Entropy of mixing

Entropy of mixing is the entropy change when substances combine, arising from the increased number of possible particle arrangements. For ideal mixtures, it depends on composition and particle count.

Configurational entropy: Entropy associated with the number of possible arrangements of distinguishable components in a system. Mixing entropy is a configurational contribution: mixing creates additional arrangements of component particles.
Entropy: A thermodynamic state function that quantifies energy dispersal and, statistically, the number of accessible microscopic states. Mixing entropy is one specific entropy change defined between separated and mixed states.
Gibbs paradox: A classical puzzle about the discontinuity in calculated mixing entropy when identical gases are treated as distinguishable. It exposes the role of particle distinguishability in calculating entropy of mixing.
Raoult's law: A relation stating that a component’s vapor pressure above an ideal solution equals its mole fraction times its pure-component vapor pressure. The ideal-solution assumptions linking vapor pressure to composition also underlie ideal mixing entropy.
Boltzmann entropy: A statistical definition of entropy proportional to the logarithm of the number of microscopic states compatible with a macroscopic state. It connects the increase in possible mixed arrangements to an entropy change.
Mole fraction: The amount of one component divided by the total amount of all components in a mixture. Ideal mixing entropy is determined by each component’s mole fraction.
Enthalpy of mixing: The enthalpy change when substances form a mixture from their separate initial states. Unlike entropy of mixing, it reflects changes in intermolecular interactions and can be nonzero for nonideal mixtures.
Flory–Huggins solution theory: A lattice model for polymer solutions that accounts for the different sizes of polymer and solvent molecules. It adapts combinatorial mixing entropy to polymer chains, whose segments occupy many lattice sites.
Gibbs entropy: A statistical-mechanical entropy defined from the probabilities of a system’s microscopic states. It provides a probability-based description of mixing when particles or states have unequal probabilities.
Ideal solution: A solution whose components obey Raoult’s law across the composition range and have zero enthalpy of mixing. Its assumptions yield the familiar composition-based entropy-of-mixing expression.

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Boltzmann's entropy formulaBroader topic: Counting arrangements illustrates how the formula predicts an entropy increase.