MCQ
Two gaseous equilibrium $\mathrm{SO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{3(\mathrm{g})}$ and $2 \mathrm{SO}_{3(\mathrm{g})} \rightleftharpoons 2 \mathrm{SO}_{2(\mathrm{g})}+\mathrm{O}_{2}(\mathrm{g})$ have  equilibrium constant $K_1$ and $K_2$ respectively at $298\, K$. Which of the following  relationship between $K_1$ and $K_2$ is correct ?
  • A
    $K_1 = K_2$
  • B
    $K_2 = (K_1)^2$
  • $K_2 = (\frac{1}{K_1})^2$
  • D
    $K_2 = \frac{1}{K_1}$

Answer

Correct option: C.
$K_2 = (\frac{1}{K_1})^2$
c
$\mathrm{SO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{3(\mathrm{g})}, \mathrm{K}_{1}$

$2 \mathrm{SO}_{3(\mathrm{g})} \rightleftharpoons 2 \mathrm{SO}_{2(\mathrm{g})}+\mathrm{O}_{2}(\mathrm{g}), \mathrm{K}_{2}$

$\mathrm{K}_{2}=\left(\frac{1}{\mathrm{K}_{1}}\right)^{2}$

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