Molecular solutes, activity coefficients

From a practical viewpoint we may conclude that molecular solutes have activity coefScients near unity up to an ionic strength of 0.1 and that deviations are moderate even at ionic strengths of the order of unity. In contrast to those of ionic solutes, activity coefficients of molecular solutes usually are slightly greater than unity. 

A conceptual difficulty arises in characterizing polymer stationary phases with gas-liquid chromatographic probe-solute specific retention volumes (1), namely, since it is a matter of experience that V remains finite, the mole fraction-based solute activity coefficient x must asymptotically approach zero as the molecular weight of the polymer stationary phase Mg becomes large . ... 

Values of K, for molecular species in NaCl solutions at 25°C are given in Table 4.5. Pytko-wicz (1983) lists additional AT, values for seawater. MINTEQA2 assumes A = 0.1 for all uncharged species. The largest Kj values in Table 4.5 equal about 0.2 for several species. In fresh, potable waters (TDS < 500 ppm, / < 0.01 m), the activity coefficients of these species still equal 1.00. Even in brackish waters with TDS values of about 5000 ppm (/ 0.1 mol/kg), for = 0.2, molecular species activity coefficients equal 1.02. Thus, to a good approximation the y, of such species can be takeri equal to unity in fresh and brackish waters. 

The ASOG method generates molecular or volume activity coefficients for each component in a mixture from a matrix of known pair interactions between each type of chemical group. Using the group counts in Table II and similar counts on the diluent, all permutations for interaction are calculated and properly weighted to give the solution activity coefficients. 

Here, R is the gas constant, Mj is the solvent s molecular weight, and P 22 are the saturated vapour pressure and second virial coefficient of the pure solvent at temperature T, respectively. The required vapour pressures and virial coefficients can be calculated or estimated from known relationships [473-477]. Other treatments for the determination of y , which include a term to correct for the free volume contribution due to differences in the size of the solute and solvent, have also been used [478, 479]. The temperature dependence of the resulting solute activity coefficient is related to the infinite dilmion partial molar excess Gibbs energy (AG ) through Eq. (9). 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

If the molecular species of the solute present in solution is the same as those present in the crystals (as would be the case for nonelectrolytes), then to a first approximation, the solubility of each enantiomer in a conglomerate is unaffected by the presence of the other enantiomer. If the solutions are not dilute, however, the presence of one enantiomer will influence the activity coefficient of the other and thereby affect its solubility to some extent. Thus, the solubility of a racemic conglomerate is equal to twice that of the individual enantiomer. This relation is known as Meyerhoffer s double solubility rule [147]. If the solubilities are expressed as mole fractions, then the solubility curves are straight lines, parallel to sides SD and SL of the triangle in Fig. 24. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

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. 

A second type of ternary electrolyte systems is solvent -supercritical molecular solute - salt systems. The concentration of supercritical molecular solutes in these systems is generally very low. Therefore, the salting out effects are essentially effects of the presence of salts on the unsymmetric activity coefficient of molecular solutes at infinite dilution. The interaction parameters for NaCl-C02 binary pair and KCI-CO2 binary pair are shown in Table 8. Water-electrolyte binary parameters were obtained from Table 1. Water-carbon dioxide binary parameters were correlated assuming dissociation of carbon dioxide in water is negligible. It is interesting to note that the Setschenow equation fits only approximately these two systems (Yasunishi and Yoshida, (24)). 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Ultraviolet spectra of benzoic acid in sulphuric acid solutions, published by Hosoya and Nagakura (1961), show a considerable medium effect on the spectrum of the unprotonated acid, but a much smaller one in concentrated acid. The former is probably connected with a hydrogen-bonding interaction of benzoic acid with sulphuric acid which is believed to be responsible for a peculiarity in the activity coefficient behaviour of unprotonated benzoic acid in these solutions (see Liler, 1971, pp. 62 and 129). The absence of a pronounced medium effect on the spectra in >85% acid is consistent with dominant carbonyl oxygen protonation. In accordance with this, Raman spectra show the disappearance in concentrated sulphuric acid of the carbonyl stretching vibration at 1650 cm (Hosoya and Nagakura, 1961). Molecular orbital calculations on the structure of the carbonyl protonated benzoic acid have also been carried out (Hosoya and Nagakura, 1964). 

By extending regular solution theory for binary mixtures of AEg in aqueous solution to the adsorption of mixture components on the surface (3,4), it is possible to calculate the mole fraction of AEg, Xg, on the mixed surface layer at tt=20, the molecular interaction parameter, 6, the activity coefficients of AEg on the mixed surface layer, fqg and f2s and mole concentration of surfactant solution, CTf=20 3t surface pressure tt=20 mn-m l (254p.l°C). The results from the following equations are shown in Table I and Table II. 

However the question of whether the salt should be considered as a molecular or ionic constituent is raised. The laws of solution theory suggest the latter. Hence, unless the salt is either fully associated or fully dissociated over the entire liquid composition range, the varying degree of salt dissociation over this range is important. In other words, since both species of ion and salt molecules contribute to the total effect caused by a partially dissociated salt, the total number of salt particles (ions and molecules) present should be considered. This would suggest that an even more correct expression of liquid composition for use in calculating liquid phase activity coefficients would be... 

So far, we have focused on how differences in molecular structure affect the solubilities and activity coefficients of organic compounds in pure water at 25°C. The next step is to evaluate the influence of some important environmental factors on these properties. In the following we consider three such factors temperature, ionic strength (i.e., dissolved salts), and organic cosolutes. The influence of pH of the aqueous solution, which is most important for acids and bases, will be discussed in Chapter 8. 

Mitchell, B. E., and P. C. Jurs, Prediction of infinite dilution activity coefficients of organic compounds in aqueous solution from molecular structure , J. Chem. Inf. Comput. Sci., 38, 200-209 (1998). 

Munz, C. H., and P. V. Roberts, The effects of solute concentration and cosolvents on the aqueous activity coefficients of low molecular weight halogenated hydrocarbons , Environ. Sci. Technol., 20, 830-836 (1986). 

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