The rate of first order reaction is `0.04 mol L^(-1) s^(-1)` at `10 min` and `0.03 mol L^(-1) s^(-1)` at `20 min` after initiation. Find the half life of the reaction.

Options

A. 44.1 s
B. 54.1 s
C. 24.1 s
D. 34.1 s

Answer

C

Explanation

c) For a first order reaction:
`k=(2.303)/(t_(2)-t_(1)) log ([A]_(1))/([A]_(2))`
`=(2.303)/(t_(2)-t_(1)) log (["rate"]_(1))/(["rate"]_(2))` `(therefore propto "rate" propto [A])`
`(2.303)/(20-10) log (0.04)/(0.03) = 0.287 s^(-1)`
`t_(1//2)= 0.693/k = 0.693/(0.287 s^(-1)) = 24.14s`