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The rate of a first order reaction is 0....

The rate of a first order reaction is 0.04 mol `"litre"^(-1)s^(-1)` after 10 minutes and 0.03 mol `"litre"^(-1)s^(-1)` after 20 minutes. Find the half life period of the reaction.

A

2.406 min

B

24.06 min

C

240.6 min

D

0.204 min

Text Solution

Verified by Experts

The correct Answer is:
B
Rate `= K x [A] , 0.04 = K[A]_(10)` and `0.03 = K[A]_(20)`
`[A]_(10)/[A]_(20) = 0.04/0.03 = 4/3`
Also, `t=2.303/K log [A]_(10)/[A]_(20)`, when t=10 min

`10 = 2.303/K log 4/3 , therefore K =2.303/10 log 4/3=0.0288 min^(-1)`
`t_(1//2) = 0.693/0.0288 = 24.06` min
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