7.7 Gibbs Free Energy and Reaction Feasibility

This section explores Gibbs Free Energy, a thermodynamic quantity used to predict the spontaneity or feasibility of a chemical reaction under constant temperature and pressure.

What is Gibbs Free Energy?

Gibbs free energy ($G$) is a measure of the amount of useable energy (or work-potential) in a system at constant temperature and pressure. It is also known as "Available Energy." It was conceptualized by the American scientist Josiah Willard Gibbs in 1876.

The Gibbs free energy of a system is defined by the equation: $G=H-TS$

Where:

• $G$ = Gibbs Free Energy
• $H$ = Enthalpy of the system
• $T$ = Absolute temperature (in Kelvin)
• $S$ = Entropy of the system

Gibbs free energy is a state function, meaning its value depends only on the current state of the system, not on the path taken to reach that state.

Gibbs Free Energy Change ($\Delta G$)

For a chemical process, we are interested in the change in Gibbs free energy ($\Delta G$). The change is given by the Gibbs-Helmholtz equation for a process at constant temperature: $\Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }$

Where:

• $\Delta G^{\circ }$ = Standard Gibbs free energy change
• $\Delta H^{\circ }$ = Standard enthalpy change
• $\Delta S^{\circ }$ = Standard entropy change
• $T$ = Absolute temperature

Predicting Reaction Spontaneity and Feasibility

The sign and magnitude of $\Delta G$ determine whether a reaction is spontaneous (feasible), non-spontaneous, or at equilibrium. A feasible reaction is one that, once started, will proceed to completion without a continuous supply of external energy.

The three possible conditions are:

Temperature Dependence of Spontaneity

The feasibility of a reaction depends on the balance between enthalpy ($\Delta H$) and entropy ($T\Delta S$).

1. Exothermic reactions with increasing entropy ($\Delta H<0,\Delta S>0$): $\Delta G$ is always negative. Spontaneous at all temperatures.
2. Endothermic reactions with decreasing entropy ($\Delta H>0,\Delta S<0$): $\Delta G$ is always positive. Non-spontaneous at all temperatures.
3. Endothermic reactions with increasing entropy ($\Delta H>0,\Delta S>0$): Spontaneous only at high temperatures where $T\Delta S>\Delta H$.
4. Exothermic reactions with decreasing entropy ($\Delta H<0,\Delta S<0$): Spontaneous only at low temperatures where $|T\Delta S|<|\Delta H|$.

Gibbs Free Energy and Phase Transitions

$\Delta G$ is also useful for understanding phase transitions, such as the melting of ice into liquid water.

Reaction: ${\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{s})}\to {\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{l})}$

• At the melting point (0°C or 273.15 K): The solid and liquid phases are in equilibrium. The rate of melting equals the rate of freezing. Here, $\Delta G=0$.
• Above the melting point (> 0°C): Melting is a spontaneous process. The liquid phase is more stable. Here, $\Delta G<0$.
• Below the melting point (< 0°C): Melting is a non-spontaneous process. The solid phase is more stable, and the reverse reaction (freezing) is spontaneous. Here, $\Delta G>0$.

Relation between $\Delta G^{\circ }$ and Equilibrium Constant ($K$)

The standard free energy change is related to the equilibrium constant of a reaction by the following expression: $\Delta G^{\circ }=-RT\ln K$ Or in terms of base 10 logarithm: $\Delta G^{\circ }=-2.303RT\log K$