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Ch.19 - Chemical Thermodynamics
Brown - Chemistry: The Central Science 15th Edition
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Capitolo 19, Problema 102

At what temperatures is the following reaction, the reduction of magnetite by graphite to elemental iron, spontaneous? Fe3O4(s) + 2 C(s, graphite) → 2 CO2(g) + 3 Fe(s)

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Identify the reaction and write it down in a balanced chemical equation format: \( \text{Fe}_3\text{O}_4(s) + 2\text{C}(s, \text{graphite}) \rightarrow 2\text{CO}_2(g) + 3\text{Fe}(s) \).
Determine the standard Gibbs free energy change (\( \Delta G^\circ \)) for the reaction using standard Gibbs free energies of formation for each compound involved in the reaction.
Use the equation \( \Delta G = \Delta G^\circ + RT \ln Q \) to relate the Gibbs free energy change at any temperature (T) and reaction quotient (Q). For spontaneity, \( \Delta G \) should be less than zero.
Since the reaction involves only solids and gases at standard state, the reaction quotient (Q) simplifies to 1 under standard conditions. Thus, the spontaneity depends solely on \( \Delta G^\circ \).
Calculate the temperature at which \( \Delta G^\circ \) changes sign using the relationship \( \Delta G^\circ = -RT \ln K \), where K is the equilibrium constant. The reaction is spontaneous at temperatures where \( \Delta G^\circ < 0 \).

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Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. A reaction is spontaneous when the change in Gibbs Free Energy (ΔG) is negative. The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.
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Gibbs Free Energy of Reactions

Entropy and Enthalpy

Entropy (S) is a measure of the disorder or randomness in a system, while enthalpy (H) is a measure of the total energy of a system, including internal energy and the energy required to make room for it. In the context of a reaction, an increase in entropy (positive ΔS) often favors spontaneity, especially at higher temperatures, while a decrease in enthalpy (negative ΔH) also promotes spontaneity.
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Entropy in Thermodynamics

Temperature's Role in Spontaneity

Temperature plays a crucial role in determining the spontaneity of a reaction through its influence on the Gibbs Free Energy equation. As temperature increases, the TΔS term becomes more significant, which can make a reaction spontaneous if ΔS is positive. Therefore, understanding how temperature affects the balance between enthalpy and entropy is essential for predicting the spontaneity of the reduction of magnetite by graphite.
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Spontaneity and Temperature
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The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane (C2H6), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: 2 CH4(g) → C2H6(g) + H2(g) In practice, this reaction is carried out in the presence of oxygen: 2 CH4(g) + 12 O2(g) → C2H6(g) + H2O(g) (b) Is the difference in ΔG° for the two reactions due primarily to the enthalpy term (ΔH) or the entropy term (-TΔS)?

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