(Solved): 2. The wet sulfuric acid process is a multi-step process which converts hydrogen sulfide \( \left(\ ...

2. The wet sulfuric acid process is a multi-step process which converts hydrogen sulfide \( \left(\mathrm{H}_{2} \mathrm{~S}\right) \) gas into sulfuric acid \( \left(\mathrm{H}_{2} \mathrm{SO}_{4}\right) \). It is used in industry to convert sulfur containing waste from various industrial processes into a useful product. There are four main reactions in the WSA process: combustion of \( \mathrm{H}_{2} \mathrm{~S} \), oxidation of \( \mathrm{SO}_{2} \), hydration of \( \mathrm{SO}_{3} \) and condensation of \( \mathrm{H}_{2} \mathrm{SO}_{4} \). Take the two middle reactions, the oxidation of \( \mathrm{SO}_{2} \) and the hydration of \( \mathrm{SO}_{3} \). (1) \( \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{3}(\mathrm{~g}) \) (2) \( \mathrm{SO}_{3}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O} \) (I) \( \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{~g}) \) Initially, the partial pressure of \( \mathrm{SO}_{2} \) was \( 0.500 \mathrm{~atm} \) and the partial pressure of \( \mathrm{O}_{2} \) was \( 0.250 \) atm. At equilibrium, the partial pressure of \( \mathrm{SO}_{3} \) was \( 0.316 \) atm. Calculate Kc for reaction (1) at \( 500 \mathrm{~K} \). Combine reaction (1) and reaction (2) to give the overall reaction and, given that \( K_{C} \) for reaction (2) is \( 0.153 \), find \( K_{C} \) for the overall process.