Question

Determine ΔG° for the following reaction: Fe₂O₃(s) + 3CO(g) → 2Fe(s) + 3CO₂(g)

Use the following reactions with known ΔG° values:

2Fe(s) + 3/2O₂(g) → Fe₂O₃(s) ΔG°rxn = -734.4kJ

CO(g) + 1/2O₂(g) → CO₂(g) ΔG°rxn = -257.2kJ

Answer 1

Apply Hess law, so we can manipulate mathematically the dGRxn values

we need Fe2O3 in the left side, so invert :

2Fe(s) + 3/2O₂(g) → Fe₂O₃(s) ΔG°rxn = -734.4kJ

to

Fe₂O₃(s) → 2Fe(s) + 3/2O₂(g) this has a -1 impact, so ΔG°rxn = -1(-734.4kJ) = +734.4 kJ

now, we need CO2 in right side, wioth a 3 coefficient, so muultiply that euqaiotn by 3

CO(g) + 1/2O₂(g) → CO₂(g) ΔG°rxn = -257.2kJ

3(CO(g) + 1/2O₂(g) → CO₂(g) ΔG°rxn = -257.2kJ)

3CO(g) + 3/2O₂(g) → 3CO₂(g) ΔG°rxn = -257.2kJ *3 = -771.6 kJ

from equaitons we got

add them both

Fe₂O₃(s) + 3CO(g) + 3/2O₂(g) → 3CO₂(g) + 2Fe(s) + 3/2O₂(g) ΔG°rxn = -771.6 kJ + 734.4 kJ

cancel common terms

Fe₂O₃(s) + 3CO(g) → 3CO₂(g) + 2Fe(s) ΔG°rxn = -37.2 kJ

which is what we needed