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The branch of physical chemistry which deals with
the rate at which the chemical reactions occur, the
mechanism by which the chemical reactions take place
and the influence of various factors such as
concentration, temperature, pressure, catalyst etc., on
the reaction rates is called the chemical kinetics.
Types of chemical reactions
On the basis of reaction rates, the chemical
reactions have been classified into the following three
types,
(1) Very fast or instantaneous reactions : These
reactions occur at a very fast rate generally these
reactions involve ionic species and known as ionic
reactions. It is almost impossible to determine the rates
of these reactions.
Examples
(i) 3 (PPt.)
AgNO 3 (^) NaCl AgCl NaNO ( Precipitation
reaction )
(ii) HCl NaOH NaCl H 2 O (acid) (base) (Salt)
( Neutralization
reaction )
(2) Moderate reaction : These reactions proceed
with a measurable rates at normal temperature and it
is these reactions are studied in chemical kinetics.
Mostly these reactions are molecular in nature.
Examples
(i) Decomposition of H 2 O 2
2 H 2 O 2 2 H 2 O O 2
(ii) Decomposition of N 2 O 5 : 2 N (^) 2 O 5 2 N 2 O 4 O 2
(3) Very slow reactions : These reactions are
extremely slow and take months together to show any
measurable change.
Examples
(i) Rusting of iron :
Hy drated ferricoxide(Rust)
Fe 2 (^) O 3 xH 2 O Fe 2 O 3. xH 2 O
(ii) H^ O H 2 O
Roomtemperature 2 2 2 2
Rate of a reaction
The rate ( speed or velocity ) of a reaction is the
change in concentration in per unit time.
t
x
or
2 1
2 1
t t
x x
dt
dx
where x or dx is the concentration change, i.e.,
( x (^) 2 x 1 )^ in the time interval^ t or^ dt, i.e.,^ ( t (^) 2 t 1 ).
Concentration is generally expressed in active mass, i.e.,
mole L
- 1
The rate measured over a long time interval is
called average rate and the rate measured for an
infinitesimally small time interval is called
instantaneous rate and
Instantaneous rate(Average rate)t 0
For the reaction aA bB cC dD
Rate of disappearance of a reactant is negative
dt
d [ A ] Rate of disappearance of A
dt
d [ B ] Rate of disappearance of B
Rate of formation of a product is positive
dt
d [ C ] Rate of formation of C
Chemical Kinetics
Chapter
dt
d [ D ] Rate of formation of D
In terms of stoichiometric coefficient rate may
be expressed as
dt
dD
dt d
dC
dt c
dB
dt b
dA
dt a
dx 1 [] 1 [ ] 1 [] 1 [ ]
The rate of reaction is always positive.
The rate of chemical reaction decreases as the
reaction proceeds.
Unit of rate of a reaction = Unitof time
Unitofconc. =mole L
- 1
time
- 1
In term of gaseous reaction the unit is atm time
and
Rate in atm time
- 1 = Rate in mole L^ time RT
1 1
Factors affecting rate of a reaction
The rate of a chemical reaction depends on the
following things
(1) Nature of reactants
(i) Physical state of reactants : This has
considerable effect over rate of reaction.
Decreasingrateofreaction
Gaseous satae Liquidstate Solidstate
(ii) Physical size of the reactants : Among the
solids, rate increases with decrease in particle size of
the solid.
(iii) Chemical nature of the reactants
(a) Reactions involving polar and ionic
substances including the proton transfer reactions are
usually very fast. On the other hand, the reaction in
which bonds is rearranged, or electrons transferred are
slow.
(b) Oxidation-reduction reactions, which
involve transfer of electrons, are also slow as
compared to the ionic substance.
(c) Substitution reactions are relatively much
slower.
(2) Effect of temperature : The rate of chemical
reaction generally increases on increasing the
temperature. The rate of a reaction becomes almost
double or tripled for every C
o 10 rise in temperature.
Temperature coefficient of a reaction is defined as
the ratio of rate constants at two temperatures
differing by (generally 25° C and 35° C ) 10° C.
C
C o o
o
k
k
k tC
k C
25
35
o
at
at(t 10 ) Temperatur ecoefficient
(3) Concentration of reactants : The rate of a
chemical reaction is directly proportional to the
concentration of the reactants means rate of reaction
decreases with decrease in concentration.
(4) Presence of catalyst : The function of a
catalyst is to lower down the activation energy. The
greater the decrease in the activation energy caused by
the catalyst, higher will be the reaction rate.
(5) Effect of sunlight : There are many chemical
reactions whose rate are influenced by radiations
particularly by ultraviolet and visible light. Such
reactions are called photochemical reactions. For
example, Photosynthesis, Photography, Blue printing,
Photochemical synthesis of compounds etc.
The radiant energy initiates the chemical reaction
by supplying the necessary activation energy required
for the reaction.
Law of mass action and Rate constant
The rate at which a substance reacts is directly
proportional to its active mass and the rate at which a
reaction proceeds is proportional to the product of the
active masses of the reacting substances.
For a reaction, aA bB product
Rate
a b A B dt
dx [ ][]
;
a b kA B dt
dx [ ][ ]
Where k is called rate constant or velocity
constant.
When [ A ][ B ] 1 mol / litre , then k dt
dx
Thus, rate constant k is also called specific
reaction rate.
The value of rate constant depends on, nature
of reactant, temperature and catalyst. It is independent
of concentration of the reactants.
Unit of rate constant
1
1
sec mol
litre (^)
^
n 1
1
sec litre
mol (^)
^
n
Where n order of reaction.
Rate law : Molecularity and Order of a reaction
Molecularity is the sum of the number of molecules
of reactants involved in the balanced chemical equation.
Molecularity of a complete reaction has no significance
and overall kinetics of the reaction depends upon the
rate determining step. Slowest step is the rate-
determining step. This was proposed by Van't Hoff.
Example : NH NO N HO 4 2 2 2 2 (Unimolecular)
NO O 3 NO 2 O 2
(Bimolecular)
Reaction path with catalyst
Ea
Ea
Reaction path Without catalyst
Energy of Reaction
Reactants
Products
Potential Energy A catalyst changes the reaction path
*Pseudo-unimolecular reactions.
Table : 11.2 Rate constant and other parameters of different order reactions
Orde
r
Rate constant Unit of rate
constant
Effect on rate by
changing conc. to m
times
(Half-life
period) T 50 =
t
x k (^) 0
conc. time
(mol L
No change
2 k 0
a
a x
a
t
k (^) 1 log 10
(^2). 303 ,
kt C C 0 e^1
kt N N e 1 0
, ( )
log ( )
2
1 10 2 1
1 a x
a x
t t
k
time
1
k
t a x a
k
2 ta ( a x )
x
(for the case
when each reactant has equal
concentration)
log ( )
2 10 ab x
ba x
ta b
k (for the case
when both reactants have different
concentration)
conc
(mol L
L mol
m
2 times
k (^) 2 a
(^322)
t a x a
k
conc
(mol L
L
2 mol
m
3 times 2 (^23)
k a
n
1 1 ()
n (^) n n n t a x a
k ; n 2
conc (1– n ) time
1
(mol L
(1– n )
s
L
( n– 1) mol
(1– n )
s
m n times
1
1
n n
n
n k a
Methods for determination of order of a reaction
(1) Integration method (Hit and Trial method)
(i) The method can be used with various sets of
a , x and t with integrated rate equations.
(ii) The value of k is determined and checked for
all sets of a , x and t.
(iii) If the value of (^) k is constant, the used
equation gives the order of reaction.
(iv) If all the reactants are at the same molar
concentration, the kinetic equations are :
log
10 a x
a
t
k
^ ( For^ first^ order
reactions )
t a a x
k
1 1 1 ( For second order
reactions )
2 2
1
( )
1
2
1
t a x a
k ( For third order
reactions )
(2) Half-life method : This method is employed
only when the rate law involved only one concentration
term.
n t a
1 1 / 2 ;
n t ka
1 (^1) / 2 ;log t (^) 1 / 2 log k ( 1 n )log a
A plotted graph of log t 1 / 2 vs log a gives a straight
line with slope ( 1 n ), determining the slope we can
find the order n. If half-life at different concentration
is given then,
1 1
1 / 21 ^ n a
t ;
1 2
1 / 22 ^ n a
t
1
1
2
1 / 22
1 / 21
( )
n
a
a
t
t
log 10 ( t 1 (^) / 2 ) 1 log 10 ( t 1 / 2 ) 2 ( n 1 )[log 10 a 2 log 10 a 1 ]
(log log )
log ( ) log ( ) 1 10 2 10 1
10 1 / 21 10 1 / 22
a a
t t n
This relation can be used to determine order of
reaction ‘ n ’
Plots of half-lives Vs concentrations (t1/2 a
1 – n )
t 1/
Conc.
Zero order
t 1/
1/a
2 nd
order
t 1/
1/a 2
3 rd
order
t 1/
Conc.
1 st order
(3) Graphical method : A graphical method
based on the respective rate laws, can also be used.
(i) If the plot of log( a x )Vs t is a straight line,
the reaction follows first order.
(ii) If the plot of ( )
a x
Vs t is a straight line, the
reaction follows second order.
(iii) If the plot of 2 ( )
a x
Vs t is a straight line,
the reaction follows third order.
(iv) In general, for a reaction of nth order, a
graph of 1 ( )
n a x
Vs t must be a straight line.
Plots from integrated rate equations
Plots of rate Vs concentrations [Rate = k(conc.) n
]
(4) Van't Haff differential method : The rate of
reaction varies as the n th power of the concentration
Where ' n 'is the order of the reaction. Thus for two
different initial concentrations C 1 and C 2 equation,
can be written in the form,
n kC dt
dC 1
1
and n kC dt
dC 2
2
Taking logarithms,
10 10 1
1 log 10 log k n log C dt
dC
…..(i)
and 10 10 2
2 log 10 log k n log C dt
dC
…..(ii)
Subtracting equation (ii) from (i),
10 1 10 2
2 10
1 10
log log
log log
C C
dt
dC
dt
dC
n
…..(iii)
dt
dC 1 and dt
dC (^) 2 are determined from
concentration Vs time graphs and the value of ' n 'can
be determined.
(5) Ostwald's isolation method (Initial rate
method)
This method can be used irrespective of the
number of reactants involved e.g., consider the
reaction, n 1 A n 2 B n 3 C Products.
This method consists in finding the initial rate of
the reaction taking known concentrations of the
different reactants ( A , B , C ).
Suppose it is observed as follows,
(i) Keeping the concentrations of B and C
constant, if concentration of A is doubled, the rate of
reaction becomes four times. This means that, Rate
2 [ A ] i.e., order with respect to A is 2
(ii) Keeping the concentrations of A and C
constant, if concentration of B is doubled, the rate of
reaction is also doubled. This means that, Rate [ B ]
i.e., order with respect to B is 1
(iii) Keeping the concentrations of A and B
constant, if concentration of C is doubled, the rate of
reaction remains unaffected. This means that rate is
independent of the concentration of C i.e., order with
respect to C is zero. Hence the overall rate law
expression will be, Rate = k [ A ]
2 [ B ] [ C ]
0
Overall order of reaction = 2 + 1 + 0 = 3.
Theories of reaction rate
(1) Collision theory
(i) The basic requirement for a reaction to occur
is that the reacting species must collide with one
another. This is the basis of collision theory for
reactions.
(ii) The number of collisions that takes place per
second per unit volume of the reaction mixture is
known as collision frequency ( Z ). The value of collision
frequency is very high of the order of
25 28 10 to 10 in
case of binary collisions.
(iii) Every collision does not bring a chemical
change. The collisions that actually produce the product
are effective collisions. The effective collisions, which
bring chemical change, are few in comparison to the
total number of collisions. The collisions that do not
form a product are ineffective elastic collisions , i.e.,
molecules just collide and disperse in different
directions with different velocities.
Conc. [A]
t
Zero order
log. [A]
t
1 st order
[ ]
A
t
2 nd order
2 [ ]
A
3 rd order
t
Rate
Conc.
Zero order
Rate
Rate
( Conc. ) 2
2 nd
order
( Conc. ) 3
3 rd
order
Rate
Conc.
1 st
order
Fraction of molecules capable of bringing effective collisions
Distribution of energies at a definite temperature
Energy (^) E
Fraction of molecules
(2) Transition state theory
(i) According to transition state theory the
activated complex is supposed to be in equilibrium with
the reactant molecules.
(ii) Once the transition state is formed it can
either return to the initial reactants or proceeds to
form the products.
(iii) Assuming that once formed the transition state
proceeds to products we can say that rate is
proportional to concentration of transition state.
Mathematically, Rate Transition state
Rate= Constant × Transition state
(iv) The activation energy for the forward
reaction,( )
f Ea and the activation energy for the reverse
reaction ( )
r Ea are related to the enthalpy ( H )of the
reaction by the equation
r a
f H Ea E.
(a) For endothermic reactions , H 0 , so that
f a
r Ea E
(b) For exothermic reaction , H 0 , so that
f a
r Ea E.
Arrhenius equation
Arrhenius proposed a quantitative relationship
between rate constant and temperature as,
EaRT k A e
/ …..(i)
The equation is called Arrhenius equation.
In which constant A is known as frequency factor.
This factor is related to number of binary molecular
collision per second per litre.
Ea is the activation energy.
T is the absolute temperature and
R is the gas constant
Both A and Ea are collectively known as
Arrhenius parameters.
Taking logarithm equation (i) may be written as,
RT
E
k A
a
- 303
log log …..(ii)
The value of activation energy( ) Ea increases, the
value of k decreases and therefore, the reaction rate
decreases.
When log k plotted against 1 / T , we get a straight
line. The intercept of this line is equal to log A and
slope equal to R
Ea
Therefore Ea 2. 303 R slope.
Rate constants for the reaction at two different
temperatures T 1 and T 2 ,
1 1 2
2 1 1
- 303
log R T T
E
k
k (^) a …..(iii)
where k 1 and k 2 are rate constant at temperatures
T 1 and T 2 respectively ( T 2 (^) T 1 ).
Mechanism of the reaction
(1) Reaction involving first order consecutive
reactions
(i) In such reactions, the reactions form a stable
intermediate compound before they are finally
converted into the products.
(ii) For example, reactants ( R ) are first converted to
intermediate ( I ) which is then converted to product ( P ) as
R I P
k k 1 2
Therefore, the reaction takes place in two steps,
both of which are first order i.e.,
Step I : R I
k 1 ; Step II : I P
k 2
This means that I is produced by step I and consumed
by step II. In these reactions, each stage will have its
own rate and rate constant the reactant concentration
will always decrease and product concentration will
always increase as shown in fig.
(2) Reaction involving slow step : When a
reaction occurs by a sequence of steps and one of the
step is slow, then the rate determining step is the slow
step. For example in the reaction
R I
k 1 ; I P
k 2 , if k 1 (^) k 2 then I is
converted into products as soon as it is formed, we can
say that
[ ]
[ ] [ ] k 1 R dt
dP
dt
d R
(3) Parallel reactions : In such type of reactions
the reactants are more reactive, which may have
different orders of the reactions taking place
simultaneously. For example, in a system containing
log k
1/T
R
Ea
- 303
Slope
Time
Concentration
Concentration profile of reactants (R), intermediate (I) and products (P) as a
function of time
R
P
I
NO 2
and SO 2 , NO 2 is consumed in the following two
reactions, 2 2 4 1 2 NO NO
k ; 2 2 3 2 NO SO NO SO
k
The rate of disappearance of NO 2 will be sum of
the rates of the two reactions i.e. ,
2 [ ] [ ][ ]
[ ] 2 2 2
2 1 2
2 k NO k NO SO dt
d NO
Photochemical reaction
Absorption of radiant energy by reactant
molecules brings in photophysical as well as
photochemical changes. According to Einstein's law of
photochemical equivalence, the basic principle of photo
processes, each reactant molecule is capable of
absorbing only one photon of radiant energy. The
absorption of photon by a reactant molecule may lead
to any of the photo process.
The chemical reactions, which are initiated as a
result of absorption of light, are known as photochemical
reactions. In such cases, the absorbed energy is
sufficient to activate the reactant molecules to cross
the energy barrier existing between the reactants and
products or in other words, energy associated with
each photon supplies activation energy to reactant
molecule required for the change.
(1) Characteristics of photochemical reactions
(i) Each molecule taking part in a photo process
absorbs only one photon of radiant energy thereby
increasing its energy level by
hc hvor
(ii) Photochemical reactions do not occur in dark.
(iii) Each photochemical reaction requires a
definite amount of energy which is characteristic of a
particular wavelength of photon. For example,
reactions needing more energy are carried out in
presence of UV light (lower , more E/Photon). A
reaction-taking place in UV light may not occur on
exposure to yellow light (lower and lesser E/Photon)
(iv) The rate of photochemical reactions depend
upon the intensity of radiation’s absorbed.
(v) The G values for light initiated reactions
may or may not be negative.
(vi) The temperature does not have marked effect
on the rate of light initiated reactions.
(2) Mechanism of some photochemical
reactions
(i) Photochemical combination of H 2 and Cl 2 : A
mixture of H 2 and Cl 2 on exposure to light give rise to
the formation of HCl , showing a chain reaction and
thereby producing
6 8 10 to 10 molecules of HCl per
photon absorbed.
H Cl HCl
sunlight 2 2 ^ ^2
The mechanism leading to very high yield of HCl
as a result of chemical change can be as follows.
Chlorine molecules absorb radiant energy to form an
excited molecule which decomposes to chlorine free
radicals ( Cl ) to give chain initiation step.
Light absorption step :
Cl 2 (^) Cl 2
hv
........(i)
Chain initiation step :
Cl Cl Cl
2
........(ii)
The chlorine free radical then combines with 2
H
molecule to form HCl and
H free radical. The
H free
radical so formed again combines with another Cl 2
molecule to give HCl and
Cl free radical back resulting
into chain propagation step.
Chain propagation step :
Cl H 2 HCl H
........(iii) H Cl 2 HCl Cl
The combination of two
Cl free radicals leads to
chain terminating step.
Chain terminating step : Cl Cl Cl 2
........(iv)
(ii) Photochemical combination of H 2 and Br 2 :
The combination of H 2 and Br 2 to form HBr in
presence of light is also an example of chain reaction
like photochemical combination of H 2 and Cl 2. Here
two Br 2 molecules absorb photon, however, inspite of
chain reaction only one molecule of HBr is formed for
each 100 photon absorbed by 100 molecules of Br 2
H Br HBr
light 2 2 ^2
Mechanism
Light absorption step :
Br 2 (^) hv Br 2
........(i)
Chain initiation step :
Br Br Br
2
........(ii)
Photochemical process (i) Oxidation
(ii) Reduction (iii) Dissociation
(iv) Double decomposition
(v) Isomeric transformation (vi) Photosensitization
Photophysical
process
(i) Fluorescence (ii) Phosphorescence
Reactant molecule
Photoelectric effect
Absorption of photon (As per Einstein law) Excitation of
electronic level
Knock out the
electron from the reactant species
Excited molecule
(c) May increase or decrease during the reaction
(d) Remains constant as the reaction proceeds
2. The rate of a reaction that not involve gases is not
dependent on [CPMT 1988; AFMC 1995]
(a) Pressure (b) Temperature
(c) Concentration (d) Catalyst
3. The rate at which a substance reacts depends on
its
[MP PMT 1987; BHU 1999; KCET 2005]
(a) Atomic weight (b) Equivalent weight
(c) Molecular weight (d) Active mass
4. The rate law for the reaction
RCl NaOH ( aq ) ROH NaCl is given by Rate
K 1 [ RCl ]. The rate of the reaction will be [IIT 1988]
(a) Doubled on doubling the concentration of
sodium hydroxide
(b) Halved on reducing the concentration of alkyl
halide to one half
(c) Decreased on increasing the temperature of
the reaction
(d) Unaffected by increasing the temperature of
the reaction
5. If doubling the concentration of a reactant `A'
increases the rate 4 times and tripling the
concentration of `A' increases the rate 9 times,
the rate is proportional to [AIIMS 1991]
(a) Concentration of `A'
(b) Square of concentration of `A'
(c) Under root of the concentration of `A'
(d) Cube of concentration of `A'
6. The rate of chemical reaction at constant
temperature is proportional to
(a) The amount of products formed
(b) The product of masses of the reactants
(c) The product of the molar concentration of the
reactants
(d) The mean free path of the reaction
7. The concentration of a reactant decreases from
0.2 M to 0.1 M in 10 minutes. The rate of the
reaction is
(a) 0.01 M (b)
2 10
(c) 0.01 mol
3 1 min
dm (d) 1 mol
3 1 min
dm
8. When a reaction is progressing
(a) The rate of the reaction goes on increasing
(b) The concentration of the products goes on
decreasing
(c) The concentration of the reactants goes on
decreasing
(d) The reaction rate always remains constant
