A) \[K_{1}^{2}=\frac{1}{{{K}_{2}}}\]
B) \[2{{K}_{1}}=K_{2}^{2}\]
C) \[{{K}_{2}}=\frac{2}{K_{1}^{2}}\]
D) \[K_{2}^{2}=\frac{1}{{{K}_{1}}}\]
Correct Answer: A
Solution :
For the reaction, \[S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)S{{O}_{3}}(g)\] Equilibrium constant, \[{{K}_{1}}=\frac{[S{{O}_{3}}]}{[S{{O}_{2}}]{{[{{O}_{2}}]}^{1/2}}}\] ?.(i) For the reaction, \[2S{{O}_{3}}(g)2S{{O}_{2}}(g)+{{O}_{2}}(g)\] Equilibrium constant, \[{{K}_{2}}=\frac{{{[S{{O}_{2}}]}^{2}}[{{O}_{2}}]}{{{[S{{O}_{3}}]}^{2}}}\].....(ii) On squaring both sides in Eq. (i), we get \[K_{1}^{2}=\frac{{{[S{{O}_{3}}]}^{2}}}{{{[S{{O}_{2}}]}^{2}}[{{O}_{2}}]}\] ??(iii) Eqs. (ii) \[\times \] Eq. (iii), we get \[K_{1}^{2}\times {{K}_{2}}=1\] or \[{{K}_{2}}=\frac{1}{K_{1}^{2}}\] or \[K_{1}^{2}=\frac{1}{{{K}_{2}}}\]
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