Metallic iron is produced in the reaction between ferrous oxide and carbon monoxide: FeO (s) + CO (g) → Fe (s) + CO2 (g), ΔH˚г = —16.480 kJ/mol the flowchart shown below depicts this process for a basis of 1 mol FeO fed at 298 K.

(a) Following is an inlet-outlet enthalpy table for the process:

Write an expression for the heat duty on the reactor, Q (kJ), in terms of the n5 and Hs in the table, the standard heat of the given reaction, and the extent of reaction. E. Then derive expressions for the quantities ε, n1, n2, n3, and n4 in terms of the variables n0 and X. Finally, derive expressions for H0 as a function of T0 and for H1, H2, H3, and H4 as functions of T. In the latter derivations, use the following formulas for Cp [kJ/(mol ∙K)] in terms of T(K adapted from Table 2-194 of Perry’s Chemical Engineers’ Handbook (see footnote 1):

FeO (s):Cp = 0.05280 + 6.243 x 10-6T — 3.188 x 102 T-2

Fe (s): Cp = 0.01728 + 2.67 x 10-5 T

CO (g): Cp 0.02761 + 5.02 x 10-6 T

CO2 (g): Cp 0.04326 + 1.146 x 10-5T — 8.180 x 102T-2

(b) Calculate the heat duty, Q (kJ), for n0 = 2.0 mol CO, T0 = 350 K. T = 550 K. and X = 0 – 00 mol FeO reacted/mol FeO fed.

(c) Prepare a spreadsheet that has the following format (a partial solution is given for one set of process variables): where DHr (= ΔH˚г) denotes the standard heat of the FeO reduction reaction arid Xi, ζ, is the extent of reaction. Use the spreadsheet to generate the four plots described in part (a) If the shapes of the plots do not match your predictions, explain why.