Mixtures solid + liquid equilibria

Since Raoult s law activities become mole fractions in ideal solutions, a simple substitution of.Y, — a, into equation (6.161) yields an equation that can be applied to (solid + liquid) equilibrium where the liquid mixtures are ideal. The result is... 

Effect of Pressure on Solid + Liquid Equilibrium Equation (6.84) is the starting point for deriving an equation that gives the effect of pressure on (solid + liquid) phase equilibria for an ideal mixture in equilibrium with a pure... 

Empirical equations of the form T = aF + bD + c, expressing the relation between total solids (T), fat (F), and density (D), have been used for years. Such derivations assume constant values for the density of the fat and of the mixture of solids-not-fat which enter into the calculation of the coefficients (a, b, and c). Since milk fat has a high coefficient of expansion and contracts as it solidifies (note that the solid-liquid equilibrium is established slowly), the temperature of measurement and the previous history of the product must be controlled carefully (see Sharp and Hart 1936). Variations in the composition of... 

Knoester, M., De Bruijne, P., and van den Tempel, M. (1972). The solid-liquid equilibrium of binary mixtures of triglycerides with palmitic and stearic chains. Chem. Phys. Lipids. 9,309-319. 

Pure water may coexist as liquid and vapor only at temperature-pressure pairs that fall on the vapor-liquid equilibrium (VLE) curve. At points above the VLE curve (but to the right of the solid-liquid equilibrium curve), water is a subcooled liquid. At points on the VLE curve, water may be saturated liquid or saturated steam (vapor) or a mixture of both. At points below the VLE curve, water is superheated steam. 

Single-phase tables are essential in uses that involve unstable phases. This includes phases that persist in a metastable region or those that are unstable at all temperatures. The real world abounds in such cases. Single-phase tables are often applied to solid-solid or solid-liquid equilibrium in mixtures, where an unstable phase is stabilized in the presence of other components. Analysis of such equilibria often requires liquid or solid properties that are many hundreds of degrees into the metastable region of each pure phase. Single-phase tables are designed to supply these properties, but their preparation is not trivial. 

To obtain the values of kaa for the binary mixture PH (1) + NA (2), the solid-liquid equilibrium data for this system [22] were used. The mole fraction of component a in the liquid phase was expressed through the modihed Schroder equation [23],... 

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... 

The combination of Eqs. (24)-(27) with the equation for the solid-liquid equilibrium provides a relation for the solubility of a solute forming a dilute solution in a ternary mixture. 

Figure 2-20 The solid liquid equilibrium relationship of a solid compound. From right to left, the solid phase at equihbrium can be pure compound A, a mixture of compounds C and A. compound C, a mixture of compounds C and B, and pure compound B. The solution phase at equihbrium can be a mixture of compounds A and B at the corresponding liquid-sohd tie hues.

The solubility of solid substances in pure and mixed solvents can be described by the usual solid-liquid equilibrium conditions (Acree Jr. 1984 Prausnitz, Lichtenthaler, and Gomes de Azevedo 1999). For the solubilities of a solid (solute, component 2) in water (component 3), cosolvent (component 1) and their mixture (mixed solvent 1-3), one can write the following equations ... 

For the synthesis and design of crystallization processes, the reliable knowledge of the solid-liquid equilibrium (SLE) behavior, respectively, the solubility of solids in a solvent or solvent mixture is of special importance. Additionally, reliable kinetic information about metastable zone nucleation and crystal growth is required. Information about the SLE behavior, respectively, the driving forces is also required to avoid blocking of, for example, in pipelines or other process units. 

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. 

Besides the pure component parameters, in particular the mixture parameters, for example of a g -model or an equation of state, should be checked carefully prior to process simulation. The procedure is shown in Figure 11.4 for the binary system acetone-cyclohexane, which may be one of the binary key systems of a multicomponent mixture. From the results shown in Figure 11.4, it can be concluded that the VLE behavior of the binary system can be reliably described in the temperature range 0-50 C with the Wilson parameters used. But from the poor -results, it seems that an extrapolation to higher or lower temperature may be dangerous, as already can be seen from the solid-liquid equilibrium (SLE) results of the eutectic system in the temperature range 0 to —lOO C and also from the incorrect temperature dependence of the calculated azeotropic data. 

Domanska, U. Lachwa, J. Thermodynamics of binary mixtures of N-methyl-2-pyrrolidinone and ketone. Experimental results and modelling of the (solid + liquid) equilibrium and the (vapour + liquid) equilibrium. The modified UNIFAC (Do) model characterization J. Chem. Thermodyn. 2005,37, 692-704... 

Phase behavior involving solid-liquid equilibrium is the basis for crystallization in chemical and materials engineering. Binary mixture systems can have up to three degrees of freedom according to the Gibbs phase rule. 

The influence of halogen substitution on the interaction energy between PAH molecules has also been investigated. Unlike the anthracene + pyrene mixture system, bromine substitution on anthracene induces a different kind of interaction in the pyrene (1) + 9,10-dibromoanthracene (2) mixture system, which also results in non-idealities in solid-liquid equilibrium (see Figure 8). The surface area and volume of the 9,10-dibromoanthracene molecule is much larger than that of pyrene. 

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