Solid-liquid equilibria predictions

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

Solid-liquid equilibrium data (1 6) for the HCl-NaCl- 0 system at 25°C were used with Equation 27 to calculate experimental activity coefficients of NaCl. Table 1 shows a comparison between the experimental activity coefficients and those calculated using Equation 12. The agreement between experimental and calculated activity coefficients is very good, and Equation 12 should be useful for predictions of solid-liquid equilibria at other temperatures. 

The application of UNIFAC to the solid-liquid equilibrium of sohds, such as naphthalene and anthracene, in nonaqueous mixed solvents provided quite accurate results [11]. Unfortunately, the accuracy of UNIFAC regarding the solubility of solids in aqueous solutions is low [7-9]. Large deviations from the experimental activity coefficients at infinite dilution and the experimental octanol/water partition coefficients have been reported [8,9] when the classical old version of UNIFAC interaction parameters [4] was used. To improve the prediction of the activity coefficients at infinite dilution and of the octanol/water partition coefficients of environmentally significant substances, special ad hoc sets of parameters were introduced [7-9]. The reason is that the UNIFAC parameters were determined mostly using the equihbrium properties of mixtures composed of low molecular weight molecules. Also, the UNIFAC method cannot be applied to the phase equilibrium in systems containing... 

Prediction of solubility is also receiving more attention, mostly limited to academic research. In comparison to the vapor-Equid equilibrium situation, which has built an extensive database for reliable prediction (Reid et al. 1977), prediction of solid-liquid equilibrium remains in its early stage (Kolaret al. 2002). However, this field is developing rapidly, and its fuUire potential cannot be overlooked (Tung et al. 2007). 

Often solid-liquid equilibrium data are not available for the system of interest, and experimental determination of the solidus-liquidus curves is required. If the system of interest is simple (ie., two to three components) and well behaved (ideal), then reliable predictive methods are available. Techniques for predicting nonideal solid-liquid phase behavior and muWcomponent equilibria are emerging. 

Other approaches to the computation of solid-liquid equilibria are shown in Table 11.2-3. The Soave-Redlich-Kwong equation of state evaluates fugacities to calculate solid-liquid equilibria,7 while Wenzel and Schmidt developed a modified van der Waals equation of state forthe representation ofphase equilibria. The Wenzel-Scbmidt approach generates fugacities, from which the authors developed a trial-and-error approach to compute solid-liquid equilibrium. Unno et a .9 recently presented a simplification of the solution of groups model (ASOG) that allows prediction of solution equilibrium from limited vapor-liquid equilibrium data. 

Muir, R.F. and Howatt, C.S. (1982) Predicting solid-liquid equilibrium data from vapour-liquid data. Chemical Engineering, 22 Feb, 89-92. 

P8.12 In the free DDBSP Explorer Version, search for solid-liquid equilibrium data for the mixture 2-propanol-benzene. Regress the two datasets simultaneously using the Wilson. NRTL, and UNIQUAC model. Check the performance of the three models. Compare the data to the results of the predictive methods UNIFAC, modified UNIFAC. and PSRK. Examine the different graphical representations. 

In Section 11.4, it was shown how suitable solvents can be selected with the help of powerful predictive thermodynamic models or direct access to the DDB using a sophisticated software package. A similar procedure for the selection of suitable solvents was also realized for other separation processes, such as physical absorption, extraction, solution crystallization, supercritical extraction, and so on. In the case of absorption processes or supercritical extraction instead of a g -model, for example, modified UNIFAC, of course an equation of state such as PSRK or VTPR has to be used. For the separation processes mentioned above instead of azeotropic data or activity coefficients at infinite dilution, now gas solubility data, liquid-liquid equilibrium data, distribution coefficients, solid-liquid equilibrium data or VLE data with supercritical compounds are required and can be accessed from the DDB. 

In the 60-80 ps section of Fig. 13.1 the benzene molecules are literally pushing the crystal lattice apart under the effect of the suddenly available kinetic energy. Diffusional and rotational freedom results and the crystal collapses to the liquid, which is then normally simulated at 300 K in the 80-120 ps section of the run. Since the part of the simulation where melting occurs is a non-equilibrium simulation, one cannot draw any conclusions from averages, nor can one claim to have simulated the actual solid-liquid equilibrium or to have predicted the melting temperature. Nevertheless, such dynamic runs offer a window over the evolution of the internal structure of the system as it goes from crystal to liquid an example taken from a study of acetic acid is shown in Fig. 13.2. One cannot say for sure that this picture is a representation of the tfue structural changes that occur when the acetic acid crystal melts molecular... 

Coon, J. E. Auwaerter, J. E. MeLaughlin, E. A comparison of solid-liquid equilibrium with vapor-liquid equilibrium for prediction of activity coefficients in systems containing polynuclear aromatics. Fluid Phase Equilib. 1989, 44, 305-345. 

Figure 9.6 Comparison of the equilibrium [equation (9.2.2)] and fractional melting [equation (9.3.15)] models for a bulk solid-liquid partition coefficient Dt of 0.1 (top) and 2 (bottom). Although the concentrations predicted by the two models diverge rapidly for incompatible elements in instantaneous melts, they remain virtually identical for compatible elements.

One aspect of the research will examine equilibrium aspects of solvation at hydro-phobic and hydrophilic interfaces. In these experiments, solvent dependent shifts in chromophore absorption spectra will be used to infer interfacial polarity. Preliminary results from these studies are presented. The polarity of solid-liquid interfaces arises from a complicated balance of anisotropic, intermolecular forces. It is hoped that results from these studies can aid in developing a general, predictive understanding of dielectric properties in inhomogeneous environments. 

Phase diagrams can be used to predict the reactions between refractories and various solid, liquid, and gaseous reactants. These diagrams are derived from phase equilibria of relatively simple pure compounds. Real systems, however, are highly complex and may contain a large number of minor impurities that significantly affect equilibria. Moreover, equilibrium between the reacting phases in real refractory systems may not be reached in actual service conditions. In fact, the successful performance of a refractory may rely on the existence of nonequilibrium conditions, eg, environment (15—19). 

For the reaction aA + bB cC + t/D, the equilibrium constant is K = [C]l[D], /[A]"(B), Solute concentrations should be expressed in moles per liter gas concentrations should be in bars and the concentrations of pure solids, liquids, and solvents are omitted. If the direction of a reaction is changed. K = UK. If two reactions are added. A", = K, K-,. The equilibrium constant can be calculated from the free-energy change for a chemical reaction K = e AcrlRT. The equation AG = AH — TAS summarizes the observations that a reaction is favored if it liberates heat (exothermic, negative AH) or increases disorder (positive AS). Le Chatelier s principle predicts the effect on a chemical reaction when reactants or products are added or temperature is changed. The reaction quotient, Q, tells how a system must change to reach equilibrium. 

There have been advances in the techniques by which solid-liquid equilibria can be correlated and, in some cases, predicted. These are described in references on phase-equilibrium thermodynamics. 

FIGURE 2. Solubilities of naphthalene (S is the mole fraction of naphthalene) in the mixtures a) methanol + water and b) ethanol + water. The experimental data (0) were taken from Ref. (2). The solid lines represent the solubilities of naphthalene predicted using equation M4. The Wilson constants were taken from Gmeling s vapor-liquid equilibrium compilation (2 ). Thus, the only solubilities in pure water and cosolvents were used for prediction. 

There has been little work done to date on the nature of the three-phase substrate-solid-liquid intersection, and there is little guidance in predicting the magnitude of the equilibrium contact angle 9 that enters into classical nucleation theory in the factor f(0). Considerably more work has been done on the contact angle in substrate-liquid-vapor equilibrium, which determines the wetting properties of the liquid for the substrate. It is possible that some of the techniques developed for that problem may be applicable to the study of surface-induced nucleation of crystallization. 

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