Physical Chemistry Third Edition

6.5 Thermodynamic Functions of Nonideal Solutions 279

Thedifferential heat of solutionof component 2 is defined by

∆Hdiff,2

(

∂∆Hmix

∂n 2

)

T,P,n′

(definition) (6.5-19)

This differential heat of solution is the enthalpy change per mol of substance 2 for

adding an infinitesimal amount of substance 2 to the solution. It is also equal to the

enthalpy change of adding 1 mol of solute to a very large solution of the given compo-

sition. The idea is that the addition changes the composition only infinitesimally. From

Eqs. (6.5-17) and (6.5-19),

∆Hdiff,iHi−Hm,∗i (6.5-20)

Equation (6.5-20) is valid for any number of components, whereas Eq. (6.5-18) is valid

only for a two-component solution.

Exercise 6.26

Write the version of Eq. (6.5-18) that applies to a solution ofccomponents.

Tabulated Thermodynamic Properties for Solutes

In Chapter 2 we discussed enthalpy changes of formation for gases and pure substances.

The enthalpy change of formation of substanceiin a solution is defined as the enthalpy

change to produce 1 mol of substanceifrom the necessary elements in their most

stable forms and then to dissolve the 1 mol of substanceiin a large amount of the

solution of the specified composition, not changing the composition of the solution.

The enthalpy change of formation therefore includes the differential heat of solution.

The standard-state enthalpy change of formation of substanceiis given by

∆Hf◦(i, in soln)H

◦

i−H

◦ (elements) (6.5-21)

The molality description is generally used, which means that the value pertains to a

hypothetical 1 mol kg−^1 solution with activity coefficient equal to unity.

The Gibbs energy change of formation is similar to the enthalpy change of formation.

It is the change in Gibbs energy to produce 1 mol of the substance from the necessary

elements in their most stable forms. The standard-state Gibbs energy of formation for

a solute is given by

∆G◦f(i, in soln)μ◦i−G◦ (elements) (6.5-22)

It includes the Gibbs energy change to dissolve 1 mol of the solute in a large amount

of the solution of the specified composition. Tabulated values of enthalpy changes and

Gibbs energy changes of formation for several solutes are given in Table A.8, using the

molality description. The notation (ao) means that the value is for an aqueous solute that

is not ionized. The notation (ai) is for an aqueous electrolyte solute that is completely

ionized or dissociated.