The entropy of mixing is the entropy change between initially separate components and their final mixture, with initial and final temperatures, pressures and component amount of substance values specified. For an ideal solution made from pure liquids at the same temperature and pressure, let . ThenThe right-hand expression is the ideal solution result; the general definition does not require ideality. Each interior mole fraction has a negative logarithm, so mixing distinct components gives positive entropy of mixing. At a pure endpoint, use the limit as .
For one mole of the chosen A/B ideal solution with ,For the same total amount of substance, equal mole fractions maximize this binary entropy of mixing: the composition function hasso its unique maximum is . This is a comparison between different prepared compositions, not a prediction that a closed sample changes its component inventory to become equimolar.
Two physically distinguishable noninteracting species with fixed particle numbers and the same single-particle partition function have the displayed canonical partition function. If , the leading large-particle-number entropy is . With and , this equals the one-species expression at total number plus . Merely attaching labels to otherwise identical indistinguishable atoms does not justify this mixing term.
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Entropy of mixing refers to the change in entropy that occurs when two or more substances (usually gases or liquids) are mixed together. It is a measure of the randomness or disorder that results from the combination of different components in a mixture. When two different substances are mixed, the number of possible arrangements or configurations of the molecules increases, leading to greater disorder. This increase in disorder contributes positively to the overall entropy of the system.