Thermodynamic parameters from phase equilibria

Fig. 4.9 Concentration dependence of the mass action law equilibrium constant /C, of the reaction 1-butanol + acetic acid butyl acetate + water at 80 °C comparison of experimental data (this work) with predictions from a thermodynamic consistent model using activity coefficients from a NRTL model with parameters from phase equilibrium data K = 22.7)...

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). 

From the outset, Flory (6) and Huggins (4,5 ) recognized that their expressions for polymer solution thermodynamics had certain shortcomings (2). Among these were the fact that the Flory-Huggins expressions do not predict the existence of the LCST (see Figure 2) and that in practice the x parameter must be composition dependent in order to fit phase equilibrium data for many polymer solutions 3,8). 

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... 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

Equilibrium constants calculated from the composition of saturated solutions are dependent on the accuracy of the thermodynamic model for the aqueous solution. The thermodynamics of single salt solutions of KC1 or KBr are very well known and have been modeled using the virial approach of Pitzer (13-15). The thermodynamics of aqueous mixtures of KC1 and KBr have also been well studied (16-17) and may be reliably modeled using the Pitzer equations. The Pitzer equations used here to calculate the solid phase equilibrium constants from the compositions of saturated aqueous solutions are given elsewhere (13-15, 18, 19). The Pitzer model parameters applicable to KCl-KBr-l O solutions are summarized in Table II. 

From measurements of the temperature dependency of the equilibrium constant, thermodynamic parameters may be deduced (section 3.4). Very few enthalpy and entropy constants have been derived for the distribution reaction MAj(aq) MA2(org) of neutral complexes such investigations give information about hydration and organic phase solvation. 

In this section we consider the thermodynamics of micellization from two points of view the law of mass action and phase equilibrium. This will reveal the equivalency of the two approaches and the conditions under which this equivalence applies. In addition, we define the thermodynamic standard state, which must be understood if derived parameters are to be meaningful. 

Thermodynamic non-idealities are taken into account while calculating necessary physical properties such as densities, viscosities, and diffusion coefficients. In addition, non-ideal phase equilibrium behavior is accounted for. In this respect, the Elec-trolyte-NRTL model (see Section 9.4.1) is used and supplied with the relevant parameters from Ref. [50]. The mass transport properties of the packing are described via the correlations from Refs. [59, 61]. This allows the mass transfer coefficients, specific contact area, hold-up and pressure drop as functions of physical properties and hydrodynamic conditions inside the column to be determined. 

If a reactant gas is introduced into the collision cell, ion-molecule collisions can lead to the observation of gas-phase reactions. Tandem-in-time instruments facilitate the observation of ion-molecule reactions. Reaction times can be extended over appropriate time periods, typically as long as several seconds. It is also possible to vary easily the reactant ion energy. The evolution of the reaction can be followed as a function of time, and equilibrium can be observed. This allows the determination of kinetic and thermodynamic parameters, and has allowed for example the determination of basicity and acidity scales in the gas phase. In tandem-in-space instruments, the time allowed for reaction will be short and can be varied over only a limited range. Moreover, it is difficult to achieve the very low collision energies that promote exothermic ion-molecule reactions. Nevertheless, product ion spectra arising from ion-molecule reactions can be recorded. These spectra can be an alternative to CID to characterize ions. 

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... 

The calculations reported in this paper and a related series of publications indicate that it is now quite feasible to obtain reasonably accurate results for phase equilibria in simple fluid mixtures directly from molecular simulation. What is the possible value of such results Clearly, because of the lack of accurate intermolecular potentials optimized for phase equilibrium calculations for most systems of practical interest, the immediate application of molecular simulation techniques as a replacement of the established modelling methods is not possible (or even desirable). For obtaining accurate results, the intermolecular potential parameters must be fitted to experimental results, in much the same way as parameters for equation-of-state or activity coefficient models. This conclusion is supported by other molecular-simulation based predictions of phase equilibria in similar systems (6). However, there is an important difference between the potential parameters in molecular simulation methods and fitted parameters of thermodynamic models. Molecular simulation calculations, such as the ones reported here, involve no approximations beyond those inherent in the potential models. The calculated behavior of a system with assumed intermolecular potentials is exact for any conditions of pressure, temperature or composition. Thus, if a good potential model for a component can be developed, it can be reliably used for predictions in the absence of experimental information. 

All these flow types appear more or less in a series one after the other during the evaporation of a liquid in a vertical tube, as Fig. 4.30 illustrates. The structure of a non-adiabatic vapour-liquid flow normally differs from that of an adiabatic two-phase flow, even when the local flow parameters, like the mass flux, quality, etc. agree with each other. The cause of this are the deviations from thermodynamic equilibrium created by the radial temperature differences, as well as the deviations from hydrodynamic equilibrium. Processes that lead to a change in the flow pattern, such as bubbles coalescing, the dragging of liquid drops in fast flowing vapour, the collapse of drops, and the like, all take time. Therefore, the quicker the evaporation takes place, the further the flow is away from hydrodynamic equilibrium. This means that certain flow patterns are more pronounced in heated than in unheated tubes, and in contrast to this some may possibly not appear at all. 

In each of these models two or more adj ustable parameters are obtained, either from data compilations such as the DECHEMA Chemistry Data Series mentioned earlier or by fitting experimental activity coefficient or phase equilibrium data, as di.scussed in standard thermodynamics textbooks. Typically binary phase behavior data are used for obtaining the model parameters, and these parameters can then be used with some caution for multicomponent mixtures such a procedure is more likely to be successful with the Wilson, NRTL, and UNIQUAC models than with the van Laar equation. However, the activity coefficient model parameters are dependent on temperamre, and thus extensive data may be needed to use these models for multicomponent mixtures over a range of temperatures. 

The main purpose of the model was to relate the ion concentration and the local electrostatic parameters. The first step towards this relation was to assume that thermodynamic equilibrium was achieved between the water pools of the reversed micelles and the excess aqueous phase. This hypothesis differs from classical thermodynamics in that the equilibrium does not take place between two macroscopic phases. Biais et already suggested in a microemulsion pseudophase model (60) that, due to the low interfacial tension, chemical potentials of any constituents depend on the composition, even in microscopic domains, but not on the geometric parameters of the structure. 

Thermodynamic parameters for the mixing of dimyristoyl lecithin (DML) and dioleoyl lecithin (DOL) with cholesterol (CHOL) in monolayers at the air-water interface were obtained by using equilibrium surface vapor pressures irv, a method first proposed by Adam and Jessop. Typically, irv was measured where the condensed film is in equilibrium with surface vapor (V < 0.1 0.001 dyne/cm) at 24.5°C this exceeded the transition temperature of gel liquid crystal for both DOL and DML. Surface solutions of DOL-CHOL and DML-CHOL are completely miscible over the entire range of mole fractions at these low surface pressures, but positive deviations from ideal solution behavior were observed. Activity coefficients of the components in the condensed surface solutions were greater than 1. The results indicate that at some elevated surface pressure, phase separation may occur. In studies of equilibrium spreading pressures with saturated aqueous solutions of DML, DOL, and CHOL only the phospholipid is present in the surface film. Thus at intermediate surface pressures, under equilibrium conditions (40 > tt > 0.1 dyne/cm), surface phase separation must occur. 

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