Solution phase activity coefficient-

Activity coefficients, which play a central role in chemical thermodynamics, are usually obtained from the analysis of phase equilibrium measurements. However, with shifts in the chemical industry and the use of combinatorial chemistry, new chemicals are being introduced for which the needed phase equilibrium data may not be available. Therefore, predictive methods for estimating activity coefficients and phase behavior are needed. Group contribution methods, such as the ASOG [analytical solution of groups... 

The activity coefficients and the equilibrium gas-phase composition have been calculated by using relationships based on Dalton s law. This also applies to Duhem s equation in the form of Eq. (8.22). For the water HP system this approach is approximately valid at T < 520 K. Comparison of activity coefficients and gas-phase composition obtained within the Redlich-Kister approximations and by numerical integration of Eq. (8.22) indicates that the modified approach of Eq. (8.23) agrees well with the solution of Eq. (8.22). With this modification, Eqs. (8.8), (8.9), (8.17), (8.18), and (8.23) provide the explicit and fairly accurate dependencies of activity coefficients on solution composition and temperature. Based on the activity coefficients, gas-phase composition can be readily obtained by using the approximations for the total pressure and Eqs. (8.3) and (8.4). Application of these formulae for estimating activity coefficients and gas-phase concentrations at higher temperatures [T > 520 K) should be considered as extrapolation. The accuracy of this extrapolation can be worse as compared to total pressure calculations. 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

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

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

When Eq. (4-282) is applied to XT E for which the vapor phase is an ideal gas and the liquid phase is an ideal solution, it reduces to a veiy simple expression. For ideal gases, fugacity coefficients and are unity, and the right-hand side of Eq. (4-283) reduces to the Poynting factor. For the systems of interest here this factor is always veiy close to unity, and for practical purposes <1 = 1. For ideal solutions, the activity coefficients are also unity. Equation (4-282) therefore reduces to... 

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. 

Y= activity coefficient of solute / = raffinate phase e = extract phase... 

The values given in this table are only approximate, but they are adequate for process screening purposes with Eqs. (16-24) and (16-25). Rigorous calculations generally require that activity coefficients be accounted for. However, for the exchange between ions of the same valence at solution concentrations of 0.1 N or less, or between any ions at 0.01 N or less, the solution-phase activity coefficients prorated to unit valence will be similar enough that they can be omitted. 

In an attempt to explain the nature of polar interactions, Martire et al. [15] developed a theory assuming that such interactions could be explained by the formation of a complex between the solute and the stationary phase with its own equilibrium constant. Martire and Riedl adopted a procedure used by Danger et al. [16], and divided the solute activity coefficient into two components. 

Yd) is the activity coefficient of the solute, and (ya) is the activity coefficient of the stationary phase. 

This relationship depends on the assumption that two similar stationary phases, irrespective of their polarity, can be considered to differ by measuring the ratio of the activity coefficients of two noncomplexing solutes (this basically implies the solute is nonpolar and will only interact with the stationary phase by dispersion forces). If this were true then. 

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. 

In Eq. (128), the superscript V stands for the vapor phase v2 is the partial molar volume of component 2 in the liquid phase y is the (unsym-metric) activity coefficient and Hffl is Henry s constant for solute 2 in solvent 1 at the (arbitrary) reference pressure Pr, all at the system temperature T. Simultaneous solution of Eqs. (126) and (128) gives the solubility (x2) of the gaseous component as a function of pressure P and solvent composition... 

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 formal Galvani potential, described by Eq. (22), practically does not depend on the concentration of ions of the electrolyte MX. Since the term containing the activity coefficients of ions in both solutions is, as experimentally shown, equal to zero it may be neglected. This results predominantly from the cross-symmetry of this term and is even more evident when the ion activity coefficients are replaced by their mean values. A decrease of the difference in the activity coefficients in both phase is, in addition, favored by partial hydration of the ions in the organic phase [31 33]. Thus, a liquid interface is practically characterized by the standard Galvani potential, usually known as the distribution potential. 

The clay ion-exchange model assumes that the interactions of the various cations in any one clay type can be generalized and that the amount of exchange will be determined by the empirically determined cation-exchange capacity (CEC) of the clays in the injection zone. The aqueous-phase activity coefficients of the cations can be determined from a distribution-of-species code. The clay-phase activity coefficients are derived by assuming that the clay phase behaves as a regular solution and by applying conventional solution theory to the experimental equilibrium data in the literature.1 2 3... 

As the components in a liquid mixture become more chemically dissimilar, their mutual solubility decreases. This is characterized by an increase in their activity coefficients (for positive deviation from Raoult s Law). If the chemical dissimilarity, and the corresponding increase in activity coefficients, become large enough, the solution can separate into two-liquid phases. 

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 ... 

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. 

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