Defining the total number of moles in the solution as nT = nA + nB, this is equivalent
to
nTSm,M = nASm,A + nBSm,B
(36)
molar entropy of the mixture, so
l
Sm,M ≡ Sm = xASm,A + xBSm,B .
(37)
The calculation of Sm,M is facilitated by defining the molar entropy of mixing,
∆mixSm,M, as
O
O
∆ mixSm,M = Sm,M xASm,A xBSm,B
(38)
O
for the mixture is also equal to the proportional sum of the molar entropies of mix-
ing for all components in the solution:
∆ mixSm,M = xA ∆ mixSm,A + xB ∆ mixSm,B
(39)
component i, the molar entropy of mixing can be calculated by
(
)
∆ mixGm,i
ln ax,i
∆ mixSm,i =
= R ln ax,i RT
(40)
T p
T
p
where ax,i is the mole-fraction-based activity of component i. So that the molar en-
tropy of a solution can be calculated by
ln ax,A
= xA Sm,A R ln ax,A RT
1
O
Sm,M ≡ Sm
T p
ln ax,B
+ xB Sm,B R ln ax,B RT
O
T p .
(41)
To evaluate this equation, the following quantities must be determined for the tem-
peratures of interest:
1. The standard-state entropy of the solvent, water
2. The standard-state entropy of the solute, NaCl(aq)
3. The activities of both water and NaCl(aq)
4. The temperature derivatives of the natural logarithms of both activities of the
solvent and solute.
Standard-state entropy of liquid water at subzero temperatures. The standard-state en-
tropy of water at subzero temperatures is estimated with the heat capacities of
supercooled water.
Speedy (1987) has presented equations for the various thermodynamic proper-
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