This presentation is based on the Topic " Chemical Kinetics" for the Chemistry undergraduate students of Mumbai University

1. Chemical Kinetics -I
Dr. Pravin U. Singare
Department of Chemistry,
N.M. Institute of Science,
Bhavan’s College, Andheri (West)

2. Introduction
• Study of chemical reactions.
• Study of reaction rate.
• Study of effect of various factors on reaction
rate.
• Study of effect of presence of catalyst on
reaction rate.

3. Complex Chemical Reactions
• Many reactions do not follow simple first
order, second order or third order reaction
kinetics.
• During such reactions many other reactions
are occurring simultaneously.
• Such reactions are called complex chemical
reactions.

4. Classification of complex chemical reactions
Complex chemical reactions
Reversible
(opposing)
reactions
Consecutive
reactions
Parallel
reactions
Monomolecular
X
monomolecular
Monomolecular
X
bimolecular
Bimolecular
X
monomolecular
Bimolecular
X
Bimolecular

5. Reversible (opposing) Reactions
• Such reactions take place in forward as well as
reverse directions.
• In such reactions, the products formed during
the reaction will recombine to form the
original reactants.
• There are different types of reversible
reactions

6. • Monomolecular reaction opposed by monomolecular
reaction
such reactions are of type
A B
here k1 is the rate constant of forward reaction
and k’1 is the rate constant of reverse reaction
Eg:
k1
k1’
N=N
k1
k1’
N=N
trans - Azobenzol cis - Azobenzol

7. Monomolecular reaction opposed by
Bimolecular reaction
such reactions are of type
Eg:- (1) Thermal decomposition of phosphorous
pentachloride
PCl5 PCl3 + Cl2
(2) Decomposition of ammonium chloride
NH4Cl NH3 + HCl
k1
k1’
A B + C
Δ
Δ

8. Bimolecular reaction opposed by Monomolecular reaction
such reactions are of type
A + B C
Eg:- 2NO2 (nitrogen dioxide) N2O4 (Dinitrogen tetroxide)
Bimolecular reaction opposed by Bimolecular reaction
such reactions are of type
A + B C + D
Eg:- (1) H2 + I2 2 HI
(2) CH3COOH + C2H5OH CH3COOC2H5 + H2O
k1
k1’
k1
k1’
Acetic acid Ethyl alcohol Ethyl acetate

9. Consecutive Reactions
The reactions which occur in sequence are called consecutive reactions.
This reactions are of type
A B C
Time
• Initially when the reaction has not
started concentration of [A] is
maximum while concentration of [B]
is zero.
• As the reaction proceed, the
concentration [A] decreases while
concentration of intermediate
product [B] increases.
• As the concentration of [B] increases
part of B will react to give final
product C and hence [C] start
increasing simultaneously.
• As the reaction proceed, [A] become
zero, [B] which was initially increasing
will start decreasing, while [C] will
increase.
k1
k2
Concentration
[C]
[B]
[A]

10. Eg:- Hydrolysis of diethyl succinate
CH2-COOC2H5
CH2-COOC2H5
H-OH CH2-COOC2H5
CH2-COOH
H-OH CH2-COOH
CH2-COOH
Diethyl succinate Monoethyl succinate Succinic Acid

11. Parallel Reactions
In such reactions, the reactants react simultaneously in
more than one route
• Such reactions are of type
• In such case
Rate of reaction of A =
Rate of formation of B
+
Rate of formation of C
A
B
C
k1
k2
Phenol
OH
k1
k2
k3
OH
NO2
o-nitro
phenol
OH
NO2
m-nitro
phenol
OH
NO2
p-nitro
phenol
Nitration

12. Thermal Chain Reactions
A reaction which take place at high temperature,
in series of successive steps, involving free
radicals (also know an reactive species) before
the final product is formed is called thermal chain
reactions.
Eg. Reaction between hydrogen and bromine in
the temperature range of 200-300oC to give
hydrogen bromide proceed in series of successive
steps as follows:

13. 1) Chain initiation
In this step reactive species or free radicals are
formed from the ordinary reactant molecules
Br Br
.Br +
.Br
(Bromine free radicals)
H H
.H +
.H
(Hydrogen free radicals)

14. 2) Chain propagation
In this step the free radicals formed in the previous step will
react with another reactant molecule to produce new reactive
intermediate free radicals
. Br + H2 HBr +
.H (Free Radical)
.H + Br2 HBr +
.Br (Free Radical)
Here
.H &
.Br are the new reactive intermediate free radicals
because they are short lived.
• This intermediate free radicals are consumed and regenerated
many times during the reaction.
• Hence one
.H &
.Br free radical is responsible for production of
several HBr molecules.

15. 3) Chain inhibition
In this step one of the reactive intermediate
free radical will attack the product molecule.
As a result the reaction get retarded.
HBr +
.H H2 +
.Br
(or)
HBr +
.Br Br2 +
.H

16. 4) Chain termination
In this step the reactive intermediate free
radicals will combine together.
.H +
.H H2
.Br +
.Br Br2
As a result, the chain reaction will get finally
terminated.

17. Effect of Temperature on Reaction Rate
• The rate of chemical reaction increases with
rise in temperature.
• Consequently, the reactions are often carried
out at elevated (higher) temperatures in order
to get good yield of product in less time.
• The effect of temperature on the rate of
reaction is expressed in terms of temperature
coefficient of the reaction.

18. • The temperature coefficient of the reaction is defined as
the ratio of the rate constants of the same reaction at two
different temperatures differing by 10oC.
• Temperature coefficient = k(T+10)
k(T)
Here k(T) is the reaction rate of chemical
reaction at room temperature
While
k(T+10) is the reaction rate of the same chemical reaction at
10oC above the room temperature.
The value of temperature coefficient is nearly equal to 2. It
means that with rise in temperature by 10oC the reaction
rate will get approximately double i.e. k(T+10) = 2 k(T)
The effect of temperature on the rate of chemical reaction
can be explained on the basis of Arrhenius theory.

19. Arrhenius Theory
• Arrhenius showed that the variation of reaction rate with
temperature can be expressed by the equation
k = A . e-Ea/RT
Here R is the Gas constant (8.314 JK-1mol-1)
T is the reaction temperature
A is the Arrhenius factor or Frequency factor which
represent the total number of collisions taking place between
the reactant molecules /mL /Sec.
Ea is the energy of activation which is the minimum energy
which the reactant molecules must acquire in order to undergo
chemical reaction leading to the formation of products.
• Reactant molecules having energy less than Ea can not react to form
product.
• Only those reactant molecules having energy equal to or greater
than Ea will undergo effective collisions with each other to form
product.

20. • According to Arrhenius theory, reactant molecules first
acquire sufficient energy and get converted into an
intermediate short lived activated complex which then
breakup forming product.
• This intermediate short lived activated complex is
unstable. It is obtained by suitable rearrangement of
atoms and bonds within the reactant molecules.
• The energy which activates the reactant molecules to
form an activated complex is called energy of activation.
• Thus any chemical reaction is represented as
Reactants Activated complex Products
Eg. 2NO + O2 2NO2
N
N
O
O
O
O

21. • In the above figures EP is the energy of product, ER is the energy
of reactants, EAc is the energy of intermediate short lived
activated complex , Ea = energy of activation =EAc – ER
• Thus according to Arrhenius concept, reactants do not directly
pass to the product, but acquire sufficient energy to pass over an
activation energy barrier as shown in the above figures.
Energy
Progress of Reaction
ER
EP
EAc
Ea
ΔE = EP-ER = - ive
(Exothermic Reaction)
Energy
Progress of Reaction
ER
EP
EAc
Ea
ΔE = EP-ER = + ive
(Endothermic Reaction)

22. • Simplifying the Arrhenius equation
k = A . e-Ea/RT
by taking log on both the sides
lnk = ln A + (-Ea/RT)
lnk = ln A – Ea/RT
2.303log10k = 2.303 log10 A – Ea/RT
Dividing the above equation through out by 2.303
log10k = log10 A – Ea/2.303RT
log10k = log10 A + 2.303RT / Ea
•Thus from the above equation rate constant (k) is
directly proportional to temperature (T) and inversely
proportional to energy of activation (Ea).
•Hence it can be said that the reactions having low energy
of activation (Ea) are performed at high temperature will
have high rate constant (k)value.

23. Experimental method to determine the Energy
of Activation
Method I
(Graphical Method)
• In this method, the same chemical reaction is performed
at different temperature (T). The rate constant (k) of the
reaction is determined for each temperature (T).
• Simplifying the Arrhenius equation
k = A.e-Ea/RT
ln (k) = ln(A) + (-Ea/RT)
2.303 log10(k) = log10(A) –Ea/RT
Dividing through out by 2.303
log10(k) = log10(A) –Ea/2.303RT

24. Rearranging the above equation
log10(k) = -Ea 1 + log10 A
2.303R T
The above equation is of the type Y = mX + C
So by plotting a graph of log10(k) on Y- axis against 1/T on X-axis
We will get a straight line graph having
intercept (C) = log10 A
Slope (m) = -Ea
2.303 R
From the slope of the graph, Energy of
Activation (Ea) can be calculated by the
Equation
Ea = slope x -2.303R
Here R is a gas constant = 8.314 J.K-1mol-1
log
10
(k)
1/T
log
10
(A)

25. Method ll
• In this method the same chemical reaction is carried out at
two different temperatures T1 & T2.
• Let k1 be the reaction rate at Temperature T1 while k2 be the
reaction rate at temperature T2.
• At temperature T1, log10(k1) = log10(A) – Ea ----------(1)
2.303RT1
• At temperature T2, log10(k2) = log10(A) – Ea -----------(2)
2.303RT2
• Subtracting eq (2) from eq(1)
log10(k2) - log10(k1) = -
log10(A) – Ea
2.303RT2
log10(A) – Ea
2.303RT1

26. log10(k2) - log10(k1) =
– Ea
2.303RT2
+ Ea
2.303RT1
log10(k2) - log10(k1) = Ea
2.303RT1
– Ea
2.303RT2
log10(k2) - log10(k1) =
Ea
2.303R
1
T1
- 1
T2
k1
log10 k2 = Ea
2.303R
T2-T1
T1.T2
log10 k2
k1
x 2.303T1.T2
Ea =
T2-T1

27. IMPORTANT FORMULAS
k = A.e-Ea/RT
k1
log10 k2 = Ea
2.303R
T2-T1
T1.T2

28. Problem 1: If the rate of reaction get double from 22oC to 32oC,
calculate the energy of activation of the reaction.
[R =8.314JK-1mol-1]
Given: T1 = 22 +273 = 295K
T2 =32 +273 = 305K
k2 = 2k1 i.e. k2/k1 =2
To Find : Ea = ?
Formula: log (k2/k1) = Ea/2.303R [1/T1 -1/T2]
Solution: log(2) = Ea/2.303(8.314) [1/295 -1/305]
0.3010 = Ea/2.303(8.314) [305-295/295 x305]
Ea = 0.3010 x 2.303 x 8.314 x 295 x305/10
Ea = 51793 J.mol-1
Ea = 51.79 kJ.mol-1

29. Problem 2: For the first order reaction, the frequency factor is 4.13x1013s-1
and Ea is 103.35kJ.mol-1. What is the rate constant at 300K ?
[R =8.314JK-1mol-1]
Given: Ea = 103.35 kJ.mol-1 = 103350 J.mol-1
A = 4.13x1013s-1
To Find: k =?
Formula: k = A.e-Ea/RT
Solution: log(k) = log(A) –Ea/2.303RT
log(k) = log(4.13x1013) –103350/(2.303)(8.314)(300)
log(k) = 13.634 – 17.992
log (k) = -4.358
k = a.log(-4.358)
k = 4.385 x10-5 s-1

30. Problem 3: In the gaseous phase reaction, the rate constant at
457.6K was found to be 3.667x10-7 s-1. Calculate the rate
constant at 480K if the energy of activation is 182.352 kJ.mol-1.
Given: Ea = 182.352 kJ.mol-1 = 182352 J mol-1
T1 = 457.6 K T2 = 480 K
k1 = 3.667x10-7 s-1
To Find: k2 = ?
Formula:
Solution: log (k2/ 3.667x10-7) = 182352 /2.303 (8.314) [480-457.6/ (480)(457.6)]
log(k2/ 3.667x10-7) = 0.9712
k2/ 3.667x10-7 = anti log (0.9712)
k2 = 9.385 (3.667x10-7 )
k2 = 34.41 x 10-7 = 3.441 x 10-6 s-1
k1
log10 k2 = Ea
2.303R
T2-T1
T1.T2

31. COLLISION THEORY
Postulates of collision theory
1. Reacting molecules are considered as a rigid sphere having only translational
motion.
2. Rate of reaction is directly proportional to the number of collisions taking place
between the reacting molecules.
3. The collisions between the reactant molecules are considered to be elastic
collisions in which there is only exchange of energy between the reactant
molecules, so that the total energy remains same.
4. Not all colliding molecules react, but only those colliding molecules having
certain minimum energy will undergo effective collisions with each other and
react to give products.
5. In order to undergo effective collisions, the reacting molecules must be properly
oriented so that they will have head on collisions.
6. When the properly oriented molecules undergo effective collisions, there will
be rearrangement of bonds in the reacting molecules giving rise to the
formation of products.

32. The number of collisions (Z) taking place per cm3 per second between
the reactant molecules is given by the equation
Z = 2n2σ2 π𝑅𝑇/𝑀
here n is the number of molecules /cm3
σ is the collision diameter i.e. distance between the center of two
colliding molecules
R is the gas constant
M is the molecular weight
T is the absolute temperature
For BIMOLECULAR REACTIONS in a mixture of gases 1 & 2,
number of collisions (Z) taking place per cm3 per second will be
2 Z(1,2) = n1.n2 σ2 8π𝑅𝑇/(𝑀1 +M2/M1.M2)
here M1 and M2 are the molecular weight of the reacting gas molecules
1 and 2
σ = σ1+ σ2/2 = average molecular diameter

33. Collision theory with respect to Bimolecular reaction
• According to the collision theory, out of Z number of molecules colliding with each
other per cm3 per second, only fraction of a molecules (q) having energy equal to
the energy of activation will undergo effective collisions resulting in the formation
of product.
• Then the rate constant (k) of the bimolecular reaction in terms of colliding
molecules will be given by the equation
k = Z.q ------------ (1)
• According to Law of distribution of energy, if ‘n’ number of molecules are present
per cm3 at temperature T, then the number of molecules (n’) possessing energy of
activation (Ea) is given by the relation
n’ = n. e-Ea/RT
𝑛′
𝑛
= e-Ea/RT ---------- (2)
But the fraction of molecules in activated state (q) is given by
q =
𝑛′
𝑛
---------- (3)
Substituting eq (3) in eq (2)
q = e-Ea/RT ---------- (4)
Substituting value of q from eq (4) in eq (1) we get
k = Z. e-Ea/RT ------------ (5)
• Comparing eq (5) with the Arrhenius equation k = A. e-Ea/RT it appears that ‘Z’, the
number of molecules colliding per cm3 per second which is twice in bimolecular
reaction will be same as the frequency factor ‘A’, i.e. A = 2Z

34. • The eq (5) can be applied to simple bimolecular reactions, but it is unable to
explain the complex molecular reactions in which the experimental determined
k value is lower than the theoretical k value calculated by eq (5).
• This is because the complex polyatomic molecules are considered to have
vibrational, rotational energies in addition to translational energy. Since this
energies are not considered while calculating the reaction rate k values, we get
the deviation in experimental and theoretical calculated k values.
• To account for this deviation, collision theory eq (5) is modified as
k = P.Z. e-Ea/RT ------------ (6)
Here P is the probability factor having value varying in the range of 1 to 10-9.
• The probability factor (P) take in to consideration the fact that not all activated
molecules will undergo reaction, but only the molecules which are properly
oriented will react to give products.
• The reactions in which the P value = 1 will obeys collision theory.

35. Lindemann Concept of Unimolecular reaction
• According to Lindemann concept
1. molecules get activated by collision with each other.
2. the activated molecules will decompose to give product only after some
time lag.
3. If the time lag is large, then there is a possibility that the activated molecules may get
deactivated by collision with low energy molecules.
• Because of the above reason, the rate of reaction will not depend on the number of activated
molecules but will depend only on those molecules which remain in the activated state and
decompose finally to give product.
• Consider a Uni molecular reaction A  Product.
• According to Lindemann, the above reaction take place in following two steps:
1. In the 1st Step two molecules of A will collide with each other and there will be exchange of
energy between the reacting molecules. As result, one molecule get activated as A* and the
rate of reaction is kf .
2. In 2nd step after a small time lag, the activated molecule will decompose to give product, and
the rate of reaction is k.
kf (activation) k (decomposition)
Step 1: A + A A* + A Step 2: A* Product
kr (deactivation)
• However, if in case of large time lag, there is a possibility that the activate A* will get
deactivated by collision with another molecule A of low energy and the reverse
process will take place having rate constant kr.
• Therefore Rate of formation of A * = kf [A].[A] = kf [A]2
Rate of removal of A* = kr[A*].[A] + k [A*]

36. • In the above reaction, A* is short lived and high energy intermediate
which is formed during the reaction.
• According to the steady state principle, for such short lived intermediate
A*
rate of formation of A* = rate of removal of A *
kf [A]2 = kr[A*].[A] + k [A*]
kf [A]2 = [A*] {kr[A] + k}
[A*] = kf [A]2 / kr .[A] + k ------- (1)
• Since the rate of reaction [-dA/dt] is proportional to the concentration of
intermediate activated complex A*
Rate of reaction =
−𝑑𝐴
𝑑𝑡
α [A*]
Rate of reaction =
−𝑑𝐴
𝑑𝑡
= k1[A*] ---------- (2)
Substituting eq (1) in eq (2)
−𝑑𝐴
𝑑𝑡
= k1.kf [A]2 / kr . [A] + k ---------- (3)

37. −𝑑𝐴
𝑑𝑡
= k1.kf [A]2 / kr . [A] + k ---------- (3)
CASE I
• At high pressure & high
concentration of A, deactivation
of A * take place to larger extent
as compared to decomposition of
A* i.e. kr . [A] >>> k and eq (3)
will be
−𝑑𝐴
𝑑𝑡
= k1.kf [A]2 / kr . [A]
−𝑑𝐴
𝑑𝑡
= k1.kf [A] / kr -----(4)
• From eq (4) it is clear that at high
pressure & high concentration of
A , the rate of reaction
−𝑑𝐴
𝑑𝑡
α [𝐴]
and the reaction will be
unimolecular.
CASE II
• At low pressure & low
concentration of A,
decomposition of A* take place to
larger extent as compared to
deactivation i.e. k >>> kr . [A]
and eq (3) will be
•
−𝑑𝐴
𝑑𝑡
= k1.kf [A]2 / k ---------- (5)
• From eq (5) it is clear that at low
pressure & low concentration of
A, the rate of reaction
−𝑑𝐴
𝑑𝑡
α [𝐴]2
and the reaction will be
bimolecular.

38. Merits & Limitations of Collision theory
Merits
1. The theory successfully explains the effect of temperature on reaction rate.
2. The theory explain variation in reaction rate with temperature for gaseous and liquid state
reactions involving simple molecules. For such reactions, experimental observed reaction
rate (k) value agrees with theoretically calculated k value.
3. The rate of unimolecular reactions in gaseous state can be explained qualitatively on the
basis of Collison theory.
Limitations
1. According to collision theory the reacting molecules having sufficient activation energy only
will go for chemical reactions, however, this theory can not explain the chemical reactions
involving transfer of electrons between the reacting molecules.
2. On the basis of collision theory, the unimolecular and bimolecular reactions are explained
on different assumptions.
3. In case of complex molecular reactions, the collision theory fails to explain the variation in
theoretical and experimental reaction rate obtained for same chemical reaction.
4. According to collision theory, the reacting molecules must be properly oriented before
undergoing collisions with each other., which is not possible for polyatomic molecules
having vibrational and rotational motions.

39. Absolute reaction rate theory / Activated complex reaction rate theory (ACRRT) / Transition
state Theory
• Absolute reaction rate theory also known as transition state theory or Activated
complex theory explains the reaction rates of elementary chemical reactions.
• The theory assumes existence of special type of chemical
equilibrium between reactants and activated transition state complexes.
• According to the absolute reaction rate theory, the energy of activation is the
difference in the energy of reactants and the energy of activated complex formed at
the transition state.
• The rate of reaction is proportional to the rate of decomposition of activated complex
forming product.
• The rate constant (k) for the reaction is given by
k =
𝑅𝑇
𝑁.ℎ
K* ----------- (1)
Here K* is the equilibrium constant of the reaction in which the reactants form
activated complex.
• The relation between free energy change ΔG* during activation and equilibrium
constant K* for the formation of activated complex is given by
ΔG* = -RTlnK*
lnK* =
−Δ𝐺∗
𝑅𝑇
K* = e
−Δ𝐺 ∗ 𝑅𝑇
---------- (2)

40. • But ΔG* = ΔH* - T ΔS* ------------- (3)
Here ΔH* & ΔS* represent enthalpy change and entropy change during activation
i.e. during the formation of activated complex.
• Substituting eq (3) in eq (2)
K* = e
−(ΔH∗ − T ΔS∗) 𝑅𝑇
K* = e
T ΔS∗ 𝑅𝑇
. e
−ΔH∗ 𝑅𝑇
K* = e
ΔS∗ 𝑅
. e
−ΔH∗ 𝑅𝑇
---------- (4)
Substituting eq (4) in eq (1)
k =
𝑅𝑇
𝑁.ℎ
e
ΔS∗ 𝑅
. e
−ΔH∗ 𝑅𝑇
----------- (5)
Comparing eq (5) with Arrhenius equation k = A. e –Ea/RT we get
A =
𝑅𝑇
𝑁.ℎ
e
ΔS∗ 𝑅
& Ea = ΔH* ------ (6)
Thus from eq (6) according to transition state theory, the frequency factor (A) also
take in to consideration the entropy change during activation (ΔS*)

41. • Comparing eq (5) with collision theory rate equation k = PZ. e –Ea/RT we get
P.Z. e –Ea/RT =
𝑅𝑇
𝑁.ℎ
e
ΔS∗ 𝑅
. e
−ΔH∗ 𝑅𝑇
--------- (7)
Thus from eq (7) it is clear that the probability factor (P) not only take into consideration
energy of activation (Ea) but also entropy change (ΔS*) and enthalpy change (ΔH*)
during the formation of activated complex.
P.Z =
𝑅𝑇
𝑁.ℎ
e
ΔS∗ 𝑅
---------- (8)
From eq 6 & 8, it is clear that the frequency factor (A) does not only take into
consideration the number of collisions (Z) taking place between the reacting molecules
/unit volume/sec but also take into consideration the entropy change (ΔS*) during the
formation of activated complex.
P =
𝑅𝑇
𝑍𝑁.ℎ
e
ΔS∗ 𝑅
& ΔH* = Ea -------- (9)
• Thus the probability factor (P) introduced as a correction term in the rate constant
equation of collision theory take into consideration the entropy change (ΔS*) which
is a measure of disorder of system during the formation of activated complex.
• For gaseous reaction system, the entropy of activation will be negative which means
that the reacting molecules will become more orderly i.e. will be properly oriented
before going for the formation of activated complex.

42. Comparison between Collision reaction rate theory (CRRT) & Activated complex
reaction rate theory (ACRRT)
Collision reaction rate theory (CRRT)
Reacting molecules undergo collision with each
other before formation of product.
Rate of reaction proportional to rate of collisions
between the activated reacting molecules.
The frequency factor (A) is equal to the number of
collisions (Z) taking place between the reacting
molecules /unit volume/sec.
k = A. e –Ea/RT (Arrhenius equation)
k = Z. e –Ea/RT (CRRT equation)
Simple molecular reactions are explained
properly but in case of complex molecular
reactions, the rate constant calculated and
measured experimentally are different.
In CRRT equation, the probability factor (P) is only
an arbitrary value varying between 1 to 10-9 and it
only emphasizes on the energy of activation (Ea).
k = P.Z. e –Ea/RT (CRRT equation)
Activated complex reaction rate theory
(ACRRT)
Reacting molecule form unstable high energy
activated complex before product formation.
Rate of reaction is proportional to decomposition
of activated complex forming product.
The frequency factor (A) does not only take into
consideration the number of collisions (Z) taking
place between the reacting molecules /unit
volume/sec but also take into consideration the
entropy change (ΔS*) during the formation of
activated complex. (Refer eq 6 & 8 of ACRRT)
Explain both the simple and complex molecular
reactions satisfactorily.
In ACRRT, the probability factor (P) not only
take into consideration energy of activation (Ea)
but also entropy change (ΔS*) and enthalpy
change (ΔH*) during the formation of activated
complex. (Refer eq 7 of ACRRT)