Question
$\text{H}_2(\text{g})+\text{I}_2(\text{g})\rightleftharpoons2\text{HI}(\text{g}),\text{K}=49$
What is the value of K, for the reaction:
$\text{H}_2(\text{g})\rightleftharpoons\frac{1}{2}\text{H}_2(\text{g})+\frac{1}{2}\text{I}_2(\text{g})?$

Answer

$\text{K}=\frac{[\text{HI}^2]}{[\text{H}_2][\text{I}_2]}$
$\text{K}=49$
$\text{K}'=\frac{[\text{H}_2]^{\frac{1}{2}}[\text{I}_2]^{\frac{1}{2}}}{[\text{HI}]}=\frac{1}{\sqrt{\text{K}}}$
$\Rightarrow\text{K}'=\frac{1}{\sqrt{49}}=\frac{1}{7}$

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