Exercise 10 | Chemical Thermodynamics

Calculate the temperature at which carbon can spontaneously reduce iron(III) oxide to iron under standard conditions by the following reaction:

2 Fe2O3 (s) + 3 C (s) → 4 Fe (s) + 3 CO2 (g)


Data: ΔS0rxn = 558.4 J.K-1

ΔH0f [Fe2O3 (s)] = -824.2 kJ.mol-1

ΔH0f [CO2 (g)] = -393.5 kJ.mol-1

ΔH0rxn = 4 x ΔH0f [Fe (s)] + 3 x ΔH0f [CO2 (g)] – 2 x ΔH0f [Fe2O3 (s)] – 3 x ΔH0f [C (s)]

ΔH0rxn = 4 x 0 + 3 x (-393.5) – 2 x (-824.2) – 3 x 0

ΔH0rxn = 467.9 kJ.mol-1


Carbon can spontaneously reduce iron(III) oxide to iron if ΔG0rxn  0

The minimum temperature is for ΔG0rxn = 0

ΔG0rxn = ΔH0rxn - TΔS0rxn = 0

T = H0rxnS0rxn

T = 467.9 × 103558.4 = 837.9 K