Let the given reaction be: (i) $2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g)$; $K_1 = 278$

The target reaction is: (ii) $\text{SO}_3(g) \rightleftharpoons \text{SO}_2(g) + \frac{1}{2}\text{O}_2(g)$

Reaction (ii) is obtained by reversing reaction (i) and dividing it by $2$ (or multiplying by $\frac{1}{2}$). When a reaction is reversed, its equilibrium constant becomes the inverse of the original . When a reaction is multiplied by a factor $n$, the new equilibrium constant is the original equilibrium constant raised to the power $n$ . Therefore, the equilibrium constant $K_2$ for reaction (ii) will be: $K_2 = \left(\frac{1}{K_1}\right)^{\frac{1}{2}} = \frac{1}{\sqrt{K_1}}$ $K_2 = \frac{1}{\sqrt{278}} = \frac{1}{16.67} \approx 0.0599 \approx 6.0 \times 10^{-2}$.