CBSE Class 12 Chemistry 2020 Delhi Set 1 Solved Paper

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Question : 37
Total: 37
(a) A first order reaction is 25% complete in 40 minutes. Calculate the value of rate constant. In what time will the reaction be 80% completed?
(b) Define order of reaction. Write the condition under which a bimolecular reaction follows first order kinetics.
OR
(a) A first order reaction is 50% completed in 30 minutes at 300K and in 10 minutes at 320 K. Calculate activation energy (Ea) for the reaction.
‌ ( ‌R=8.314JK−1mol−1‌ ) ‌
(b) Write the two conditions for collisions to be effective collisions.
(c) How order of reaction and molecularity differ towards a complex reaction?
[Given : log‌2=0.3010,log‌3=0.4771,log‌4= 0.6021,log‌5=0.6991]
Solution:  
(a) t=‌
2303
k
‌log
‌
[A]0
[A]
.
(i) 40‌min=‌
2.303
k
‌log
‌
100
75
........(i)
(ii) t=‌
2.303
k
‌log
‌
100
20
........(ii)
Dividing (i) by (ii)
‌‌
40
t
=‌
2.303
k
‌log
‌
100
75
∕‌
2.303
k
‌log
‌
100
20

‌‌
40
t
=‌
‌
2.303
k
‌log
‌
4
3
2.303‌log‌5

‌‌
40
t
=‌
0.6021∕4.771
0.6991

‌‌
40
t
=‌
0.1250
0.6991

‌t=‌
0.6691×40
0.1250
=223.712‌min.

‌k=‌
2.303
t
‌log
‌
100
100−0.25
=‌
2.303
40
‌log
‌
100
75

‌=‌
2.303
40
(log‌4−log‌3)

‌=‌
2.303
40
(0.6021−0.4771)

‌=‌
2.303
40
×0.125
=0.007196

‌=7.196×10−3min−1
(b) Order of reaction: The sum of the coefficients of the reacting species that are involved in the rate equation for the reaction, is called order of reaction.
The condition under which a bimolecular reaction follows first order kinetics is when one of the reactants is taken in large excess that its concentration changes hardly.
OR
(a) At 300K,t1∕2=30‌min.
‌t1∕2=‌
0.693
k
‌ or
‌k
=‌
0.693
t1∕2

‌k1=‌
0.693
30
=0.0231min−1

At 320K,t1∕2=10‌min
‌t1∕2=‌
0.693
k
‌ or
‌k
=‌
0.693
t1∕2

‌k2=‌
0.693
10
=0.0693min−1

According to Arrhenius equation:
‌log‌
k2
k1
=‌
Ea
2.303R
[‌
1
T1
−‌
1
T2
]

‌=log‌
0.0693
0.0231
=‌
Ea
2.303R
[‌
T2−T1
T1T2
]

‌=log‌
0.0693
0.0231
=‌
Ea
2.303×8.314
[‌
320−300
300×320
]

‌‌‌[∵R=8.314JK−1mol−1]
‌=log‌3=‌
Ea×20
2.303×8.314×300×320

‌Ea=‌
log‌3×2.303×8.314×300×320
20

‌=‌
0.4771×2.303×8.314×300×320
20

‌=43848.5Jmol−1=43.85‌kJ‌mol−1
(b) Two conditions for collisions to be effective collision are :
(i) The reactant molecules must have attained sufficient energy to break chemical bonds
(ii) The reactant molecules must have the proper orientation.
(c) The number of the reacting species that collide simultaneously in a chemical reaction is called as molecularity of a reaction. The sum of the coefficients of the reacting species is the order of reaction.
For complex reactions, molecularity has no significance while the order of reaction is applicable.
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