Electrolyte solutions, activity coefficient weak electrolytes

Note that we have only spoken of neutral species of the type that can be obtained as the dominant species in a solution activity coefficients for the neutral species of weak electrolytes and other neutral species in a matrix of charged particles constitute a more difficult problem. Their activity coefficients are usually assumed to be 1.0, or are taken as equal to those of some other neutral species such as H2S or CO2 under the same conditions. The activity coefficients of neutral species in electrolyte solutions... 

Due to the need to model the equilibria of solutions containing multiple weak electrolytes, such as the H2O - NHs CO2 system, it became necessary to go beyond the Setschenow equation for activity coefficient calculations. For such solutions to be modeled well, the ion-molecule interactions must affect not only the molecular activity coefficients, but also the ionic activity coefficients and water activities. An early attempt by Edwards. Newman and Prausnitz (P5) used the Guggenheim equation for activity coefficients and assumed the water activity to be unity. This application was felt to be good for low weak electrolyte concentrations at temperatures no higher than 80° C. 

Further on, Kunz et al could show that this failure of the simplified dispersion model is not a consequence of the weakness of the Poisson-Boitzmann equation. More elaborate statistical mechanics, using the so-called hypernetted chain equation (HNC), yielded basically the same result. Obviously the problem comes from the neglect of ion-water interactions and their changes near the surface. To introduce such interactions in primitive model calculations, Bostrom et al [see also Refs. 13(b)-13(d)] used Jungwirth s water profile perpendicular to the surface as a basis to model a distance-dependent electrostatic function, instead of a static dielectric constant. Such ideas were used several times over the years, for instance to model activity coefficients of electrolyte solutions. ... 

The secondary salt effect is important when the catalytically active ions are produced by the dissociation of a weak electrolyte. In solutions of weak acids and weak bases, added salts, even if they do not exert a common ion effect, can influence hydrogen and hydroxide ion concentrations through their influence on activity coefficients. 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (2), Pitzer and co-workers (4, ,j5), and" Cruz and Renon (7j, presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. 

Which electrolytes are called strong, and which are called weak In what form can the law of mass action be applied to strong electrolytes Define the activity, the activity coefficient, and the ionic strength of a solution. 

Activity coefficients of non-ionized molecules do not differ appreciably from unity. In dilute solutions of weak electrolytes the differences between activities and concentrations (calculated from the degree of dissociation) is negligible. 

From all that has been said about activity and activity coefficients, it is apparent that whenever precise results are to be expected, activities should be used when expressing equilibrium constants or other thermodynamic functions. In the present text however we shall be using simply concentrations. For the dilute solutions of strong and weak electrolytes that are mainly used in qualitative analysis, errors introduced into calculations are not considerable. 

Nonetheless, the activity coefficient is not determined by the dielectric constant alone. In this connection, it is interesting to note that acetic acid is much weaker in NMP than in water (13). When NMP is added to the aqueous solvent, the dissociation of the protonated form of tris-(hydroxymethyl )aminomethane is enhanced initially (12). In pure NMP, however, this acid is weaker than in water (14), despite the greatly increased dielectric constant (e = 176 at 25°C). These results point to the controlling influence of solute-solvent interactions on the behavior of these weak electrolytes. 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

A kinetic electrolyte effect ascribable solely to the influence of the ionic strength on activity coefficients of ionic reactants and transition states is called a primary kinetic electrolyte effect. A kinetic electrolyte effect arising from the influence of the ionic strength of the solution upon the pre-equilibrium concentration of an ionic species that is involved in a subsequent rate-limiting step of a reaction is called a secondary kinetic electrolyte effect. A common case encountered in practice is the effect on the concentration of a hydrogen ion (acting as catalyst) produced from the ionization of a weak acid in a buffer solution. 

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

The reason why Qstwald s dilution law, equation (17), Chapter 3, is moderately successful in accounting for the conductances of weak electrolytes is now evident. Arrhenius equation, a = A/Ao, yields degrees of dissociation which are too low. This error, from our present point of view, was more or less offset by the tacit assumption made by Arrhenius and Ostwald, that activity coefficients are unity, whereas, for dilute solutions at least, they are less than unity. 

Figure 7.2 summarizes the relative weathering rates of major minerals in igneous and metamorphic rocks. Actual weathering rates depend also on soil temperature and moisture, particle size, and planes of physical weakness (cleavage) in the crystal. The effect of moisture includes both the flow rate of soil solution past mineral surfaces and the composition of the solution. Solids dissolve more slowly if the solution already contains their constituent ions. High electrolyte concentrations, on the other hand, can maintain higher ion concentrations at equilibrium because of lower activity coefficients and because of complex-ion and ion-pair formation. 

In this chapter we discuss some of the properties of electrolyte solutions. In Sec. 12-1, the chemical potential and activity coefficient of an electrolyte are expressed in terms of the chemical potentials and activity coefficients of its constituent ions. In addition, the zeroth-order approximation to the form of the chemical potential is discussed and the solubility product rule is derived. In Sec. 12-2, deviations from ideality in strong-electrolyte solutions are discussed and the results of the Debye-Hiickel theory are presented. In Sec. 12-3, the thermodynamic treatment of weak-electrolyte solutions is given and use of strong-electrolyte and nonelectrolyte conventions is discussed. 

Thus it is useful to associate a with an activity coefficient at low concentrations. At low concentrations, it is useful to represent Pha by Eq. (12-59). Equation (12-59) is similar to Eq. (12-30) which expresses //ha in terms of strong-electrolyte conventions. This completes our discussion of weak-electrolyte solutions. [More details concerning computations involving Eq. (12-56) can be found in F. H. MacDougall, Thermodynamics and Chemistry, chap. XV, 3d ed., John Wiley, Sons, Inc., New York, 1939.]... 

This last condition is fulfilled when the ionic concentrations are very low, as they are in fact in dilute solutions of weak electrolytes. The dissociation constants of substances such as weak organic acids can be determined by a combination of the formulae of Ostwald and Arrhenius, but the procedure is quite inadmissible for salts. Here the degree of dissociation is large. In fact the value of a is often indistinguishable from unity, and the mutual influences of the ions are considerable. They are calculable in principle by methods due to Debye and Hiickel, and operate differently on different properties. The procedure outlined on p. 276 allows the calculation of the activity coefiicients. In general the thermodynamic properties of the salt in solution correspond to those of a system with apparently incomplete dissociation, not because the concentrations of the ions are reduced by molecule formation but because the activity coefficients are lowered by mutual ionic influences. 

Although Pitzer s method of calculating activity coefficients has been applied with some success to solutions containing weak electrolytes (OPl, OP14, it s form is best suited to strong electrolyte solutions. This is becausei in solutions of weak electrolytes, significant concentrations of molecular solutes are present. While... 

The last paper (S30) presented activity coefficients for the undissociated part of the following weak electrolyte acids benzoic, ortho toluylic, salicylic, ortho-nitrobenzoic, acetic, monochloracetic and dichloracetic acids. In a study of binary solutions of sodium and potassium acetate. RandaU. McBain and White (S26) found the ionic activity coefficients to be very close in value to the ionic activity coefficients for binary sodium and potassium chloride solutions. Consequently, in Randall and Failey s paper on the activity coefficients of the undissociated part of weak electrolytes, the activity coefficients of the monobasic acids in salt solutions oi varying concentrations were assumed to be equal to the activity coefficient of hydrochloric acid in the same or similar salt solution at the same concentration. This meant that ... 

Randall and Failey felt that, while not completely accurate, such assumptions could be safely made for such dilute solutions and would not have much effect on the calculations for the activity coefficients of the undissociated portion the weak electrolyte acid. 

The following calculations were then done using ternary weak acid - salt water solubility data in which the solution is saturated with the weak electrolyte to get the activity coefficient of the undissociated portion of the weak acid ... 

Equation (7.9) equating the activities in binary and ternary solutions applies to the undissociated weak acid also the molalities of the undissociated part of the weak acid are known for the binary and ternary solutions and since the activity coefficient in the binary solution was assumed to be unity, equation (7.9) may be rearranged in order to calculate the activity coefficient of the undissociated portion of the weak electrolyte in the ternary solution ... 

The impact of these liquid phase reactions on the phase equilibrium properties is thus an increased solubility of NH3, CO2, H2S and HCN compared with the one calculated using the ideal Henry s constants. The reason for the change in solubility is that only the compounds present as molecules have a vapour pressure, whereas the ionic species have not. The change thus depends on the pH of the mixture. The mathematical solution of the physical model is conveniently formulated as an equilibrium problem using coupled chemical reactions. For all practical applications the system is diluted and the liquid electrolyte solution is weak, so activity coefficients can be neglected. 

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