A) \[\frac{2{{\mu }_{0}}i}{3\pi R}\]respectively
B) \[\frac{5{{\mu }_{0}}i}{12R}\]
C) \[\frac{6{{\mu }_{0}}i}{11R}\]
D) \[\frac{3{{\mu }_{0}}i}{7R}\]
Correct Answer: D
Solution :
The rate expression for the decomposition of \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{5}}}\]is \[\frac{-d[{{N}_{2}}{{O}_{5}}]}{dt}=\,\frac{1}{2}\frac{d[N{{O}_{2}}]}{dt}=2\frac{d[{{O}_{2}}]}{dt}\] \[\therefore \] \[\frac{d[N{{O}_{2}}]}{dt}=2\frac{d[{{N}_{2}}{{O}_{5}}]}{dt}=2\times 24\times {{10}^{-4}}\] \[=4.8\times {{10}^{-4}}mol\,\,{{L}^{-1}}\,\,{{\min }^{-1}}\] It is point to be noted that rate is also positive and hence is \[\frac{-d[{{N}_{2}}{{O}_{5}}]}{dt}\] taken positive. Similarly. \[\frac{d[{{O}_{2}}]}{dt}=\frac{1}{2}\,\,\frac{d[{{N}_{2}}{{O}_{5}}]}{dt}=\frac{1}{2}\times 2.4\times {{10}^{-4}}\] \[=\text{1}.\text{2}\times \text{l}{{0}^{-\text{4}}}\text{ mol}\,{{\text{L}}^{\text{-1}}}\text{ mi}{{\text{n}}^{\text{-1}}}\]
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