Partial specific volume

The partial specific volume $$\bar{v_i},$$ 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.
 * $$V=\sum _{i=1}^n m_i \bar{v_i},$$

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


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

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. 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.
 * $$v = \sum_i w_i\cdot \bar{v_i} = \frac {1}{\rho}$$


 * $$\sum_i \rho_i \cdot \bar{v_i} = 1$$