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 Page 1


Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
1
www.learnershabitat.ac.in
This branch of chemistry which deals with the study of rates of chemical reactions and the mechanism
by which they occur. While studying reaction, one deals with :
(a) how fast (or slow) the reactants get converted into products
(b) the steps or paths through which the products are formed (reaction mechanism)
Chemical reaction kinetics deals with the rates of chemical processes. Any chemical process may be
broken down into a sequence of one or more single-step processes known either as elementary
processes, elementary reactions, or elementary steps. Elementary reactions usually involve either a
single reactive collision between two molecules, which we refer to as a a bimolecular step, or dissocia-
tion/isomerisation of a single reactant molecule, which we refer to as a unimolecular step. Very rarely,
under conditions of extremely high pressure, a termolecular step may occur, which involves simulta-
neous collision of three reactant molecules. An important point to recognise is that many reactions
that are written as a single reaction equation in actual fact consist of a series of elementary steps.
This will become extremely important as we learn more about the theory of chemical reaction rates.
As a general rule, elementary processes involve a transition between two atomic or molecular states
separated by a potential barrier. The potential barrier constitutes the activation energy of the pro-
cess, and determines the rate at which it occurs. When the barrier is low, the thermal energy of the
reactants will generally be high enough to surmount the barrier and move over to products, and the
reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient
energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the
source of the temperature dependence of reaction rates. The huge variety of chemical species, types
of reaction, and the accompanying potential energy surfaces involved means that the timescale over
which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as
iron rusting, to extremely fast reactions, such as the electron transfer processes involved in many
biological systems or the combustion reactions occurring in flames. A study into the kinetics of a
chemical reaction is usually carried out with one or both of two main goals in mind:
1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e. the reaction
mechanism.
2. Determination of the absolute rate of the reaction and/or its individual elementary steps.
RATE OF A REACTION
In general, for a reaction : R ? P, the behaviour of the concentration of the reactant and product, as
the reaction proceeds is shown graphically
CHEMICAL KINETICS
CHEMICAL KINETICS
Page 2


Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
1
www.learnershabitat.ac.in
This branch of chemistry which deals with the study of rates of chemical reactions and the mechanism
by which they occur. While studying reaction, one deals with :
(a) how fast (or slow) the reactants get converted into products
(b) the steps or paths through which the products are formed (reaction mechanism)
Chemical reaction kinetics deals with the rates of chemical processes. Any chemical process may be
broken down into a sequence of one or more single-step processes known either as elementary
processes, elementary reactions, or elementary steps. Elementary reactions usually involve either a
single reactive collision between two molecules, which we refer to as a a bimolecular step, or dissocia-
tion/isomerisation of a single reactant molecule, which we refer to as a unimolecular step. Very rarely,
under conditions of extremely high pressure, a termolecular step may occur, which involves simulta-
neous collision of three reactant molecules. An important point to recognise is that many reactions
that are written as a single reaction equation in actual fact consist of a series of elementary steps.
This will become extremely important as we learn more about the theory of chemical reaction rates.
As a general rule, elementary processes involve a transition between two atomic or molecular states
separated by a potential barrier. The potential barrier constitutes the activation energy of the pro-
cess, and determines the rate at which it occurs. When the barrier is low, the thermal energy of the
reactants will generally be high enough to surmount the barrier and move over to products, and the
reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient
energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the
source of the temperature dependence of reaction rates. The huge variety of chemical species, types
of reaction, and the accompanying potential energy surfaces involved means that the timescale over
which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as
iron rusting, to extremely fast reactions, such as the electron transfer processes involved in many
biological systems or the combustion reactions occurring in flames. A study into the kinetics of a
chemical reaction is usually carried out with one or both of two main goals in mind:
1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e. the reaction
mechanism.
2. Determination of the absolute rate of the reaction and/or its individual elementary steps.
RATE OF A REACTION
In general, for a reaction : R ? P, the behaviour of the concentration of the reactant and product, as
the reaction proceeds is shown graphically
CHEMICAL KINETICS
CHEMICAL KINETICS
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
2
www.learnershabitat.ac.in
From the graph, it is clear that the concentration of the reactant decreases and that of the product
increases as the reaction proceeds and the rate of the change of the concentration of the reactant as
well as that of the product is also changing.
Rate of a reaction can, now, be defined in two ways :
Average Rate of reaction (r
av
) given by for the reaction R ? P :
r
av
 = 
[R]
–
t
?
?
 = 
[P]
t
?
?
where ?[R] and ?[P] represents the change in the concentrations of 'R' and 'P' respectively over a time
interval ?t
The average rate of the reaction between a time interval (t
f
 – t
i 
= ?t) can be determined from the above
graph by locating the concentration of 'R' of 'P' on this graph at the time instants t
f
 and t
i
 as shown.
If [R]
f
 and [R]
i
 are the concentrations of the reactant 'A' at the time instants t
f
 and t
i
 then :
av
[R] –[R]
r –
t – t
? ?
?
? ?
? ?
f i
f i
Similarly from the plot of 'P' as a function of 't', we have : av
[P] –[P]
r
t – t
? ?
?
? ?
? ?
f i
f i
Note :
The above expression for r
av
 is equivalent to the slope of the line joining the points (t
f 
, [A]
f
)
and (t
i 
, [R]
i
) or (t
f 
, [P]
f
) and (t
i 
, [P]
i
) as shown.
Instantaneous Rate of reaction (r
inst.
) can be calculated from r
av
in the limit ?t ? 0 and is represented as :
r
inst.
 = 
d[R] d[P]
–
dt dt
?
Note : The above expression for r
inst. 
is equivalent to the slope of the tangent from the plot of the
concentration of 'R' or 'P' at any time instant 't'.
The rate of the reaction (r
inst.
 or r
av
) is always calculated as a positive quantity.
The rate of a reaction at any temperature depends on the concentration of the reactants and
sometimes on the concentration of some foreign substances (e.g a catalyst) being used in the
reaction as well. The representation of this dependence of the rate of the reaction on the
concentrations is known as rate law and this rate law is determined experimentally.
Units of rate of a reaction
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 gas is
expressed in terms of their partial pressures, then the units of the rate equation will be atm s
–1
.
Relation between various rates :
In general for a reaction : aA + bB ? cC + dD
The rate of reaction can be expressed as follows :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
Page 3


Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
1
www.learnershabitat.ac.in
This branch of chemistry which deals with the study of rates of chemical reactions and the mechanism
by which they occur. While studying reaction, one deals with :
(a) how fast (or slow) the reactants get converted into products
(b) the steps or paths through which the products are formed (reaction mechanism)
Chemical reaction kinetics deals with the rates of chemical processes. Any chemical process may be
broken down into a sequence of one or more single-step processes known either as elementary
processes, elementary reactions, or elementary steps. Elementary reactions usually involve either a
single reactive collision between two molecules, which we refer to as a a bimolecular step, or dissocia-
tion/isomerisation of a single reactant molecule, which we refer to as a unimolecular step. Very rarely,
under conditions of extremely high pressure, a termolecular step may occur, which involves simulta-
neous collision of three reactant molecules. An important point to recognise is that many reactions
that are written as a single reaction equation in actual fact consist of a series of elementary steps.
This will become extremely important as we learn more about the theory of chemical reaction rates.
As a general rule, elementary processes involve a transition between two atomic or molecular states
separated by a potential barrier. The potential barrier constitutes the activation energy of the pro-
cess, and determines the rate at which it occurs. When the barrier is low, the thermal energy of the
reactants will generally be high enough to surmount the barrier and move over to products, and the
reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient
energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the
source of the temperature dependence of reaction rates. The huge variety of chemical species, types
of reaction, and the accompanying potential energy surfaces involved means that the timescale over
which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as
iron rusting, to extremely fast reactions, such as the electron transfer processes involved in many
biological systems or the combustion reactions occurring in flames. A study into the kinetics of a
chemical reaction is usually carried out with one or both of two main goals in mind:
1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e. the reaction
mechanism.
2. Determination of the absolute rate of the reaction and/or its individual elementary steps.
RATE OF A REACTION
In general, for a reaction : R ? P, the behaviour of the concentration of the reactant and product, as
the reaction proceeds is shown graphically
CHEMICAL KINETICS
CHEMICAL KINETICS
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
2
www.learnershabitat.ac.in
From the graph, it is clear that the concentration of the reactant decreases and that of the product
increases as the reaction proceeds and the rate of the change of the concentration of the reactant as
well as that of the product is also changing.
Rate of a reaction can, now, be defined in two ways :
Average Rate of reaction (r
av
) given by for the reaction R ? P :
r
av
 = 
[R]
–
t
?
?
 = 
[P]
t
?
?
where ?[R] and ?[P] represents the change in the concentrations of 'R' and 'P' respectively over a time
interval ?t
The average rate of the reaction between a time interval (t
f
 – t
i 
= ?t) can be determined from the above
graph by locating the concentration of 'R' of 'P' on this graph at the time instants t
f
 and t
i
 as shown.
If [R]
f
 and [R]
i
 are the concentrations of the reactant 'A' at the time instants t
f
 and t
i
 then :
av
[R] –[R]
r –
t – t
? ?
?
? ?
? ?
f i
f i
Similarly from the plot of 'P' as a function of 't', we have : av
[P] –[P]
r
t – t
? ?
?
? ?
? ?
f i
f i
Note :
The above expression for r
av
 is equivalent to the slope of the line joining the points (t
f 
, [A]
f
)
and (t
i 
, [R]
i
) or (t
f 
, [P]
f
) and (t
i 
, [P]
i
) as shown.
Instantaneous Rate of reaction (r
inst.
) can be calculated from r
av
in the limit ?t ? 0 and is represented as :
r
inst.
 = 
d[R] d[P]
–
dt dt
?
Note : The above expression for r
inst. 
is equivalent to the slope of the tangent from the plot of the
concentration of 'R' or 'P' at any time instant 't'.
The rate of the reaction (r
inst.
 or r
av
) is always calculated as a positive quantity.
The rate of a reaction at any temperature depends on the concentration of the reactants and
sometimes on the concentration of some foreign substances (e.g a catalyst) being used in the
reaction as well. The representation of this dependence of the rate of the reaction on the
concentrations is known as rate law and this rate law is determined experimentally.
Units of rate of a reaction
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 gas is
expressed in terms of their partial pressures, then the units of the rate equation will be atm s
–1
.
Relation between various rates :
In general for a reaction : aA + bB ? cC + dD
The rate of reaction can be expressed as follows :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
3
www.learnershabitat.ac.in
ORDER OF A REACTION
By performing a reaction in actual in laboratory and carefully examining it, it is possible to express the
rate law as the product of concentrations of reactants each raised to some power. For example
consider the reaction : aA + bB ? cC + dD. The differential rate law is written as :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
where k
r
 is called as rate constant of the reaction or velocity constant or specific reaction rate.
k is a characteristic of a reaction at a given temperature. It changing only when the temperature changes.
The powers m and n are integers or fractions. m is called as order of reaction with respect to A and n
is called as order of reaction with respect to B.The overall order of reaction = m + n
Hence, the sum of powers of the concentration of the reactants in the rate law expression is
called the order of that chemical reaction.
The values of m and n are calculated from the experimental data obtained for a reaction and
the powers m and n are not related to the stoichiometric coefficients of the reactants
Order can be fractional,  zero or negative.
For example consider the following reaction :
(i) H
2
(g) + Br
2
(g) ? 2 HBr (g) rate = k[H
2
] [Br
2
]
1/2
 
(by experiment), order of reaction = 1 + 1/2 = 3/2
(ii) CH
3
CHO(g) ? CH
4
(g) + CO(g), rate = k[CH
3
CHO]
3/2 
, order of reaction = 3/2
Units of k :
In general, the rate law for a n
th
 order reaction can be taken as :
dc
dt
kc
n
? –
where k : rate constant; c : concentrationand n : order of reaction
?
k
dc dt
c
n
?
/
? Units of k ? (mol/L)
1–n
 (time)
–1
For a 'zero' order reaction (n = 0) : Units of k = (mol/L)
1
 (time)
–1
   or  mol/L/sec
For a first order reaction (n = 1) : Units of k ? (time)
–1
 e.g. sec
–1
, min
–1
, hrs
–1
 etc.
For a second order reaction (n = 2) : Units of k ? (mol/L)
–1
 (time)
–1
?or L/mol/sec.
MOLECULARITY
As already discussed, the order of a reaction is an experimental concept.
A complex chemical reaction is understood in terms of various indirect steps called elementary processes.
The study of a reaction in terms of elementary processes is called as reaction mechanism. Now various
elementary steps occur at different rates.
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction,
which must collide simultaneously in order to bring about a chemical reaction is called
molecularity of a reaction.
In the rate determining step, when one molecule takes part, it is said to be a unimolecular reaction ;
two molecules take part, it is said to be a bimolecular reaction; three molecules take part, it is said to
be a termolecular reaction.
Unimolecular :
1. Cyclopropane ? propene
2. O
3
(g) ? O
2
(g) + O(g)
3. N
2
O
5
(g) ? N
2
O
4
(g) + 1/2O
2
(g)
Page 4


Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
1
www.learnershabitat.ac.in
This branch of chemistry which deals with the study of rates of chemical reactions and the mechanism
by which they occur. While studying reaction, one deals with :
(a) how fast (or slow) the reactants get converted into products
(b) the steps or paths through which the products are formed (reaction mechanism)
Chemical reaction kinetics deals with the rates of chemical processes. Any chemical process may be
broken down into a sequence of one or more single-step processes known either as elementary
processes, elementary reactions, or elementary steps. Elementary reactions usually involve either a
single reactive collision between two molecules, which we refer to as a a bimolecular step, or dissocia-
tion/isomerisation of a single reactant molecule, which we refer to as a unimolecular step. Very rarely,
under conditions of extremely high pressure, a termolecular step may occur, which involves simulta-
neous collision of three reactant molecules. An important point to recognise is that many reactions
that are written as a single reaction equation in actual fact consist of a series of elementary steps.
This will become extremely important as we learn more about the theory of chemical reaction rates.
As a general rule, elementary processes involve a transition between two atomic or molecular states
separated by a potential barrier. The potential barrier constitutes the activation energy of the pro-
cess, and determines the rate at which it occurs. When the barrier is low, the thermal energy of the
reactants will generally be high enough to surmount the barrier and move over to products, and the
reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient
energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the
source of the temperature dependence of reaction rates. The huge variety of chemical species, types
of reaction, and the accompanying potential energy surfaces involved means that the timescale over
which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as
iron rusting, to extremely fast reactions, such as the electron transfer processes involved in many
biological systems or the combustion reactions occurring in flames. A study into the kinetics of a
chemical reaction is usually carried out with one or both of two main goals in mind:
1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e. the reaction
mechanism.
2. Determination of the absolute rate of the reaction and/or its individual elementary steps.
RATE OF A REACTION
In general, for a reaction : R ? P, the behaviour of the concentration of the reactant and product, as
the reaction proceeds is shown graphically
CHEMICAL KINETICS
CHEMICAL KINETICS
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
2
www.learnershabitat.ac.in
From the graph, it is clear that the concentration of the reactant decreases and that of the product
increases as the reaction proceeds and the rate of the change of the concentration of the reactant as
well as that of the product is also changing.
Rate of a reaction can, now, be defined in two ways :
Average Rate of reaction (r
av
) given by for the reaction R ? P :
r
av
 = 
[R]
–
t
?
?
 = 
[P]
t
?
?
where ?[R] and ?[P] represents the change in the concentrations of 'R' and 'P' respectively over a time
interval ?t
The average rate of the reaction between a time interval (t
f
 – t
i 
= ?t) can be determined from the above
graph by locating the concentration of 'R' of 'P' on this graph at the time instants t
f
 and t
i
 as shown.
If [R]
f
 and [R]
i
 are the concentrations of the reactant 'A' at the time instants t
f
 and t
i
 then :
av
[R] –[R]
r –
t – t
? ?
?
? ?
? ?
f i
f i
Similarly from the plot of 'P' as a function of 't', we have : av
[P] –[P]
r
t – t
? ?
?
? ?
? ?
f i
f i
Note :
The above expression for r
av
 is equivalent to the slope of the line joining the points (t
f 
, [A]
f
)
and (t
i 
, [R]
i
) or (t
f 
, [P]
f
) and (t
i 
, [P]
i
) as shown.
Instantaneous Rate of reaction (r
inst.
) can be calculated from r
av
in the limit ?t ? 0 and is represented as :
r
inst.
 = 
d[R] d[P]
–
dt dt
?
Note : The above expression for r
inst. 
is equivalent to the slope of the tangent from the plot of the
concentration of 'R' or 'P' at any time instant 't'.
The rate of the reaction (r
inst.
 or r
av
) is always calculated as a positive quantity.
The rate of a reaction at any temperature depends on the concentration of the reactants and
sometimes on the concentration of some foreign substances (e.g a catalyst) being used in the
reaction as well. The representation of this dependence of the rate of the reaction on the
concentrations is known as rate law and this rate law is determined experimentally.
Units of rate of a reaction
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 gas is
expressed in terms of their partial pressures, then the units of the rate equation will be atm s
–1
.
Relation between various rates :
In general for a reaction : aA + bB ? cC + dD
The rate of reaction can be expressed as follows :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
3
www.learnershabitat.ac.in
ORDER OF A REACTION
By performing a reaction in actual in laboratory and carefully examining it, it is possible to express the
rate law as the product of concentrations of reactants each raised to some power. For example
consider the reaction : aA + bB ? cC + dD. The differential rate law is written as :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
where k
r
 is called as rate constant of the reaction or velocity constant or specific reaction rate.
k is a characteristic of a reaction at a given temperature. It changing only when the temperature changes.
The powers m and n are integers or fractions. m is called as order of reaction with respect to A and n
is called as order of reaction with respect to B.The overall order of reaction = m + n
Hence, the sum of powers of the concentration of the reactants in the rate law expression is
called the order of that chemical reaction.
The values of m and n are calculated from the experimental data obtained for a reaction and
the powers m and n are not related to the stoichiometric coefficients of the reactants
Order can be fractional,  zero or negative.
For example consider the following reaction :
(i) H
2
(g) + Br
2
(g) ? 2 HBr (g) rate = k[H
2
] [Br
2
]
1/2
 
(by experiment), order of reaction = 1 + 1/2 = 3/2
(ii) CH
3
CHO(g) ? CH
4
(g) + CO(g), rate = k[CH
3
CHO]
3/2 
, order of reaction = 3/2
Units of k :
In general, the rate law for a n
th
 order reaction can be taken as :
dc
dt
kc
n
? –
where k : rate constant; c : concentrationand n : order of reaction
?
k
dc dt
c
n
?
/
? Units of k ? (mol/L)
1–n
 (time)
–1
For a 'zero' order reaction (n = 0) : Units of k = (mol/L)
1
 (time)
–1
   or  mol/L/sec
For a first order reaction (n = 1) : Units of k ? (time)
–1
 e.g. sec
–1
, min
–1
, hrs
–1
 etc.
For a second order reaction (n = 2) : Units of k ? (mol/L)
–1
 (time)
–1
?or L/mol/sec.
MOLECULARITY
As already discussed, the order of a reaction is an experimental concept.
A complex chemical reaction is understood in terms of various indirect steps called elementary processes.
The study of a reaction in terms of elementary processes is called as reaction mechanism. Now various
elementary steps occur at different rates.
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction,
which must collide simultaneously in order to bring about a chemical reaction is called
molecularity of a reaction.
In the rate determining step, when one molecule takes part, it is said to be a unimolecular reaction ;
two molecules take part, it is said to be a bimolecular reaction; three molecules take part, it is said to
be a termolecular reaction.
Unimolecular :
1. Cyclopropane ? propene
2. O
3
(g) ? O
2
(g) + O(g)
3. N
2
O
5
(g) ? N
2
O
4
(g) + 1/2O
2
(g)
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
4
www.learnershabitat.ac.in
Bimolecular :
1. NO(g) + O
3
 (g) ? NO
2
(g) + O
2
(g)
2. 2HI(g) ? H
2
(g) + I
2
(g)
Termolecular :
1. 2NO(g) + O
2
(g) ? 2NO
2
 (g)
The probability that more than three molecules can collide and react simultaneously is very small.
Hence, reactions with the molecularity three are very rare and slow to proceed. It is, therefore,
evident that complex reactions involving more than three molecules in the stoichiometric equation
must take place in more than one step.
KClO
3
 + 6FeSO
4
 + 3H
2
SO
4
 ? KCl + 3Fe
2
(SO
4
)
3
 + 3H
2
O
This reaction which apparently seems to be of tenth order is actually a second order reaction. This shows
that this reaction takes place in several steps. Which step controls the rate of the overall reaction? The
question can be answered if we go through the mechanism of reaction, for example, chances to win the
relay race competition by a team depend upon the slowest person in the team. Similarly, the overall rate of
the reaction is controlled by the slowest step in a reaction called the rate determining step.
(i) Order of a reaction is an experimental quantity. It can be zero and even a fraction but
molecularity cannot be zero or a non integer.
(ii) Order is applicable to elementary as well as complex reactions whereas molecularity is appli-
cable only for elementary reactions. For complex reaction molecularity has no meaning. 103
Chemical Kinetics
(iii) For complex reaction, order is given by the slowest step and molecularity of the slowest step
is same as the order of the overall reaction.
For a reaction : A ? B in the rate law : rate = k[A]
m
 [B]
n
Neither the order of reaction (m + n) nor the molecularity of a reaction can be predicted from
stoichiometric coefficient of a balanced reaction. The order of reaction is always to be determined
experimentally and molecularity is determined theoretically after studying the reaction mechanism.
However as a theoretical idea sometime, we can have an approximate order of reaction equal to
molecularity (i.e., the number of molecules taking part in slowest elementary for complex reactions).
Problem 1 :
The rate of formation of NO(g) in the reaction NOBr(g) ? NO(g) + Br
2
(g) is found to be 1.6 × 10
–4
 M/s.
Find the rate of overall reaction rate and rate of consumption of NOBr.
We have :
d NO
dt
[ ]
? 1.6 × 10
–4
 M/s.
First write a balanced chemical equation. 2NOBr(g) ? 2NO(g) + Br
2
(g)
Now, Rate of overall reaction = –
[ ] 1
2
d NOBr
dt
 = ?
1
2
d NO
dt
[ ]
 = 
1
1
2
d Br
dt
[ ]
 = 0.8 × 10
–4
 M/s
Rate of consumption of NOBr = –
d NOBr
dt
[ ]
 = +1.6 × 10
–4
 M/s
Problem 2 :
The rate constant for a given reaction is k = 3 × 10
–5
 s
–1
 atm
–1
. Express it in units of L mol
–1
 sec
–1
.
Sol. PV = nRT ? P = cRT (c : concentration in mol/L)
Substitute R = 0.0821  L–atm/mol/K ; T = 273 K ; P = 1 atm  ? c = 0.04462 mol/L
? k ?
? 3 10
0 04462
–5
.
 = 6.73 × 10
–4
 L/mol/s.
Page 5


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This branch of chemistry which deals with the study of rates of chemical reactions and the mechanism
by which they occur. While studying reaction, one deals with :
(a) how fast (or slow) the reactants get converted into products
(b) the steps or paths through which the products are formed (reaction mechanism)
Chemical reaction kinetics deals with the rates of chemical processes. Any chemical process may be
broken down into a sequence of one or more single-step processes known either as elementary
processes, elementary reactions, or elementary steps. Elementary reactions usually involve either a
single reactive collision between two molecules, which we refer to as a a bimolecular step, or dissocia-
tion/isomerisation of a single reactant molecule, which we refer to as a unimolecular step. Very rarely,
under conditions of extremely high pressure, a termolecular step may occur, which involves simulta-
neous collision of three reactant molecules. An important point to recognise is that many reactions
that are written as a single reaction equation in actual fact consist of a series of elementary steps.
This will become extremely important as we learn more about the theory of chemical reaction rates.
As a general rule, elementary processes involve a transition between two atomic or molecular states
separated by a potential barrier. The potential barrier constitutes the activation energy of the pro-
cess, and determines the rate at which it occurs. When the barrier is low, the thermal energy of the
reactants will generally be high enough to surmount the barrier and move over to products, and the
reaction will be fast. However, when the barrier is high, only a few reactants will have sufficient
energy, and the reaction will be much slower. The presence of a potential barrier to reaction is also the
source of the temperature dependence of reaction rates. The huge variety of chemical species, types
of reaction, and the accompanying potential energy surfaces involved means that the timescale over
which chemical reactions occur covers many orders of magnitude, from very slow reactions, such as
iron rusting, to extremely fast reactions, such as the electron transfer processes involved in many
biological systems or the combustion reactions occurring in flames. A study into the kinetics of a
chemical reaction is usually carried out with one or both of two main goals in mind:
1. Analysis of the sequence of elementary steps giving rise to the overall reaction. i.e. the reaction
mechanism.
2. Determination of the absolute rate of the reaction and/or its individual elementary steps.
RATE OF A REACTION
In general, for a reaction : R ? P, the behaviour of the concentration of the reactant and product, as
the reaction proceeds is shown graphically
CHEMICAL KINETICS
CHEMICAL KINETICS
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
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From the graph, it is clear that the concentration of the reactant decreases and that of the product
increases as the reaction proceeds and the rate of the change of the concentration of the reactant as
well as that of the product is also changing.
Rate of a reaction can, now, be defined in two ways :
Average Rate of reaction (r
av
) given by for the reaction R ? P :
r
av
 = 
[R]
–
t
?
?
 = 
[P]
t
?
?
where ?[R] and ?[P] represents the change in the concentrations of 'R' and 'P' respectively over a time
interval ?t
The average rate of the reaction between a time interval (t
f
 – t
i 
= ?t) can be determined from the above
graph by locating the concentration of 'R' of 'P' on this graph at the time instants t
f
 and t
i
 as shown.
If [R]
f
 and [R]
i
 are the concentrations of the reactant 'A' at the time instants t
f
 and t
i
 then :
av
[R] –[R]
r –
t – t
? ?
?
? ?
? ?
f i
f i
Similarly from the plot of 'P' as a function of 't', we have : av
[P] –[P]
r
t – t
? ?
?
? ?
? ?
f i
f i
Note :
The above expression for r
av
 is equivalent to the slope of the line joining the points (t
f 
, [A]
f
)
and (t
i 
, [R]
i
) or (t
f 
, [P]
f
) and (t
i 
, [P]
i
) as shown.
Instantaneous Rate of reaction (r
inst.
) can be calculated from r
av
in the limit ?t ? 0 and is represented as :
r
inst.
 = 
d[R] d[P]
–
dt dt
?
Note : The above expression for r
inst. 
is equivalent to the slope of the tangent from the plot of the
concentration of 'R' or 'P' at any time instant 't'.
The rate of the reaction (r
inst.
 or r
av
) is always calculated as a positive quantity.
The rate of a reaction at any temperature depends on the concentration of the reactants and
sometimes on the concentration of some foreign substances (e.g a catalyst) being used in the
reaction as well. The representation of this dependence of the rate of the reaction on the
concentrations is known as rate law and this rate law is determined experimentally.
Units of rate of a reaction
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 gas is
expressed in terms of their partial pressures, then the units of the rate equation will be atm s
–1
.
Relation between various rates :
In general for a reaction : aA + bB ? cC + dD
The rate of reaction can be expressed as follows :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
Chemical Kinetics – Nirmaan TYCRP
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ORDER OF A REACTION
By performing a reaction in actual in laboratory and carefully examining it, it is possible to express the
rate law as the product of concentrations of reactants each raised to some power. For example
consider the reaction : aA + bB ? cC + dD. The differential rate law is written as :
Rate = 
1 d[A]
–
a dt
 = 
1 d[B]
–
b dt
 = + 
1 d[C]
c dt
 = 
1 d[D]
d dt
?
 = k
r
[A]
m
[B]
n
where k
r
 is called as rate constant of the reaction or velocity constant or specific reaction rate.
k is a characteristic of a reaction at a given temperature. It changing only when the temperature changes.
The powers m and n are integers or fractions. m is called as order of reaction with respect to A and n
is called as order of reaction with respect to B.The overall order of reaction = m + n
Hence, the sum of powers of the concentration of the reactants in the rate law expression is
called the order of that chemical reaction.
The values of m and n are calculated from the experimental data obtained for a reaction and
the powers m and n are not related to the stoichiometric coefficients of the reactants
Order can be fractional,  zero or negative.
For example consider the following reaction :
(i) H
2
(g) + Br
2
(g) ? 2 HBr (g) rate = k[H
2
] [Br
2
]
1/2
 
(by experiment), order of reaction = 1 + 1/2 = 3/2
(ii) CH
3
CHO(g) ? CH
4
(g) + CO(g), rate = k[CH
3
CHO]
3/2 
, order of reaction = 3/2
Units of k :
In general, the rate law for a n
th
 order reaction can be taken as :
dc
dt
kc
n
? –
where k : rate constant; c : concentrationand n : order of reaction
?
k
dc dt
c
n
?
/
? Units of k ? (mol/L)
1–n
 (time)
–1
For a 'zero' order reaction (n = 0) : Units of k = (mol/L)
1
 (time)
–1
   or  mol/L/sec
For a first order reaction (n = 1) : Units of k ? (time)
–1
 e.g. sec
–1
, min
–1
, hrs
–1
 etc.
For a second order reaction (n = 2) : Units of k ? (mol/L)
–1
 (time)
–1
?or L/mol/sec.
MOLECULARITY
As already discussed, the order of a reaction is an experimental concept.
A complex chemical reaction is understood in terms of various indirect steps called elementary processes.
The study of a reaction in terms of elementary processes is called as reaction mechanism. Now various
elementary steps occur at different rates.
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction,
which must collide simultaneously in order to bring about a chemical reaction is called
molecularity of a reaction.
In the rate determining step, when one molecule takes part, it is said to be a unimolecular reaction ;
two molecules take part, it is said to be a bimolecular reaction; three molecules take part, it is said to
be a termolecular reaction.
Unimolecular :
1. Cyclopropane ? propene
2. O
3
(g) ? O
2
(g) + O(g)
3. N
2
O
5
(g) ? N
2
O
4
(g) + 1/2O
2
(g)
Chemical Kinetics – Nirmaan TYCRP
LEARNERS HABITAT EXPERTS Pvt. Ltd.: 97/1, IIIrd Floor, Near NCERT, Adchini, New Delhi, 011-32044009
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Bimolecular :
1. NO(g) + O
3
 (g) ? NO
2
(g) + O
2
(g)
2. 2HI(g) ? H
2
(g) + I
2
(g)
Termolecular :
1. 2NO(g) + O
2
(g) ? 2NO
2
 (g)
The probability that more than three molecules can collide and react simultaneously is very small.
Hence, reactions with the molecularity three are very rare and slow to proceed. It is, therefore,
evident that complex reactions involving more than three molecules in the stoichiometric equation
must take place in more than one step.
KClO
3
 + 6FeSO
4
 + 3H
2
SO
4
 ? KCl + 3Fe
2
(SO
4
)
3
 + 3H
2
O
This reaction which apparently seems to be of tenth order is actually a second order reaction. This shows
that this reaction takes place in several steps. Which step controls the rate of the overall reaction? The
question can be answered if we go through the mechanism of reaction, for example, chances to win the
relay race competition by a team depend upon the slowest person in the team. Similarly, the overall rate of
the reaction is controlled by the slowest step in a reaction called the rate determining step.
(i) Order of a reaction is an experimental quantity. It can be zero and even a fraction but
molecularity cannot be zero or a non integer.
(ii) Order is applicable to elementary as well as complex reactions whereas molecularity is appli-
cable only for elementary reactions. For complex reaction molecularity has no meaning. 103
Chemical Kinetics
(iii) For complex reaction, order is given by the slowest step and molecularity of the slowest step
is same as the order of the overall reaction.
For a reaction : A ? B in the rate law : rate = k[A]
m
 [B]
n
Neither the order of reaction (m + n) nor the molecularity of a reaction can be predicted from
stoichiometric coefficient of a balanced reaction. The order of reaction is always to be determined
experimentally and molecularity is determined theoretically after studying the reaction mechanism.
However as a theoretical idea sometime, we can have an approximate order of reaction equal to
molecularity (i.e., the number of molecules taking part in slowest elementary for complex reactions).
Problem 1 :
The rate of formation of NO(g) in the reaction NOBr(g) ? NO(g) + Br
2
(g) is found to be 1.6 × 10
–4
 M/s.
Find the rate of overall reaction rate and rate of consumption of NOBr.
We have :
d NO
dt
[ ]
? 1.6 × 10
–4
 M/s.
First write a balanced chemical equation. 2NOBr(g) ? 2NO(g) + Br
2
(g)
Now, Rate of overall reaction = –
[ ] 1
2
d NOBr
dt
 = ?
1
2
d NO
dt
[ ]
 = 
1
1
2
d Br
dt
[ ]
 = 0.8 × 10
–4
 M/s
Rate of consumption of NOBr = –
d NOBr
dt
[ ]
 = +1.6 × 10
–4
 M/s
Problem 2 :
The rate constant for a given reaction is k = 3 × 10
–5
 s
–1
 atm
–1
. Express it in units of L mol
–1
 sec
–1
.
Sol. PV = nRT ? P = cRT (c : concentration in mol/L)
Substitute R = 0.0821  L–atm/mol/K ; T = 273 K ; P = 1 atm  ? c = 0.04462 mol/L
? k ?
? 3 10
0 04462
–5
.
 = 6.73 × 10
–4
 L/mol/s.
Chemical Kinetics – Nirmaan TYCRP
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Problem 3 :
From the rate laws for the reactions given below, determine the order with respect to each
species and the overall order :
(i) 2HCrO
4
–
 + 6I
–
 + 14H
+
 ?  2Cr
3+
 + 3I
2
 + 8H
2
O, Rate = k[HCrO
4
–
] [I
–
]
2
 [H
+
]
2
(ii) H
2
O
2
 + 2I
–
 + 2H
+
 ? I
2
 + 2H
2
O, Rate = k[H
2
O
2
] [I
–
]
Sol. (i) The order of the reaction with respect to [HCrO
4
–
] is 1; with respect to [I
–
] is 2 and with
respect to [H
+
] is 2. The overall order of the reaction is 1 + 2 + 2 = 5
(ii) The order of the reaction with  respect to [H
2
O
2
] is 1 and with respect to [I
–
] is 1. The overall
order of the reaction is 1 + 1= 2.
In (i) stoichiometric coefficient of I
–
 is 6 whereas the power coefficient (n) in the rate law is 2.
Reaction (i) may not take place in a single step. It may not be possible for all the 22 molecules
to be in a state to collide with each other simultaneously. Such a reaction is called a complex reaction.
A complex reaction takes place in a series of a number of elementary reactions.
Zero Order Reactions :
The rate law for zero order reactions (n = 0) is written as :
  A        
 
    product
        t=o a = [A]
o
o
        t=t a – x = [A] x
? ? [A] k   
dt
[A] d
  –
Slope = –k
[A]
0
t
[A]
– k  
dt
[A] 
?
d
– 
? ?
?
[A] 
[A] 
t 
o 
o
dt k   [A] d 
[A]
o
 – [A] = kt
t
[A] – [A]
   k
o
?
 = 
x
t
? Half life (t
 1/2
) :
Time in which half of initial amount is left.
[A]
o 
 ? ? ? [A]
o
/2
t = o     t = t
1/2
A
0
t
1 2 /
k = 
1/2
o o
t
/2 [A] – [A]
t
1/2
 = 
k 2
[A]
o
Thus, for a Zero order reaction, half life is directly proportional to initial concentration of the reactant.
Clearly, zero order reactions are those, whose rates are not affected by change in concentrations of
reactants (i.e., independent of concentration). The rates of such reactions only depend upon
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