DETERMINING WHETHER A REACTION IS SPONTANEOUS Consider the oxidation of iron metal: 4 Fe(s) + 3 O2(g) → 2 Fe2O3(s) By determining the sign of ΔStotal, show whether the reaction is spontaneous at 25 °C.

Question

DETERMINING WHETHER A REACTION IS SPONTANEOUS

Consider the oxidation of iron metal:

[latex]4 Fe(s) + 3 O_{2}(g) → 2 Fe_{2}O_{3}(s)[/latex]

By determining the sign of [latex]ΔS_{total}[/latex], show whether the reaction is spontaneous at 25 °C.

STRATEGY
To determine the sign of [latex]ΔS_{total} = ΔS_{sys} + ΔS_{surr}[/latex], we need to calculate the values of [latex]ΔS_{sys} and ΔS_{surr}[/latex] The entropy change in the system equals the standard entropy of reaction and can be calculated using the standard molar entropies in Table 16.1. To obtain [latex]ΔS_{surr}[/latex] = -ΔH°/T , calculate ΔH° for the reaction from standard enthalpies of formation (Section 8.9).

Accepted Answer

[latex]ΔS_{sys} = ΔS° = 2 S°(Fe_{2}O_{3}) - [4 S°(Fe) + 3 S°(O_{2})][/latex]

= [latex](2 mol)\left(87.4 \frac{J}{K · mol} \right) - \left[(4 mol)\left(27.3 \frac{J}{K · mol}\right) + (3 mol)\left(205.0 \frac{J}{K · mol}\right)\right][/latex]

= -549.5 J/K

ΔH° = 2 [latex]ΔH°_{f}(Fe_{2}O_{3}) - [4 ΔH°_{f}(Fe) + 3 ΔH°_{f}(O_{2})][/latex]

Because [latex]ΔH°_{f}[/latex] = 0 for elements and [latex]ΔH°_{f}[/latex] = -824.2 kJ/mol for [latex]Fe_{2}O_{3}[/latex] (Appendix B), ΔH° for the reaction is

ΔH° = 2 [latex]ΔH°_{f}(Fe_{2}O_{3})[/latex] = (2 mol)(-824.2 kJ/mol) = -1648.4 kJ

Therefore, at 25 °C = 298.15 K,

[latex]ΔS_{surr} = \frac{- ΔH°}{T} = \frac{-(-1,648,400 J)}{298.15 K}[/latex] = 5529 J/K

[latex]ΔS_{total} = ΔS_{sys} + ΔS_{surr}[/latex] = -549.5 J/K + 5529 J/K = 4980 J/K

Because the total entropy change is positive, the reaction is spontaneous under standardstate conditions at 25 °C.

BALLPARK CHECK
Since the reaction consumes 3 mol of gas, [latex]ΔS_{sys}[/latex] is negative. Because the oxidation (burning) of iron metal is highly exothermic, [latex]ΔS_{surr}[/latex] = -ΔH°/T is positive and very large. The value [latex]ΔS_{surr}[/latex] of is greater than the absolute value of [latex]ΔS_{sys}[/latex] , and so [latex]ΔS_{total}[/latex] is positive, in agreement with the solution.

Question 16.4: DETERMINING WHETHER A REACTION IS SPONTANEOUS Consider the o...

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