Liquid solutions activity coefficient

We define the standard state of a liquid as ay = 1 and for gases as an ideal gas pressure of 1 bar, Pj = I- For ideal liquid solutions (activity coefficients of unity), we write ay = Cy so at chemical equilibrium... 

For gases, pure solids, pure liquids, and nonionic solutes, activity coefficients are approximately unity under most reasonable experimental conditions. For reactions involving only these species, differences between activity and concentration are negligible. Activity coefficients for ionic solutes, however, depend on the ionic composition of the solution. It is possible, using the extended Debye-Htickel theory, to calculate activity coefficients using equation 6.50... 

In the previous sections, we emphasized that at constant temperature, the liquid-phase activity coefficient is a function of both pressure and composition. Therefore, any thermodynamic treatment of gas solubility in liquids must consider the question of how the activity coefficient of the gaseous solute in the liquid phase varies with pressure and with composition under isothermal conditions. 

Any convenient model for liquid phase activity coefficients can be used. In the absence of any data, the ideal solution model can permit adequate design. 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

Given a prediction of the liquid-phase activity coefficients, from say the NRTL or UNIQUAC equations, then Equations 4.69 and 4.70 can be solved simultaneously for x and x . There are a number of solutions to these equations, including a trivial solution corresponding with x[ = x[. For a solution to be meaningful ... 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

The solubility values are functions of pure component properties of the solute (a// /uv, 7ffl ) and the liquid phase activity coefficients of the components in solution. Solubility is calculated using the following equation... 

Heintz, A., Kulikov, D.V., and Verevkin, S.R, Thermodynamic properties of mixtures containing ionic liquids. 2. Activity coefficients at infinite dilution of hydrocarbon and polar solutes in l-methyl-3-ethyl-imidazolium bis(trifluoromethyl-sulfonyl)amide and in l,2-dimethyl-3-ethyl-imidazolium bis(trifluoromethyl-sulfonyl)amide using gas-liquid chromatography, /. Chem. Eng. Data, 47, 894, 2002. 

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... 

In equation 21 the vapor phase is considered to be ideal, and all nonideality effects are attributed to the liquid-phase activity coefficient, y. For an ideal solution (7t = 1), equation 21 becomes Raoult s law for the partial pressure,, exerted by the liquid mixture ... 

Perhaps the most significant of the partial molar properties, because of its application to equilibrium thermodynamics, is the chemical potential, i. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equilibrium problems. The natural logarithm of the liquid-phase activity coefficient, lny, is also defined as a partial molar quantity. For liquid mixtures, the activity coefficient, y describes nonideal liquid-phase behavior. 

The program estimates the liquid phase activity coefficients at specified temperatures and liquid compositions from molecular structure of the molecules. Binary or multicomponent solutions can be considered. 

Experimental vapor-liquid-equilibrium data for benzene(l)/n-heptane(2) system at 80°C (176°F) are given in Table 1.8. Calculate the vapor compositions in equilibrium with the corresponding liquid compositions, using the Scatchard-Hildebrand regular-solution model for the liquid-phase activity coefficient, and compare the calculated results with the experimentally determined composition. Ignore the nonideality in the vapor phase. Also calculate the solubility parameters for benzene and n-heptane using heat-of-vaporization data. 

In this definition, the activity coefficient takes account of nonideal liquid-phase behavior for an ideal liquid solution, the coefficient for each species equals 1. Similarly, the fugacity coefficient represents deviation of the vapor phase from ideal gas behavior and is equal to 1 for each species when the gas obeys the ideal gas law. Finally, the fugacity takes the place of vapor pressure when the pure vapor fails to show ideal gas behavior, either because of high pressure or as a result of vapor-phase association or dissociation. Methods for calculating all three of these follow. 

Data are available for equilibrium pressure-volume-temperature of pure polymer liquids, solvent activity coefficients at infinite dilution, solvent activity coefficients at finite concentrations, and liquid-liquid phase equilibria of binary and ternary polymer solutions. 

Many nonionizable organic solutes in water are described thermodynamically on the mole fraction scale, although their solubilities may commonly be reported in practical units, for example, molality. [Refer to Schwarzenbach et al. (1993) and Klotz (1964) for detailed discussion of such aqueous solutions.] Here, the standard state is the pure liquid state of the organic solute, that is, Xj = 1. The reference state is Xi - 1, that is, a solution in which the organic solute molecules interact with one another entirely. Activity coefficients of solute molecules in dilute aqueous solutions are generally much greater than unity for this reference state choice, jc, 1. For example, with this reference state, aqueous benzene has an experimental infinitely dilute solution activity coefficient, T nzeno of 2400 for an infinite dilution reference state, jc, - 0, the activity coefficient would be approximately 1 (Tanford, 1991). 

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 . ... 

It was reported by Dixon and Johnston (56) that up to a moderate pressure, the liquid phase activity coefficient of the solid component 73 could be obtained by any activity coefficient model or, more conveniently, from the regular solution theory, as... 

For an ideal-liquid mixture, this equation shows a linear plot of In D vs. molar concentration. The term is the liquid-phase activity coefficient, and the term d InjJdXi is the slope of the conventional plot of the logarithm of the activity coefficient versus mole fraction (see Figures 12.7 and 12.9 in Chapter 12, or see Chapter 4). Thus, for the value of the liquid diffusion coefficient of a concentrated binary mixture i-j, Equations (8.5) or (8.6) should be used, depending on ideality of the solution. 

As in vapor-liquid equilibria and in liquid-liquid equilibria, exparimental arixhire data are required to find liquid-phase activity coefficients. For some so]id-liquid systems, estimates for 7 can be mede using regular-solution theory (Preston and Prausnitz2) or UNIFAC (Cmehling el al,3), but for reliable work a few exparimental measurements are necessary. 

Perhaps the most important term in Eq. (5.2-3) is the liquid-phase activity coefficient, and mathods for its prediction have been developed in many forms and by many workers. For binery systems die Van Laar [Eq. (1.4-18)]. Wilson [Eq. (1.4-23)]. NRTL (Eq. (1.4-27)], and UNIQUAC [Eq. (1.4-3 )] relationships are useful for predicting liquid-phase nonidealities, but they require some experimental data. When no data are available, and an approximate nonideality correction will suffice, the UNiFAC approach Eq-(1.4-31)], which utilizes functional group contributions, may be used. For special cases Involving regular solutions (no excess entropy of mixing), the Scatchard-Hiidebmod mathod provides liquid-phase activity coefficients based on easily obtained pane-component properties. 

Next, one frequently would like to be able to make some assessment of the accuracy of a set of experimental vapor-liquid or activity coefficient measurements. Basic thermodynamic theory (as opposed to the solution modeling of Chapter 9) provides no means of predicting the values of liquid-phase activity coefficients to which the experimental results could be compared. Also, since the liquid solution models discussed in Chapter 9 only approximate real solution behavior, any discrepancy between these models and experiment is undoubtedly more a reflection of the inadequacy of the model than a test of the experimental results. 

The question of evaluating the liquid-phase activity coefficient of the solute species still remains. Although experimental data for y would be preferable, such data may not be available. Consequently, various liquid solution models and correlations are used. If the regular solution model is used, we have... 

The purpose of this section is to study some aspects of the partitioning phenomenon and to relate the distribution coefficient to more fundamental thermodynamic quantities, so that we can (1) predict the distribution coefficient for a solute among two given solvents if experimental data are not available, or (2) use experimental distribution coefficient data to obtain information on liquid-phase activity coefficients. 

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