Volume fraction
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Volume fractions φi are useful alternatives to mole fractions xi when dealing with mixtures in which there is a large disparity between the sizes of the various kinds of molecules; e.g., polymer solutions. They provide a more appropriate way to express the relative amounts of the various components.
In any ideal mixture, the total volume is the sum of the individual volumes prior to mixing.
- Caution: in non-ideal cases the additivity of volume is no longer guaranteed. Volumes can contract or expand upon mixing and molar volume becomes a function of both concentration and temperature. This is why mole fractions are a safer unit to use.
If vi is the volume of one molecule of component i, its volume fraction in the mixture is
where the total volume of the system is the sum of the contributions from all the chemical species
The volume fraction can also be expressed in terms of the numbers of moles by transferring Avogadro's number NA ≈ 6.023 x 1023 between the factors in the numerator.
where ni = Ni / NA is the number of moles of i and Vi is the molar volume, and
As with mole fractions, the dimensionless volume fractions sum to one by virtue of their definition.
Thermodynamic functions using volume fractions reduce to mole-fraction expressions for mixtures of rigid molecules of roughly equal size. For macromolecules, there is a question about whether they behave as flexible, random coils (see Flory-Huggins solution theory), or whether they have compact structures like globular proteins. In addition to entropic questions, there are others concerning energy.
For real mixtures, see Partial molar volume.
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