The Gibb's free energy is an additional state function defined to keep track of the available energy. The entropy of a substance diminishes available energy. For each substance, the Gibb's free energy is defined as:
G = H - TS
The Gibb's free energy is an extensive property (dependent on the moles of material) and a state function (independent of the path of the reaction).
It may help to think of the enthalpy of a substance as being made up of two parts. One part is associated with the entropy of a substance and can not be transferred outside that substance to the surroundings. The second part may be transferred outside the substance to do work or increase the entropy of the surroundings. That second part is the Gibb's free energy.
H = TS + G
The Gibb's free energy change, ΔG, during a reaction at constant temperature is:
ΔG = ΔH - TΔS
You can experiment with free energy calculations with an interactive graph.
When doing calculations using this equation, students must be sure that all units are the same. In thermodynamic tables, entropies are frequently listed as calories/mole degree at the same time that enthalpies are listed in kcal/mole. If the entropy change term seems large, be sure to check the units. Dimensional analysis will resolve this problem.
The Gibb's free energy change is also a measure of spontaneity of a reaction. A reaction is spontaneous when the entropy of the universe is increasing. At first, one might assume that a reaction must be exothermic (enthalpy, ΔH, is negative) to be spontaneous, but that does not account for the change in entropy of the reactants and products. The free energy state function accounts for that change in entropy of the reactants and products. If ΔG is negative, the reaction is spontaneous. An endothermic process may be spontaneous if the entropy of the products is larger than the entropy of the reactants. One common example is the solution of salts in water. The temperature of some solutions drop as the salts dissolve because the process is endothermic. The salt itself changes from an ordered solid to highly disordered ions moving around the entire container of water. The process results in a large increase in entropy of the system which can drive the process if it is not too endothermic.
You can use tables of standard enthalpies and entropies to calculate the standard free energy of reactants and products and in turn the free energy of the reaction using the equation:
Alternatively, if you have tables of free energies of formation at standard conditions, you may calculate the standard free energy of the reaction in the same manner that you calculate enthalpies using Hess's law.
Chemists are frequently most interested in the Gibb's free energy which is of interest at constant pressure (open to the atmospheric pressure). However, another free energy term is appropriate at constant volume (reaction in a closed rigid container). Gibb's free energy (constant P and T) and the Helmholtz free energy (constant V and T) are compared.
