(c) In general, under which condition is ΔG°_f more positive (less negative) than ΔH°_f ? (i) When the temperature is high, (ii) when the reaction is reversible, (iii) when ΔS°_f is negative.

Verified step by step guidance

1. Understand the relationship between Gibbs free energy (\( \Delta G^\circ \)) and enthalpy (\( \Delta H^\circ \)) using the equation: \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \).
2. Identify the condition where \( \Delta G^\circ \) is more positive (or less negative) than \( \Delta H^\circ \). This occurs when the term \( -T\Delta S^\circ \) is positive, which means \( \Delta S^\circ \) must be negative.
3. Consider the effect of temperature (\( T \)) on the equation. A higher temperature would increase the magnitude of the \( -T\Delta S^\circ \) term, making \( \Delta G^\circ \) more positive if \( \Delta S^\circ \) is negative.
4. Evaluate the options given: (i) High temperature would make \( \Delta G^\circ \) more positive if \( \Delta S^\circ \) is negative. (ii) Reversibility of the reaction does not directly affect the relationship between \( \Delta G^\circ \) and \( \Delta H^\circ \). (iii) A negative \( \Delta S^\circ \) would directly contribute to \( \Delta G^\circ \) being more positive.
5. Conclude that the condition where \( \Delta G^\circ \) is more positive than \( \Delta H^\circ \) is when \( \Delta S^\circ \) is negative, especially at high temperatures.

Key Concepts

Gibbs Free Energy (ΔG°)

Gibbs Free Energy (ΔG°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It combines the system's enthalpy (ΔH°) and entropy (ΔS°) to determine spontaneity; a negative ΔG° indicates a spontaneous process. Understanding how ΔG° relates to temperature and entropy is crucial for predicting reaction behavior.

Enthalpy (ΔH°)

Enthalpy (ΔH°) is a measure of the total heat content of a system, reflecting the energy required to create a system at constant pressure. It is a key factor in determining the heat absorbed or released during a chemical reaction. The relationship between ΔH° and ΔG° is essential for understanding how temperature influences reaction spontaneity, particularly when considering the signs of ΔH° and ΔS°.

Entropy (ΔS°)

Entropy (ΔS°) is a measure of the disorder or randomness in a system. It plays a critical role in thermodynamics, as it influences the spontaneity of reactions. A negative ΔS° indicates a decrease in disorder, which can lead to a more positive ΔG° at high temperatures, affecting the overall feasibility of a reaction. Understanding the interplay between ΔS° and temperature is vital for analyzing the conditions under which ΔG° becomes less negative.