**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 *= *n*A + *n*B + K + *n*N

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where *n*A, *n*B ... are the amounts of components A, B ... (mol) and *n*T 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 *= *n*A + *n*B .

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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 *

*V*B =

*T*

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∂*n*B p,*T *,*n*

*i *∋*i *≠ B

where *V*T 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 *= *n*AVA + *n*BVB .

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We can perform a similar operation on the total Gibbs energy1 (*G*T, J) of the mixture,

*GT *= *n*AGA + *n*BGB

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where the partial molar Gibbs energy,

def ∂*G*T

*G*B =

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∂*n*B 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 *= *n*AGA + *n*BGB .

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The partial molar Gibbs energy is also known as the chemical potential

def

B = *G*B .

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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 *= *H*T - *T S*T

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