(Solved): In the modern chemical industry, synthesis of most sulfuric acid utilizes elemental sulfur as a fee ...

In the modern chemical industry, synthesis of most sulfuric acid utilizes elemental sulfur as a feedstock. However, an alternative and historically important source of sulfuric acid was the conversion of an ore containing iron pyrites ( \( \mathrm{FeS}_{2} \) ) to sulfur oxides by roasting (burning) the ore with air. The following reactions occurred in an oven: \[ \begin{array}{c} 2 \mathrm{FeS}_{2}(\mathrm{~s})+\frac{11}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+4 \mathrm{SO}_{2}(\mathrm{~g}) \\ \mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{SO}_{3}(\mathrm{~g}) \end{array} \] The gases leaving the oven were fed to a catalytic converter in which most of the remaining \( \mathrm{SO}_{2} \) produced was oxidized to \( \mathrm{SO}_{3} \). Finally, the gas leaving the converter was sent to an absorption column where the \( \mathrm{SO}_{3} \) was taken up by water to produce sulfuric acid \( \left(\mathrm{H}_{2} \mathrm{SO}_{4}\right) \). (a) The ore fed to the oven was \( 90.0 \mathrm{wt} \% \mathrm{FeS}_{2} \), and the remaining material may be considered inert. Dry air was fed to the oven in \( 30.0 \% \) excess of the amount required to oxidize all of the sulfur in the ore to \( \mathrm{SO}_{3} \). Eighty-five percent of the \( \mathrm{FeS}_{2} \) was oxidized, and \( 60 \% \) of the \( \mathrm{SO}_{2} \) produced was oxidized to \( \mathrm{SO}_{3} \). Leaving the roaster were (i) a gas stream containing \( \mathrm{SO}_{2}, \mathrm{SO}_{3}, \mathrm{O}_{2} \), and \( \mathrm{N}_{2} \) and (ii) a solid stream containing unconverted pyrites, ferric oxide ( \( \left.\mathrm{Fe}_{2} \mathrm{O}_{3}\right) \), and the inert material. Calculate the required feed rate of air in standard cubic meters per \( 100 \mathrm{~kg} \) of ore fed to the process. Also determine the molar composition and volume \( (\mathrm{SCM} / 100 \mathrm{~kg} \) ore) of the gas leaving the oven. (b) The gas leaving the oven entered the catalytic converter. Reaction (2) proceeded to equilibrium, at which point the component partial pressures are related by the expression \[ K_{\mathrm{P}}(T)=\frac{p_{\mathrm{SO}_{3}}}{p_{\mathrm{SO}_{2}} p_{\mathrm{O}_{2}}^{0.5}} \] Assume the converter operated at constant temperature (T) and pressure (P). List the equations that are required to calculate the extent of reaction \( E \) at the equilibrium of \( \mathrm{SO}_{2} \) using \( \mathrm{K}_{\boldsymbol{p}}(\mathrm{T}), \mathrm{P}, E_{2} \).