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

Answer

B

Explanation

For a first order reaction, `A to` products and for concentration of the reactant at two different times.
`k = (2.303)/( t_2 - t_1) log"" ([A]_1)/([A]_2)`
`k = (2.303)/( t_2 - t_1) log "" (("rate")_1)/(("rate")_2) ( because " rate" prop [A])`
`k = (2.303)/( (20 - 10) ) log"" ((0.04)/( 0.03)) = 0.0287" sec"^(-1)`
`t_(1//2) = (0.693)/( k) = (0.693)/( 0.0287" sec"^(-1) ) = 24.14` sec