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Question : 15
Total: 26
Following data are obtained for the reaction:
N 2 O 5 → 2 NO 2 + 1 ∕ 2 O 2
(a) Show that it follows first order reaction.
(b) Calculate the half-life.
(Givenlog 2 = 0.3010 , log 4 = 0.6021 )
| 0 | 300 | 600 |
| | | |
(a) Show that it follows first order reaction.
(b) Calculate the half-life.
(Given
Solution:
(a) For first order reaction the integral rate law is:
k t = ln (
)
Given,a 0 = 1.6 × 10 − 2 mol L − 1
Fort = 300 s , a t = 0.8 × 10 − 2 mol L − 1
Fort = 600 s , a t = 0.4 × 10 − 2 mol L − 1
Using first set of data in the rate law,
k × 300 = ln
k = 0.00231 s − 1
Using second set of data in the rate law,
k × 600 = ln
k = 0.00231 s − 1
The value ofk is consistent,therefore it follows first order reaction.
(b) The half-life of first order reaction is given by the following equation :
t 1 ∕ 2 =
= 2.303 ×
∴ t 1 ∕ 2 = 2.303 ×
= 300.08 s .
Given,
For
For
Using first set of data in the rate law,
Using second set of data in the rate law,
The value of
(b) The half-life of first order reaction is given by the following equation :
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