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In
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
and fluid mechanics, 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: :$\phi_i = \frac$ 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 solution In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, str ...
s 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: :$\sum_^ V_i = V ; \qquad \sum_^ \phi_i = 1$ The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a
dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or ...
; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

# Volume concentration and volume percent

Volume percent is the
concentration In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, s ...
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, rather than the total of all the individual component's volumes prior to mixing: :$\text = \frac\text\text \times 100% = \text \times 100%$ :$\varphi_i = \phi_i \left(1 - \frac\right)$
Volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
percent is usually used when the solution is made by mixing two
fluid In physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...
s, such as liquids or gases. However, percentages are only additive for
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law The ideal gas law, also called the ge ...
es.''Volume-volume percentage''Chembuddy
website A website (also written as a web site) is a collection of web pages and related content that is identified by a common domain name and published on at least one web server. Examples of notable websites are Google, Facebook, Amazon, and ...
The percentage by volume (vol%) is one way of expressing the composition of a mixture with a
dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or ...
; 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. The "enough water" is actually slightly more than 60 volume units, since water-ethanol mixture loses volume due to intermolecular attraction.

# Relation to mass fraction

Volume fraction is related to mass fraction, $Y_i \equiv\frac = \frac$ by $Y_i = \frac , \rho _\equiv , \rho_m\equiv\sum_j$ where $\rho_i\$is the constituent density, and $\rho_m$ is the mixture density.