The rate constant `k`, for the reaction `N_(2)O_(5)(g) rarr 2NO_(2) (g) + (1)/(2) O_(2)(g)` is `2.3 xx 10^(-2) s^(-1)`. Which equation given below describes the change of `[N_(2)O_(5)]` with time ? `[N_(2)O_(5)]_(0)` and `[N_(2)O_(5)]_(t)` correspond to concentration of `N_(2)O_(5)` initially and at time, `t` ?

Options

A. `[N_(2)O_(5)]t=[N_(2)O_(5)]_(0)+kt`
B. `[N_(2)O_(5)]_(0)=[N_(2)O_(5)]_(t)^(e^(kt))`
C. `log[N_(2)O_(5)]_(t)=log[N_(2)O_(5)]_(0)+kt`
D. In`([N_(2)O_(5)]_(0))/([N_(2)O_(5)]_(t))`=kt.

Answer

D

Explanation

`k=(1)/(t)` In`(a("initial"))/(a-x("after time t"))`
`k_(t)=In([N_(2)O_(5)]_(0))/([N_(2)O_(5)]_(t))`.