The production of steel from iron ore is endothermic. To reduce the heat that must be supplied, engineers need to find the lowest temperature at which the desired reactions are spontaneous. Estimate the temperature at which it is thermodynamically possible for carbon to reduce iron(III) oxide to iron under standard conditions by the endothermic reaction 2 Fe₂O₃(s) + 3 C(s) → 4 Fe(s) + 3 CO₂(g).

ANTICIPATE Because a gas is produced, ΔS° > 0; because (as asserted) ΔH° > 0 also, you should expect the reaction to become spontaneous at a high temperature.

PLAN At low temperatures, ΔG° = ΔH° – TΔS° and ΔH° is positive (the reaction is endothermic). If the temperature is increased there will come a point, at T = ΔH°/ΔS°, at which ΔG° = 0. Above that temperature it is negative.