Partial specific volume

The partial specific volume ${\displaystyle {\bar {v_{i}}},}$ express the variation of the extensive volume of a mixture in respect to composition of the masses. It is the partial derivative of volume with respect to the mass of the component of interest.

${\displaystyle V=\sum _{i=1}^{n}m_{i}{\bar {v_{i}}},}$

where ${\displaystyle {\bar {v_{i}}}}$ is the partial specific volume of a component ${\displaystyle i}$ defined as:

${\displaystyle {\bar {v_{i}}}=\left({\frac {\partial V}{\partial m_{i}}}\right)_{T,P,m_{j\neq i}}.}$

The PSV is usually measured in milliLiters (mL) per gram (g), proteins > 30 kDa can be assumed to have a partial specific volume of 0.708 mL/g.^[1] Experimental determination is possible by measuring the natural frequency of a U-shaped tube filled successively with air, buffer and protein solution.^[2]

Properties

The weighted sum of partial specific volumes of a mixture or solution is an inverse of density of the mixture namely the specific volume of the mixture.

${\displaystyle v=\sum _{i}w_{i}\cdot {\bar {v_{i}}}={\frac {1}{\rho }}}$

${\displaystyle \sum _{i}\rho _{i}\cdot {\bar {v_{i}}}=1}$

See also

• Partial molar property
• Apparent molar property