In: Chemistry
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
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