Thermodynamics and Chemistry

CHAPTER 10 ELECTROLYTE SOLUTIONS

10.2 SOLUTION OF ASYMMETRICALELECTROLYTE 288

The single-ion activity coefficients approach unity in the limit of infinite dilution:

(^) C! 1 and (^) ! 1 as mB! 0 (10.1.11)
(constantT,p, and)
In other words, we assume that in an extremely dilute electrolyte solution each individual
ion behaves like a nonelectrolyte solute species in an ideal-dilute solution. At a finite solute
molality, the values of (^) Cand (^) are the ones that allow Eq.10.1.10to give the correct
values of the quantities.CrefC/and.ref/. We have no way to actually measure
these quantities experimentally, so we cannot evaluate either (^) Cor (^) .
We can define single-ion pressure factorsCandas follows:

C

def

D exp

refCC

RT

!

exp



VC^1 .pp/

RT



(10.1.12)

def

D exp



ref 

RT



exp



V^1 .pp/

RT



(10.1.13)

The approximations in these equations are like those in Table9.6for nonelectrolyte solutes;
they are based on the assumption that the partial molar volumesVCandVare independent
of pressure.
From Eqs.10.1.7,10.1.10,10.1.12, and10.1.13, the single-ion activities are related to
the solution composition by

aCDC (^) C
mC
m
aD (^)
m
m

(10.1.14)

Then, from Eq.10.1.9, we have the following relations between the chemical potentials and
molalities of the ions:

CDCCRTln.C (^) CmC=m/CzCF (10.1.15)
DCRTln. (^) m=m/CzF (10.1.16)
Like the values of (^) Cand (^) , values of the single-ion quantitiesaC,a,C, and
cannot be determined by experiment.

10.2 Solution of a Symmetrical Electrolyte

Let us consider properties of an electrolyte solute as a whole. The simplest case is that of a
binary solution in which the solute is a symmetrical strong electrolyte—a substance whose
formula unit has one cation and one anion that dissociate completely. This condition will be
indicated byD 2 , whereis the number of ions per formula unit. In an aqueous solution,
the solute withequal to 2 might be a 1:1 salt such as NaCl, a 2:2 salt such as MgSO 4 , or
a strong monoprotic acid such as HCl.
In this binary solution, the chemical potential of the solute as a whole is defined in the
usual way as the partial molar Gibbs energy

B

def

D



@G

@nB



T;p;nA

(10.2.1)