Properties of the partial molar volume

suppose we know the volume of an equimolar mixture of water and alcohol. We now add 18 cm of water. If the initial volume is sufficiently large, the increase in volume is not 18 cm, but only 16-5 cm this is the partial molar volume of water in the given solution. 

It sometimes happens that Vi is negative. Thus, for example, if a little magnesium sulphate is added to an aqueous solution of this salt, the volume decreases whence MgS04 - 

Calculation of Partial Molar Volumes by the BaJchuis-Rooseboom Method, For a two component system the partial molar volumes may be evaluated graphically by plotting 

We know, however, that by employing mole fractions we can express partial molar volumes in terms of intensive variables, so that if we choose 0 2 as the independent variable we may write 

It is thus easily shown that equation (1.33) can be written 

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The properties of the partial molar volume which were studied in chapter I, 3 transpose immediately to the case of chemical potentials. If we consider a binary mixture and take the mole fraction Xg as independent variable we have, dropping the subscripts T and p for the rest of this paragraph ... 

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