(
)
BC ) Tf 4 Trw 4
(4
*
Tf
Cp,H 2O(l)
p
∫
dT =
4Ts4
T
Trw
(
)
B(3) 4B(4) T 3 T 3
Cp
Cp f
rw
+
3Ts3
(
)
B(2) 3B(3) + 6B(4) T 2 T 2
Cp
Cp f
rw
Cp
+
2Ts2
B(1) 2B(2) + 3B(3) 4B(4) T T
Cp ( f
rw )
Cp
Cp
Cp
+
Ts
T
+ 2CCp arctan f 1
Ts
T
2CCp arctan rw 1
Ts
[
]
+ BC ) BC ) + BC ) BC ) + BC ) ln(Tf ) ln(Trw ) .
(0
(1
(2
(3
(4
(43)
p
p
p
p
p
lated similarly. Initially, we can define the apparent molal constant pressure heat
capacity of the solute, φCp,NaCl(aq) (J K1 mol1), in a NaCl aqueous solution as
[C
]
O
nH 2O(l)Cp,H 2O(l)
p,m
φ
=
Cp,NaCl(aq)
(44)
nNaCl(aq)
where Cp,m = constant-pressure molar heat capacity of the solution
(J K1 mol1)
O
Cp,H 2O(l) = constant-pressure heat capacity of liquid water in its
standard state (i.e., pure) (J K1 mol1)
nH2O(l) = amount of water in the solution (mol)
nNaCl(aq) = amount of NaCl in the solution (mol).
The change in entropy for the solute in its reference state is calculated from
T φCp,NaCl(aq)
O
O
∆SNaCl(aq)
=∫
dT .
(45)
T
Tr
The apparent molal constant-pressure heat capacity was estimated with the Pitzer
model:
Cp (mr )
O
1 + b Im
ν zNa zCl AC
Cp,H 2O(l)
φ
Cp,NaCl(aq) +
=
+
ln
1 + b Ir
2b
nr
nr
[
]
(
)
2νNa νCl RT 2 (m mr )BNaCl + m2 mr νNa zNaCNaCl
C
C
2
(46)
17
Previous Page
