Given that the equilibrium constant for the reaction \( 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \...

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Given that the equilibrium constant for the reaction \( 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) \)
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?
\[\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\]
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