A mixture of \(\text{SO}_2(g)\), \(\text{O}_2(g)\), and \(\text{SO}_3(g)\) is held at equilibrium inside a cylinder fitted with a movable piston at a constant temperature according to the following equation: \[ 2\,\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\,\text{SO}_3(g) \qquad \Delta H^\circ = -198\text{ kJ/mol}_{\text{rxn}} \] The volume of the container is suddenly halved at constant temperature. Which of the following correctly predicts the direction the reaction shifts to re-establish equilibrium, along with the correct justification comparing \(Q_c\) and \(K_c\) immediately following the volume change?