Volume fraction

Volume fraction

Volume fractions phi_i are useful alternatives to mole fractions x_i 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 v_i is the volume of one molecule of component i, its volume fraction in the mixture is

: phi_i equiv frac{N_iv_i}{V}

where the total volume of the system is the sum of the contributions from all the chemical species

: V = sum_j N_jv_j ,

The volume fraction can also be expressed in terms of the numbers of moles by transferring Avogadro's number N_A ≈ 6.023 x 1023 between the factors in the numerator.

: phi_i equiv frac{n_iV_i}{V}

where n_i = N_i / N_A is the number of moles of i and V_i is the molar volume, and

: V = sum_j n_jV_j ,

As with mole fractions, the dimensionless volume fractions sum to one by virtue of their definition.

: sum_i phi_i equiv 1 ,

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.

:chemistry-stub


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