(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system?

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Identify the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \).

Recognize that \( \Delta G \) represents the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

Understand that at constant temperature, \( T \) remains unchanged, so the equation simplifies to show that \( \Delta G \) depends on \( \Delta H \) and \Delta S \).

Consider how changes in \( \Delta H \) and \( \Delta S \) affect \( \Delta G \): an increase in \( \Delta H \) increases \( \Delta G \), while an increase in \( \Delta S \) decreases \( \Delta G \) (since \( T \Delta S \) is subtracted).

Conclude that at constant temperature, the change in Gibbs free energy is indeed dependent on the changes in enthalpy and entropy of the system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. It is defined by the equation G = H - TS, where H is enthalpy, T is temperature, and S is entropy. The change in Gibbs free energy (ΔG) indicates the spontaneity of a process: if ΔG is negative, the process is spontaneous, while a positive ΔG indicates non-spontaneity.

Enthalpy

Enthalpy (H) is a thermodynamic quantity that represents the total heat content of a system. It accounts for the internal energy of the system plus the product of its pressure and volume (H = U + PV). Changes in enthalpy (ΔH) during a process can indicate whether the process absorbs heat (endothermic, ΔH > 0) or releases heat (exothermic, ΔH < 0), which is crucial for understanding energy changes in chemical reactions.

Entropy

Entropy (S) is a measure of the disorder or randomness in a system. It quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. In thermodynamics, changes in entropy (ΔS) are important for predicting the direction of spontaneous processes. According to the second law of thermodynamics, the total entropy of an isolated system can never decrease over time, which plays a key role in determining the feasibility of reactions.