Metallic iron is produced in the reaction between ferrous oxide and carbon monoxide:

The flowchart shown below depicts this process for a basis of 1 mol FeO fed at 298 K.

(a) We wish to explore the effects of the variables n₀ (the molar feed ratio of CO to FeO), T₀ (the feed temperature of the carbon monoxide), X (the fractional conversion of FeO), and T (the product temperature) on Q (the heat duty on the reactor). Without doing any calculations, sketch the shapes of the curves you would expect to obtain for the following plots:

(i) Let n₀ = 1 mol CO fed/mol FeO fed, T₀ = 400 K, and X = 1. Vary T from 298K to 1000 K, calculate Q for each T, and plot Q versus T.

(ii) Let n₀ = 1 mol CO fed/mol FeO fed, T = 700 K, and X = 1. Vary T₀ from 298K to 1000 K, calculate Q for each T₀, and plot Q versus T₀.

(iii) Let n₀ = 1 mol CO fed/mol FeO fed, T₀ = 400 K, and T = 500 K. Vary X from 0 to 1, calculate Q for each X, and plot Q versus X.

(iv) Let X = 0:5, T₀ = 400 K, and T = 400 K. Vary n₀ from 0.5 to 2 mol CO fed/mol FeO fed, calculate Q for each n₀, and plot Q versus n₀.

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

References: FeO(s), CO(g), Fe(s), CO₂(g) at 25°C

Write an expression for the heat duty on the reactor, Q(kJ), in terms of the n_s and Ĥ_s in the table, the standard heat of the given reaction, and the extent of reaction, ξ. Then derive expressions for the quantities ξ, n₁, n₂, n₃, and n₄ in terms of the variables n₀ and X. Finally, derive expressions for Ĥ₀ as a function of T₀ and for Ĥ₁, Ĥ₂, Ĥ₃, and Ĥ₄ 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 2-151 of Perry’s Chemical Engineers’ Handbook:

(c) Calculate the heat duty, Q(kJ), for n₀ = 2:0 mol CO, T₀ = 350 K, T = 550 K, and X = 0:700mol FeO reacted/mol FeO fed.

(d) Prepare a spreadsheet that has the following format (a partial solution is given for one set of process variables):

where DHr (= ΔH_r) denotes the standard heat of the FeO reduction reaction and Xi (ξ) 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.

Transcribed Image Text:

FeO(s) + CO(g) CO(g) Fe(s) + CO2(g), AH = -16.480 kJ