At a particular temperature, the equilibrium constant \(K_c\) for the reaction represented below is \(2.5 \times 10^3\).

\[ 2\,\text{SO}_3\text{(g)} \rightleftharpoons 2\,\text{SO}_2\text{(g)} + \text{O}_2\text{(g)} \]

What is the value of \(K_c\) for the following reaction at the same temperature?

\[ \text{SO}_2\text{(g)} + \frac{1}{2}\,\text{O}_2\text{(g)} \rightleftharpoons \text{SO}_3\text{(g)} \]