The rate constant $k$,for the reaction ${N_2}{O_5}_{(g)} \to 2N{O_2}_{(g)} + \frac{1}{2}{O_2}_{(g)}$ is $2.3 \times 10^{-2} \ s^{-1}$. 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 $t$.

• 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
  $\ln \frac{[{N_2}{O_5}]_0}{[{N_2}{O_5}]_t} = kt$