Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.2 PARTIALMOLARQUANTITIES 234

ion. Consider an aqueous solution of a fully-dissociated electrolyte solute with the

formula MCX, whereCandare the numbers of cations and anions per solute

formula unit. The partial molar volumeVBof the solute, which can be determined

experimentally, is related to the (unmeasurable) partial molar volumesVCandVof

the constituent ions by

VBDCVCCV (9.2.28)

For aqueous solutions, the usual reference ion is HC, and the partial molar volume of

this ion at infinite dilution is arbitrarily set equal to zero:VH^1 CD 0.

For example, given the value (at298:15K and 1 bar) of the partial molar volume

at infinite dilution of aqueous hydrogen chloride

VHCl^1 D17:82cm^3 mol^1 (9.2.29)

we can find the so-called “conventional” partial molar volume of Clion:

VCl^1 DVHCl^1 VH^1 CD17:82cm^3 mol^1 (9.2.30)

Going one step further, the measured valueVNaCl^1 D16:61cm^3 mol^1 gives, for NaC

ion, the conventional value

VNa^1 CDVNaCl^1 VCl^1 D.16:6117:82/cm^3 mol^1 D1:21cm^3 mol^1 (9.2.31)

9.2.5 Partial specific quantities

Apartial specific quantityof a substance is the partial molar quantity divided by the molar
mass, and has dimensions of volume divided by mass. For example, the partial specific
volumevBof solute B in a binary solution is given by

vBD

VB

MB

D



@V

@m.B/



T;p;m.A/

(9.2.32)

wherem.A/andm.B/are the masses of solvent and solute.
Although this book makes little use of specific quantities and partial specific quantities,
in some applications they have an advantage over molar quantities and partial molar quanti-
ties because they can be evaluated without knowledge of the molar mass. For instance, the
value of a solute’s partial specific volume is used to determine its molar mass by the method
of sedimentation equilibrium (Sec.9.8.2).
The general relations in Sec.9.2.4involving partial molar quantities may be turned
into relations involving partial specific quantities by replacing amounts by masses, mole
fractions by mass fractions, and partial molar quantities by partial specific quantities. Using
volume as an example, we can write an additivity relationV D

P

im.i/vi, and Gibbs–
Duhem relations

P

im.i/dviD^0 and

P

iwidviD^0. For a binary mixture of A and B,
we can plot the specific volumevversus the mass fractionwB; then the tangent to the curve
at a given composition has intercepts equal tovAatwBD 0 andvBatwBD 1. A variant of
this plot is

vwAvAwBvB

versuswB; the intercepts are then equal tovAvAand
vBvB.