Question

Given that the equilibrium constant for the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$ 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?
$SO_3(g) \rightleftharpoons SO_2(g) + \frac{1}{2} O_2(g)$

• A. $1.8 \times 10^{-3}$
• B. $3.6 \times 10^{-3}$
• C. $6.0 \times 10^{-2}$
• D. $1.3 \times 10^{-5}$

Answer 1

Answer: (C)

$2SO_2(g) + O_2(g)\rightleftharpoons 2SO_3(g) \,\,\,K = 278$ (given)
$SO_3(g) \rightleftharpoons SO_2(g) + \frac{1}{2} O_2(g)\,\,\,K' = \left(\sqrt{\frac{1}{K}}\right)$
$= \sqrt{\frac{1}{278}} = \sqrt{35.97\times10^{-4}} = 6\times10^{-2}$