https://doi.org/10.1351/goldbook.14656
State of a system in which the macroscopic properties of the system become uniform and independent of time. If the temperature is uniform throughout the system, a state of thermal equilibrium has been reached; if the pressure is uniform, a state of hydrostatic equilibrium has been reached; and if the chemical potential of each component is uniform, a state of chemical equilibrium has been reached. If all these quantities become uniform, the system is said to be in a state of complete thermodynamic equilibrium.
Notes:
- Complete thermodynamic equilibrium can be expressed in many ways, depending on which variables are of interest. For solubility purposes, the important variables are \(T\), \(p\) and the chemical potentials \(\mu_{i}\) of the \(C\) components. Equilibrium conditions involving these variables may be obtained by the condition that the variation of the Gibbs energy, expressed in terms of \(T\), \(p\) and the amount of substance \(n_{i}\) of the \(C\) components, is zero, \(\updelta G(T,p,n_{i}) = 0\), i.e., the Gibbs energy is a minimum. If the variation is negative, an irreversible change of the system can occur.
- Solubility equilibrium is an example of a state of complete thermodynamic equilibrium. For example, a saturated solution of a solid in a liquid at a fixed temperature and pressure is in a state of complete thermodynamic equilibrium. If the system is subjected to a small increase in temperature, a small portion of solid will dissolve to restore the equilibrium (if the solubility increases with temperature), while if there is a small decrease in temperature, a small portion of solid will precipitate. This is the basis for determining accurate values of solubility by approaching the equilibrium solubility from both supersaturation and undersaturation directions.