Carbon disulfide, a key component in the manufacture of rayon fibers, is produced in the reaction between methane and sulfur vapor over a metal oxide catalyst: CH4 (g) + 4 S (v) → CS2 (g) + 2 H2S (g) ΔHг (700°C) = – 274 kJ/mol Methane and molten sulfur, each at 150°C, are fed to a heat exchanger in stoichiometric proportion. Heat is exchanged between the reactor feed and product streams, and the sulfur in the feed is vaporized. The gaseous methane and sulfur leave the exchanger and pass through a second pre-heater in which they are heated to 700°C, the temperature at which they enter the reactor. Heat is transferred from the reactor at a rate of 41.0k mol of feed. The reaction products emerge from the reactor at 800°C, pass through the heat exchanger, and emerge at 200°C with sulfur as a liquid. Use the heat capacity data given below to perform the following calculations.

Heat capacities: Cp [J/ (mol∙°C)] ≈ 29.4 for S (l), 36.4 for S (v), 71.4 for CH4 (g), 31.8 for CS2, and 44.8 for H2S (g).

(a) Estimate the fractional conversion achieved in the reactor.

(b) Estimate the quantity of heat (kJ/mol feed) that must be transferred in the second pre-heater to brine the feed up to 700°C.

(c) Suggest a method to improve the energy economy of the process.