The partial molar volumes of acetone and chloroform in a mixture in which the mole fraction of chloroform is 0.47 are 74.1 ml/mol and 80.2 ml/mol, respectively. What is the volume of a solution of mass 100 g?

Solution:

The total volume of a mixture is :

V= n_AV_A + n_BV_B .

We need to find n_A and n_B. From the definition of molar fractions (chapter 1.2(d)), one can easily show that

x_An_B = x_Bn_A.

Then, using the equation for the total mass of the solution:

m= n_AM_A + n_BM_B,

we can easily solve for n_A and n_B. Substituting n_A and n_B to the final equation, we get:

V= m(x_AV_A + x_BV_B)/(x_AM_A + x_BM_B).

If we choose that A is acetone and B is chloroform, the volume of the mixture is

V= 88.8 ml.