Physical Chemistry , 1st ed.

In the case of gas mixtures, we defined activity as related to the partial pres-

sure piof the gas. For ions in solution, the activity of the ionic solute is related

to the concentration of the solute, in this case the molality:

aimi (8.38)

We do the same thing mathematically with equation 8.38 as we have done with

previous proportionalities. In order to remove the unit of molality, we divide

the right side of equation 8.38 by some standard concentration m°, which we

set at exactly 1 molal. We also use the proportionality constant i, called the

activity coefficient,for an ion:

aii

m

m

°

i (8.39)

The value of the activity coefficient ivaries with concentration, so we must

either tabulate the values versus concentration or have a way of calculating

them. However, in the limit of infinite dilution, ionic solutions should behave

as if their molal concentration is directly related to the chemical potential;

that is,

mlim

i→^0

i 1 (8.40)

As concentrations of ions get larger,igets smaller, and the activity gets pro-

gressively smaller and smaller than the true molal concentration of the ions.

The subscript ion the variables in the above equations implies that each in-

dividual species has its own molality, activity, activity coefficient, and so on.

For example, in a 1.00-molal solution of sodium sulfate (Na 2 SO 4 ),

mNa^ 2.00 m

mSO 42

 1.00 m

(Notice how we are subscripting the molal symbol with the appropriate ion.)

The fact that the total positive charge must equal the total negative charge

implies a relationship between the charges on the ions and their molal con-

centrations. For a simple binary salt An Bn ,where n and n are the formula

subscripts for the cation and anion, respectively, ionic solutions require that

the molalities of the cation and anion satisfy the formula



m

n

^ m

n

^ (8.41)

It is easy to verify this expression using our sodium sulfate solution. From the

formula Na 2 SO 4 , we find by inspection that n 2 and n 1 :



2.0

2

0 m



1.0

1

0 m



Substituting for the activities of the cation a and the anion a in equation

8.37, the chemical potentials of the cation and anion are

 ° RTln  

m

m

°



 ° RTln  

m

m

°



Because the ° values and molalities of the positive and negative ions are not

necessarily the same, the chemical potentials of the cation and anions will

226 CHAPTER 8 Electrochemistry and Ionic Solutions