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

Options

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

Answer

A

Explanation

`K=(2.303)/((t_(2)-t_(1)))log.((a-x_(1))/((a-x_(2)))`
`K=(2.303)/((20-10))log.((0.04)/(0.03))`
`K=(2.303xx0.1249)/(10)`
`(2.303xxlog2)/(t_(1//2))=(2.303xx0.1249)/(10)`
`t_(1//2)=(0.3010xx10)/(0.1249)=24.1s`