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.                 \[\text{In}\frac{{{\text{ }\!\![\!\!\text{ }{{\text{N}}_{\text{2}}}{{O}_{5}}]}_{0}}}{{{\text{ }\!\![\!\!\text{ }{{\text{N}}_{\text{2}}}{{O}_{5}}]}_{t}}}=kt\]