Thermodynamics and Chemistry

CHAPTER 10 ELECTROLYTE SOLUTIONS

10.3 ELECTROLYTES INGENERAL 292

in place of Eq.10.2.4. The cations and anions are in the same phase of electric potential.
We use Eqs.10.1.4and10.1.5to obtain

CC./C./

DCC.0/C.0/C.CzCCz/F (10.3.4)

Electrical neutrality requires that.CzCCz/be zero, giving

BDCC.0/C.0/ (10.3.5)

By combining Eq.10.3.5with Eqs.10.1.10,10.3.1, and10.3.3, we obtain

BDrefB CRTln

h



C

C 





C

C



(^) 

mB
m
i
(10.3.6)
whererefB DCrefCCref is the chemical potential of the solute in the hypothetical
reference state atD 0 in which B is at the standard molality and behaves as at infinite
dilution. Equation10.3.6is the generalization of Eq.10.2.6. It shows that althoughCand
depend on,Bdoes not.
The mean ionic activity coefficient (^) is defined in general by
(^)  D



C

C



(^) 

(10.3.7)

or

(^) D



C

C^



1=

(10.3.8)

Thus (^) is a geometric average of (^) Cand (^) weighted by the numbers of the cations and
anions in the solute formula unit. With a substitution from Eq.10.3.7, Eq.10.3.6becomes
BDrefB CRTln
h
CC



(^) 
m
B
m
i
(10.3.9)
SinceBrefB is a measurable quantity, so also is (^) .
The solute activity, defined byBDm;BCRTlnam;B, is
am;BD





C

C





m;B (^) 
m
B
m



(10.3.10)

wherem;Bis the pressure factor that we can evaluate with Eq.10.2.12. Equation10.3.10is
the generalization of Eq.10.2.10. From Eqs.10.1.12,10.1.13, and10.2.11and the relations
refB DCrefCCref andBDCCC, we obtain the relation

m;BDCC (10.3.11)

10.3.2 Multisolute solution

Equation10.3.3relates the chemical potential of electrolyte B in a binary solution to the
single-ion chemical potentials of its constituent ions:

BDCCC (10.3.12)