Evaluation of partial molar volumes in binary mixtures

3 Evaluation of partial molar volumes in binary mixtures 

The partial molar volumes Va and Fb in a binary mixture can be evaluated by the method of intercepts. To use this method, we plot experimental values of the quantity V/n (where is A + b) versus the mole fraction xb. V/n is called the mean molar volume. 

See Fig. 9.3(a) on the next page for an example. In this figme, the tangent to the curve drawn at the point on the curve at the composition of interest (the composition used as an illustration in Sec. 9.2.1) intercepts the vertical line where xb equals 0 at F/n = Fa = 17.7 cm mol and intercepts the vertical line where xb equals 1 at V/n = Fb = 38.8 cm mol .  

To derive this property of a tangent line for the plot of F/n versus xb, we use Eq. 9.2.9 

When we differentiate this expression for V/n with respect to xb, keeping in mind that Fa and Fb are functions of xb, we obtain 

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