A) \[\frac{2{{k}_{1}}}{{{k}_{2}}}{{[N{{O}_{2}}]}^{2}}\]
B) \[2{{k}_{1}}{{[N{{O}_{2}}]}^{2}}-2{{k}_{2}}[{{N}_{2}}{{O}_{4}}]\]
C) \[2{{k}_{1}}{{[N{{O}_{2}}]}^{2}}-{{k}_{2}}[{{N}_{2}}{{O}_{4}}]\]
D) \[(2{{k}_{1}}-{{k}_{2}})[N{{O}_{2}}]\]
Correct Answer: B
Solution :
\[2N{{O}_{2}}{{N}_{2}}{{O}_{4}}\] Rate \[=-\frac{1}{2}\frac{d[N{{O}_{2}}]}{dt}={{k}_{1}}{{[N{{O}_{2}}]}^{2}}-{{k}_{2}}[{{N}_{2}}{{O}_{4}}]\] \[\therefore \] Rate of disappearance of \[N{{O}_{2}}\] i.e., \[-\frac{d[N{{O}_{2}}]}{dt}=2{{k}_{1}}{{[N{{O}_{2}}]}^{2}}-2{{k}_{2}}[{{N}_{2}}{{O}_{4}}]\]
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