A rigid container at \(500\text{ K}\) is charged with \(\text{PCl}_3\text{(g)}\), \(\text{Cl}_2\text{(g)}\), and \(\text{PCl}_5\text{(g)}\) such that the initial partial pressures are \(P_{\text{PCl}_3} = 0.50\text{ atm}\), \(P_{\text{Cl}_2} = 0.20\text{ atm}\), and \(P_{\text{PCl}_5} = 0.40\text{ atm}\). The reversible reaction is represented by the following equation:

\[\text{PCl}_3\text{(g)} + \text{Cl}_2\text{(g)} \rightleftharpoons \text{PCl}_5\text{(g)} \quad K_p = 2.0 \text{ at } 500\text{ K}\]

Which of the following correctly predicts the direction the reaction will proceed to establish equilibrium and provides the appropriate comparison between \(Q_p\) and \(K_p\)?