A) \[4{{k}_{1}}=2k_{1}^{'}=k_{1}^{''}\]
B) \[4{{k}_{1}}=k_{1}^{'}=2k_{1}^{''}\]
C) \[{{k}_{1}}=2k_{1}^{'}=k_{1}^{''}\]
D) \[2{{k}_{1}}=2k_{1}^{'}=4k_{1}^{''}\]
Correct Answer: D
Solution :
The rate of reaction is given by \[\frac{-d\left[ {{N}_{2}}{{O}_{5}} \right]}{dt}=\frac{1}{2}\frac{d\left[ N{{O}_{2}} \right]}{dt}=2\frac{d\left[ {{O}_{2}} \right]}{dt}={{k}_{1}}[{{N}_{2}}{{O}_{5}}]\] Therefore, \[\frac{-d\left[ {{N}_{2}}{{O}_{5}} \right]}{dt}={{k}_{1}}[{{N}_{2}}{{O}_{5}}]\] \[\frac{+d\left[ N{{O}_{2}} \right]}{dt}=2{{k}_{1}}[{{N}_{2}}{{O}_{5}}]\] \[k_{1}^{'}[{{N}_{2}}{{O}_{5}}]\] \[\frac{d\left[ {{O}_{2}} \right]}{dt}=\frac{1}{2}{{k}_{1}}[{{N}_{2}}{{O}_{5}}]=k_{1}^{''}[{{N}_{2}}{{O}_{5}}]\] Hence, the correct option is [d].
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