question_answer

Consider the decomposition of \[{{N}_{2}}{{O}_{5}}\] as \[{{N}_{2}}{{O}_{5}}\xrightarrow{{}}2N{{O}_{2}}+\frac{1}{2}{{O}_{2}}\] The rate of reaction is given by \[\frac{-d[{{N}_{2}}{{O}_{5}}]}{dt}=\frac{1}{2}\frac{d[N{{O}_{2}}]}{dt}=2\frac{d[{{O}_{2}}]}{dt}={{k}_{1}}[{{N}_{2}}{{O}_{5}}]\] Therefore, \[\frac{-d[{{N}_{2}}{{O}_{5}}]}{dt}={{k}_{1}}[{{N}_{2}}{{O}_{5}}]\]                                 \[\frac{+d\,[N{{O}_{2}}]}{dt}=2{{k}_{1}}[{{N}_{2}}{{O}_{5}}]=k_{1}^{}[{{N}_{2}}{{O}_{5}}]\]                                 \[\frac{+d\,\,[{{O}_{2}}]}{dt}=\frac{1}{2}{{k}_{1}}[{{N}_{2}}{{O}_{5}}]=k_{1}^{}[{{N}_{2}}{{O}_{5}}]\] Choose the correct option.

A)  \[{{k}_{1}}=k{{}_{1}}={{k}_{1}}\]                             

B)  \[{{k}_{1}}=2k_{1}^{}=k_{1}^{}\]

C)  \[4{{k}_{1}}=k_{1}^{}=2k_{1}^{}\]          

D)  \[4{{k}_{1}}=2k_{1}^{}=k_{1}^{}\]