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 hlaf-life period of the reaction is :

Options

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

Answer

B

Explanation

For first-order kinetics, rate is directly proportinal to concentration of reactants. Thus,
`Rate_(1)=k(a-x)_(1)`
`Rate_(2)=k(a-x)_(2)`
:. `(Rate_(1))/(Rate_(2))=((a-x)_(1))/((a-x)_(2))=(0.04)/(0.03)`
Considering the integrated rate law:
`k=(2.303)/((t_(2)-t_(1)))`log`(a-x)_(1)/((a-x)_(2))`
`=(2.303)/((20-10)s)log((0.04)/(0.03))`
`=(2.303)/(10s)(0.1249)`
For first order kinetic
`t_(1//2)=0.693//k=(0.693)/((2.303)(0.1249)//10)s=24.1s`