In a first order reaction, the concentration of the reactant decreases form `800 "mol dm"^(-3)` to `50 "mol dm"^(-3)` in `2 xx 10^(4) s`. The rate constant of the reaction (in `s^(-1)`) is

Options

A. `2 xx 10^(4)`
B. `3.45 xx 10^(-5)`
C. `1.386 xx 10^(-4)`
D. `2 xx 10^(-4)`

Answer

C

Explanation

`800 rarr 400 rarr 200 rarr 100 rarr 50`
There are four half lives involved.
Half life `= (2 xx 10^(4))/(4) = 5 xx 10^(3)s`
Rate constant, `k = (0.693)/(5 xx 10^(3)) =1.386 xx 10^(-4) s^(-1)`