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. 24.1 s
B. 34.1 s
C. 44.1 s
D. 54.15 s

Answer

A

Explanation

For a first order reaction
`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=(2.303 xx 0.1249)/(10)`
`(0.6932)/(t_(1 // 2))=(2.303 xx 0.1249)/(10)`
`t_(1 // 2)=(0.6932 xx 10)/(2.303 xx 0.1249)=24.1` sec