How does the Gibbs energy vary with temperature according to the Gibbs-Helmholtz equation?

The Gibbs-Helmholtz equation provides a relationship between Gibbs free energy, temperature, and enthalpy. Specifically, it states that the Gibbs energy (G) can be expressed in terms of the enthalpy (H), temperature (T), and entropy (S) as follows:

G = H - TS

As temperature changes, the contributions of both enthalpy and entropy to the Gibbs free energy vary. According to the Gibbs-Helmholtz equation, the derivative of Gibbs free energy with respect to temperature can provide insight into how G changes as T varies. The relationship indicates that the Gibbs energy's variations are influenced not only by changes in enthalpy but also by the entropy term scaled by temperature.

The correct interpretation, aligned with choice B, involves recognizing that as temperature increases, the term TS grows, which leads to a modification in G. Specifically, if the entropy is positive, an increase in temperature results in a decreasing Gibbs free energy, due to the stronger impact of the negative TS term. Therefore, it can be said that Gibbs free energy decreases with increasing temperature in proportion to that temperature's impact on entropy.

In this context, while the other options suggest different characteristics of the relationship between Gibbs free energy and temperature