DETERMINATION OF ACTIVITIES OF STRONG ELECTROLYTES

19.2 DETERMINATION OF ACTIVITIES OF STRONG ELECTROLYTES

All methods used in the study of nonelectrolytes also can be applied in principle to the determination of activities of electrolyte solutes. However, in practice, several methods are difficult to adapt to electrolytes because it is impractical to obtain data for solutions sufficiently dilute to allow the necessary extrapolation to infinite dilution. For example, some data are available for the vapor pressures of the hydrogen halides in their aqueous solutions, but these measurements by themselves do not permit us to determine the activity of the solute because significant data cannot be obtained at concentrations below 4 molal.

449 Activity data for electrolytes usually are obtained by one or more of three

19.2 DETERMINATION OF ACTIVITIES OF STRONG ELECTROLYTES

independent experimental methods: measurement of the potentials of electrochemical cells, measurement of the solubility, and measurement of the properties of the solvent, such as vapor pressure, freezing point depression, boiling point elevation, and osmotic pressure. All these solvent properties may be subsumed under the rubric colligative properties.

A great deal of information on activities of electrolytes also has been obtained by the isopiestic method, in which a comparison is made of the concentrations of two solutions with equal solvent vapor pressure. The principles of this method were discussed in Section 17.5.

Once activity coefficients have been determined at one temperature by one of the methods mentioned above, calorimetric measurement of enthalpies of dilution can be used to determine activity coefficients at other temperatures.

Measurement of Cell Potentials For the cell composed of a hydrogen electrode and a silver – silver chloride

(Ag – AgCl) electrode immersed in a solution of HCl, represented by the notation

(19 :26) the convention that we have adopted (see Section 17.4) describes the cell reaction as

H 2 (g), HCl(m 2 ), AgCl(s), Ag(s)

H 2 (g) þ AgCl(s) ¼ HCl(m 2 ) þ Ag(s) (19 :27)

2 By this convention, the potential of the cell is defined as the potential of the electrode

on the right, at which reduction occurs, minus the potential of the electrode on the left, at which oxidation occurs.

We know from Equation (7.84) that the free energy change of the reaction is related to the cell potential by

and from Equation (16.23) that DG is related to the activities of reactants and products by

a H 2 a AgCl

Substituting from Equation (7.84) into Equation (19.28), we obtain

a 1 H 2 a AgCl

ACTIVITY, ACTIVITY COEFFICIENTS, AND OSMOTIC COEFFICIENTS

nF a 1 H =2 2 a AgCl

If the pressure of hydrogen gas is maintained at the standard pressure of 1 bar, a pressure that is essentially equal to the fugacity, then the hydrogen can be considered to be in its standard state, with an activity equal to 1. As pure solid Ag and pure solid AgCl are in their standard states, their activities also are equal to 1. Thus, Equation (19.30) can be written as

Hence, the cell indicated by Equation (19.26) can be used to determine the activity of dissolved HCl.

To apply Equation (19.31) to experimental data, we must specify our choice of standard states, because the values of E8 and of a HCl depend on this choice. We shall use the hypothetical unit molality ratio standard state obtained by extrapolation from the infinitely dilute solution. By convention, m8 is taken equal

to 1 mol kg 21 . From Equations (19.5), (19.9), (19.10), and (19.18), we can write, for dissolved HCl,

a HCl ¼ (a H þ )(a Cl )

¼ [(m H þ =m8)g H þ ][m Cl =m8)g Cl ] ¼ (m + =m8) 2 (g + ) 2 (19 :32)

Substituting from Equation (19.32) into Equation (19.31), we have

E RT ln (m + =m8) 2 (g ) 2

nF