Weak electrolyte models

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

Weak electrolytes in which dimerization (as opposed to ion pairing) is the result of chemical bonding between oppositely charged ions have been studied using a sticky electrolyte model (SEM). In this model, a delta fiinction interaction is introduced in the Mayer/-fiinction for the oppositely charged ions at a distance L = a, where a is the hard sphere diameter. The delta fiinction mimics bonding and tire Mayer /-function... 

Zhu J and Rasaiah J C 1989 Solvent effects in weak electrolytes II. Dipolar hard sphere solvent an the sticky electrolyte model with L = a J. Chem. Phys. 91 505... 

The first rigorous method for weak electrolyte solutions was that of Edwards et al. ( 5). Because comparisons with the models of other workers will be made, the thermodynamic framework will be outlined and the assumptions that were made stated. For a single solute which dissociates only in the aqueous solution, the model is based on four principles ... 

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. 

However, in most aqueous electrolyte systems of industrial interest, not only strong electrolytes but also weak electrolytes and molecular nonelectrolytes are present. While the modified Pitzer equation appears to be a useful tool for the representation of aqueous strong electrolytes including mixed electrolytes, it cannot be used in the form just presented to represent the important case of systems containing molecular solutes. A unified thermodynamic model for both ionic solutes and molecular solutes is required to model these kinds of systems. 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

VAN AKEN et al. 0) and EDWARDS et al. (2) made clear that two sets of fundamental parameters are useful in describing vapor-liquid equilibria of volatile weak electrolytes, (1) the dissociation constant(s) K of acids, bases and water, and (2) the Henry s constants H of undissociated volatile molecules. A thermodynamic model can be built incorporating the definitions of these parameters and appropriate equations for mass balance and electric neutrality. It is complete if deviations to ideality are taken into account. The basic framework developped by EDWARDS, NEWMAN and PRAUSNITZ (2) (table 1) was used by authors who worked on volatile electrolyte systems the difference among their models are in the choice of parameters and in the representation of deviations to ideality. 

Appendix. Formalism of BEUTIER S Model of Volatile Weak Electrolytes Vapor-Liquid Equilibria... 

It is evident from the title of this symposium that as a result of recent requirements to reduce pollutant levels in process wastewater streams, improved techniques for predicting the vapor-liquid-solid equilibria of multicomponent aqueous solutions of strong and/or weak electrolytes are needed. In addition to the thermodynamic models necessary for such predictions, tools have to be developed so that the engineer or scientist can use these thermodynamic models correctly and with relative ease. 

The absorption rate of carbon dioxide increases in the presence of amines or ammonia. Therefore, the reaction kinetics of NH3 and C02 has been considered in the model equations, too. The rate constant as a function of the temperature has been determined according to Ref. 136. The coefficients for the calculation of the chemical equilibrium constants in this system of volatile weak electrolytes are taken from Ref. 137. 

The ultimate extension of FRACHEM/ECES is to combine the ability to model rate limiting kinetics with the electrolyte equilibria capabilities of ECES. A need for such a tower model arose recently in the development of a new pollution control process. In this process certain organic species in dilute concentrations in waste water streams undergo reactions to form weak electrolytes which are then stripped from the waste water. In order to simulate and optimize the process a suitable tower model was needed. 

Our primary objective was to develop a computational technique which would correlate the ionization constant of a weak electrolyte (e.g., weak acid, ionic complexes) in water and the ionization constant of the same electrolyte in a mixed-aqueous solvent. Consideration of Equations 8, 22, and 28 suggested that plots of experimental pKa vs. some linear combination of the reciprocals of bulk dielectric constants of the two solvents might yield the desirable functions. However, an acceptable plot should have the following properties it should be continuous without any maximum or minimum the plot should include the pKa values of an acid for as many systems as possible and the plot should be preferably linear. The empirical equation that fits this plot would be the function sought. Furthermore, the function should be analogous to some theoretical model so that a physical interpretation of the ionization process is still possible. 

It can be seen that the added complexity of ion association is likely to make any simple model of ion-ion interactions very difficult to apply without a number of ad hoc assumptions concerning ionic radii. This is particularly true for ionic strengths in excess of 0.01 M or for low-dielectric-constant media. However, a further difficulty is raised by the problem of the nature of an ion pair. If we consider the simple case of univalent ions A+ B forming an ion pair, it is possible to picture the pair as varying in character from one in which the charges remain separated by the sum of the ionic radii of A+ + B to a molecule in which A and B form a covalent bond, not necessarily even polar in character. Nor is it necessarily true that a given species will behave the same in different solvents. If there is a tendency to covalent bond formation, then it is quite possible that the polarity of the A—B bond will depend on the dielectric constant of the solvent. Covalently bound molecules which ionize are considered as weak electrolytes, and they are not treated by the methods of Bjerrum, which are meant for strong electrolytes. The differences may not always be clear, but the important interactions for the weak electrolyte are with the solvent, and these we shall consider next. 

This continuum model predicts that all of these thermodynamic properties should preserve their sign and increase in magnitude as D is decreased. This is, of course, subject to the behavior of the derivatives (din D/d In T) and (din D/d In F) as D changes. In the case of weak electrolytes this is qualitatively the observed behavior. Some values are given in Table XV.7 for the dissociation of HaO and acetic acid in water-dioxane mixtures. Since the derivatives of D and F are not the same as the values in pure HaO, the values cannot be expected to follow D in any simple fashion. However, it is seen that qualitative agreement is obtained. If one uses Eqs. (XV.12.2) to (XV.12.5) and the experimental values of the derivatives for water, it is possible to calculate AFp from the experimental values of each of the thermodynamic quantities in turn. For acetic acid the values are 4.7 Kcal from AS, 0.3 Kcal from AH, 5.5 Kcal from ACp, and 5 Kcal from AF. Except for AH, this can be considered quite good correlation compared to AFion = 6.5 Kcal observed directly. For H2O the values are 4 Kcal from AS, 6 Kcal from ACp, 33 Kcal from AH, and... 

Recent models for ion transport in glasses inclnde the weak electrolyte , the random site , and the Anderson and Stnart models. ... 

Weak electrolyte model of RS has been employed to calculate activity coefficients and to use activity coefficients to detennine the activation barriers for conductivity. The agreement between the experimental and theoretical activation energies has been found to be satisfactory (Ravine and Souquet, 1977). 

Figure 4.6 Surface pH hypothesis for weak acids and bases. A model for the influence of the microclimate pH in rat proximal jejunum on weak electrolyte permeation. The weak acid A is converted to neutral by the presence of H+ in the microclimate. The undissociated form can easily be absorbed through the mucosa. In contrast, the weak base B is protonated by the H+ to BH+ which is less absorbed through the membrane.

Further efforts based upon the Pitzer equation approach should allow one to model reasonably accurately the complex thermodynamics occurring in flue-gas-desulfurization aqueous scrubbers. Tasks to be pursued to this end include (1) Replacing important estimated parameters by ones based upon experiment, particularly for sulfites. (2) Including higher-order terms (three-body, electrostatic, temperature dependence) where data are available. (3) Extending the treatment to include weak electrolytes. 

To calculate gas solubility in natural geochemical systems, basic thermodynamic properties such as the Henry s law constant and, in the case of weak electrolytes the dissociation constant, must be combined with a thermodynamic model of aqueous solution behavior. An analogous approach has been used to predict mineral solubilities in concentrated brines (1). Such systems are also relevant to the atmosphere where very concentrated solutions occur as micrometer sized aerosol particles and droplets, which contain very small amounts of water relative to the surrounding gas phase. The ambient relative humidity (RH) controls solute concentrations in the droplets, which will be very dilute near 1(X)% RH, but become supersaturated with respect to soluble constituents (such as NaCl) below about 75% RH. The chemistry of the aerosol is complicated by the non-ideality inherent in concentrated electrolyte solutions. 

SOLUBILITY OF A WEAK ELECTROLYTE IN SALT SOLUTIONS. Calculation of the solubility of a volatile strong electrolyte, such as HCl, in aqueous salt solutions is straightforward. However, solubilities of weak electrolytes are more difficult to model accurately, since the dissolved speciation must frequently be determined in addition to the activity of the component of interest. Thus, in the case of NH3, the relevant ionic interactions involving NH4 and OH" must be known in addition to parameters for the interaction of dissolved salts with the neutral NH3 molecule. See, for example, the work of Maeda et al. (47) on the dissociation of NH3 in LiCl solutions. 

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