlling
the rate of a chemical reaction for its complete
understanding. For example, which parameters
determine as to how rapidly food gets spoiled? How
to design a rapidly setting material for dental filling?
Or what controls the rate at which fuel burns in an
auto engine? All these questions can be answered by
the branch of chemistry, which deals with the study
of reaction rates and their mechanisms, called
chemical kinetics. The word kinetics is derived from
the Greek word ‘kinesis’ meaning movement.
Thermodynamics tells only about the feasibility of a
reaction whereas chemical kinetics tells about the rate
of a reaction.  For example, thermodynamic data
indicate that diamond shall convert to graphite but
in reality the conversion rate is so slow that the change
is not perceptible at all. Therefore, most people think
After studying this Unit, you will be
able to
· define the average and
instantaneous rate of a reaction;
· express the rate of a reaction in
terms of change in concentration
of either of the reactants or
products with time;
· distinguish between elementary
and complex reactions;
· differentiate between the
molecularity and order of a
reaction;
· define rate constant;
· discuss the dependence of rate of
reactions on concentration,
temperature and catalyst;
· derive integrated rate equations
for the zero and first order
reactions;
· determine the rate constants for
zeroth and first order reactions;
· describe collision theory.
Objectives
Chemical Kinetics helps us to understand how chemical reactions
occur.
3
Chemical Kinetics
Unit Unit Unit Unit Unit
3
Chemical Kinetics
Reprint 2024-25
62 Chemistry
that diamond is forever. Kinetic studies not only help us to determine
the speed or rate of a chemical reaction but also describe the
conditions by which the reaction rates can be altered. The factors
such as concentration, temperature, pressure and catalyst affect the
rate of a reaction. At the macroscopic level, we are interested in
amounts reacted or formed and the rates of their consumption or
formation. At the molecular level, the reaction mechanisms involving
orientation and energy of molecules undergoing collisions,
are discussed.
In this Unit, we shall be dealing with average and instantaneous
rate of reaction and the factors affecting these. Some elementary
ideas about the collision theory of reaction rates are also given.
However, in order to understand all these, let us first learn about the
reaction rate.
Some reactions such as ionic reactions occur very fast, for example,
precipitation of silver chloride occurs instantaneously by mixing of
aqueous solutions of silver nitrate and sodium chloride. On the other
hand, some reactions are very slow, for example, rusting of iron in
the presence of air and moisture. Also there are reactions like inversion
of cane sugar and hydrolysis of starch, which proceed with a moderate
speed. Can you think of more examples from each category?
You must be knowing that speed of an automobile is expressed in
terms of change in the position or distance covered by it in a certain
period of time. Similarly, the speed of  a reaction or  the rate of a
reaction can be defined as the change in concentration of  a reactant
or product in unit time. To be more specific, it can be expressed in
terms of:
(i) the rate of decrease in concentration of any one of the
reactants,or
(ii) the rate of increase in concentration of any one of the products.
Consider a hypothetical reaction, assuming that the volume of the
system remains constant.
R ® P
One mole of the reactant R produces one mole of the product P. If
[R]
1
  and [P]
1
 are the concentrations of R and P respectively at time t
1
and [R]
2
 and [P]
2
 are their concentrations at time  t
2
 then,
Dt = t
2
 – t
1
D[R] = [R]
2 
– [R]
1
D [P] = [P]
2
 – [P]
1
The square brackets in the above expressions are used to express
molar concentration.
Rate of disappearance of R
[ ] Decrease in concentration of R
R
=
Time taken t
?
= - ?
(3.1)
3.1 3.1 3.1 3.1 3.1 Rate of a Rate of a Rate of a Rate of a Rate of a
Chemical Chemical Chemical Chemical Chemical
Reaction Reaction Reaction Reaction Reaction
Reprint 2024-25
63 Chemical Kinetics
Rate of appearance of P
[ ] Increase in concentration of P
P
=
Time taken t
?
= +
?
(3.2)
Since, D[R] is a negative quantity (as concentration of reactants is
decreasing), it is multiplied with –1 to make the rate of the reaction a
positive quantity.
Equations (3.1) and (3.2) given above represent the average rate of
a reaction, r
av
.
Average rate depends upon the change in concentration of reactants
or products and the time taken for that change to occur (Fig. 3.1).
Fig. 3.1:  Instantaneous and average rate of a reaction
Units of rate of a reaction
From equations (3.1) and (3.2), it is clear that units of rate are
concentration time
–1
. For example, if concentration is in  mol L
–1
  and
time is in seconds then the units will be mol L
-1
s
–1
. However, in gaseous
reactions, when the concentration of gases is expressed in terms of their
partial pressures, then the units of the rate equation will be atm s
–1
.
From the concentrations of C
4
H
9
Cl (butyl chloride) at different times given
below, calculate the average rate of the reaction:
C
4
H
9
Cl  +  H
2
O  ®  C
4
H
9
OH + HCl
during different intervals of time.
t/s 0 50 100 150 200 300 400 700 800
 [C
4
H
9
Cl]/mol L
–1
0.100 0.0905 0.0820 0.0741 0.0671 0.0549 0.0439 0.0210 0.017
We can determine the difference in concentration over different intervals
of time and thus determine the average rate by dividing D[R] by Dt
(Table 3.1).
{         }
Example 3.1 Example 3.1 Example 3.1 Example 3.1 Example 3.1
Solution Solution Solution Solution Solution
Reprint 2024-25
64 Chemistry
It can be seen (Table 3.1) that the average rate falls from 1.90× 0
-4
 mol L
-1
s
-1
 to
0.4 × 10
-4
 mol L
-1
s
-1
. However, average rate cannot be used to predict the
rate of a reaction at a particular instant as it would be constant for the
time interval for which it is calculated. So, to express the rate at a particular
moment of time we determine the instantaneous rate. It is obtained
when we consider the average rate at the smallest time interval say dt ( i.e.
when Dt approaches zero). Hence, mathematically for an infinitesimally
small dt instantaneous rate is given by
[ ] [ ] -? ?
= =
? ?
av
R P
r
t t
(3.3)
As  Dt ® 0 or
? ? ? ?
inst
d d
R P
d d
r
t t
?
? ?
Table 3.1: Average rates of hydrolysis of butyl chloride
[C
4
H
9
CI]
t
1
 / [C
4
H
9
CI]
t
2
 / t
1
/s t
2
/s r
av
 × 10
4
/mol L
–1
s
–1
 mol L
–1
mol L
–1
[ ] [ ] ( )
{ }
= – - ×
2 1
4
4 9 4 9 2 1
t t
C H Cl – C H Cl / t t 10
0.100 0.0905 0 50 1.90
0.0905 0.0820 50 100 1.70
0.0820 0.0741 100 150 1.58
0.0741 0.0671 150 200 1.40
0.0671 0.0549 200 300 1.22
0.0549 0.0439 300 400 1.10
0.0439 0.0335 400 500 1.04
0.0210 0.017 700 800 0.4
Fig 3.2
Instantaneous rate
of hydrolysis of butyl
chloride(C
4
H
9
Cl)
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65 Chemical Kinetics
It can be determined graphically by drawing a tangent at time t on
either of the curves for concentration of R and P vs time t and calculating
its slope (Fig. 3.1). So in problem 3.1, r
inst 
at 600s for example, can be
calculated by plotting concentration of butyl chloride as a function of
time. A tangent is drawn that touches the curve at t = 600 s (Fig. 3.2).
The slope of this tangent gives the instantaneous rate.
So, r
inst   
at 600 s = –   mol L
–1
 = 5.12 × 10
–5
 mol L
–1
s
–1
At t = 250 s r
inst
 = 1.22 × 10
–4
 
mol L
–1
s
–1
     t = 350 s r
inst
 = 1.0 × 10
–4
 mol L
–1
s
–1
     t = 450 s r
inst
 = 6.4 ×× 10
–5
 mol L
–1
s
–1
Now consider a reaction
Hg(l) + Cl
2 
(g) ®
 
HgCl
2
(s)
Where stoichiometric coefficients of the reactants and products are
same, then rate of the reaction is given as
[ ] [ ] [ ]
2 2
Hg Cl HgCl
Rate of reaction = – –
t t t
? ? ?
= =
? ? ?
i.e., rate of disappearance of any of the reactants is same as   the rate
of appearance of the products. But in the following reaction, two moles of
HI decompose to produce one mole each of H
2 
and I
2,
2HI(g)   ®
   
H
2
(g)   +   I
2
(g)
For expressing the rate of such a reaction where stoichiometric
coefficients of reactants or products are not equal to one, rate of
disappearance of any of the reactants or  the rate of appearance of
products is divided by their respective stoichiometric coefficients. Since
rate of consumption of HI is twice the rate of formation of H
2
 or I
2
, to
make them equal, the term D[HI]  is divided by 2. The rate of this reaction
is given by
Rate  of reaction  
[ ] [ ] [ ]
2 2
H I 1
HI
2 t t t
? ? ?
= - = =
? ? ?
Similarly, for the reaction
5 Br
- 
(aq) + BrO
3
–
 (aq) + 6 H
+
 (aq)  ®  3 Br
2
 (aq) + 3 H
2
O (l)
Rate
Br
BrO
H
Br H
= - [ ]
= - ?
?
?
?
= - [ ]
=
[ ]
=
- - +
1
5
1
6
1
3
1
3
3 2 2
?
?
?
?
?
?
?
?
?
t t t t
O O
[ ]
?t
For a gaseous reaction at constant temperature, concentration is
directly proportional to the partial pressure of a species and hence, rate
can also be expressed as rate of change in partial pressure of the reactant
or the product.
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