Concise Physical Chemistry

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

PARTIAL MOLAR VOLUME 131

V

n 2

FIGURE 9.6 Partial molar volume as the slope ofVvs.n 2. The lower line givesVm 2 as

n 2 →0, and the upper tangent line givesVm 2 at a specific concentrationn 2 =0.

component as the solute and the greater component as the solvent. In many cases, the

choice is obvious, for example, in KCl solutions in water, KCl is clearly the solute.

Evidently, from Fig. 9.6, the partial molar volume of one component, which we

have chosen to call the solute, is the slope of one of the solid lines found by measuring

the volume increment upon adding small amounts of component 2 to large amounts

of component 1. In real solutions, these lines need not be straight; the partial molar

volume of the solute is found in the limit asdn 2 →0.

RecognizingVm 2 as the slope of the function ofVvs.n 2 means that we have the

definition

Vm 2 =

(

∂V

∂n 2

)

T,p,n 1

This slope can be found anywhere on the entire curve of experimentally measured

total volume vs.X 2 , whereXn 2 =n 2 /(n 1 +n 2 ). NowVm 2 is defined as the volume

change found upon adding an infinitesimal amount of component 2 to a solution of

compositionX 2 specified by a horizontal distance along theX 2 axis; for example,

X 2 = 0 .20 in Fig. 9.7.

0 1

X 2

Vm1

Vm2

V

0.20

FIGURE 9.7 Volume behavior of a nonideal binary solution.X 2 is the mole fraction of

component 2.