Chemical kinetics -Notes and Problems with Solutions JEE Notes | EduRev

JEE : Chemical kinetics -Notes and Problems with Solutions JEE Notes | EduRev

 Page 1


1 . CLASSIFICATION OF REACTIONS : [IN TERMS OF R ATES]
(i) There are certain reactions which are too slow e.g. rusting of iron, weathering of rocks.
(ii) Instantaneous reactions i.e. too fast e.g. Detonation of explosives, acid-base neutralization,
precipitation of AgCl by NaCl and AgNO
3
.
(iii) Neither too fast nor too slow e.g. combination of H
2
 and Cl
2
 in presence of light, hydrolysis of ethyl
acetate catalysed by acid, decomposition of azomethane
2 . RATE OF REACTION :
The change in concentration of either reactant or product per unit time.
Formula : v = ± 
dc
dt
dc = change in concentration in a small interval dt.
[–] sign is used when we refer to reactant concentration.
[+] sign is used when we refer to product concentration.
? Example : N
2
 + 3H
2
 ? 2NH
3
(i) Rate of formation of ammonia = +
3
d[NH ]
dt
(ii) Rate of disappearance of nitrogen = –
2
d [N ]
dt
(iii) Rate of disappearance of hydrogen = –
2
d [H ]
dt
Rate of reaction = + 
1
2
3
d[NH ]
dt
 = – 
2
d [N ]
dt
 = – 
1
3
2
d [H ]
dt
Thus, Rate of reaction = – 
2
d [N ]
dt
 = 
1
2
3
d[NH ]
dt
or rate of formation of ammonia = Twice the rate of disappearance of nitrogen
i.e.
3
d[NH ]
dt
 = 
2
3
 
2
d [H ]
–
dt
? ?
? ?
? ?
3 . AVERAGE VELOCITY OF REACTION  :
Change in the concentration of reactants or products per unit time is called average reaction velocity. If ?c
is the change in the concentration of reactants and product in ?t time, then
Average velocity = ± 
c
t
?
?
or Average velocity = 
(–) Change in the concentration of reactants
Time
   
(+ ) Change in the concentration of products
Time
CHEMICAL KINETICS
JEEMAIN.GURU
Page 2


1 . CLASSIFICATION OF REACTIONS : [IN TERMS OF R ATES]
(i) There are certain reactions which are too slow e.g. rusting of iron, weathering of rocks.
(ii) Instantaneous reactions i.e. too fast e.g. Detonation of explosives, acid-base neutralization,
precipitation of AgCl by NaCl and AgNO
3
.
(iii) Neither too fast nor too slow e.g. combination of H
2
 and Cl
2
 in presence of light, hydrolysis of ethyl
acetate catalysed by acid, decomposition of azomethane
2 . RATE OF REACTION :
The change in concentration of either reactant or product per unit time.
Formula : v = ± 
dc
dt
dc = change in concentration in a small interval dt.
[–] sign is used when we refer to reactant concentration.
[+] sign is used when we refer to product concentration.
? Example : N
2
 + 3H
2
 ? 2NH
3
(i) Rate of formation of ammonia = +
3
d[NH ]
dt
(ii) Rate of disappearance of nitrogen = –
2
d [N ]
dt
(iii) Rate of disappearance of hydrogen = –
2
d [H ]
dt
Rate of reaction = + 
1
2
3
d[NH ]
dt
 = – 
2
d [N ]
dt
 = – 
1
3
2
d [H ]
dt
Thus, Rate of reaction = – 
2
d [N ]
dt
 = 
1
2
3
d[NH ]
dt
or rate of formation of ammonia = Twice the rate of disappearance of nitrogen
i.e.
3
d[NH ]
dt
 = 
2
3
 
2
d [H ]
–
dt
? ?
? ?
? ?
3 . AVERAGE VELOCITY OF REACTION  :
Change in the concentration of reactants or products per unit time is called average reaction velocity. If ?c
is the change in the concentration of reactants and product in ?t time, then
Average velocity = ± 
c
t
?
?
or Average velocity = 
(–) Change in the concentration of reactants
Time
   
(+ ) Change in the concentration of products
Time
CHEMICAL KINETICS
JEEMAIN.GURU
Concentration
Product
Reactant
Tim e
Unit of average velocity = 
Unit of concentration
Unit of time
 = 
gram mole
litre× Second
 =  gram mole litre
–1
 second
–1
4 . INSTANTANEOUS RATE OF THE REACTION :
The rate of reaction determined at specified concentration or specified time      
B
Tim e
Concentration
is called instantaneous rate.
The instantaneous rate of the reaction can be determined by measuring
concentration of reactant or product at a instant of time and plotting con-
centration versus time.
The instantaneous rate at any time is determined by the slope of the tan-
gent at a point on the time-concentration curve corresponding to the speci-
fied time. The slope of the tangent at a point is the limiting value of 
c
t
?
?
.
t 0
c
Lim
t ? ?
?
?
=
dc
dt
In terms of the concentration of reactant, the rate of the reaction = –
dc
dt
. The –sign indicates that the e
concentration of reactant decreases with time.
In terms of the concentration of product, the rate of the reaction = +
dc
dt
. The +sign indicates that the e
concentration of product increases with time. In the reaction if at a time t the concentration of product is x and
at time t + dt, the concentration becomes x + dx then the reaction rate =
dx
dt
.
? For example the rate of reaction : N
2
 + 3H
2
 
? ? ? ?
? ? ? ? 2NH
3
in terms of the concentrations of N
2
, H
2
 and NH
3
 can be expressed as :
– 
2
d[N ]
dt
, –
1
3
2
d[H ]
dt
, + 
1
2
3
d[NH ]
dt
E x . 1 What should be (a) the rate of disappearance of B and (b) the rate of formation of C, if the rate
of disappearance of A for the reaction A + B ? 2C is 10
–2
 mole/litre/second at a particular
temperature ?
S o l . (a) Rate of disappearance of A = Rate of disappearance of B
       = 10
–2
 mole/litre/second
(b) Rate of disappearance of A = 
1
2
 ×  Rate of formation of C
Rate of formation of C = 2 ×  Rate of disappearance of A
 = 2 × 10
–2
 mole/litre/second
JEEMAIN.GURU
Page 3


1 . CLASSIFICATION OF REACTIONS : [IN TERMS OF R ATES]
(i) There are certain reactions which are too slow e.g. rusting of iron, weathering of rocks.
(ii) Instantaneous reactions i.e. too fast e.g. Detonation of explosives, acid-base neutralization,
precipitation of AgCl by NaCl and AgNO
3
.
(iii) Neither too fast nor too slow e.g. combination of H
2
 and Cl
2
 in presence of light, hydrolysis of ethyl
acetate catalysed by acid, decomposition of azomethane
2 . RATE OF REACTION :
The change in concentration of either reactant or product per unit time.
Formula : v = ± 
dc
dt
dc = change in concentration in a small interval dt.
[–] sign is used when we refer to reactant concentration.
[+] sign is used when we refer to product concentration.
? Example : N
2
 + 3H
2
 ? 2NH
3
(i) Rate of formation of ammonia = +
3
d[NH ]
dt
(ii) Rate of disappearance of nitrogen = –
2
d [N ]
dt
(iii) Rate of disappearance of hydrogen = –
2
d [H ]
dt
Rate of reaction = + 
1
2
3
d[NH ]
dt
 = – 
2
d [N ]
dt
 = – 
1
3
2
d [H ]
dt
Thus, Rate of reaction = – 
2
d [N ]
dt
 = 
1
2
3
d[NH ]
dt
or rate of formation of ammonia = Twice the rate of disappearance of nitrogen
i.e.
3
d[NH ]
dt
 = 
2
3
 
2
d [H ]
–
dt
? ?
? ?
? ?
3 . AVERAGE VELOCITY OF REACTION  :
Change in the concentration of reactants or products per unit time is called average reaction velocity. If ?c
is the change in the concentration of reactants and product in ?t time, then
Average velocity = ± 
c
t
?
?
or Average velocity = 
(–) Change in the concentration of reactants
Time
   
(+ ) Change in the concentration of products
Time
CHEMICAL KINETICS
JEEMAIN.GURU
Concentration
Product
Reactant
Tim e
Unit of average velocity = 
Unit of concentration
Unit of time
 = 
gram mole
litre× Second
 =  gram mole litre
–1
 second
–1
4 . INSTANTANEOUS RATE OF THE REACTION :
The rate of reaction determined at specified concentration or specified time      
B
Tim e
Concentration
is called instantaneous rate.
The instantaneous rate of the reaction can be determined by measuring
concentration of reactant or product at a instant of time and plotting con-
centration versus time.
The instantaneous rate at any time is determined by the slope of the tan-
gent at a point on the time-concentration curve corresponding to the speci-
fied time. The slope of the tangent at a point is the limiting value of 
c
t
?
?
.
t 0
c
Lim
t ? ?
?
?
=
dc
dt
In terms of the concentration of reactant, the rate of the reaction = –
dc
dt
. The –sign indicates that the e
concentration of reactant decreases with time.
In terms of the concentration of product, the rate of the reaction = +
dc
dt
. The +sign indicates that the e
concentration of product increases with time. In the reaction if at a time t the concentration of product is x and
at time t + dt, the concentration becomes x + dx then the reaction rate =
dx
dt
.
? For example the rate of reaction : N
2
 + 3H
2
 
? ? ? ?
? ? ? ? 2NH
3
in terms of the concentrations of N
2
, H
2
 and NH
3
 can be expressed as :
– 
2
d[N ]
dt
, –
1
3
2
d[H ]
dt
, + 
1
2
3
d[NH ]
dt
E x . 1 What should be (a) the rate of disappearance of B and (b) the rate of formation of C, if the rate
of disappearance of A for the reaction A + B ? 2C is 10
–2
 mole/litre/second at a particular
temperature ?
S o l . (a) Rate of disappearance of A = Rate of disappearance of B
       = 10
–2
 mole/litre/second
(b) Rate of disappearance of A = 
1
2
 ×  Rate of formation of C
Rate of formation of C = 2 ×  Rate of disappearance of A
 = 2 × 10
–2
 mole/litre/second
JEEMAIN.GURU
Ex.2 A gaseous reaction : 2A(g) + B(g) ? 2C(g),
Show a decrease in pressure from 120 mm to 100 mm in 10 minutes. The rate of appearance of C is -
[A] 2 mm/min [B] 4 mm/min [C] 10 mm/min [D] 12 mm/min. Ans. [B]
Sol. Suppose 2p is the pressure of C after 10 min.
Fall in pressure of A = 2p ; Fall in pressure of B = p
Total fall in pressure = (2p + p) – 2p = p = 20 mm
Pressure of C = 2p = 40 mm
Rate of appearance of C = 40/10 = 4 mm/min
Ex.3 The term 
dx
dt
 in the rate expression refers to the -
[A] concentration of the reactants [B] increase in concentration of the reactants
[C] instantaneous rate of the reaction [D] average rate of the reaction Ans. [C]
Sol. It is expression for instantaneous rate
Ex.4 Which of the following expression can be used to describe the instantaneous rate of the reaction ?
2A + B ? ? A
2
B
[A] – 
1 d [A]
2 dt
[B] –
d [A]
dt
[C] 
2
1 d[A B]
2 dt
[D] –
1 d [A] d [B]
.
2 dt dt
Ans. [A]
Sol. The instantaneous rate of the reaction can be expressed by any of the following expressions
1 d [A]
–
2 dt
   or   –
d[B]
dt
   or   
2
d [A B]
dt
Ex.5 Which of the following will react at the highest rate ?
[A] 1 mol of A and 1 mol of B in a 1 L vessel [B] 2 mol of A and 2 mol of B in a 2 L vessel
[C] 3 mol of A and 3 mol of B in a 3 L vessel [D] All would react at the same rate Ans. [D]
Sol. Since all have same conc. of reactants, all would react at same rate.
5 . FACTORS AFFECTING THE RATE OF REACTION :
(i) Concentration : Law of mass action enunciates that greater is the conc. of the reactants, the more
rapidly the reaction proceeds.
(i i) Pressure (Gaseous reaction) : On increasing the pressure, volume decreases and conc. increases
and hence the rate increases.
(iii) Temperature : It is generally observed that rise in temperature increases the reaction rate.
( i v) Nature of the reactants : The rate depends upon specific bonds involved and hence on the nature
of reactants.
g s ? ? ?
( v ) Surface area of the reactants : In heterogeneous reactions, more powdered is the form of
reactants, more is the velocity. [as more active centres are provided]
( v i ) Catalyst : Affects the rate immensely.
E x . 6 For the reaction :
4NH
3
(g) + 5O
2
(g) ? 4NO(g) + 6H
2
O(g)
Given : 
d [NO]
dt
= 3.6 × 10
–3
 mol L
–1
 s
–1
Calculate  : (i) rate of disappearance of ammonia
       (ii) rate of formation of water
JEEMAIN.GURU
Page 4


1 . CLASSIFICATION OF REACTIONS : [IN TERMS OF R ATES]
(i) There are certain reactions which are too slow e.g. rusting of iron, weathering of rocks.
(ii) Instantaneous reactions i.e. too fast e.g. Detonation of explosives, acid-base neutralization,
precipitation of AgCl by NaCl and AgNO
3
.
(iii) Neither too fast nor too slow e.g. combination of H
2
 and Cl
2
 in presence of light, hydrolysis of ethyl
acetate catalysed by acid, decomposition of azomethane
2 . RATE OF REACTION :
The change in concentration of either reactant or product per unit time.
Formula : v = ± 
dc
dt
dc = change in concentration in a small interval dt.
[–] sign is used when we refer to reactant concentration.
[+] sign is used when we refer to product concentration.
? Example : N
2
 + 3H
2
 ? 2NH
3
(i) Rate of formation of ammonia = +
3
d[NH ]
dt
(ii) Rate of disappearance of nitrogen = –
2
d [N ]
dt
(iii) Rate of disappearance of hydrogen = –
2
d [H ]
dt
Rate of reaction = + 
1
2
3
d[NH ]
dt
 = – 
2
d [N ]
dt
 = – 
1
3
2
d [H ]
dt
Thus, Rate of reaction = – 
2
d [N ]
dt
 = 
1
2
3
d[NH ]
dt
or rate of formation of ammonia = Twice the rate of disappearance of nitrogen
i.e.
3
d[NH ]
dt
 = 
2
3
 
2
d [H ]
–
dt
? ?
? ?
? ?
3 . AVERAGE VELOCITY OF REACTION  :
Change in the concentration of reactants or products per unit time is called average reaction velocity. If ?c
is the change in the concentration of reactants and product in ?t time, then
Average velocity = ± 
c
t
?
?
or Average velocity = 
(–) Change in the concentration of reactants
Time
   
(+ ) Change in the concentration of products
Time
CHEMICAL KINETICS
JEEMAIN.GURU
Concentration
Product
Reactant
Tim e
Unit of average velocity = 
Unit of concentration
Unit of time
 = 
gram mole
litre× Second
 =  gram mole litre
–1
 second
–1
4 . INSTANTANEOUS RATE OF THE REACTION :
The rate of reaction determined at specified concentration or specified time      
B
Tim e
Concentration
is called instantaneous rate.
The instantaneous rate of the reaction can be determined by measuring
concentration of reactant or product at a instant of time and plotting con-
centration versus time.
The instantaneous rate at any time is determined by the slope of the tan-
gent at a point on the time-concentration curve corresponding to the speci-
fied time. The slope of the tangent at a point is the limiting value of 
c
t
?
?
.
t 0
c
Lim
t ? ?
?
?
=
dc
dt
In terms of the concentration of reactant, the rate of the reaction = –
dc
dt
. The –sign indicates that the e
concentration of reactant decreases with time.
In terms of the concentration of product, the rate of the reaction = +
dc
dt
. The +sign indicates that the e
concentration of product increases with time. In the reaction if at a time t the concentration of product is x and
at time t + dt, the concentration becomes x + dx then the reaction rate =
dx
dt
.
? For example the rate of reaction : N
2
 + 3H
2
 
? ? ? ?
? ? ? ? 2NH
3
in terms of the concentrations of N
2
, H
2
 and NH
3
 can be expressed as :
– 
2
d[N ]
dt
, –
1
3
2
d[H ]
dt
, + 
1
2
3
d[NH ]
dt
E x . 1 What should be (a) the rate of disappearance of B and (b) the rate of formation of C, if the rate
of disappearance of A for the reaction A + B ? 2C is 10
–2
 mole/litre/second at a particular
temperature ?
S o l . (a) Rate of disappearance of A = Rate of disappearance of B
       = 10
–2
 mole/litre/second
(b) Rate of disappearance of A = 
1
2
 ×  Rate of formation of C
Rate of formation of C = 2 ×  Rate of disappearance of A
 = 2 × 10
–2
 mole/litre/second
JEEMAIN.GURU
Ex.2 A gaseous reaction : 2A(g) + B(g) ? 2C(g),
Show a decrease in pressure from 120 mm to 100 mm in 10 minutes. The rate of appearance of C is -
[A] 2 mm/min [B] 4 mm/min [C] 10 mm/min [D] 12 mm/min. Ans. [B]
Sol. Suppose 2p is the pressure of C after 10 min.
Fall in pressure of A = 2p ; Fall in pressure of B = p
Total fall in pressure = (2p + p) – 2p = p = 20 mm
Pressure of C = 2p = 40 mm
Rate of appearance of C = 40/10 = 4 mm/min
Ex.3 The term 
dx
dt
 in the rate expression refers to the -
[A] concentration of the reactants [B] increase in concentration of the reactants
[C] instantaneous rate of the reaction [D] average rate of the reaction Ans. [C]
Sol. It is expression for instantaneous rate
Ex.4 Which of the following expression can be used to describe the instantaneous rate of the reaction ?
2A + B ? ? A
2
B
[A] – 
1 d [A]
2 dt
[B] –
d [A]
dt
[C] 
2
1 d[A B]
2 dt
[D] –
1 d [A] d [B]
.
2 dt dt
Ans. [A]
Sol. The instantaneous rate of the reaction can be expressed by any of the following expressions
1 d [A]
–
2 dt
   or   –
d[B]
dt
   or   
2
d [A B]
dt
Ex.5 Which of the following will react at the highest rate ?
[A] 1 mol of A and 1 mol of B in a 1 L vessel [B] 2 mol of A and 2 mol of B in a 2 L vessel
[C] 3 mol of A and 3 mol of B in a 3 L vessel [D] All would react at the same rate Ans. [D]
Sol. Since all have same conc. of reactants, all would react at same rate.
5 . FACTORS AFFECTING THE RATE OF REACTION :
(i) Concentration : Law of mass action enunciates that greater is the conc. of the reactants, the more
rapidly the reaction proceeds.
(i i) Pressure (Gaseous reaction) : On increasing the pressure, volume decreases and conc. increases
and hence the rate increases.
(iii) Temperature : It is generally observed that rise in temperature increases the reaction rate.
( i v) Nature of the reactants : The rate depends upon specific bonds involved and hence on the nature
of reactants.
g s ? ? ?
( v ) Surface area of the reactants : In heterogeneous reactions, more powdered is the form of
reactants, more is the velocity. [as more active centres are provided]
( v i ) Catalyst : Affects the rate immensely.
E x . 6 For the reaction :
4NH
3
(g) + 5O
2
(g) ? 4NO(g) + 6H
2
O(g)
Given : 
d [NO]
dt
= 3.6 × 10
–3
 mol L
–1
 s
–1
Calculate  : (i) rate of disappearance of ammonia
       (ii) rate of formation of water
JEEMAIN.GURU
Sol. From the eqn. it is clear that
Rate = – 
1
4
 
3
d[NH ]
dt
 = 
1
4
d [NO]
dt
 = 
1
6
2
d[H O]
dt
           Thus :      – 
1
4
3
d[NH ]
dt
 = 
1
4
d [N O ]
dt
or –
3
d[NH ]
dt
 = 
d [NO]
dt
= 3.6 × 10
–3
 mol L
–1
 s
–1
   Also    
1
4
d [NO]
dt
 = 
1
6
2
d[H O]
dt
3
2
d [NO]
dt
=
2
d[H O]
dt
3
2
 × 3.6 × 10
–3
 = 
2
d[H O]
dt
2
d[H O]
dt
= 5.4 × 10
–3
 mol L
–1 
s
–1
E x . 7 The following reaction was studied in a closed vessel.
2N
2
O
5
(g) 
? ? ?
? ? ?
 4NO
2
(g) + O
2
(g)
It was found that concentration of NO
2
 increases by 4.0 × 10
–2
 mol L
–1
 in five seconds, calculate
(a) the rate of reaction
(b) the rate of change of concentration N
2
O
5
.
S o l . (a) Rate =
2
d[NO ] 1
4 dt
But 
2 1
2
d [NO ] 4.0 10 mol L
dt 5 sec
? ?
?
?
= 8 × 10
–3
 mol L
–1
 s
–1
? Rate of reaction = 
1
4
× 8 × 10
–3
 mol L
–1
 s
–1
 = 2 × 10
–3
 mol L
–1
 s
–1
(b) Rate of change of conc. of N
2
O
5
= 
?
? ?
2 5
d[N O ] 1
dt 2
× Rate of formation of NO
2
= – 
1
2
2 5
[d[N O ]]
dt
 = –
1
2
 × 8 × 10
–3
 = 4 × 10
–3
 mol L
–1 
s
–1
E x . 8 The rate of change in concentration of R in the reaction, 2P + Q ? ? ? 2R + 3S, was reported as
1.0 mol L
–1
 sec
–1
. Calculate the reaction rate as well as rate of change of concentration of P, Q and S.
S o l .
?1
2
d[P]
dt
d[Q] 1 d[R] 1 d[S]
dt 2 dt 3 dt
? ? ? ?
= Rate of reaction
?
d[R]
dt
 = 1.0 molL
–1
 s
–1
?
d[P] d[R]
dt dt
? ?
= 1.0 mol L
–1
 s
–1
d[Q] 1 d[R] 1
dt 2 dt 2
?
? ?
 = 0.5 molL
–1 
s
–1
d[S] 3 d[R] 3
dt 2 dt 2
?
? ?
 × 1 = 1.5 molL
–1
 s
–1
Rate of reaction =
1
2
d[C]
dt
=
1
2
× 1 = 0.5 mol L
–1
s
–1
JEEMAIN.GURU
Page 5


1 . CLASSIFICATION OF REACTIONS : [IN TERMS OF R ATES]
(i) There are certain reactions which are too slow e.g. rusting of iron, weathering of rocks.
(ii) Instantaneous reactions i.e. too fast e.g. Detonation of explosives, acid-base neutralization,
precipitation of AgCl by NaCl and AgNO
3
.
(iii) Neither too fast nor too slow e.g. combination of H
2
 and Cl
2
 in presence of light, hydrolysis of ethyl
acetate catalysed by acid, decomposition of azomethane
2 . RATE OF REACTION :
The change in concentration of either reactant or product per unit time.
Formula : v = ± 
dc
dt
dc = change in concentration in a small interval dt.
[–] sign is used when we refer to reactant concentration.
[+] sign is used when we refer to product concentration.
? Example : N
2
 + 3H
2
 ? 2NH
3
(i) Rate of formation of ammonia = +
3
d[NH ]
dt
(ii) Rate of disappearance of nitrogen = –
2
d [N ]
dt
(iii) Rate of disappearance of hydrogen = –
2
d [H ]
dt
Rate of reaction = + 
1
2
3
d[NH ]
dt
 = – 
2
d [N ]
dt
 = – 
1
3
2
d [H ]
dt
Thus, Rate of reaction = – 
2
d [N ]
dt
 = 
1
2
3
d[NH ]
dt
or rate of formation of ammonia = Twice the rate of disappearance of nitrogen
i.e.
3
d[NH ]
dt
 = 
2
3
 
2
d [H ]
–
dt
? ?
? ?
? ?
3 . AVERAGE VELOCITY OF REACTION  :
Change in the concentration of reactants or products per unit time is called average reaction velocity. If ?c
is the change in the concentration of reactants and product in ?t time, then
Average velocity = ± 
c
t
?
?
or Average velocity = 
(–) Change in the concentration of reactants
Time
   
(+ ) Change in the concentration of products
Time
CHEMICAL KINETICS
JEEMAIN.GURU
Concentration
Product
Reactant
Tim e
Unit of average velocity = 
Unit of concentration
Unit of time
 = 
gram mole
litre× Second
 =  gram mole litre
–1
 second
–1
4 . INSTANTANEOUS RATE OF THE REACTION :
The rate of reaction determined at specified concentration or specified time      
B
Tim e
Concentration
is called instantaneous rate.
The instantaneous rate of the reaction can be determined by measuring
concentration of reactant or product at a instant of time and plotting con-
centration versus time.
The instantaneous rate at any time is determined by the slope of the tan-
gent at a point on the time-concentration curve corresponding to the speci-
fied time. The slope of the tangent at a point is the limiting value of 
c
t
?
?
.
t 0
c
Lim
t ? ?
?
?
=
dc
dt
In terms of the concentration of reactant, the rate of the reaction = –
dc
dt
. The –sign indicates that the e
concentration of reactant decreases with time.
In terms of the concentration of product, the rate of the reaction = +
dc
dt
. The +sign indicates that the e
concentration of product increases with time. In the reaction if at a time t the concentration of product is x and
at time t + dt, the concentration becomes x + dx then the reaction rate =
dx
dt
.
? For example the rate of reaction : N
2
 + 3H
2
 
? ? ? ?
? ? ? ? 2NH
3
in terms of the concentrations of N
2
, H
2
 and NH
3
 can be expressed as :
– 
2
d[N ]
dt
, –
1
3
2
d[H ]
dt
, + 
1
2
3
d[NH ]
dt
E x . 1 What should be (a) the rate of disappearance of B and (b) the rate of formation of C, if the rate
of disappearance of A for the reaction A + B ? 2C is 10
–2
 mole/litre/second at a particular
temperature ?
S o l . (a) Rate of disappearance of A = Rate of disappearance of B
       = 10
–2
 mole/litre/second
(b) Rate of disappearance of A = 
1
2
 ×  Rate of formation of C
Rate of formation of C = 2 ×  Rate of disappearance of A
 = 2 × 10
–2
 mole/litre/second
JEEMAIN.GURU
Ex.2 A gaseous reaction : 2A(g) + B(g) ? 2C(g),
Show a decrease in pressure from 120 mm to 100 mm in 10 minutes. The rate of appearance of C is -
[A] 2 mm/min [B] 4 mm/min [C] 10 mm/min [D] 12 mm/min. Ans. [B]
Sol. Suppose 2p is the pressure of C after 10 min.
Fall in pressure of A = 2p ; Fall in pressure of B = p
Total fall in pressure = (2p + p) – 2p = p = 20 mm
Pressure of C = 2p = 40 mm
Rate of appearance of C = 40/10 = 4 mm/min
Ex.3 The term 
dx
dt
 in the rate expression refers to the -
[A] concentration of the reactants [B] increase in concentration of the reactants
[C] instantaneous rate of the reaction [D] average rate of the reaction Ans. [C]
Sol. It is expression for instantaneous rate
Ex.4 Which of the following expression can be used to describe the instantaneous rate of the reaction ?
2A + B ? ? A
2
B
[A] – 
1 d [A]
2 dt
[B] –
d [A]
dt
[C] 
2
1 d[A B]
2 dt
[D] –
1 d [A] d [B]
.
2 dt dt
Ans. [A]
Sol. The instantaneous rate of the reaction can be expressed by any of the following expressions
1 d [A]
–
2 dt
   or   –
d[B]
dt
   or   
2
d [A B]
dt
Ex.5 Which of the following will react at the highest rate ?
[A] 1 mol of A and 1 mol of B in a 1 L vessel [B] 2 mol of A and 2 mol of B in a 2 L vessel
[C] 3 mol of A and 3 mol of B in a 3 L vessel [D] All would react at the same rate Ans. [D]
Sol. Since all have same conc. of reactants, all would react at same rate.
5 . FACTORS AFFECTING THE RATE OF REACTION :
(i) Concentration : Law of mass action enunciates that greater is the conc. of the reactants, the more
rapidly the reaction proceeds.
(i i) Pressure (Gaseous reaction) : On increasing the pressure, volume decreases and conc. increases
and hence the rate increases.
(iii) Temperature : It is generally observed that rise in temperature increases the reaction rate.
( i v) Nature of the reactants : The rate depends upon specific bonds involved and hence on the nature
of reactants.
g s ? ? ?
( v ) Surface area of the reactants : In heterogeneous reactions, more powdered is the form of
reactants, more is the velocity. [as more active centres are provided]
( v i ) Catalyst : Affects the rate immensely.
E x . 6 For the reaction :
4NH
3
(g) + 5O
2
(g) ? 4NO(g) + 6H
2
O(g)
Given : 
d [NO]
dt
= 3.6 × 10
–3
 mol L
–1
 s
–1
Calculate  : (i) rate of disappearance of ammonia
       (ii) rate of formation of water
JEEMAIN.GURU
Sol. From the eqn. it is clear that
Rate = – 
1
4
 
3
d[NH ]
dt
 = 
1
4
d [NO]
dt
 = 
1
6
2
d[H O]
dt
           Thus :      – 
1
4
3
d[NH ]
dt
 = 
1
4
d [N O ]
dt
or –
3
d[NH ]
dt
 = 
d [NO]
dt
= 3.6 × 10
–3
 mol L
–1
 s
–1
   Also    
1
4
d [NO]
dt
 = 
1
6
2
d[H O]
dt
3
2
d [NO]
dt
=
2
d[H O]
dt
3
2
 × 3.6 × 10
–3
 = 
2
d[H O]
dt
2
d[H O]
dt
= 5.4 × 10
–3
 mol L
–1 
s
–1
E x . 7 The following reaction was studied in a closed vessel.
2N
2
O
5
(g) 
? ? ?
? ? ?
 4NO
2
(g) + O
2
(g)
It was found that concentration of NO
2
 increases by 4.0 × 10
–2
 mol L
–1
 in five seconds, calculate
(a) the rate of reaction
(b) the rate of change of concentration N
2
O
5
.
S o l . (a) Rate =
2
d[NO ] 1
4 dt
But 
2 1
2
d [NO ] 4.0 10 mol L
dt 5 sec
? ?
?
?
= 8 × 10
–3
 mol L
–1
 s
–1
? Rate of reaction = 
1
4
× 8 × 10
–3
 mol L
–1
 s
–1
 = 2 × 10
–3
 mol L
–1
 s
–1
(b) Rate of change of conc. of N
2
O
5
= 
?
? ?
2 5
d[N O ] 1
dt 2
× Rate of formation of NO
2
= – 
1
2
2 5
[d[N O ]]
dt
 = –
1
2
 × 8 × 10
–3
 = 4 × 10
–3
 mol L
–1 
s
–1
E x . 8 The rate of change in concentration of R in the reaction, 2P + Q ? ? ? 2R + 3S, was reported as
1.0 mol L
–1
 sec
–1
. Calculate the reaction rate as well as rate of change of concentration of P, Q and S.
S o l .
?1
2
d[P]
dt
d[Q] 1 d[R] 1 d[S]
dt 2 dt 3 dt
? ? ? ?
= Rate of reaction
?
d[R]
dt
 = 1.0 molL
–1
 s
–1
?
d[P] d[R]
dt dt
? ?
= 1.0 mol L
–1
 s
–1
d[Q] 1 d[R] 1
dt 2 dt 2
?
? ?
 = 0.5 molL
–1 
s
–1
d[S] 3 d[R] 3
dt 2 dt 2
?
? ?
 × 1 = 1.5 molL
–1
 s
–1
Rate of reaction =
1
2
d[C]
dt
=
1
2
× 1 = 0.5 mol L
–1
s
–1
JEEMAIN.GURU
6 . SPECIFIC REACTION RATE :
Applying law of mass action to the reaction :
m
1
A + m
2
B ? n
1
C + n
2
D
Rate ? 
1
m
[A] 
2
m
[B]
or v = k
1
m
[A] 
2
m
[B]
This equation is known as rate law. Where k is the proportionality constant and is called
(i) Velocity constant or (ii) Velocity coefficient or (iii) Specific reaction rate.
On putting [A] = [B] = 1, where have : v = k
Hence specific reaction rate is the rate of the reaction when the concentration of each reactant is taken as
unit.
? Unit of Specific Reaction Rate
v = k 
1
m
[A] . 
2
m
[B]
conc.
time
= k
1 2
m +m
[conc.]
1 2
[1–(m + m )]
[conc.]
 ×  [time]
–1
 = k or k =
[1–(m + m )]
1 2
mole
litre
? ?
? ?
? ?
. [second
–1
]
7 . DISTINCTION BETWEEN UNIT OF RATE AND RATE CONSTANT :
? Rate of a reaction : Its units are always mole litre
–1
 time
–1
.
? Rate constant : Its unit depends upon the order of reaction.
8 . RATE LAW :
( a ) It may also not depend upon the concentration of each reactant or product of the reaction.
Suppose, mA + nB ? Product
m n
R [A] [B] ?
(b ) Rate of a chemical reaction is directly proportional to the product of the concentration of reactants
raise to the power of their stoichiometric coffecient.
( c ) The rate law represents the experimentally observed rate of reaction which depends upon the slowest
step of the reaction.
( d ) Rate law cannot be deduce from the equation for a given reaction. It can be find by experiments
only.
(e) The rate law may not bear a simple relationship of the stoichiometric equation.
Ex.9 In the reaction, A + 2B ? 6C + 2D, if the initial rate –
d [A]
dt
 at t = 0 is 2.6 × 10
–2
 M sec
–1
, what will be the
value of –
d [B]
dt
 at t = 0 ?
[A] 8.5 × 10
–2
 M sec
–1
[B] 2.5 × 10
–2
 M sec
–1
[C] 5.2 × 10
–2
 M sec
–1
[D] 7.5 × 10
–2
 M sec
–1
Ans. [C]
S o l . From the reaction it is evident that when a mole of A is reacting, 2 moles of B must react. Hence the
decrease in the concentration of B must be twice that of A
? –  
d [B]
dt
= 2 
d [A]
–
dt
? ?
? ?
? ?
= 2 × 2.6 × 10
–2 
= 5.2 × 10
–2
 M sec
–1
JEEMAIN.GURU
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