Читать книгу Geochemistry - William M. White - Страница 108

The ideal solution model provides a useful reference for solution behavior. Comparing real solutions with ideal ones leads to the concept of excess functions, for example:

(3.51)

which can be resolved into contributions of excess enthalpy and entropy:

(3.52)

The excess enthalpy is a measure of the heat released during mixing the pure end-members to form the solution, and the excess entropy is a measure of all the energetic effects resulting from a nonrandom distribution of species in solution. We can express excess enthalpy change in the same way as excess free energy:

(3.53)

But since ΔH_{ideal mixing} = 0, ΔH_excess = ΔH_real; in other words, the enthalpy change upon mixing is the excess enthalpy change. Similar expressions may, of course, be written for volume and entropy (bearing in mind that unlike volume and enthalpy, ΔS_ideal is not zero).

Combining eqn. 3.46 with eqn. 3.48 leads to the following:

(3.54)

We can rewrite this as:

(3.55)

Equation 3.55 shows how activity coefficients relate to Henry's and Raoult's laws. Comparing eqn. 3.55 with eqn. 3.39, we see that in the region where Henry's law holds, that is, dilute solutions, the activity coefficient is equal to Henry's law constant. In the region where Raoult's law holds, the activity coefficient is 1 and eqn. 3.55 reduces to eqn. 3.26 since RT ln λ_i = 0.

Since we know that

comparing equations 3.51 and 3.55, we find that:

(3.56)

which is the same as:

(3.56a)

so that the molar excess free energy associated with component i is simply RT times the log of the activity coefficient. The total molar excess free energy of the solution is then:

(3.57)

We will see the usefulness of the concept of excess free energy shortly when we consider activities in electrolyte solutions. It will also prove important in our treatment of nonideal solid solutions and exsolution phenomena in the next chapter.