Activity Coefficients in Mixtures of Nonelectrolytes

Substance i in a liquid or solid mixture Pure i in the same physical state as the mixture  

Solute B, mole fraction basis B at mole fraction 1, behavior extrapolated from infinite dilution on a mole fraction basis  

Solute B, molality basis B at molality m°, behavior extrapolated from infinite dUulion on a molality basis  

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Concentrated, Binary Mixtures of Nonelectrolytes Several correlations that predict the composition dependence of Dab. re summarized in Table 5-19. Most are based on known values of D°g and Dba- In fact, a rule of thumb states that, for many binary systems, D°g and Dba bound the Dab vs. Xa cuiwe. CuUinan s equation predicts dif-fusivities even in hen of values at infinite dilution, but requires accurate density, viscosity, and activity coefficient data. 

Various functions have been used to express the deviation of observed behavior of solutions from that expected for ideal systems. Some functions, such as the activity coefficient, are most convenient for measuring deviations from ideality for a particular component of a solution. However, the most convenient measure for the solution as a whole, especially for mixtures of nonelectrolytes, is the series of excess functions (1) (3), which are defined in the foUowing way. 

In a previous paper regarding the gas solubility in mixtures of two nonelectrolytes, the ideality approximation for the binary solvent was employed to obtain an expression for the gas solubility. The ideality of the mixed solvents constituted a good approximation because usually the nonideality of the mixture of two nonelectrolytes is much lower than those between each of them and the gas. A similar assumption can be made for dilute aqueous salt solutions. Indeed, the data regarding the activity coefficient of water (yw) in dilute aqueous solutions of sodium chloride indicate that 1(9 In 7w/9xw)p,tI 0.01 for a molality of sodium chloride smaller than 0.8. Considering, in addition, that (Ai2 - A2s)4=o is independent of composition, eq 13 becomes... 

Section l. 4 discusses fogacities (through activity coefficients) in the liquid phase, Illustrative examples ate given using semiempirical models for liquid mixtures of nonelectrolytes. 

Nonelectrolyte G mcxlels only account for the short-range interaction among non-charged molecules (—One widely used G model is the Non-Random-Two-Liquid (NRTL) theory developed in 1968. To extend this to electrolyte solutions, it was combined with either the DH or the MSA theory to explicitly account for the Coulomb forces among the ions. Examples for electrolyte models are the electrolyte NRTL (eNRTL) [4] or the Pitzer model [5] which both include the Debye-Hiickel theory. Nasirzadeh et al. [6] used a MSA-NRTL model [7] (combination of NRTL with MSA) as well as an extended Pitzer model of Archer [8] which are excellent models for the description of activity coefficients in electrolyte solutions. Examples for electrolyte G models which were applied to solutions with more than one solvent or more than one solute are a modified Pitzer approach by Ye et al. [9] or the MSA-NRTL by Papaiconomou et al. [7]. However, both groups applied ternary mixture parameters to correlate activity coefficients. Salimi et al. [10] defined concentration-dependent and salt-dependent ion parameters which allows for correlations only but not for predictions or extrapolations. 

Table 8-8 gives some nonelectrolyte transfer free energies, and Table 8-9 lists single ion transfer activity coefficients. Note especially the remarkable values for anions in dipolar aprotic solvents, indicating extensive desolvation in these solvents relative to methanol. This is consistent with the enhanced nucleophilic reactivity of anions in dipolar aprotic solvents. Parker and Blandamer have considered transfer activity coefficients for binary aqueous mixtures. 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

The present paper is concerned with mixtures composed of a highly nonideal solute and a multicomponent ideal solvent. A model-free methodology, based on the Kirkwood—Buff (KB) theory of solutions, was employed. The quaternary mixture was considered as an example, and the full set of expressions for the derivatives of the chemical potentials with respect to the number of particles, the partial molar volumes, and the isothermal compressibility were derived on the basis of the KB theory of solutions. Further, the expressions for the derivatives of the activity coefficients were applied to quaternary mixtures composed of a solute and an ideal ternary solvent. It was shown that the activity coefBcient of a solute at infinite dilution in an ideal ternary solvent can be predicted in terms of the activity coefBcients of the solute at infinite dilution in subsystems (solute + the individual three solvents, or solute + two binaries among the solvent species). The methodology could be extended to a system formed of a solute + a multicomponent ideal mixed solvent. The obtained equations were used to predict the gas solubilities and the solubilities of crystalline nonelectrolytes in multicomponent ideal mixed solvents. Good agreement between the predicted and experimental solubilities was obtained. 

In contrast, a solution of nonelectrolytes can be treated as a mixture of ideal clusters because the activity coefficient can be expanded in terms of a power series in concentration, each term of which corresponds to the existence in solution of the appropriate n cluster. 

The introductory discussion of models for liquid-phase activity coefficients, presented in Chapter 5, included a description of the Wilson equation, which is appropriate for many nonelectrolyte mixtures that exhibit large deviations from ideality. However, the Wilson model cannot correlate liquid-liquid equilibrium data, and therefore it cannot be used in LLE and VLLE calculations. To overcome this deficiency, Renon and Prausnitz [1] devised the NRTL model for (NonRandom, Two-Liquid). 

Suppose we equilibrate a liquid mixture with a gas phase. If component i of the liquid mixture is a volatile nonelectrolyte, and we are able to evaluate its fugacity fi in the gas phase, we have a convenient way to evaluate the activity coefficient y,- in the liquid. The relation between yt and fi will now be derived. 

In principle, everybody knows that an activity coefficient has no significance unless there is a clear definition of the standard state to which it refers. In practice, however, there is all too often a tendency to neglect precise specification of the standard state and in some cases failure to give this exact specification can lead to serious difficulties. This problem is especially important when we consider supercritical components or electrolytes in liquid mixtures and, a little later, I shall have a few comments on that situation. But for now, let us consider mixtures of typical nonelectrolyte liquids at a temperature where every component can exist as a pure liquid. In that event, the standard-state fugacity is the fugacity of the pure liquid at system temperature and pressure and that fugacity is determined primarily by the pure liquid s vapor pressure. 

The Center for Energy Resources Engineering (CERE) of the Technical University of Denmark (DTU) is operating a data bank for electrolyte solutions [18]. It is a compilation of experimental data for (mainly) aqueous solutions of electrolytes and/or nonelectrolytes. The database is a mixture between a literature reference database and a numerical database. Currently references to more than 3,000 papers are stored in the database together with around 150,000 experimental data. The main properties are activity and osmotic coefficients, enthalpies, heat capacities, gas solubilities, and phase equihhria like VLE, LLE, and SLE. The access to the htera-ture reference database is free of charge. The numerical values must be ordered at CERE. 

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