Question 17.6: Iron metal is produced commercially by reducing iron(III) ox......
Iron metal is produced commercially by reducing iron(III) oxide in iron ore with carbon monoxide:
Fe_{2}O_{3}(s) + 3 CO(g)\longrightarrow 2 Fe(s) + 3 CO_{2}(g)(a) Calculate the standard free-energy change for this reaction at 25 °C.
(b) Is the reaction spontaneous under standard-state conditions at 25 °C?
(c) Does the reverse reaction become spontaneous at higher temperatures? Explain.
STRATEGY
(a) We can calculate the standard free-energy change from the relation ΔG° = ΔH° – TΔS°, but first we must find ΔH° and ΔS° from standard heats of formation (ΔH°_{f}) and standard molar entropies (S°).
(b) The reaction is spontaneous under standard-state conditions if ΔG° is negative.
(c) The spontaneity of the reaction at higher temperatures depends on the signs and magnitudes of ΔH° and ΔS°.
| IDENTIFY | |
| Known | Unknown |
| Temperature (25 °C) | ΔG° |
| Values of ΔH°_{f} and S° (Appendix B) | Spontaneous or nonspontaneous at 25 °C Conditions for spontaneity |
(a) The following values of ΔH°_{f} and S° are found in Appendix B:
Table 1
So we have
ΔH° = [2 ΔH°_{f}(Fe) + 3 ΔH°_{f}(CO_{2})] – [ΔH°_{f}(Fe_{2}O_{3}) + 3 ΔH°_{f}(CO)]= [(2 mol)(0 kJ/mol) + (3 mol)(-393.5 kJ/mol)] – [(1 mol)(-824.2 kJ/mol) + (3 mol)(-110.5 kJ/mol)]
ΔH° = -24.8 kJ
and
ΔS° = [2 S°(Fe) + 3 S°(CO_{2})] – [S°(Fe_{2}O_{3}) + 3 S°(CO)]= [(2 mol)(27.3\frac{J}{K \cdot mol}) + (3 mol)(213.6\frac{J}{K \cdot mol})] – [(1 mol)(87.4\frac{J}{K \cdot mol}) + (3 mol)(197.6\frac{J}{K \cdot mol})]
ΔS° = +15.2 J/K or 0.0152 kJ/K
Therefore,
ΔG° = ΔH° – TΔS°
= (-24.8 kJ) – (298 K)(0.0152 kJ/K)
ΔG° = -29.3 kJ
(b) Because ΔG° is negative, the reaction is spontaneous at 25 °C. This means that a mixture of Fe_{2}O_{3}(s), CO(g), Fe(s), and CO_{2}(g), with each gas at a partial pressure of 1 atm, will react at 25 °C to produce more iron metal.
(c) Because ΔH° is negative and ΔS° is positive, ΔG° will be negative at all temperatures. The forward reaction is therefore spontaneous at all temperatures, and the reverse reaction does not become spontaneous at higher temperatures.
Table 1
| Fe_{2}O_{3}(s) | CO(g) | Fe(s) | CO_{2}(g) | |
| ΔH°_{f} (kJ/mol) | -824.2 | -110.5 | 0 | -393.5 |
| S°[J/(K · mol)] | 87.4 | 197.6 | 27.3 | 213.6 |