Thermodynamics and Chemistry

CHAPTER 10 ELECTROLYTE SOLUTIONS

10.2 SOLUTION OF ASYMMETRICALELECTROLYTE 289

and is a function ofT,p, and the solute molalitymB. AlthoughBunder given conditions
must in principle have a definite value, we are not able to actually evaluate it because we
have no way to measure precisely the energy brought into the system by the solute. This
energy contributes to the internal energy and thus toG. We can, however, evaluate the
differencesBrefm;BandBm;B.

We can write the additivity rule (Eq.9.2.25) forGas either

GDnAACnBB (10.2.2)

or

GDnAACnCCCn (10.2.3)

A comparison of these equations for a symmetrical electrolyte (nBDnCDn) gives us
the relation

BDCC (10.2.4)

(D 2 )

We see that the solute chemical potential in this case is thesumof the single-ion chemical
potentials.
The solution is a phase of electric potential. From Eqs.10.1.4and10.1.5, the sum
CCappearing in Eq.10.2.4is

C./C./DC.0/C.0/C.zCCz/F (10.2.5)

For the symmetrical electrolyte, the sum.zCCz/is zero, so thatBis equal toC.0/C
.0/. We substitute the expressions of Eq.10.1.10, use the relationrefm;BDrefCCref
with reference states atD 0 , set the ion molalitiesmCandmequal tomB, and obtain

BDrefm;BCRTln



(^) C (^)
m
B
m

 2 

(10.2.6)

(D 2 )

The important feature of this relation is the appearance of thesecondpower ofmB=m,
instead of the first power as in the case of a nonelectrolyte. Also note thatBdoes not
depend on, unlikeCand.

Although we cannot evaluate (^) Cor (^) individually, we can evaluate the product (^) C (^) .
This product is the square of themean ionic activity coefficient (^) , defined for a symmet-
rical electrolyte by
(^)  defD
p
(^) C (^) (10.2.7)
(D 2 )
With this definition, Eq.10.2.6becomes
BDrefm;BCRTln



.

/^2

m

B

m

 2 

(10.2.8)

(D 2 )

Since it is possible to determine the value ofBrefm;Bfor a solution of known molality,

(^) is a measurable quantity.