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

Answer

C

Explanation

For a first order reaction. `A to` product, and for concentration of the reactant at two different times
`k = (2*303)/((2)-t_(1)) log""([A]_(1))/([A]_(2))`
Also for first order reaction, rate `alpha` [A]. Hence
`k=(2*303)/(t_(2)-t_(1))log""(("Rate")_(1))/(("Rate")_(2))`
`=(2*303)/((20-10))log((0*04)/(0*03))=0*0287 s^(-1)`
`t_(1//2)=(0*693)/(k)=(0*693)/(0*0287s^(-1))=24*14s`