Mean activity coefficient mixtures

If the validity of Eq. (1.3.31) is assumed for the mean activity coefficient of a given electrolyte even in a mixture of electrolytes, and quantity a is calculated for the same measured electrolyte in various mixtures, then different values are, in fact, obtained which differ for a single total solution molality depending on the relative representation and individual properties of the ionic components. 

A number of authors have suggested various mixing rules, according to which the quantity a could be calculated for a measured electrolyte in a mixture, starting from the known individual parameters of the single electrolytes and the known composition of the solution. However, none of the proposed mixing relationships has found broad application. Thus, the question about the dependence of the mean activity coefficients of the individual electrolytes on the relative contents of the various electrolytic components was solved in a different way. 

Methodically, there is no great difference between measuring the mean activity coefficient in a solution of one electrolyte and measuring this quantity in a mixture of electrolytes. Binary mixtures have been studied most extensively. If osmotic methods are used, then the coefficients ocx and... 

Note that in all ion interaction approaches, the equation for mean activity coefficients can be split up to give equations for conventional single ion activity coefficients in mixtures, e.g., Eq. (6.1). The latter are strictly valid only when used in combinations that yield electroneutrality. Thus, while estimating medium effects on standard potentials, a combination of redox equilibria with H " + e 5112(g) is necessary (see Example 3). 

Meissner et al. (10,11,12) have presented a method of estimating the activity coefficient of an electrolyte in a single component or in a solution. The technique is based on graphical analysis of the reduced mean activity coefficient for a broad class of electrolytes. The method has good estimates of activity coefficients when compared with the published values for single components and mixtures of eleotrolytes. 

This equation contains a parameter B that must be calculated from the experimental data. In addition, information about the molar volume of the mixture and the mean activity coefficient of the salt on the molality in the binary mixture water (1)—salt (3) is necessary. 

For NaCl, the results are not too accurate at high molalities. However, it is well-known that most models fail to represent accurately the mean activity coefficient for the NaCl + H2O mixtures at high molalities. One can, therefore, conclude that the gas solubility in aqueous salt solutions can be well described by eq 24 when accurate expressions for the mean activity coefficient of the salt in the binary water + salt mixtures are used. 

The Kirkwood-Buff formalism can be also used to derive the composition dependence of the Henry constant for a sparingly soluble gas dissolved in a mixed solvent containing water-r electrolyte [27]. The obtained equation requires information about the molar volume and the mean activity coefficient of the electrolyte in the binary (water-H electrolyte) mixture. Several expressions for the mean activity coefficient of the electrolyte were tested and it was concluded that the accuracy in... 

Eq. (B.l) will allow fairly accurate estimates of the aetivity coefficients in mixtures of electrolytes if the ion interaction coefficients are known. Ion interaction coefficients for simple ions can be obtained from tabulated data of mean activity coefficients of strong electrolytes or from the corresponding osmotic coefficients. Ion interaction coefficients for complexes can either be estimated from the charge and size of the ion or determined experimentally from the variation of the equilibrium constant with the ionic strength. 

Kwak JCT, Nelson RWP. Mean activity coefficients for the simple electrolyte in aqueous mixtures of polyelectrolyte and simple electrolyte. 4. The systems nickel chloride—nickel poly(styrenesulfonate), zinc chloride—zinc poly-(styrenesulfonate), and cadmium chloride—cadmium poly(styrenesulfonate). J Phys Chem 1978 82 2388-2391. 

Nesbitt (44,45) has pointed out that ratios of the activity coefficients of ions of the same charge in mixtures can be obtained without ambiguity from mean activity coefficients of electrolytes with a common anion or cation. If HCl is one of the electrolytes, a pH measurement might provide a reference point for calculating the activity coefficient of a second cation as well as that of the anion involved. Equilibrium theory suggests that pH measurements of saturated solutions of a metal hydroxide or carbonate might also lead to the activity coefficient of the metal ion concerned (46). In these cases, a convention is necessary to provide numerical values of the pH. 

The ionic interaction theories of Brrfnsted-Guggenheim (48) and Pitzer (49,50) have been conspicuously successful in accounting for the mean activity coefficients and other thermodynamic properties of electrolytes, singly and in mixtures of ionic solutes. They have proved especially useful in salt mixtures such as seawater (51,52). Unfortunately, specific parameters characteristic of single ions do not appear in the theory. For a single 1 1 electrolyte, the equations lead to equality of the activity coefficients of cation and anion, as in Equation 7. 

K. Jackowska, Rocz. Chem., 45, 87 (1971). Determination of mean activity coefficients of CsCl in methanol-water mixtures using cells with liquid junction. 

H. Sadek, T. F. Tadros, and A. A. El-Harakany, Electrochim. Acta, 16, 353 (1971). Mean activity coefficients and medium effects of HCl in H20-methylcellosolve mixtures. 

In this equation x, is the liquid perfume concentration, Mt the molecular weight, R the ideal gas constant, and T the absolute temperature. Equation 2 relates the liquid perfume composition, x, with the human sensory reaction of the evaporated perfume. A key factor of Equation 2 is the activity coefficient, y, because it represents the affinity of a molecule to its neighboring medium. High value of y means an increased inclination for a given substance to be released from the mixture and low value of y means a low concentration in the headspace. This means that the OV values of a particular component can change if it is diluted in different solvents or mixed with different fragrance components. 

It may be conjectured that collective behavior implies that the surfactants that make up the mixture are not too different, the presence of an intermediate being a way to reduce the discrepancy. When the activity coefficient is calculated from non-ideal models it is often taken to be proportional to the difference in solubihty parameters [42,43], which in case of a binary is the difference (3i - if the system is multicomponent, then the dil -ference is - Sm) y which is often less, because the mean value exhibits an average lower deviation. In other terms, it means that for a ternary in which the third term is close to the average of the two first terms, then the introduction of the third component reduces the nonideahty because (5i - 53) + ( 2 - < (5i - 52) -... 

For the systems with alcohols, the description of SLE given by the UNIQUAC ASM equation (assuming the association of alcohols) did not provide any better results. It can be understood as a picture of a very complicated interaction between the molecules in the solution it means that it exists not only in the association of alcohol molecules but also between alcohol and IL molecules and between IL molecules themselves. Parameters shown in Table 1.7 may be helpful to describe activity coefficients for any concentration, temperature, and to describe ternary mixtures. They are also useful for the complete thermod5mamic description of the solution. 

In addition to its direct influence via the water activity in the system, the amount of water also influences the activity coefficients of the other components in the mixture, and therefore equiUbrium constants like K0 can vary with the water activity in the system (Table 1.5) [29, 63, 64]. This can be seen as a solvent effect on the equilibrium constant The tendency in esterification reactions is that increases with decreasing water activity, which means that it is favorable to use low water activity because of both the direct effect of water activity on the equilibrium and the influence of water on K0. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

These interactions exist in real systems for which the activity has the physical meaning of the effective concentration. Thus, only for dilute real solutions does A = a. In mixtures, the activity coefficient is usually, but not always, less than one and is affected by all the species in the multicomponent mixture. 

In both of the above examples, we used an anionic buffer (MOPS or cacodylate). The buffer anions have only repulsive interactions with RNA and can be grouped with chloride ions when calculating mean ion activities. Thus, we apply mean ionic activity coefficients measured with KC1 solutions to solutions in which K+ ions are contributed both by KC1 and K-buffer salts. We strongly advise against the use of cationic buffers such as Tris, because of its idiosyncratic interactions with nucleic acids as compared to group I ions, and particularly against mixing KC1 with Tris buffer, which creates a cationic mixture of unknown activity. 

Mixtures of hydrocarbons are assumed to be athermal by UNIFAC, meaning there is no residual contribution to the activity coefficient. The free volume contribution is considered significant only for mixtures containing polymers and is equal to zero for liquid mixtures. The combinatorial activity coefficient contribution is calculated from the volume and surface area fractions of the molecule or polymer segment. The molecule structural parameters needed to do this are the van der Waals or hard core volumes and surface areas of the molecule relative to those of a standardized polyethylene methylene CH2 segment. UNIFAC for polymers (UNIFAC-FV) calculates in terms of activity (a,-) instead of the activity coefficient and uses weight fractions... 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

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