The rate constant k, for the reaction ${N_2}{O_5}(g) \to $ $2N{O_2}(g) + \frac{1}{2}{0_2}(g)$ 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 $t$.

  • [AIIMS 2004]
  • 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

    ${\rm{ln}}\frac{{{{{\rm{[}}{{\rm{N}}_{\rm{2}}}{O_5}]}_0}}}{{{{{\rm{[}}{{\rm{N}}_{\rm{2}}}{O_5}]}_t}}} = kt$

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