In chemistry, the volume fraction \( \phi _{i} \) is defined as the volume of a constituent Vi 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 the concentration of a certain solute, measured by volume, in a solution. It has as a denominator the volume of the mixture itself, as usual for expressions of concentration,[2] rather than the total of all the individual component's volumes prior to mixing:
\( {\displaystyle {\text{volume percent}}={\frac {\text{volume of solute}}{\text{volume of solution}}}\times 100} \)
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.[3]
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
Alcohol meter
Alcohol proof
Apparent molar property
For non-ideal mixtures, see Partial molar volume and Excess molar quantity
Percentage
References
IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "volume fraction". doi:10.1351/goldbook.V06643
IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "concentration". doi:10.1351/goldbook.C01222
Volume-volume percentage, Chembuddy website
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Solutions
Solution
Ideal solution Aqueous solution Solid solution Buffer solution Flory–Huggins Mixture Suspension Colloid Phase diagram Phase separation Eutectic point Alloy Saturation Supersaturation Serial dilution Dilution (equation) Apparent molar property Miscibility gap
Concentration
and related quantities
Molar concentration Mass concentration Number concentration Volume concentration Normality Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio Ternary plot
Solubility
Solubility equilibrium Total dissolved solids Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart
Solvent
(Category) Acid dissociation constant Protic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion Lyate ion
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