Electrolyte solution activity coefficient

Pytkowicz (1969) writes Thermodynamic constants give a superficial appearance of convenience because they do not depend upon the composition of the medium, while apparent constants do. However, in the application of thermodynamic constants to the calculation of concentrations in concentrated multi-electrolyte solutions, activity coefficients have to be determined as a function of composition thereby cancelling what may have seemed to be an advantage. ... 

If the dependence of the relative permittivity of the solvent on the electric field strength of the ions is also taken into account, then other thermodynamic parameters of electrolyte solutions (activity coefficient, heat of dilution, partial molar enthalpy content of the solute etc.) can likewise be calculated in better agreement with the experimental data. Although the introduction of the field-dependent relative permittivity into the ion-ion and ion-solvent interactions is accompanied by very great mathematical difficulties, the problem can be solved successfully by employing various approximations. 

O Connell, J. P., Y. Q. Hu, and K. A. Marshall. 1999. Aqueous strong electrolyte solution activity coefficients and densities from fluctuation solution theory. Fluid Phase Equilibria,... 

I. 46. The magnitude of the coefficient reflects the electric charge distribution of the ionic species. A 0.1 molal solution of Al2(S04)3 has an activity coefficient of only 0.035. It should also be noted that, in dilute solutions, activity coefficients of electrolytes decrease in magnitude with increasing concentration. A minimum is reached and the coefficient then increases with concentration. See Activity Debye-Huckel Law Biomineralization... 

Studies of the solution properties of heteropoly acids have been somewhat spares despite the general interest in these compounds for many years. Deterents to such studies have been primarily the instability of the compounds and the uncertainty concerning their composition. Conductivity and pH measurements on the heteropoly acids H4[PMonVO40] and H5[PMoi0V2O40] in aqueous solutions and mixed solvents has already been discussed. The acids are strong 1-4 and 1-5 electrolytes, respectively. Activity coefficients of ammonium 6-heteropolymolybdates have been reported and shown these to be 1 3 electrolytes197. ... 

Empirically, the Setchenov equation [37,39] has been found to express the variation of the neutral solute activity coefficient (7 ) with the electrolyte concentration (Ce), at least for low electrolyte concentrations (a few tens molar) ... 

Equation (7-4) indicates that the solubility product includes an activity-coefficient term, a term which has been assumed to be unity up to this time. The introduction to this chapter pointed out that errors arising from neglect of the effects of the activity coefficient are usually small when compared with several uncertainties or side reactions. The activity coefficient in Equation (7-4) depends on the kind and concentration of all electrolytes in solution, not merely those involved directly with the precipitate. The correction to solubility calculations that must be made to account for the activity-coefficient effect is known as the diverse ion effect. The appropriate background is discussed in Chapter 2, and Problems 2-1,2-2, and 2-3 are examples of the calculations. For 1 1 electrolytes in solution, activity coefficients can usually be assumed to be unity when concentrations are much less than 0.1 M. Common ion and diverse ion effects can be significant at the same time, for example, when a large excess of common ion is added in a precipitation. The diverse ion effect is one of the reasons that the haphazard addition of a large excess of precipitant should be avoided. 

Second, we need an equation-of-state for electrolyte solutions. Equations-of-state are needed for modeling high-pressure applications with electrolyte solutions. Significant advances are being made in this area. Given that the electrolyte NRTL model has been widely applied for low-pressure applications, we are hopeful that, some day, there will be an equation-of-state for electrolytes that is compatible with the electrolyte NRTL activity coefficient model. 

Other methods are used to describe me behavior of ionic species (electrolytes). The activity coefficient of an ion in solution may be expressed in terms of modified Debye-Hiickel theory. A common expression suitable for low concentrations has the form... 

For a dilute solution, also, p is not greatly different from the density po of the pure solvent, and since this and its molecular weight Jlfo are constant, it follows from equation (32.32) that the concentration (molarity) of any aolvte in a dilute solution is approximately proportional to its mole fraction. It is possible, therefore, to modify equation (32.25) in the following manner. In the first place, if the solution is dilute, and particularly if it contains no electrolytes, the activity coefficient factor may be taken as unity, so that equation (32.25) reduces to (32.26). If the mole fractions are replaced by the corresponding molarities, utilizing equation (32.32), it is found that... 

For most electrolytes k lies between zero and 0.1 hence, by equation (39.74), in a solution of ionic strength 0.1, 7/70 for the nonelectrolyte varies from unity to 1.023. It is frequently assumed, therefore, that in dilute solutions of electrolytes, the activity coefficient of a nonelectrolyte, or of the undissociated portion of an electrolyte, is virtually unity. 

There are two points in connection with equation (39.74) to which attention may be drawn. First, it is seen that the activity coefficient of the nonelectrolyte varies directly with the ionic strength for electrolytes, in dilute solution, the activity coefficient depends on the square root of the ionic strength of the medium (see Chapter XVII). Second, the activity coefficient of the nonelectrolyte increases with the ionic strength whereas for an electrolyte the activity coefficient at first decreases. The subsequent increase observed in many cases is attributed to a type of salting-out effect. ... 

We see from equation (1) that, in very dilute solutions of a strong electrolyte, the activity coefficient is determined only by the concentration and valence of ions, the specific nature of the ions having no appreciable influence. 

JOH/PYT] Johnson, K. S., Pytkowicz, R. M., Ion association and activity coefficients in multicomponent solutions, Activity coefficients in electrolyte solutions, Pytkowicz, R. M., Ed., II, pp.I-62, CRC Press, Boca Raton, Florida, (1979). Cited on page 588. 

Since solutions with low electrolyte concentrations are of most interest, the solute activity coefficients in electrolyte solutions could, in principle, be defined, following Eq. 9.7-20, by... 

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... 

Garnsey and Prue made measurements by a heating-curve method on solutions of the perchlorates of lithium and potassium, and of lithium chloride. Measurements were made up to a molality of about 0.25 mol kg . The first two salts behave as strong electrolytes with activity coefficients given by the equation (cf. eqn. 2.9.14)... 

In an electrolyte, the activity coefficient of the metal ions cannot be neglected and deviates considerably from one. The activity coefficient depends on the ionic strength /, defined in Eq. (1.12). Eor diluted solutions (c<10 mol kg i), it can be calculated by the Debye-Hiickel theory in the first approximation (Eq. (1.15)). In practice, if working with an excess of supporting electrolytes, the activity coefficient is approximately constant. The variation of the equilibrium potential with the concentration is determined by the Nemst factor 2.303 RTIF=59.2 mV at 25 °C for z+ = l (decadal logarithm). 

A rigorous test of multicomponent solution activity coefficient prediction methods is the calculation of the mutual solubilities of salts and the calculation of salt solubilities in aqueous electrolyte solutions. The salt solubilities are affected by the solution composition. In order to calculate the saturation molalities, the activity coefficients must be adequately predicted. 

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 ... 

As it can be observed from Fig. 1, electrolyte solutions are highly nonideal from the thermodynamic point-of-view, i.e., the solvent activity coefficient as well as the salt activity coefficient strongly deviates from unity (ideal solution). Activity coefficients fr depend on temperature and composition of the considered electrolyte... 

Rosene and Manes studied the effect of pH on the total adsorption from aqueous solutions of sodium benzoate + benzoic acid by activated charcoal. They interpreted their data in terms of the Polanyi potential theory applied to bisolute adsorption (see later p. 117), in which the concentrations of neutral benzoic acid and benzoate anions depend on the pH of the solution (activity coefficient corrections were ignored). They confirmed that, at constant total equilibrium concentration, the adsorption dropped from a relatively high plateau for pH <2 down to a small adsorption at pH >10. The analysis of results is somewhat more complex than with essentially non-electrolyte adsorption, and in this case there were additional effects involving chemisorption of benzoate ion by residual ash in the carbon which had, therefore, to be eliminated. Even with ash-extracted carbon there was evidence of some residual chemisorption. The theoretical analysis correlated satisfactorily with the experimental data on the basis that at pH >10 sodium benzoate is not physically adsorbed and that the effect of pH is completely accounted for by its effect on the concentration of free acid. In addition the theory explains successfully the increase in pH (called by the authors hydrolytic adsorption ) when solutions of sodium benzoate are treated with neutral carbon. However, no account is taken in this paper of the effect of pH on the surface charge of the carbon. 

The prediction from the theoretical argument above, that a solute activity coefficient in a dilute solution is a linear function of the composition variable, is borne out experimentally as illustrated in Fig. 9.10 on page 264. This prediction applies only to a nonelectrolyte solute for an electrolyte, the slope of activity coefficient versus molality approaches —oo at low molality (page 290). 

The Arrhenius theory of electrolytic solutions was quantitatively restored by explaining the properties of strong electrolytes without activity coefficients on basis of ionic solvation and incomplete dissociation [263-266],... 

Apelblat A (2008) The boiling point elevations of electrolyte solutions. Activity and osmotic coefficients at the boiling point temperatures. In Bostrelli DV (ed) Solution Chemistry Research Progress. Nova Science, Inc., New York, pp 133-148... 

Debye-Hiickel theory The activity coefficient of an electrolyte depends markedly upon concentration. Jn dilute solutions, due to the Coulombic forces of attraction and repulsion, the ions tend to surround themselves with an atmosphere of oppositely charged ions. Debye and Hiickel showed that it was possible to explain the abnormal activity coefficients at least for very dilute solutions of electrolytes. 

Derive the equation of state, that is, the relationship between t and a, of the adsorbed film for the case of a surface active electrolyte. Assume that the activity coefficient for the electrolyte is unity, that the solution is dilute enough so that surface tension is a linear function of the concentration of the electrolyte, and that the electrolyte itself (and not some hydrolyzed form) is the surface-adsorbed species. Do this for the case of a strong 1 1 electrolyte and a strong 1 3 electrolyte. 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

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