Solved Example: Chemical Kinetics | Chemistry for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Example on Chemical Kinetics 
JEE Mains 
Q1: For a first order reaction, 
(a) the degree of dissociation is equal to ( ?? - ?? ????
). 
(b) a plot of the reciprocal concentration of the reactant vs time gives a straight line. 
(c) the time taken for the completion of ???? % reaction is twice the ?? ?? /?? of the reaction. 
(d) the pre-exponential factor in the Arrhenius equation has the dimension of ?? . 
Ans: (c) 
t
3/4
= 2t
1/2
 
Q2: In a certain reaction ?? % of the reactant decomposes in 30 minutes, ???? % in 90 minutes 
and ???? % in 180 minutes. What are the dimensions of the rate constant? 
(a) hour  
-?? 
(b) ?????? ?????? -?? ?????? -?? 
(c) lit ?????? -?? ?????? -?? 
(d) ?????? ?????? -?? 
Ans: b 
 
Q3: Figure shows a graph in ??????
????
 ?? vs 
?? ?? where ?? is rate constant and ?? is temperature. 
The straight line BC has 
 
Ans: Slope, m =
-E
a
2.303R
= -
1
2.303
 
? E
a
= R = 2cal . 
 
 
 
 
Page 2


JEE Solved Example on Chemical Kinetics 
JEE Mains 
Q1: For a first order reaction, 
(a) the degree of dissociation is equal to ( ?? - ?? ????
). 
(b) a plot of the reciprocal concentration of the reactant vs time gives a straight line. 
(c) the time taken for the completion of ???? % reaction is twice the ?? ?? /?? of the reaction. 
(d) the pre-exponential factor in the Arrhenius equation has the dimension of ?? . 
Ans: (c) 
t
3/4
= 2t
1/2
 
Q2: In a certain reaction ?? % of the reactant decomposes in 30 minutes, ???? % in 90 minutes 
and ???? % in 180 minutes. What are the dimensions of the rate constant? 
(a) hour  
-?? 
(b) ?????? ?????? -?? ?????? -?? 
(c) lit ?????? -?? ?????? -?? 
(d) ?????? ?????? -?? 
Ans: b 
 
Q3: Figure shows a graph in ??????
????
 ?? vs 
?? ?? where ?? is rate constant and ?? is temperature. 
The straight line BC has 
 
Ans: Slope, m =
-E
a
2.303R
= -
1
2.303
 
? E
a
= R = 2cal . 
 
 
 
 
Q4: The hydrolysis of ethyl acetate  ????
?? ???????? + ?? ?? ?? ?? ???? in aqueous solution is first order 
w.r.t ethyl acetate. Upon varying the ???? of the solution, the first order rate constant varies 
as follows 
???? 3 2 1 
?? ?? /????
-?? ( ?? -?? ) 1.1 11 110 
 
What is the order w.r.t ?? +
and value of rate constant? 
(a) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(b) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(c) 1 and ?? . ?? × ????
?? ????
?? ?????? -?? ?? -?? 
(d) Data is inadequate. 
Ans: (a) 
 rate = k
'
[ Ester ][H
3
O
+
]
?? = k[ Ester ]
k = k
'
[H
3
O
+
]
?? (
10
-3
10
-2
)
?? =
1.1
11
( 10
-1
)
?? = 10
-1
 ? ?? = 1
k = 1.1 × 10
-4
= k
'
( 10
-3
) ?
k
'
= ?? . ?? × ????
-1
????
3
?????? -1
?? -1
.
 
Q5: For a reaction, ?? ? ?? + ?? , it was found that at the end of ???? ?????? from the start the 
total optical rotation of the system was ????
°
 and when the reaction is complete it was ??????
°
. 
Assuming that only B and ?? are optically active and dextro rotatory, the rate constant of this 
first order reaction would be 
(a) ?? . ?????? ??????
-?? 
(b) ?? . ???? ??????
-?? 
(c) ?? . ?? ??????
-?? 
(d) ?? . ?? × ????
-?? ??????
-?? 
Ans: (a) 
A ? B + C 
R
o
= 0, R
t
= 50
°
 and R
8
= 100
°
 
Rate constant of the above reaction is given by 
k =
2.303
t
log 
R
8
- R
o
R
8
- R
t
 =
2.303
t
log 
100
50
= ?? . ?????? ??????
-1
. 
 
 
 
 
Page 3


JEE Solved Example on Chemical Kinetics 
JEE Mains 
Q1: For a first order reaction, 
(a) the degree of dissociation is equal to ( ?? - ?? ????
). 
(b) a plot of the reciprocal concentration of the reactant vs time gives a straight line. 
(c) the time taken for the completion of ???? % reaction is twice the ?? ?? /?? of the reaction. 
(d) the pre-exponential factor in the Arrhenius equation has the dimension of ?? . 
Ans: (c) 
t
3/4
= 2t
1/2
 
Q2: In a certain reaction ?? % of the reactant decomposes in 30 minutes, ???? % in 90 minutes 
and ???? % in 180 minutes. What are the dimensions of the rate constant? 
(a) hour  
-?? 
(b) ?????? ?????? -?? ?????? -?? 
(c) lit ?????? -?? ?????? -?? 
(d) ?????? ?????? -?? 
Ans: b 
 
Q3: Figure shows a graph in ??????
????
 ?? vs 
?? ?? where ?? is rate constant and ?? is temperature. 
The straight line BC has 
 
Ans: Slope, m =
-E
a
2.303R
= -
1
2.303
 
? E
a
= R = 2cal . 
 
 
 
 
Q4: The hydrolysis of ethyl acetate  ????
?? ???????? + ?? ?? ?? ?? ???? in aqueous solution is first order 
w.r.t ethyl acetate. Upon varying the ???? of the solution, the first order rate constant varies 
as follows 
???? 3 2 1 
?? ?? /????
-?? ( ?? -?? ) 1.1 11 110 
 
What is the order w.r.t ?? +
and value of rate constant? 
(a) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(b) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(c) 1 and ?? . ?? × ????
?? ????
?? ?????? -?? ?? -?? 
(d) Data is inadequate. 
Ans: (a) 
 rate = k
'
[ Ester ][H
3
O
+
]
?? = k[ Ester ]
k = k
'
[H
3
O
+
]
?? (
10
-3
10
-2
)
?? =
1.1
11
( 10
-1
)
?? = 10
-1
 ? ?? = 1
k = 1.1 × 10
-4
= k
'
( 10
-3
) ?
k
'
= ?? . ?? × ????
-1
????
3
?????? -1
?? -1
.
 
Q5: For a reaction, ?? ? ?? + ?? , it was found that at the end of ???? ?????? from the start the 
total optical rotation of the system was ????
°
 and when the reaction is complete it was ??????
°
. 
Assuming that only B and ?? are optically active and dextro rotatory, the rate constant of this 
first order reaction would be 
(a) ?? . ?????? ??????
-?? 
(b) ?? . ???? ??????
-?? 
(c) ?? . ?? ??????
-?? 
(d) ?? . ?? × ????
-?? ??????
-?? 
Ans: (a) 
A ? B + C 
R
o
= 0, R
t
= 50
°
 and R
8
= 100
°
 
Rate constant of the above reaction is given by 
k =
2.303
t
log 
R
8
- R
o
R
8
- R
t
 =
2.303
t
log 
100
50
= ?? . ?????? ??????
-1
. 
 
 
 
 
Q6: If 'I' is the intensity of absorbed light and ' ?? ' is the concentration of ???? for the 
photochemical process ???? + ?? ?? ???? * the rate of formation of ????
*
 is directly proportional to: 
(a) c 
(b) I 
(c) ?? ?? 
(d) c . I 
Ans: (b) Rate determining step for all photoprimary processes is given as ?? = ?? . ?? 
Q7: The rate constant of a reaction at ?????? ?? , in presence of catalyst is same as that of 
?????? ?? in absence of catalyst if use of catalyst lowers down the energy barrier by ???? ?? then 
what will be the value of activation energy of uncatalysed reaction? 
(a) ?????? ?? 
(b) ?????? ?? 
(c) ?????? ?? 
(d) ?????? ?? 
Ans: (d) 
Let in absence of catalyst activation energy to be E
a
 then in presence of catalyst will be 
E
a
- 60 
 ? K
catalyst 
= K
without catalyst 
E
a
- 60
RT
=
E
a
RT
E
a
- 60
500
=
E
a
800
E
a
= ?????? ?? .
 
Q8: For a hypothetical reaction ?? ?
?
?? ?
?? ?? stow 
?? assuming rate of formation of ?? is equal to its rate of 
disappearance, the rate expression is: 
(a) rate =
?? ?? ?? ?? [?? ]
?? ?? +?? ?? 
(b) rate =
?? ?? ?? ?? [?? ]
?? -?? +?? ?? 
(c) rate =
?? ?? [-?? ]
[?? ????
+?? ?? ]
 
(d) rate =
?? ?? +?? ?? ?? ?? 
Ans: (b) 
 rate = ?? 2
[?? ] … ( 1)
?? [?? ]
????
= ?? 1
[?? ] - ?? -1
[?? ] - ?? 2
[?? ] = ?? 1
[?? ] - [?? ][?? -1
+ ?? 2
]
 but 
?? [?? ]
????
= 0
[?? ] =
?? 1
[?? ]
?? -1
+ ?? 2
 ? ( 2) in (1) 
 rate =
?? 1
?? 2
?? -1
+ ?? 2
[?? ].
 
Page 4


JEE Solved Example on Chemical Kinetics 
JEE Mains 
Q1: For a first order reaction, 
(a) the degree of dissociation is equal to ( ?? - ?? ????
). 
(b) a plot of the reciprocal concentration of the reactant vs time gives a straight line. 
(c) the time taken for the completion of ???? % reaction is twice the ?? ?? /?? of the reaction. 
(d) the pre-exponential factor in the Arrhenius equation has the dimension of ?? . 
Ans: (c) 
t
3/4
= 2t
1/2
 
Q2: In a certain reaction ?? % of the reactant decomposes in 30 minutes, ???? % in 90 minutes 
and ???? % in 180 minutes. What are the dimensions of the rate constant? 
(a) hour  
-?? 
(b) ?????? ?????? -?? ?????? -?? 
(c) lit ?????? -?? ?????? -?? 
(d) ?????? ?????? -?? 
Ans: b 
 
Q3: Figure shows a graph in ??????
????
 ?? vs 
?? ?? where ?? is rate constant and ?? is temperature. 
The straight line BC has 
 
Ans: Slope, m =
-E
a
2.303R
= -
1
2.303
 
? E
a
= R = 2cal . 
 
 
 
 
Q4: The hydrolysis of ethyl acetate  ????
?? ???????? + ?? ?? ?? ?? ???? in aqueous solution is first order 
w.r.t ethyl acetate. Upon varying the ???? of the solution, the first order rate constant varies 
as follows 
???? 3 2 1 
?? ?? /????
-?? ( ?? -?? ) 1.1 11 110 
 
What is the order w.r.t ?? +
and value of rate constant? 
(a) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(b) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(c) 1 and ?? . ?? × ????
?? ????
?? ?????? -?? ?? -?? 
(d) Data is inadequate. 
Ans: (a) 
 rate = k
'
[ Ester ][H
3
O
+
]
?? = k[ Ester ]
k = k
'
[H
3
O
+
]
?? (
10
-3
10
-2
)
?? =
1.1
11
( 10
-1
)
?? = 10
-1
 ? ?? = 1
k = 1.1 × 10
-4
= k
'
( 10
-3
) ?
k
'
= ?? . ?? × ????
-1
????
3
?????? -1
?? -1
.
 
Q5: For a reaction, ?? ? ?? + ?? , it was found that at the end of ???? ?????? from the start the 
total optical rotation of the system was ????
°
 and when the reaction is complete it was ??????
°
. 
Assuming that only B and ?? are optically active and dextro rotatory, the rate constant of this 
first order reaction would be 
(a) ?? . ?????? ??????
-?? 
(b) ?? . ???? ??????
-?? 
(c) ?? . ?? ??????
-?? 
(d) ?? . ?? × ????
-?? ??????
-?? 
Ans: (a) 
A ? B + C 
R
o
= 0, R
t
= 50
°
 and R
8
= 100
°
 
Rate constant of the above reaction is given by 
k =
2.303
t
log 
R
8
- R
o
R
8
- R
t
 =
2.303
t
log 
100
50
= ?? . ?????? ??????
-1
. 
 
 
 
 
Q6: If 'I' is the intensity of absorbed light and ' ?? ' is the concentration of ???? for the 
photochemical process ???? + ?? ?? ???? * the rate of formation of ????
*
 is directly proportional to: 
(a) c 
(b) I 
(c) ?? ?? 
(d) c . I 
Ans: (b) Rate determining step for all photoprimary processes is given as ?? = ?? . ?? 
Q7: The rate constant of a reaction at ?????? ?? , in presence of catalyst is same as that of 
?????? ?? in absence of catalyst if use of catalyst lowers down the energy barrier by ???? ?? then 
what will be the value of activation energy of uncatalysed reaction? 
(a) ?????? ?? 
(b) ?????? ?? 
(c) ?????? ?? 
(d) ?????? ?? 
Ans: (d) 
Let in absence of catalyst activation energy to be E
a
 then in presence of catalyst will be 
E
a
- 60 
 ? K
catalyst 
= K
without catalyst 
E
a
- 60
RT
=
E
a
RT
E
a
- 60
500
=
E
a
800
E
a
= ?????? ?? .
 
Q8: For a hypothetical reaction ?? ?
?
?? ?
?? ?? stow 
?? assuming rate of formation of ?? is equal to its rate of 
disappearance, the rate expression is: 
(a) rate =
?? ?? ?? ?? [?? ]
?? ?? +?? ?? 
(b) rate =
?? ?? ?? ?? [?? ]
?? -?? +?? ?? 
(c) rate =
?? ?? [-?? ]
[?? ????
+?? ?? ]
 
(d) rate =
?? ?? +?? ?? ?? ?? 
Ans: (b) 
 rate = ?? 2
[?? ] … ( 1)
?? [?? ]
????
= ?? 1
[?? ] - ?? -1
[?? ] - ?? 2
[?? ] = ?? 1
[?? ] - [?? ][?? -1
+ ?? 2
]
 but 
?? [?? ]
????
= 0
[?? ] =
?? 1
[?? ]
?? -1
+ ?? 2
 ? ( 2) in (1) 
 rate =
?? 1
?? 2
?? -1
+ ?? 2
[?? ].
 
Q9: For a first order reaction ?? ( ?? ) ? ?? ( ?? )+ ?? ( ?? ) , the total pressure of ?? + ?? + ?? at time ' ?? ' and 
8 are ?? ?? and ?? ?? respectively. The rate constant ?? of the reaction is 
(a) 
?? ?? ???? 
?? ?? ?? ?? ?? -?? ?? 
(b) 
?? ?? ???? 
?? ?? ?? ?? -?? ?? 
(c) 
?? ?? ???? 
?? ?? ?? ?? ?? -?? ?? 
(d) 
?? ?? ???? 
?? ?? ?? ( ?? ?? -?? ?? )
 
Sol. (d) 
Q10: Which of the following is incorrect statement about Arrhenius equation? 
?? = ?????? -?? ?? /????
= ????
-?? ?? /????
 
(a) 'A' represents the number of effective collisions having correct orientation. 
(b) ' ?? ' represents the number of collisions per unit time when the concentration of each reactant 
is one molar. 
(c) ?? -?? ?? /????
 represents the fraction of collisions having energy less than activation energy. 
(d) ?? -?? ?? /????
 represents the fraction of collisions having energy more than or equal to activation 
energy. 
Ans: (c) 
Q11: The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction 
at ????
°
?? are ?? × ????
-?? ?? -?? , ?????? . ?? ???? ?????? -?? and ?? × ????
????
 ?? -?? respectively. The value of the rate 
constant as ?? ? 8 is 
(a) ?? × ????
????
 ?? -?? 
(b) ?? × ????
????
 ?? -?? 
(c) 8 
(d) ?? . ?? × ????
????
 ?? -?? 
Ans: (b) 
k = Ac
-E
2
RT
, when T ? 8 ? k = A. 
Q12: In the first order reaction, ?? ? ?? ; the concentration of ' ?? ' changes from ?? . ???? to ?? . ???????? 
is ???? ?????? . The rate of reactions ( ?????? ?? -?? ?????? -?? ) when concentration of ' ?? ' is 0.01 M would be 
(a) ?? . ???? × ????
-?? 
(b) ?? . ???? × ????
-?? 
(c) ?? . ?? × ????
-?? 
(d) ?? . ?? × ????
-?? 
Ans: (b) 
X ? Y 
Number of half-lives when [X] changes from 0.1M to 
0.025M = 2.
t
1/2
=
40
2
= 20 min
k =
0.693
20
 min
-1
 
Page 5


JEE Solved Example on Chemical Kinetics 
JEE Mains 
Q1: For a first order reaction, 
(a) the degree of dissociation is equal to ( ?? - ?? ????
). 
(b) a plot of the reciprocal concentration of the reactant vs time gives a straight line. 
(c) the time taken for the completion of ???? % reaction is twice the ?? ?? /?? of the reaction. 
(d) the pre-exponential factor in the Arrhenius equation has the dimension of ?? . 
Ans: (c) 
t
3/4
= 2t
1/2
 
Q2: In a certain reaction ?? % of the reactant decomposes in 30 minutes, ???? % in 90 minutes 
and ???? % in 180 minutes. What are the dimensions of the rate constant? 
(a) hour  
-?? 
(b) ?????? ?????? -?? ?????? -?? 
(c) lit ?????? -?? ?????? -?? 
(d) ?????? ?????? -?? 
Ans: b 
 
Q3: Figure shows a graph in ??????
????
 ?? vs 
?? ?? where ?? is rate constant and ?? is temperature. 
The straight line BC has 
 
Ans: Slope, m =
-E
a
2.303R
= -
1
2.303
 
? E
a
= R = 2cal . 
 
 
 
 
Q4: The hydrolysis of ethyl acetate  ????
?? ???????? + ?? ?? ?? ?? ???? in aqueous solution is first order 
w.r.t ethyl acetate. Upon varying the ???? of the solution, the first order rate constant varies 
as follows 
???? 3 2 1 
?? ?? /????
-?? ( ?? -?? ) 1.1 11 110 
 
What is the order w.r.t ?? +
and value of rate constant? 
(a) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(b) 1 and ?? . ?? × ????
-?? ????
?? ?????? -?? ?? -?? 
(c) 1 and ?? . ?? × ????
?? ????
?? ?????? -?? ?? -?? 
(d) Data is inadequate. 
Ans: (a) 
 rate = k
'
[ Ester ][H
3
O
+
]
?? = k[ Ester ]
k = k
'
[H
3
O
+
]
?? (
10
-3
10
-2
)
?? =
1.1
11
( 10
-1
)
?? = 10
-1
 ? ?? = 1
k = 1.1 × 10
-4
= k
'
( 10
-3
) ?
k
'
= ?? . ?? × ????
-1
????
3
?????? -1
?? -1
.
 
Q5: For a reaction, ?? ? ?? + ?? , it was found that at the end of ???? ?????? from the start the 
total optical rotation of the system was ????
°
 and when the reaction is complete it was ??????
°
. 
Assuming that only B and ?? are optically active and dextro rotatory, the rate constant of this 
first order reaction would be 
(a) ?? . ?????? ??????
-?? 
(b) ?? . ???? ??????
-?? 
(c) ?? . ?? ??????
-?? 
(d) ?? . ?? × ????
-?? ??????
-?? 
Ans: (a) 
A ? B + C 
R
o
= 0, R
t
= 50
°
 and R
8
= 100
°
 
Rate constant of the above reaction is given by 
k =
2.303
t
log 
R
8
- R
o
R
8
- R
t
 =
2.303
t
log 
100
50
= ?? . ?????? ??????
-1
. 
 
 
 
 
Q6: If 'I' is the intensity of absorbed light and ' ?? ' is the concentration of ???? for the 
photochemical process ???? + ?? ?? ???? * the rate of formation of ????
*
 is directly proportional to: 
(a) c 
(b) I 
(c) ?? ?? 
(d) c . I 
Ans: (b) Rate determining step for all photoprimary processes is given as ?? = ?? . ?? 
Q7: The rate constant of a reaction at ?????? ?? , in presence of catalyst is same as that of 
?????? ?? in absence of catalyst if use of catalyst lowers down the energy barrier by ???? ?? then 
what will be the value of activation energy of uncatalysed reaction? 
(a) ?????? ?? 
(b) ?????? ?? 
(c) ?????? ?? 
(d) ?????? ?? 
Ans: (d) 
Let in absence of catalyst activation energy to be E
a
 then in presence of catalyst will be 
E
a
- 60 
 ? K
catalyst 
= K
without catalyst 
E
a
- 60
RT
=
E
a
RT
E
a
- 60
500
=
E
a
800
E
a
= ?????? ?? .
 
Q8: For a hypothetical reaction ?? ?
?
?? ?
?? ?? stow 
?? assuming rate of formation of ?? is equal to its rate of 
disappearance, the rate expression is: 
(a) rate =
?? ?? ?? ?? [?? ]
?? ?? +?? ?? 
(b) rate =
?? ?? ?? ?? [?? ]
?? -?? +?? ?? 
(c) rate =
?? ?? [-?? ]
[?? ????
+?? ?? ]
 
(d) rate =
?? ?? +?? ?? ?? ?? 
Ans: (b) 
 rate = ?? 2
[?? ] … ( 1)
?? [?? ]
????
= ?? 1
[?? ] - ?? -1
[?? ] - ?? 2
[?? ] = ?? 1
[?? ] - [?? ][?? -1
+ ?? 2
]
 but 
?? [?? ]
????
= 0
[?? ] =
?? 1
[?? ]
?? -1
+ ?? 2
 ? ( 2) in (1) 
 rate =
?? 1
?? 2
?? -1
+ ?? 2
[?? ].
 
Q9: For a first order reaction ?? ( ?? ) ? ?? ( ?? )+ ?? ( ?? ) , the total pressure of ?? + ?? + ?? at time ' ?? ' and 
8 are ?? ?? and ?? ?? respectively. The rate constant ?? of the reaction is 
(a) 
?? ?? ???? 
?? ?? ?? ?? ?? -?? ?? 
(b) 
?? ?? ???? 
?? ?? ?? ?? -?? ?? 
(c) 
?? ?? ???? 
?? ?? ?? ?? ?? -?? ?? 
(d) 
?? ?? ???? 
?? ?? ?? ( ?? ?? -?? ?? )
 
Sol. (d) 
Q10: Which of the following is incorrect statement about Arrhenius equation? 
?? = ?????? -?? ?? /????
= ????
-?? ?? /????
 
(a) 'A' represents the number of effective collisions having correct orientation. 
(b) ' ?? ' represents the number of collisions per unit time when the concentration of each reactant 
is one molar. 
(c) ?? -?? ?? /????
 represents the fraction of collisions having energy less than activation energy. 
(d) ?? -?? ?? /????
 represents the fraction of collisions having energy more than or equal to activation 
energy. 
Ans: (c) 
Q11: The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction 
at ????
°
?? are ?? × ????
-?? ?? -?? , ?????? . ?? ???? ?????? -?? and ?? × ????
????
 ?? -?? respectively. The value of the rate 
constant as ?? ? 8 is 
(a) ?? × ????
????
 ?? -?? 
(b) ?? × ????
????
 ?? -?? 
(c) 8 
(d) ?? . ?? × ????
????
 ?? -?? 
Ans: (b) 
k = Ac
-E
2
RT
, when T ? 8 ? k = A. 
Q12: In the first order reaction, ?? ? ?? ; the concentration of ' ?? ' changes from ?? . ???? to ?? . ???????? 
is ???? ?????? . The rate of reactions ( ?????? ?? -?? ?????? -?? ) when concentration of ' ?? ' is 0.01 M would be 
(a) ?? . ???? × ????
-?? 
(b) ?? . ???? × ????
-?? 
(c) ?? . ?? × ????
-?? 
(d) ?? . ?? × ????
-?? 
Ans: (b) 
X ? Y 
Number of half-lives when [X] changes from 0.1M to 
0.025M = 2.
t
1/2
=
40
2
= 20 min
k =
0.693
20
 min
-1
 
Q13: For the reaction, ?? ?? ?? ?? ? ?? ????
?? + ?? /?? ?? ?? , 
 -
?? [?? ?? ?? ?? ]
????
= ?? ?? [ ?? ?? ?? ?? ]
?? [????
?? ]
????
= ?? ?? [ ?? ?? ?? ?? ]
?? [?? ?? ]
????
= ?? ?? [ ?? ?? ?? ?? ]
 
The relation in between ?? ?? , ?? ?? and ?? ?? is 
(a) ?? ?? ?? = ?? ?? = ?? ?? ?? 
(b) ?? ?? = ?? ?? = ?? ?? 
(c) ?? ?? ?? = ?? ?? ?? = ?? ?? 
(d) none of these 
Ans: (a) 
N
2
O
5
? 2NO
2
+
1
2
O
2
 
Rate of the given reaction is expressed by -
?? [ N
2
O
5
]
????
 
 =
1
2
d[NO
2
]
dt
=
2 d[O
2
]
dt
k
1
[ N
2
O
5
] =
1
2
k
2
[ N
2
O
5
] = 2k
3
[ N
2
O
5
]
 or ?? ?? 1
= ?? 2
= 4?? 3
.
 
 
Q14: How will the rate ?? = ?? [????
?? ][?? ?? ] of reaction, ?? ????
?? + ?? ?? ? ?? ????
?? , change if the volume of 
the reaction vessel is tripled? 
(a) It will be 
?? ?? rd of its initial value. 
(b) It will be 3 times of its initial value. 
(c) It will be 9 times of its initial value. 
(d) It will be 
?? ?? th of its initial value. 
Ans: (d) 
2SO
2
+ O
2
? 2SO
3
 
Rate law expression of the above reaction is given by R = k[SO
2
][O
2
] 
Let [SO
2
] = ?? M and [O
2
] = yM at any time then, rate R , is given by R
1
= k( ?? y) . 
If the volume of the reaction vessel is tripled, then [SO
2
] = 
?? 3
M and [O
2
] =
y
3
M 
? New rate, R
2
= k (
x
3
)(
y
3
) =
R
1
9
.