- $phi\_i\; equiv\; frac\{N\_iv\_i\}\{V\}$

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 $N\_A$ ≈ 6023 x 10

- $phi\_i\; equiv\; frac\{n\_iV\_i\}\{V\}$

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

- $sum\_i\; phi\_i\; equiv\; 1$

For ideal mixtures thermodynamic functions expressed in terms of volume fractions asymptotically approach the mole fraction representation as the various molecular volumes become equal

For real mixtures there is usually a contraction or expansion on mixing due to interstitial packing and different molecular interactions so the volumes of the separate initial components do not sum to the total Even in that case the total volume is the sum of the

- $V(lambda\; n\_1\; lambda\; n\_2\; lambda\; n\_z)\; =\; lambda\; V$

For example if the amount of everything in the system is doubled the volume doubles regardless of the molecular interactions

- $V\; =\; sum\_j\; n\_joverline\; V\_j$

in which

- $overline\; V\_i\; equiv\; frac\{partial\; V\}\{partial\; n\_i\}$