Concise Physical Chemistry

c09 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

130 THE PHASE RULE

0 1

X 2

Vm1

Vm2

V

FIGURE 9.4 Total volume of an ideal binary solution.X 2 is the mole fraction of compo-

nent 2.

In reality, life is not that simple. The total volume of the solution will not usually

be the sum of the molar volumes weighted by their relative amounts. The volume

actually occupied by the solute in the solution is called thepartial molar volume,

which can be greater than or smaller than its molar volume in the pure state. The

volume of the solution will then be greater or smaller than the sum of its parts.

Addition of some potassium salts to one mole of pure water results in a volume

of solution that is even smaller than the initial volume of water (shrinkage occurs).

These three possibilities are shown in Fig. 9.5.

9.4.1 Generalization

We have been completely arbitrary in designating component 2 with amountn 2 as the

solute andn 1 as the number of moles of solvent, so we can switch designations just as

arbitrarily. Thus everything we have said about component 2 in a binary solution also

applies to component 1 treated as though it is the solute in solution with component 2.

In a solution of completely miscible liquids, it is conventional to take the lesser

V

n 2

Von 2

FIGURE 9.5 Volume increase (or decrease) upon adding small amounts of soluten 2 to pure

solvent. Three cases are shown forVn 2 >Vn◦ 2 ,Vn 2 <Vn◦ 2 ,andVn 2 <0.