Consider the following gaseous equilibria with equilibrium constants $K_1$ and $K_2$ respectively. $SO_2\text{(g)} + \frac{1}{2} O_2\text{(g)} \rightleftharpoons SO_3\text{(g)}$ $2SO_3\text{(g)} \rightleftharpoons 2SO_2\text{(g)} + O_2\text{(g)}$ The equilibrium constants are related as …

Question

Consider the following gaseous equilibria with equilibrium constants $K_1$ and $K_2$ respectively.
$SO_2\text{(g)} + \frac{1}{2} O_2\text{(g)} \rightleftharpoons SO_3\text{(g)}$
$2SO_3\text{(g)} \rightleftharpoons 2SO_2\text{(g)} + O_2\text{(g)}$
The equilibrium constants are related as …

$2K_1 = K_2^2$

$K_1^2 = \frac{1}{K_2}$

$K_2^2 = \frac{1}{K_1}$

$K_2 = \frac{2}{K_1^2}$

Solution

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