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: ΔS⁰_rxn = 558.4 J.K^-1

ΔH⁰_f [Fe₂O₃ (s)] = -824.2 kJ.mol^-1

ΔH⁰_f [CO₂ (g)] = -393.5 kJ.mol^-1

Question

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: ΔS⁰_rxn = 558.4 J.K^-1

ΔH⁰_f [Fe₂O₃ (s)] = -824.2 kJ.mol^-1

ΔH⁰_f [CO₂ (g)] = -393.5 kJ.mol^-1

| General Chemistry 3

Accepted Answer

ΔH⁰_rxn = 4 x ΔH⁰_f [Fe (s)] + 3 x ΔH⁰_f [CO₂ (g)] – 2 x ΔH⁰_f [Fe₂O₃ (s)] – 3 x ΔH⁰_f [C (s)]

ΔH⁰_rxn = 4 x 0 + 3 x (-393.5) – 2 x (-824.2) – 3 x 0

ΔH⁰_rxn = 467.9 kJ.mol^-1

Carbon can spontaneously reduce iron(III) oxide to iron if ΔG⁰_rxn $\leq$ 0

The minimum temperature is for ΔG⁰_rxn = 0

ΔG⁰_rxn = ΔH⁰_rxn - TΔS⁰_rxn = 0

T =

\frac{∆ {H^{0}}_{rxn}}{∆ {S^{0}}_{rxn}}

T =

\frac{467.9 \times 10^{3}}{558.4}

= 837.9 K

Exercise 10 | Entropy, Free Energy, and Equilibrium