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_(10)[N_(2)O_(5)]_(t)=log_(10)[N_(2)O_(5)]_(0)-kt`
D. `ln.([N_(2)O_(5)]_(0))/([N_(2)O_(5)]_(t))=kt`

Answer

D

Explanation

Rate constant `=2.3xx10^(-2)s^(-1)`
It means it is a first order reaction (because unit of rate constant is `s^(-1)`)
For first order reaction `K=(1)/(t)ln.(a)/(a-x)`
`Kt=ln.(a)/(a-x)=ln.([N_(2)O_(5)]_(0))/([N_(2)O_(5)]_(t))`