• Source: Partial specific volume

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 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
=

∑

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

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