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Q. Two gaseous equilibria $SO_{2(g)} + \frac{1}{2}O_{2}(g) \rightleftharpoons SO_{3(g)}$ and
$2SO_{3(g)} \rightleftharpoons 2SO_{2(g)} + O_{2(g)}$ have equilibrium constants $K_{1}$ and $K_{2}$ respectively at $298\, K.$ Which of the following relationships between $K_{1}$ and $K_{2}$ is correct?

Equilibrium

Solution:

$K_{1} =\frac{[SO_{3}]}{[SO_{2}][O_{2}]^{1/2}}$ and $K_{2}=\frac{[SO_{2}]^{2}[O_{2}]}{[SO_{3}]^{2}} ; K_{2} =\frac {1}{K^{2}_{1}}$