Phase equilibria activity

This chapter reviews developments in physical-chemical properties, thermophysical properties, phase equilibria, activity coefficients, modeling, and electrochemistry. 

The computer subroutines for calculation of vapor-phase and liquid-phase fugacity (activity) coefficients, reference fugac-ities, and molar enthalpies, as well as vapor-liquid and liquid-liquid equilibrium ratios, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements and CDC 6400 execution times for these subroutines are given in Appendix J. 

The activity coefficient y can be defined as the escaping tendency of a component relative to Raonlt s law in vapor-liqnid eqnihbrinm (see Sec. 4 in this handbook or Null, Phase Equilibrium in Process Design, Wiley-Interscience, 1970). 

In this example of the corrosion of zinc in a reducing acid of pH = 4, the corrosion product is Zn (aq.), but at higher pHs the thermodynamically stable phase will be Zn(OH)j and the equilibrium activity of Zn will be governed by the solubility product of Zn(OH)j and the pH of the solution at still higher pHs ZnOj-anions will become the stable phase and both Zn and Zn(OH)2 will become unstable. However, a similar thermodynamic approach may be adopted to that shown in this example. 

There is a similar expression for polymer activity. However, if the fluid being sorbed by the polymer is a supercritical gas, it is most useful to use chemical potential for phase equilibrium calculations rather than activity. For example, at equilibrium between the fluid phase (gas) and polymer phase, the chemical potential of the gas in the fluid phase is equal to that in the liquid phase. An expression for the equality of chemical potentials is given by Cheng (12). 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

The activity coefficients are evaluated from the above phase equilibrium data by procedures widely available in the thermodynamics literature (Tassios, 1993 Prausnitz et al. 1986). Since the objective in this book is parameter estimation we will provide evaluated values of the activity coefficients based on... 

When the standard states for the solid and liquid species correspond to the pure species at 1 atm pressure or at a low equilibrium vapor pressure of the condensed phase, the activities of the pure species at equilibrium are taken as unity at all moderate pressures. Consequently, the gas phase composition at equilibrium will not be... 

The most fundamental manner of demonstrating the relationship between sorbed water vapor and a solid is the water sorption-desorption isotherm. The water sorption-desorption isotherm describes the relationship between the equilibrium amount of water vapor sorbed to a solid (usually expressed as amount per unit mass or per unit surface area of solid) and the thermodynamic quantity, water activity (aw), at constant temperature and pressure. At equilibrium the chemical potential of water sorbed to the solid must equal the chemical potential of water in the vapor phase. Water activity in the vapor phase is related to chemical potential by... 

The equilibrium conditions given by eqs. (4.15) and (4.16) can in general be expressed through the activity coefficients. Using a solid-liquid phase equilibrium as an example we obtain... 

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. 

Mixture property Define the model to be used for liquid activity coefficient calculation, specify the binary mixture (composition, temperature, pressure), select the solute to be extracted, the type of phase equilibrium calculation (VLE or LLE) and finally, specify desired solvent performance related properties (solvent power, selectivity, etc.)... 

A very fine example was provided by the extensive use of Professor Pitzer s electrolyte activity coefficient theory within several acid gas phase equilibrium models. 

HS, S, HCCU, CO3, RR NH, RR NCOO", H+, OH- and H2O. Hence there are twenty-three unknowns (m and Yj for all species except water plus x ). To solve for trie unknowns there are twenty-three independent equations Seven chemical equilibria, three mass balances, electroneutrality, the use of Equation (6) for the eleven activity coefficients and the phase equilibrium for xw. The problem is one of solving a system of nonlinear algebraic equations. Brown s method (21, 22) was used for this purpose. It is an efficient procedure, based on a partial pivoting technique, and is analogous to Gaussian elimination in linear systems of equations. 

At present there are two fundamentally different approaches available for calculating phase equilibria, one utilising activity coefficients and the other an equation of state. In the case of vapour-liquid equilibrium (VLE), the first method is an extension of Raoult s Law. For binary systems it requires typically three Antoine parameters for each component and two parameters for the activity coefficients to describe the pure-component vapour pressure and the phase equilibrium. Further parameters are needed to represent the temperature dependence of the activity coefficients, therebly allowing the heat of mixing to be calculated. 

Therefore, the physical meaning of the solubility curve of a surfactant is different from that of ordinary substances. Above the critical micelle concentration the thermodynamic functions, for example, the partial molar free energy, the activity, the enthalpy, remain more or less constant. For that reason, micelle formation can be considered as the formation of a new phase. Therefore, the Krafft Point depends on a complicated three phase equilibrium. 

On the other hand, micelle formation has sometimes been considered to be a phase separation of the surfactant-rich phase from the dilute aqueous solution of surfactant. The micellar phase and the monomer in solution are regarded to be in phase equilibrium and cmc can be considered to be the solubility of the surfactant. When the activity coefficient of the monomer is assumed to be unity, the free energy of micelle formation, Ag, is calculated by an equation... 

Thermodynamic activity coefficients can be determined from the phase equilibrium measurements, and they are a measure of deviations from Raoult s law. Data of the activity coefficients covering the whole range of liquid composition of IL + molecular solvent mixtures have been reported in the literature and discussed in sections 1.6,1.7, and 1.8 as the values obtained from the SLE, LLE, and VLE data. When a strong interaction between the IL and the solvent exists, negative deviations from ideality should be expected with the activity coefficients lower than one. 

Discusses structure and physicochemical properties, activity coefficients, phase equilibrium with other liquids, and modeling... 

Several reviews have been published about ILs and analytical chemistry, fortunately now we have main players in this field in one place who kindly agreed f o provide f heir contributions. This book is an attempt to collect experience and knowledge about the use of ILs in different areas of analytical chemistry such as separation science, spectroscopy, and mass spectrometry that could lead others to new ideas and discoveries. In addition, there are chapters providing information of studies on determination of physicochemical properties, fhermophysical properties and activity coefficients, phase equilibrium with other liquids, and discussion about modeling, which are essential to know beforehand, also for wider applications in analytical chemistry. 

VOCs), and to a decrease in production yields. Quantitation of these phenomena and determination of material balances and conversion yields remain the bases for process analysis and optimisation. Two kinds of parameters are required. The first is of thermodynamic nature, i.e. phase equilibrium, which requires the vapour pressure of each pure compound involved in the system, and its activity. The second is mass-transfer coefficients related to exchanges between all phases (gas and liquids) existing in the reaction process. 

As already stated, one of the important pieces of data for biotransformation processes is knowledge of phase equilibrium and the activity of solutes involved. Hence, assuming that gas and liquid phases are at thermodynamic equilibrium, we can write... 

Use of equation 247 for actual calculations requires explicit introduction of composition variables. As in phase-equilibrium calculations, this is normally done for gas phases through the fugacity coefficient and for liquid phases through the activity coefficient. Thus, either... 

The dashed line in Fig. 19.7 gives the concentration in zone B expressed as the corresponding A-phase equilibrium concentration. This modified representation is like an extrapolation of the A-phase concentration scheme into system B. In fact, it is the same as considering the variability of activity or fugacity of the chemical, rather than its concentration, through the adjacent media. Consequently, the concentration jump at the phase boundary disappears the concentration profile (or more accurately the chemical activity profile) across the boundary looks like that shown in Fig. 19.6. 

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. 

Many additional consistency tests can be derived from phase equilibrium 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 solubility, and solubility of water in chemicals are related to solution activity coefficients and other properties through fundamental equilibrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equilibrium models may permit a missing property value to be calculated from those values that are known (2). 

The same reference (standard) state, f is chosen for the two phases, so that it cancels on both sides of equation 39. The products stffi and y" are referred to as activities. Because equation 39 holds for each component of a liquid—liquid system, it is possible to predict liquid—liquid phase splitting when the activity coefficients of the individual components in a multicomponent system are known. These values can come from vapor—liquid equilibrium experiments or from prediction methods developed for phase-equilibrium problems (4,5,10). Some binary systems can be modeled satisfactorily in this manner, but only rough estimations appear to be possible for multicomponent systems because activity coefficient models are not yet sufficiendy developed in this area. 

Aqueous Solubility. Solubility of a chemical in water can be calculated rigorously from equilibrium thermodynamic equations. Because activity coefficient data are often not available from the literature or direct experiments, models such as UNIFAC can be used for structure—activity estimations (24). Phase-equilibrium relationships can then be applied to predict miscibility. Simplified calculations are possible for low miscibility, however, when there is a high degree of miscibility, the phase-equilibrium relationships must be solved rigorously. 

In applying equation 33, Cpsl (the constant-pressure molar heat capacity of the stoichiometric liquid) is usually extrapolated from high-temperature measurements or assumed to be equal to Cpij of the compound, whereas the activity product, afXTjafXT), is estimated by interjection of a solution model with the parameters estimated from phase-equilibrium data involving the liquid phase (e.g., solid-liquid or vapor-liquid equilibrium systems). To relate equation 33 to an available data base, the activity product is expressed... 

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