Partial specific volume

The partial specific volume $\overline{v_i},$ 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.

$V=\sum _{i=1}^n{m}_i\overline{v_i},$

where $\overline{v_i}$ is the partial specific volume of a component $i$ defined as:

$\overline{v_i}={\left(\frac{\partial V}{\partial m_i}\right)}_{T,P,m_{j\ne i}}.$

The PSV is usually measured in milliLiters (mL) per gram (g), proteins > 30 kDa can often be assumed to have a partial specific volume of 0.708 mL/g, though this estimate varies depending on the amount of volume accessible by solvent or bound molecules. Experimental determination is possible by measuring the natural frequency of a U-shaped tube filled successively with air, buffer and protein solution.

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.

$v=\sum _i{w}_i\cdot \overline{v_i}=\frac{1}{\rho }$

$\sum _i{\rho }_i\cdot \overline{v_i}=1$

See also

• Partial molar property
• Apparent molar property