The reaction $$ \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 3 \mathrm{~S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is the basis of a suggested method for removal of \(\mathrm{SO}_{2}\) from power-plant stack gases. The standard free energy of each substance is given in Appendix \(\mathrm{C}\). (a) What is the equilibrium constant for the reaction at \(298 \mathrm{~K}\) ? (b) In principle, is this reaction a feasible method of removing \(\mathrm{SO}_{2} ?\) (c) If \(P_{\mathrm{SO}_{2}}=P_{\mathrm{H}_{2} \mathrm{~S}}\) and the vapor pressure of water is 25 torr, calculate the equilibrium \(\mathrm{SO}_{2}\) pressure in the system at \(298 \mathrm{~K}\). (d) Would you expect the process to be more or less effective at higher temperatures?

(a) Using provided standard free energies and the equation, the equilibrium constant (K) at 298 K can be calculated using \(K = e^{\frac{-\Delta G^{\circ}}{RT}}\). (b) The reaction is feasible for removing SO2 if K > 1, which would indicate that the forward reaction is favored at equilibrium. (c) The equilibrium SO2 pressure at 298 K can be found by substituting the given conditions into the K expression: \(K = \frac{(25 \,\text{torr})^{2}}{P_{\mathrm{SO}_{2}}(P_{\mathrm{H}_{2}\mathrm{S}})^{2}}\) and solving for \(P_{\mathrm{SO}_{2}}\). (d) Based on the calculated standard enthalpy change (∆H°), the temperature dependency of the process's effectiveness can be determined. If the reaction is endothermic (positive ∆H°), it will be more effective at higher temperatures; if exothermic (negative ∆H°), it will be less effective at higher temperatures.