where m = molal concentration of the solute (mol kg1)
nr = amount of NaCl in reference solution (mol)
νNa = stoichiometric number of Na in NaCl (dimensionless)
νCl = stoichiometric number of Cl in NaCl (dimensionless)
ν = νNa +νCl (dimensionless)
Cp(mr) = constant-pressure heat capacity of a solution with a molality equal
to mr (J K1 mol1)
zNa = charge number of the Na+ cation (dimensionless)
zCl = charge number of the Cl anion (dimensionless)
AC = DebyeHckel coefficient for apparent molar constant-pressure heat
capacity (J K1 mol1)
b = constant equal to 1.2 (kg1/2 mol1/2)
Im = molality-based ionic strength (mol kg1)
Ir = molality-based ionic strength of the reference solution (mol kg1).
C
C
The quantities BNaCl (kg K2 mol1) and CNaCl (kg2 K2 mol2) are defined by
2β(0) 2 β(0) 2β(1) Cl
2 βNaCl
(1)
NaCl +
Na +
C
BNaCl =
NaCl +
(47)
T2
T
T
2
T
T
p
p
T
(
)(
)
1 1 + α Im exp α Im
α 2 Im
and
2 (1)
2 CNaCl
2 CNaCl
2 (0)
(0)
(1)
CNaCl
CNaCl
C
=
+
+
+
CNaCl
2
T2
T
T
T
T
T
p
p
p
p
(
)
3
6 6 + α 2 Im + 3α 2 Im + α 2 Im 2 exp α 2 Im
3
2
(48)
42
α 2 Im
where β(0) Cl and β(1) Cl are ion-interaction parameters of the Pitzer model (kg
Na
Na
1); C(0)
(1)
and CNaCl are ion-interaction parameters of the Pitzer model (kg2
mol
NaCl
mol2); α is a constant in the Pitzer model (= 2.0 kg1/2 mol1/2); and α2 is a con-
stant in the Pitzer model (as revised by Archer) (= 2.0 kg1/2 mol1/2). As can be
inferred from eq 47 and 48, β(0) Cl , β(1) Cl , CNaCl , and CNaCl are functions of T and
(0)
(1)
Na
Na
p. Archer (1992) deveoped lengthy formulae to calculate these parameters.
Activity of H2O. The activity of water, aH2O(l) , in an aqueous NaCl solution can be
calculated by
[
]
aH 2O(l) = exp φH 2O(l)vmNaCl(aq)
(49)
where φH 2O(l) is the osmotic coefficient of water (dimensionless) (Stokes 1991).
The osmotic coefficient was calculated from the Pitzer model via
18
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