Final answer:
The correct temperature dependence of the Gibbs energy is represented by the equation ∆G = ∆H - T∆S; this equation is used to determine if a process is spontaneous based on changes in Gibbs free energy, enthalpy, and entropy.
Step-by-step explanation:
The temperature dependence of the Gibbs energy is given by the equation ∆G = ∆H - T∆S, where ∆G is the change in Gibbs free energy, ∆H is the change in enthalpy, T is the absolute temperature in Kelvin, and ∆S is the change in entropy. This relationship is known as the Gibbs-Helmholtz equation. It's important to remember that the Gibbs free energy, enthalpy, and entropy are all state functions, and their changes are used to predict the spontaneity of a process at constant temperature and pressure. A process will occur spontaneously if it leads to a decrease in the Gibbs free energy (∆G° < 0), which is synonymous with an overall increase in the entropy of the system and its surroundings (∆S_total).