[

]

*Im*

φH 2O(l) 1 = *z*Na zCl Aφ

1 + *b I*m

[

)]

(

2νNa νCl (0)

βNaCl + β(1) Cl exp α *I*m

+* m*

ν

Na

[

)] .

(

4νNa 2 νCl (0)

2

(1)

*C*NaCl + *C*NaCl exp α 2 Im

+* m*

(50)

ν

*Activity of NaCl(aq). *The mole-fraction-based activities (see App. A) that are called

for by eq 41 are related to the molality-based activities typically calculated in solu-

tion chemistry by

(

)

O

ln *a*x,B = ln *a*x,B + ln *M*AmB

(51)

where *M*A is the molar mass of solvent A (kg mol1). The mean-ionic activity of

NaCl(aq), *a*NaCl(aq) (dimensionless) is calculated by

γ NaCl(aq)mNaCl(aq)

*a*NaCl(aq) =

(52)

O

*m*NaCl(aq)

where γ NaCl(aq) = mean-ionic activity coefficient of NaCl(aq) (dimensionless)

*m * NaCl(aq) = mean-ionic molality of NaCl(aq) (mol kg1)

O

*m*

= standard-state mean-ionic molality of NaCl(aq)

NaCl(aq)

(mol kg1).

The mean-ionic activity coefficient, in turn, is calculated with the Pitzer model

for a mean-ionic activity coefficient in a one-electrolyte aqueous solution:

(

)

*Im*

2

ln γ = *z*Na zCl Aφ

+ ln 1 + b *I*m

1 + b *I*m b

α 2 Im

β(1) Cl

(

)

2ν ν

(0)

1 1 + α *I*m

exp α *I*m

2βNaCl +

+ *m * Na Cl

Na

2

α 2 Im

ν

4νNa2 νCl

2

+* m*

(53)

ν

3 3/2 α 2 Im

(

)

42

2

6 6 + 6α 2 Im + 3α 2 Im + 3α 2 Im

exp α 2 Im

2

(0)

3*C*NaCl + 4*C*N) Cl

(1

a

4

α 2 Im2

.

*Temperature derivatives of the natural logarithms of activities of both H2O(l) and NaCl(aq).*

Temperature derivatives were calculated numerically. The derivative of a function

*f *at *T *was estimated by a five-point numerical approximation,

[

]

1

*f *′(Tf ) ≈

*f *(Tf 2δ*T *) 8 *f *(Tf δ*T *) + 8 *f *(Tf + δ*T *) *f *(Tf + 2δ*T *)

(54)

12δ*T*

where δ*T *is a small increment chosen to be 0.1 K. The expected error of this esti-

mate should be on the order of δ*T*4 (Burden and Faires 1989).

19