Chemical thermodynamics of mixtures and aqueous solutions
Before considering the properties of electrolyte solutions at subzero temperatures, this
discussion surveys briefly the chemical thermodynamics of mixtures and solutions. Con-
sider a mixture of N components:
nT = nA + nB + K + nN
(19)
where nA, nB ... are the amounts of components A, B ... (mol) and nT total number of mole-
cules in the mixture (mol). If the number of molecules of one component is much greater
than all the other components, the mixture is called a solution. The dominant mixture com-
ponent is called the solvent, and the other mixture components are called solutes. If the
mixture being discussed is a solution, by convention the letter A is reserved to represent the
solvent.
Consider now a binary mixture or solution:
nT = nA + nB .
(20)
For all extensive thermodynamic properties of the mixture or solution, the partial molar
quantities can be defined; for example, the partial molar volume of B (m3 mol1) is
def ∂V
VB =
T
(21)
∂nB p,T ,n
i ∋i ≠ B
where VT is the total volume of the mixture (m3) and ∋ is a logical symbol for "such that."
The total volume of the binary mixture is therefore
VT = nAVA + nBVB .
(22)
We can perform a similar operation on the total Gibbs energy1 (GT, J) of the mixture,
GT = nAGA + nBGB
(24)
where the partial molar Gibbs energy,
def ∂GT
GB =
(25)
∂nB p,T ,n
i ∋i ≠ B
is defined similarly to before. And, as before, the total Gibbs energy can be represented in
terms of partial molar quantities:
GT = nAGA + nBGB .
(26)
The partial molar Gibbs energy is also known as the chemical potential
def
B = GB .
(27)
In a mixture, the chemical potential of each component differs from some defined standard
state. This difference defines the activity of the mixture component,
1
This quantity is defined by:
def
GT = HT - T ST
(23)
12
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