from a thermodynamics book Given that the volume change on m

from a thermodynamics book.

Given that the volume change on mixing of a solution obeys the relation delta V_mix = 2.7 X_1 X^2_2 (cc/mole) Derive expressions for the partial molar volumes of each of the components as functions of composition. Demonstrate that your result is correct by using it to compute delta V_mix demonstrating that the equation above is recovered.

Solution

By defn of partial molar volume,

Va = dV/Dx | xb

Vb = dV/Dx| xa

Given Delta (Vmix) = 2.7*X1X2^2

b) d(delta V) = 2.7 X2^2 dX1 + 5.4 X1*X2 * dX2

The partial inegration gives back the original function

Partial molar volume of component 1 is 2.7 X2^2

Partial molar volume of component 2 is 2.7* 2* X1*X2 =5.4*X1*X2