A) \[{K}'=\frac{1}{{{K}^{2}}}\]
B) \[{K}'=\frac{1}{K}\]
C) \[{K}'=\frac{1}{\sqrt{K}}\]
D) None of these
Correct Answer: C
Solution :
\[2N{{O}_{2}}\]⇌\[2NO+{{O}_{2}}\] ??(i) \[K=1.6\times {{10}^{-12}}\] \[NO+\frac{1}{2}{{O}_{2}}\]⇌\[N{{O}_{2}}\] ??(ii) Reaction (ii) is half of reaction (i) \[K=\frac{{{[NO]}^{2}}[{{O}_{2}}]}{{{[N{{O}_{2}}]}^{2}}}\] ??(i) \[{{K}^{'}}=\frac{[N{{O}_{2}}]}{[NO]\,\,{{[{{O}_{2}}]}^{{1}/{2}\;}}}\] ??(ii) On multiplying (i) and (ii) \[K\times {{K}^{'}}=\frac{{{[NO]}^{2}}[{{O}_{2}}]}{{{[N{{O}_{2}}]}^{2}}}\times \frac{[N{{O}_{2}}]}{[NO]\,\,{{[{{O}_{2}}]}^{{1}/{2}\;}}}\] \[=\frac{[NO]\,\,{{[{{O}_{2}}]}^{{1}/{2}\;}}}{[N{{O}_{2}}]}=\frac{1}{{{K}^{'}}}\] \[K\times {{K}^{'}}=\frac{1}{{{K}^{'}}}\]; \[K=\frac{1}{{{K}^{'2}}}\]; \[{{K}^{'}}=\frac{1}{\sqrt{K}}\].
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