Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively:
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$
$2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$
The equilibrium constants are related as:

  • A
    $2 K_{1} = K_{2}^{2}$
  • B
    $K_{1}^{2} = \frac{1}{K_{2}}$
  • C
    $K_{2}^{2} = \frac{1}{K_{1}}$
  • D
    $K_{2} = \frac{2}{K_{1}^{2}}$

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Difficult
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For the reaction,$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$,the equilibrium constant is $K_1$. The equilibrium constant is $K_2$ for the reaction,$2NO_{(g)} + O_{2(g)} \rightleftharpoons 2NO_{2(g)}$. What is $K$ for the reaction,$NO_{2(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + O_{2(g)}$?

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