A student investigates four different reversible gas-phase reactions at \(500\text{ K}\). Each reaction is allowed to reach chemical equilibrium in a separate rigid container. The balanced chemical equations and the measured equilibrium partial pressures of all species are shown in the table below.

System	Balanced equation	Equilibrium partial pressures (\(\text{atm}\))
1	\(2\,\text{NO}_2(g) \rightleftharpoons \text{N}_2\text{O}_4(g)\)	\(P_{\text{NO}_2} = 2.0\), \(P_{\text{N}_2\text{O}_4} = 0.40\)
2	\(\text{CO}(g) + \text{Cl}_2(g) \rightleftharpoons \text{COCl}_2(g)\)	\(P_{\text{CO}} = 0.10\), \(P_{\text{Cl}_2} = 0.10\), \(P_{\text{COCl}_2} = 4.0\)
3	\(2\,\text{NOCl}(g) \rightleftharpoons 2\,\text{NO}(g) + \text{Cl}_2(g)\)	\(P_{\text{NOCl}} = 1.0\), \(P_{\text{NO}} = 0.20\), \(P_{\text{Cl}_2} = 0.10\)
4	\(\text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g)\)	\(P_{\text{PCl}_5} = 2.0\), \(P_{\text{PCl}_3} = 0.50\), \(P_{\text{Cl}_2} = 0.50\)

Based on the data in the table, which system is product-favored at \(500\text{ K}\), and why?