Given that the equilibrium constant for the reaction $2 {SO}_{2} (g) + O_{2} (g) ⇌ 2 {SO}_{3} (g)$ has a value of 278 at aparticular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature?
${SO}_{3} (g) ⇌ {SO}_{2} (g) + \frac{1}{2} O_{2} (g)$

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1.8 x 10^-3

3.6 x 10^-3

6.0 x 10^-2

1.3 x 10^-5

answer is C.

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Detailed Solution

$2 {SO}_{2} + O_{2} ⇌ 2 {SO}_{3}; K = 278$
${SO}_{3} ⇌ {SO}_{2} + \frac{1}{2} O_{2}; K^{'} = \frac{1}{\sqrt{K}}$
$K^{'} = \frac{1}{\sqrt{K}} = \frac{1}{\sqrt{278}} = 6 \times 10^{- 2}$

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