Entropy of Mixing

In thermodynamics the entropy of mixing is the increase in the total entropy of a compound system, when different and chemically non-reacting chemical substances or material components are mixed by removing partition(s) between the system's initially separate volumes.

In general, the mixing may be constrained to occur under various prescribed conditions. In the customarily prescribed conditions, the materials are each at a common temperature and pressure, and the whole compound system may change its volume, while being maintained at constant temperature, pressure, and chemical component masses. The volume available for each material to explore is increased, from that of its initially separate compartment, to the total common final volume. The final volume need not be the sum of the initially separate volumes, so that work can be done on or by the system during the process of mixing, as well as heat being transferred to or from the surroundings, because of the maintenance of constant pressure and temperature.

For concision in this article, the term 'ideal material' is used to refer to an ideal gas (mixture) or an ideal solution.

In a process of mixing of ideal materials, the final common volume is the sum of the initial separate compartment volumes. There is no heat transfer and no work is done. The entropy of mixing is entirely accounted for by the diffusive expansion of each material into a final volume not initially accessible to it.

On the mixing of non-ideal materials, the total final common volume may be different from the sum of the separate initial volumes, and there may occur transfer of work or heat, to or from the surroundings; also there may be a departure of the entropy of mixing from that of the corresponding ideal case. That departure is the main reason for interest in entropy of mixing. These energy and entropy variables and their temperature dependences provide valuable information about the properties of the materials.

On a molecular level, the entropy of mixing is of interest because it is a macroscopic variable that provides information about molecular properties. In ideal materials, intermolecular forces are the same between every pair of molecular kinds, so that a molecule feels no difference between itself and its molecular neighbours. Consequently, there may be differences of intermolecular forces or specific molecular effects between different species, even though they are chemically non-reacting. The entropy of mixing provides information about differences of intermolecular forces or specific molecular effects in the materials.

The statistical concept of randomness is used for statistical mechanical explanation of the entropy of mixing. Mixing of ideal materials is regarded as random at a molecular level, and, correspondingly, mixing of non-ideal materials may be non-random.