1. Tardigrade
  2. Question
  3. Chemistry
  4. Consider the following gaseous equilibria with equilibrium constants K1 and K2 respectively SO2(g)+(1/2)O2(g)SO3(g) 2SO3(g)2SO2(g)+O2(g) The equilibrium constants are related as

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Q. Consider the following gaseous equilibria with equilibrium constants $ {{K}_{1}} $ and $ {{K}_{2}} $ respectively $ S{{O}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)S{{O}_{3}}(g) $ $ 2S{{O}_{3}}(g)2S{{O}_{2}}(g)+{{O}_{2}}(g) $ The equilibrium constants are related as

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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}}} $