A mixture of \(\text{SO}_2\text{(g)}\), \(\text{O}_2\text{(g)}\), and \(\text{SO}_3\text{(g)}\) is held at equilibrium in a rigid \(2.0\text{ L}\) container at a constant temperature according to the following equation.

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

At equilibrium, the concentration of each gas is \([\text{SO}_2] = 0.40\text{ M}\), \([\text{O}_2] = 0.10\text{ M}\), and \([\text{SO}_3] = 0.20\text{ M}\). Based on this information, what is the value of the equilibrium constant, \(K_c\), for the reaction at this temperature?