The partial specific volume v i ¯ , {\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.
V = ∑ i = 1 n m i v i ¯ , {\displaystyle V=\sum _{i=1}^{n}m_{i}{\bar {v_{i}}},}
where v i ¯ {\displaystyle {\bar {v_{i}}}} is the partial specific volume of a component i {\displaystyle i} defined as:
v i ¯ = ( ∂ V ∂ m i ) T , P , m j ≠ i . {\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 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 = ∑ i w i ⋅ v i ¯ = 1 ρ {\displaystyle v=\sum _{i}w_{i}\cdot {\bar {v_{i}}}={\frac {1}{\rho }}}
∑ i ρ i ⋅ v i ¯ = 1 {\displaystyle \sum _{i}\rho _{i}\cdot {\bar {v_{i}}}=1}
See also Partial molar property Apparent molar property
References