Two gaseous equilibria SO_{2(g)} + frac{1}{2} | vedclass

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(C) For the first reaction: $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$,the equilibrium constant is $K_{1} = \frac{[SO_{3}]}{[SO_{

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$K_{2} = (\frac{1}{K_{1}})^{2}$

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(C) For the first reaction: $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$,the equilibrium constant is $K_{1} = \frac{[SO_{3}]}{[SO_{2}][O_{2}]^{1/2}}$.For the second reaction: $2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$,the equilibrium constant is $K_{2} = \frac{[SO_{2}]^{2}[O_{2}]}{[SO_{3}]^{2}}$.Comparing the two expressions,we can see that $K_{2} = \left( \frac{[SO_{2}][O_{2}]^{1/2}}{[SO_{3}]} \right)^{2}$.Since $\frac{[SO_{2}][O_{2}]^{1/2}}{[SO_{3}]} = \frac{1}{K_{1}}$,it follows that $K_{2} = (\frac{1}{K_{1}})^{2}$.

Two gaseous equilibria $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$ and $2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$ 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?

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