Barium sulfate is reduced with carbon as part of the manufacture of lithopone, a white pigment: 2 BaSO4 (s) + 4 C (s) — 2BaS (s) + 4 CO2 (g) A mixture of crushed barite (an ore containing xB kg BaSO4/kg barite) and coal (containing xC kg C/kg coal) at temperature T0 (K) is fed to a furnace. Essentially all of the barium sulfate in the feed is converted. As part of the furnace design, you must specify for a basis of 100 kg barite ore the masses of coal fed and of carbon, barium sulfide, carbon dioxide, and other solids emerging from the reactor, as well as the product temperature and required heat input to the furnace.

(a) Draw and label a flowchart, and calculate the degrees of freedom of the process.

(b) Outline the solution procedure (i.e., list in order the equations you would write and the variables you would determine) if you are given values of xB, xC, T0, the percent excess coal fed, and the product temperature. If a solution involves iteration or is impossible say so.

(c) Repeat part (b), assuming that the specified variables are xB, xC, T0, the mass of BaS produced, and the heat input to the furnace.

(d) Repeat part (b), assuming that the specified variables are xB, xC, T0, the percent excess coal fed, and the heat input to the furnace.