Activity coefficient nonelectrolytes

The use of UNIFAC for estimating activity coefficients in binary and multicomponent organic and organic—water systems is recommended for those systems composed of nonelectrolyte, nonpolymer substances for which only stmctural information is known. UNIFAC is not recommended for systems for which some reUable experimental data are available. The method, including revisions through 1987 (39), is available in commercial software packages such as AspenPlus (174). 

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. 

By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

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. 

If one of the partners in a second-order reaction is not an ion, then in ideal solutions there will be little effect of added salts on the rate. The activity coefficient of a nonelectrolyte does not depend strongly on ionic strength the way that the activity coefficients of ions do. In a reaction with only one participating ion, it and the transition... 

Figure 7.4 shows such functions for binary solutions of a number of strong electrolytes and for the purposes of comparison, for solutions of certain nonelectrolytes (/ ). We can see that in electrolyte solutions the values of the activity coefficients vary within much wider limits than in solutions of nonelectrolytes. In dilute electrolyte solutions the values of/+ always decrease with increasing concentration. For... 

Fig. 1.1 The activity coefficient y of a nonelectrolyte and mean activity coefficients y of electrolytes as functions of molality...

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

Li, J., Dallas, A.J., Eikens, D.I., Carr, P.W., Bergmann, D.L., Hait, M.J., Eckert, C.A. (1993) Measurement of large infinite dilution activity coefficients of nonelectrolytes in water by inert gas stripping and gas chromatography. Anal. Chem. 65, 3212-3218. 

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. 

Long, F.A. McDevit, W.F. "Activity Coefficients of Nonelectrolyte Solutes in Aqueous Salt Solutions," Chem. Rev.,... 

Roughly half of the data on the activities of electrolytes in aqueous solutions and most of the data for nonelectrolytes, have been obtained by isopiestic technique. It has two main disadvantages. A great deal of skill and time is needed to obtain reliable data in this way. It is impractical to measure vapor pressures of solutions much below one molal by the isopiestic technique because of the length of time required to reach equilibrium. This is generally sufficient to permit the calculation of activity coefficients of nonelectrolytes, but the calculation for electrolytes requires data at lower concentrations, which must be obtained by other means. 

Our approach is different from previous methods in two basic aspects. First, we define our standard state as the saturated solution and, second, we define our activity coefficients in a way similar to that commonly used for nonelectrolytes. 

For concentrated solutions, the activity coefficient of an electrolyte is conveniently defined as though it were a nonelectrolyte. This is a practical definition for the description of phase equilibria involving electrolytes. This new activity coefficient f. can be related to the mean ionic activity coefficient by equating expressions for the liquid-phase fugacity written in terms of each of the activity coefficients. For any 1-1 electrolyte, the relation is ... 

There are, however, many specific and anomalous kinetic salt effects, especially at higher salt concentrations, the origin of which lies in the effects on nonelectrolyte reactant activity coefficients. This is often the most interesting effect for enzymes, because the charge on the substrate is frequently zero, making the product ZiZ also zero. The exact charge on the enzyme molecules can be difficult to determine if one is working at a pH removed from the isoelectric point of the enzyme. 

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. 

Elaborate procedures have been developed for obtaining activity coefficients from freezing-point and thermochemical data. However, to avoid duplication, the details will not be outlined here, because a completely general discussion, which is applicable to solutions of electrolytes as well as to nonelectrolytes, is presented in Chapter 21 of the Third Edition of this book [6]. 

In Chapters 16 and 17, we developed procedures for defining standard states for nonelectrolyte solutes and for determining the numeric values of the corresponding activities and activity coefficients from experimental measurements. The activity of the solute is defined by Equation (16.1) and by either Equation (16.3) or Equation (16.4) for the hypothetical unit mole fraction standard state (X2° = 1) or the hypothetical 1-molal standard state (m = 1), respectively. The activity of the solute is obtained from the activity of the solvent by use of the Gibbs-Duhem equation, as in Section 17.5. When the solute activity is plotted against the appropriate composition variable, the portion of the resulting curve in the dilute region in which the solute follows Henry s law is extrapolated to X2 = 1 or (m2/m°) = 1 to find the standard state. 

As we saw in Section 17.5, the activity coefficient of a nonelectrolyte solute can be calculated from the activity coefficient of the solvent, which, in turn, can be obtained from the measurement of colligative properties such as vapor pressure lowering, freezing point depression, or osmotic pressure. We used the Gibbs-Duhem equation in the form [Equation (17.33)]... 

The activity coefficients of solute and solvent are of comparable magnitudes in dilute solutions of nonelectrolytes, so that Equation (17.33) is a useful relationship. But the activity coefficients of an electrolyte solute differ substantially from unity even in very dilute solutions in which the activity coefficient of the solvent differs from unity by less than 1 x 10 . The data in the first three columns of Table 19.3 illustrate the situation. It can be observed that the calculation of the activity coefficient of solute from the activity coefficient of water would be imprecise at best. 

Bretti. C.. Crea. F.. Foti. C.. and Sammartano. S. Solnbility and acivity coefficients of acidic and basic nonelectrolytes in aqueous salt solutions. 1. Solnbility and activity coefficients o-phthalic and L-cystine in NaCl(aq). (CHsl NCUaq). and (C2Hs) NI(aq) at different ionic strengths and at t= 25 °C. Ind. Eng. Chem., 50(5) 1761-1767. 2005. 

This expression is analogous to Eiq. (2.3), in that (1 — (p) expresses the contribution of the solvent and In y+ that of the electrolyte to the excess Gibbs energy of the solution. The calculation of the mean ionic activity coefficient of an electrolyte in solution is required for its activity and the effects of the latter in solvent extraction systems to be estimated. The osmotic coefficient or the activity of the water is also an important quantity related to the ability of the solution to dissolve other electrolytes and nonelectrolytes. 

In any event, the activity coefficient of the nonelectrolyte, designated by subscript N, generally follows the Setchenov equation ... 

With the use of thermodynamic relations and numerical procedure, the activity coefficients of the solutes in a ternary system are expressed as a function of binary data and the water activity of the ternary system. The isopiestic method was used to obtain water activity data. The systems KCl-H20-PEG-200 and KBr-H20-PEG-200 were measured. The activity coefficient of potassium chloride is higher in the mixed solvent than in pure water. The activity coefficient of potassium bromide is smaller and changes very little with the increasing nonelectrolyte concentration. PEG-200 is salted out from the system with KCl, but it is salted in in the system with KBr within a certain concentration range. 

The activity coefficients of the nonelectrolyte and electrolyte were calculated by means of Equations 14 and 15 for chosen concentrations, and are listed in Tables V-VIII. 

The trend of activity coefficients of potassium chloride and potassium bromide is different in measured mixed solvent. The activity coefficient of potassium chloride is higher in the mixed solvent than in the pure water and rises smoothly with the nonelectrolyte content. The minimum value, about 2.0-3.0m in pure water, can be observed in the mixed solvent also. Because of the activity coefficient of the nonelectrolyte in the ternary system (also higher than that in pure water), both components are mutually salted out. 

The activity coefficient of potassium bromide is smaller in the mixed solvent than in pure water and changes very little with the increasing nonelectrolyte concentration. 

The theoretical picture is expressed by the Debye and McAulay equation [50], which relates the salt effects on nonelectrolytes to the dielectric constant of the solution, e and ionic radius, rj of individual ions. In this theory, the ions make the solution a poorer solvent for a nonelectrolyte, so that its activity coefficient, f , is increased as follows ... 

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