$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$
has a value of $278$ at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature?
$SO_{3(g)} \rightleftharpoons SO_{2(g)} + \frac{1}{2} O_{2(g)}$
By reversing the equation (i), we get
$25 \mathrm{O}_{3(\mathrm{g})} \leftrightharpoons 2 \mathrm{SO}_{2(\mathrm{g})}+\mathrm{O}_{2(\mathrm{g})}$
Equilibrium constant for this reaction is
$\mathrm{K}^{\prime}=1 / \mathrm{K}=1 / 278$
By dividing the equation (ii) by $2,$ we get desired equation.
$\mathrm{SO}_{3(\mathrm{g})} \leftrightharpoons \mathrm{SO}_{2(g)}+\frac 12 \mathrm{O}_{2(\mathrm{g})}$
Equilibrium constant for this reaction
$K^{\prime \prime}=\sqrt{K^{\prime}}=\sqrt{\frac{1}{K}}=\sqrt{\frac{1}{278}}$
$=0.0599 \approx 0.06$
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