A first-order reaction was started with a decimolar solution of the reactant, `8` minutes and `20 `seconds later its concentration was found to `M//100`. So the rate constant of the reaction is

Options

A. `2.303 xx 10^(-5) sec^(-1)`
B. `2.303 xx 10^(-4) sec^(-1)`
C. `2.606 xx 10^(-3) sec^(-1)`
D. `2.606 xx 10^(-5) sec^(-1)`

Answer

C

Explanation

`[A]_(0)=M//10`
`[A]_(t)=M//10`
`t=8min20s`
`=(8xx60+20)s`
`=(480 +20)=500s`
`k=(2.303)/(t)"log"([A]_(0))/([A]_(t))`
`=(2.303)/(500)log10=4.606xx10^(-3)s`.