\[NO(g)+\frac{1}{2}{{O}_{2}}\] \[N{{O}_{2}}(g)\] and \[2N{{O}_{2}}(g)\] \[2NO(g)+{{O}_{2}}(g)\] are related as
A) \[{{K}_{2}}=\frac{1}{{{K}_{1}}}\]
B) \[{{K}_{2}}=K_{1}^{2}\]
C) \[{{K}_{2}}=\frac{{{K}_{1}}}{2}\]
D) \[{{K}_{2}}=\frac{1}{K_{1}^{2}}\]
Correct Answer: D
Solution :
| [d] \[{{K}_{1}}=\frac{[N{{O}_{2}}]}{[NO]{{[{{O}_{2}}]}^{1/2}}}\]; \[{{K}_{2}}=\frac{{{[NO]}^{2}}[{{O}_{2}}]}{{{[N{{O}_{2}}]}^{2}}}\] |
| \[\Rightarrow \] \[\frac{{{[N{{O}_{2}}]}^{2}}}{{{[NO]}^{2}}[{{O}_{2}}]}=\frac{1}{{{K}_{2}}}\]\[\Rightarrow \] \[\frac{[N{{O}_{2}}]}{[NO]\ {{[{{O}_{2}}]}^{1/2}}}=\frac{1}{\sqrt{{{K}_{2}}}}\] |
| \[\Rightarrow \] \[{{K}_{1}}=\frac{1}{\sqrt{{{K}_{2}}}}\]; \[{{K}_{2}}=\frac{1}{K_{1}^{2}}\]. |
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