# Partial specific volume

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The '''partial specific volume''' '''<math>\bar{v_i},</math>''' express the variation of the extensive volume of a mixture in respect to composition of the masses. It is the [partial derivative](/source/partial_derivative) of volume with respect to the mass of the component of interest.
:<math>V=\sum _{i=1}^n m_i \bar{v_i},</math>

where <math>\bar{v_i}</math> is the partial specific volume of a component <math>i</math> defined as:

:<math>\bar{v_i}=\left( \frac{\partial V}{\partial m_i} \right)_{T,P,m_{j\neq i}}.</math>

The PSV is usually measured in [milliLiters](/source/Litre) (mL) per [gram](/source/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.<ref>{{cite book |last1=Buxbaum |first1=Engelbert |title=Biophysical Chemistry of Proteins |url=https://archive.org/details/biophysicalchemi00buxb_979 |url-access=limited |date=2011 |publisher=Springer |location=New York, Dordrecht, Heidelberg, London |isbn=978-1-4419-7250-7 |pages=[https://archive.org/details/biophysicalchemi00buxb_979/page/n236 237]–249 |chapter=25: Centrifugation|doi=10.1007/978-1-4419-7251-4_25 }}</ref> Experimental determination is possible by measuring the natural frequency of a U-shaped tube filled successively with air, buffer and protein solution.<ref>{{cite book |author1=Kratky, O. |author2=Leopold, H. |author3=Stabinger, H. |editor1=Hirs, C.H.W. |editor2=Timasheff, S.N. |title=Meth. Enzymol. Vol. 27: Enzyme Structure Part D|date=1973 |isbn=978-0-12-181890-6 |pages= 98–110 |chapter=5: The determination of the partial specific volume of proteins by the mechanical oscillator technique}}</ref>

==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](/source/specific_volume) of the mixture.
:<math>v = \sum_i w_i\cdot \bar{v_i} = \frac {1}{\rho}</math>

:<math>\sum_i \rho_i \cdot \bar{v_i} = 1</math>

==See also==
*[Partial molar property](/source/Partial_molar_property)
*[Apparent molar property](/source/Apparent_molar_property)

==References==
<references/>

Category:Mass density

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