Iron(III) oxide can be reduced by carbon monoxide. Fe₂O₃(s) + 3CO(g) ⇄ 2Fe(s) + 3CO₂(g)
Use the following thermodynamic data at 298 K to determine the equilibrium constant at this temperature.

Question

Iron(III) oxide can be reduced by carbon monoxide. Fe₂O₃(s) + 3CO(g) ⇄ 2Fe(s) + 3CO₂(g) Use the following thermodynamic data at 298 K to determine the equilibrium constant at this temperature.

Quizplus · Accepted Answer

The equilibrium constant can be calculated using the formula:
ΔG° = -RTlnK
where ΔG° is the standard free energy change, R is the gas constant, T is the temperature in Kelvin and K is the equilibrium constant.

Using the given thermodynamic data at 298K, we can calculate ΔG° for the reaction:
ΔG° = ΣΔG°f(products) - ΣΔG°f(reactants)
ΔG° = [2(0) + 3(-110.5)] - [(-288.1) + (0) + 2(-393.5) + 3(-26.4)]
ΔG° = 26.3 kJ/mol

Substituting the values into the formula:
ΔG° = -RTlnK
26.3 = -(8.314 J/mol*K)(298 K) lnK
lnK = -0.0101
K = e^(-0.0101) = 1.4 × 10^-3

Therefore, the equilibrium constant at 298K is 1.4 × 10^-3, which corresponds to option D.

Iron(III) Oxide Can Be Reduced by Carbon Monoxide