For a first-order reaction `A rarr B` the reaction rate at reactant concentration of `0.10 M` is found to be `2.0 xx 10^(-5) "mol" L^(-1) s^(-1)`. The half-life period of the reaction is

Options

A. 220s
B. 30s
C. 300s
D. 347s

Answer

D

Explanation

For a first order reaction `ArarrB` , the differential rate law is
Rate `=k[A]`
`2.0xx10^(-5)molL^(-1)s^(-1)=k(0.01M)`
`k=(2.0xx10^(-5)molL^(-1)s^(-1))/(0.01M)`
`=2.0xx10^(-3)s^(-1)`
For the first order reaction
`t_(1//2)=(0.693)/(k)`
Thus,
`t_(1//2)=(0.693)/(2.0xx10^(-3)s^(-1))`
`=346.5s`
`=347s`