[
]
Im
φH 2O(l) 1 = zNa zCl Aφ
1 + b Im
[
)]
(
2νNa νCl (0)
βNaCl + β(1) Cl exp α Im
+ m
ν
Na
[
)] .
(
4νNa 2 νCl (0)
2
(1)
CNaCl + CNaCl 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 ax,B = ln ax,B + ln MAmB
(51)
where MA is the molar mass of solvent A (kg mol1). The mean-ionic activity of
NaCl(aq), aNaCl(aq) (dimensionless) is calculated by
γ NaCl(aq)mNaCl(aq)
aNaCl(aq) =
(52)
O
mNaCl(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 = zNa zCl Aφ
+ ln 1 + b Im
1 + b Im b
α 2 Im
β(1) Cl
(
)
2ν ν
(0)
1 1 + α Im
exp α Im
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)
3CNaCl + 4CN) 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 2δT ) 8 f (Tf δT ) + 8 f (Tf + δT ) f (Tf + 2δT )
(54)
12δT
where δT is a small increment chosen to be 0.1 K. The expected error of this esti-
mate should be on the order of δT4 (Burden and Faires 1989).
19
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