Volume fraction

In chemistry, the volume fraction φ_i is defined as the volume of a constituent V_i divided by the volume of all constituents of the mixture V prior to mixing:^[1]

$\phi_i = \frac {V_i}{\sum_j V_j}$

Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same concept as volume percent (vol%) except that the latter is expressed with a denominator of 100, e.g., 18%.

The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients).

The sum of all volume fractions of a mixture is equal to 1:

$\sum_{i=1}^{N} V_i = V ; \qquad \sum_{i=1}^{N} \phi_i = 1$

The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

Volume percent

Volume percent is a common expression of a solution's concentration. It is the volume fraction expressed with a denominator of 100, and thus is defined as:

$\textrm{volume\ percent} = \frac{\textrm{volume\ of\ solute}}{\textrm{volume\ of\ solution}} \times 100$

Volume percent is usually used when the solution is made by mixing two fluids, such as liquids or gases. However, percentages are only additive for ideal gases.^[2]

The percentage by volume (vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

In the case of a mixture of ethanol and water, which are miscible in all proportions, the designation of solvent and solute is arbitrary. The volume of such a mixture is slightly less than the sum of the volumes of the components. Thus, by the above definition, the term "40% alcohol by volume" refers to a mixture of 40 volume units of ethanol with enough water to make a final volume of 100 units, rather than a mixture of 40 units of ethanol with 60 units of water.

See also

• Alcohol by volume
• For non-ideal mixtures, see Partial molar volume and Excess molar quantity
• Alcohol proof
• Alcohol meter
• Apparent molar property
• Percentage

References

1. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "volume fraction".
2. Volume-volume percentage, Chembuddy website