How is the standard Gibbs energy of reaction expressed mathematically?

The standard Gibbs energy of reaction is expressed mathematically as the difference between the standard enthalpy change and the temperature multiplied by the standard entropy change of the reaction. This relationship is derived from the fundamental definition of Gibbs free energy, which accounts for both the energy changes due to the heat transfer at constant temperature and the entropy changes associated with the disorder of the system.

In this expression, Δ_rH® represents the standard enthalpy change of the reaction, which quantifies the heat absorbed or released under standard conditions. T is the absolute temperature in Kelvin, reflecting how temperature influences the system's entropy. Δ_rS® is the standard entropy change of the reaction, which indicates the change in disorder or randomness of the system during the reaction.

This equation effectively captures the thermodynamic balance of energy and entropy, illustrating how they interact to determine the spontaneity of a reaction at a given temperature. A negative value of Gibbs energy indicates that the reaction is spontaneous, whereas a positive value suggests non-spontaneity.

Understanding this equation is fundamental in thermochemistry, as it links the energy and entropy contributions to predict reaction behavior under standard conditions.