Mean activity, strong electrolytes

It is important to realise that whilst complete dissociation occurs with strong electrolytes in aqueous solution, this does not mean that the effective concentrations of the ions are identical with their molar concentrations in any solution of the electrolyte if this were the case the variation of the osmotic properties of the solution with dilution could not be accounted for. The variation of colligative, e.g. osmotic, properties with dilution is ascribed to changes in the activity of the ions these are dependent upon the electrical forces between the ions. Expressions for the variations of the activity or of related quantities, applicable to dilute solutions, have also been deduced by the Debye-Hiickel theory. Further consideration of the concept of activity follows in Section 2.5. 

The beginning of the twentieth century also marked a continuation of studies of the structure and properties of electrolyte solution and of the electrode-electrolyte interface. In 1907, Gilbert Newton Lewis (1875-1946) introduced the notion of thermodynamic activity, which proved to be extremally valuable for the description of properties of solutions of strong electrolytes. In 1923, Peter Debye (1884-1966 Nobel prize, 1936) and Erich Hiickel (1896-1981) developed their theory of strong electrolyte solutions, which for the first time allowed calculation of a hitherto purely empiric parameter—the mean activity coefficients of ions in solutions. 

For strong electrolytes, the activity of molecules cannot be considered, as no molecules are present, and thus the concept of the dissociation constant loses its meaning. However, the experimentally determined values of the dissociation constant are finite and the values of the degree of dissociation differ from unity. This is not the result of incomplete dissociation, but is rather connected with non-ideal behaviour (Section 1.3) and with ion association occurring in these solutions (see Section 1.2.4). 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

Hamer, W. J. "Theoretical Mean Activity Coefficients of Strong Electrolytes in Aqueous Solution from 0 to 100 C" NSRDS-NBS 24, U.S. Department of Commerce, National Bureau of Standards, December 1968. 

Figure 8.3 Schematic plot of mean ionic activity coefficient y versus molality (m) for typical strong electrolytes [1 1 (e.g., HC1), light dashed line 2 1 (e.g., H2S04), heavy dashed line], showing the extreme deviations from ideality (dotted line) even in dilute solutions.

In the previous chapter, we described the thermodynamic properties of nonelectrolyte solutions. In this chapter, we focus on electrolytes as solutes. Electrolytes behave quite differently in solution than do nonelectrolytes. In Chapter 11, we described the strong electrolyte standard state and summarized relationships between the activity of the solute ai, the mean activity coefficient 7 , and the molality m in Table 11.3. 

These equations are used whenever we need an expression for the chemical potential of a strong electrolyte in solution. We have based the development only on a binary system. The equations are exactly the same when several strong electrolytes are present as solutes. In such cases the chemical potential of a given solute is a function of the molalities of all solutes through the mean activity coefficients. In general the reference state is defined as the solution in which the molality of all solutes is infinitesimally small. In special cases a mixed solvent consisting of the pure solvent and one or more solutes at a fixed molality may be used. The reference state in such cases is the infinitely dilute solution of all solutes except those whose concentrations are kept constant. Again, when two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be made and clearly stated. 

Debye and Hiickel were working out their conceptions mathematically, and found that the mean activity coefficient of a strong electrolyte A y B 7 may be expressed by the equation ... 

The original form of the Debye-Hiickel equation permits the calculation of the mean activity coefficients of strong electrolytes in solutions defined by their molarity c. Should the value of this coefficient be expressed by molality, whioh is more advantageous in electrochemistry, it will be possible in the case of a sufficiently diluted solution to substitute into the equation (V-58) for = y m (see V-41e) and for molarities of all ions the product of their molalities and the density of the solvent s wqp°, so that ... 

Fig. 27.2. Mean ionic activity coefficients of some strong electrolytes.

The mean activity coefficients of a number of strong 1 1 electrolytes are shown in fig. 27.2. It is seen that these curves tend towards the same limiting line in very dilute solutions. 

Relationships analogous to those given above may be derived in an exactb similar manner for the activities referred to mole fractions or molarities. As seen in 37c, the activities for the various standard states, based on the ideal dilute solution, can be related to one another by equation (37.7). The result is, however, applicable to a single molecular species the corresponding relationships between the mean ionic activity coefficients of a strong electrolyte, assumed to be completely ionized, are found to be... 

For dilute electrolyte solutions, Lewis and Randall observed that the mean activity coefficient of a strong electrolyte does not depend on the kind of ion, but only on the concentration and charge numbers of all ions present in solution. So, the individual properties of the ions are not decisive for interionic interactions in dilute electrolyte solutions. These observations paved the way for the introduction of the concept of ionic strength / ... 

The Macinnes convention leads to = Tci = 7 kci, We can now compute individual ion activity coefficients from their mean values measured in solutions of strong electrolytes using y Kci values as our starting point. (In the ideal strong electrolyte, cations and anions are unassociated with each other and thus do not form complexes [see Chap. 3].) It is important to remember that all such calculations must be done with y values for KCl and other salts measured at the same ionic strength, which is not the same molality except for monovalent-monovalent salts. 

Define the mean ion activity coefficient of a salt and comment on its significance in a weak versus a strong electrolyte solution. 

Eq. (B.l) will allow fairly accurate estimates of the aetivity coefficients in mixtures of electrolytes if the ion interaction coefficients are known. Ion interaction coefficients for simple ions can be obtained from tabulated data of mean activity coefficients of strong electrolytes or from the corresponding osmotic coefficients. Ion interaction coefficients for complexes can either be estimated from the charge and size of the ion or determined experimentally from the variation of the equilibrium constant with the ionic strength. 

For an electrolyte (strong) MX, the mean activity coefficient (Y ) and mean activity (a ) is defined this way. 

Solubility of a Pure Component Strong Electrolyte. The calculation of the solubility of a pure component solid in solution requires that the mean ionic activity coefficient be known along with a thermodynamic solubility product (a solubility product based on activity). Thermodynamic solubility products can be calculated from standard state Gibbs free energy of formation data. If, for example, we wished to calculate the solubility of KCI in water at 25 °C,... 

Figure 7.4 Mean logarithmic ionic activity coefficient for different aqueous systems with strong electrolytes as a function of the ionic strength.

In Chapters IV and V considerable effort was spent describing strong electrolytes and alternative formulations for their corresponding mean and/or ionic activity coefficients. A strict definition of a strong electrolyte is a species which completely dissociates in water. In reality, very few species fit this definition of strong electrolytes. The following definitions are offered in order to provide a practical classification of electrolytes ... 

W. J. Hamer, Theoretical Mean Activity Coefficients of Strong Electrolytes in Aqueous Solutions from 0 to 100°C, NBS No. 24, U. S. Government Printing Office, Washington, D. C., 1968. 

Lewis and Randall (Ref. [99]) introduced the term ionic strength, defined by this equation, two years before the Debye-HUckel theory was published. They found empirically that in dilute solutions, the mean ionic activity coefficient of a given strong electrolyte is the same in all solutions having the same ionic strength. 

Recall that y is the mean ionic activity coefficient of a strong electrolyte, or the stoichiometric activity coefficient of an electrolyte that does not dissociate completely. 

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