For the reaction 2 Hg(l) + O₂(g) → 2 HgO(s), ∆H = –43 kcal/mol (–180 kJ/mol).
b. Under what conditions would you expect this process to be spontaneous?

Verified step by step guidance

1. Determine the thermodynamic criteria for spontaneity: A process is spontaneous when the Gibbs free energy change (ΔG) is negative. The relationship is given by the equation: $\Delta G=\Delta H-T\Delta S$, where ΔH is the enthalpy change, T is the temperature in Kelvin, and ΔS is the entropy change.
2. Analyze the given data: The reaction has a negative enthalpy change (ΔH = -43 kcal/mol or -180 kJ/mol), indicating that it is exothermic. This means the system releases heat to the surroundings.
3. Consider the entropy change (ΔS): The reaction involves the combination of liquid mercury (Hg) and oxygen gas (O2) to form solid mercury(II) oxide (HgO). Since gases have higher entropy than solids, the entropy of the system likely decreases (ΔS < 0).
4. Evaluate the temperature dependence: Since ΔH is negative and ΔS is negative, the term $-T\Delta S$ becomes positive as temperature increases. For the reaction to remain spontaneous (ΔG < 0), the magnitude of ΔH must outweigh the positive $-T\Delta S$ term, which is more likely at lower temperatures.
5. Conclude the conditions for spontaneity: This reaction is expected to be spontaneous at lower temperatures where the exothermic enthalpy change (ΔH) dominates over the unfavorable entropy change (ΔS).

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a process at constant temperature and pressure. A reaction is spontaneous if the change in Gibbs Free Energy (∆G) is negative. The relationship between enthalpy (∆H), entropy (∆S), and temperature (T) is given by the equation ∆G = ∆H - T∆S, where a negative ∆G indicates a spontaneous reaction.

Enthalpy and Exothermic Reactions

Enthalpy (H) is a measure of the total energy of a thermodynamic system, and reactions that release energy, such as the given reaction with ∆H = -43 kcal/mol, are termed exothermic. Exothermic reactions tend to favor spontaneity because they result in a decrease in enthalpy, which contributes to a negative ∆G under appropriate conditions, particularly at lower temperatures.

Entropy and Disorder

Entropy (S) is a measure of the disorder or randomness in a system. In general, processes that increase the entropy of the universe are favored. For the reaction 2 Hg(l) + O2 → 2HgO(s), the formation of a solid from liquids and gases typically results in a decrease in entropy, which can affect spontaneity. Understanding the balance between enthalpy and entropy is crucial for determining the conditions under which the reaction is spontaneous.