Activities, stoichiometric liquid

Activities, stoichiometric liquid component, Group III-V materials, 286-88... 

In equation 33, the superscript I refers to the use of method I, a T) is the activity of component i in the stoichiometric liquid (si) at the temperature of interest, AHj is the molar enthalpy of fusion of the compound ij, and ACp[ij] is the difference between the molar heat capacities of the stoichiometric liquid and the compound ij. This representation requires values of the Gibbs energy of mixing and heat capacity for the stoichiometric liquid mixture as a function of temperature in a range for which the mixture is not stable and thus generally not observable. When equation 33 is combined with equations 23 and 24 in the limit of the AC binary system, it is termed the fusion equation for the liquidus (107-111). 

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... 

From a Solution Model. Calculation of the difference in reduced standard-state chemical potentials by methods I or III in the absence of experimental thermodynamic properties for the liquid phase necessitates the imposition of a solution model to represent the activity coefficients of the stoichiometric liquid. Method I is equivalent to the equation of Vieland (106) and has been used almost exclusively in the literature. The principal difference between methods I and III is in the evaluation of the activity coefficients... 

Here a. (T) is the activity of component i in a stoichiometric liquid at the liquidus temperature, T, AS (IC) is the entropy of fusion of compound IC at the melting temperature, T, and AC (IC) is the difference in heat capacity between themstoichiom6tric liquid and the solid compound. This sequence is the same as that proposed for binary III-V systems by Vieland (5.). 

Each of the above three methods employs a different data base. Most of the property values required for the evaluation of in Equations 7-9 have been experimentally determined for III—V systems and these three relationships can be used as a test for thermodynamic consistency. The first method, Equation 7, is most reliable at or near the binary compound melting temperature. As the temperature is lowered below the melting one, uncertainties in the extrapolated stoichiometric liquid heat capacity and component activity coefficients become important. The second method, Equation 8, is limited to the temperature range in which an experimental determination of AG. is feasible (e.g., high temperature galvanic cell). Method II is also valuable for "pinning down" the low temperature values of 0yp. Method III is the preferred procedure when estimating solution model parameters from liquidus data. Since the activity coefficients of the stochiometric liquid... 

For the first case, Equation 7 was used in which the activity product of the stoichiometric liquid at the liquidus temperature of interest was calculated from the NRTL equation. The enthalpy of fusion and melting temperature for the compound as well as the heat capacity difference, however, were specified. The values chosen for these properties were those recommended by Chang et al. (4-). Figure 4 compares the calculated values of 9p for each data set with the recommended values (solid line). In these data reductions the NRTL equation had four adjustable parameters and the non-randomness factor was fixed at -0.001. The results given in Figure 4 are an extreme example of the possible discrepancy between the values of 9 calculated by this procedure and the recommended values. The ability of the parameter estimates obtained in these fits to reproduce the data sets is within the reported experimental error for each data set. Thus, errors in the extrapolated values of 9 are canceled by errors in the calculated values of Using values of 9 determined in this way to extrapolate data sets in temperature or to predict multicom-... 

For the second case, Equation 9 was used with Equations 3 and 4 to reduce the same binary Ga-Sb data sets. The stoichiometric liquid mixture activity product was fixed at the melting temperature by the NRTL model parameters. The remaining thermodynamic properties found in Equation 9 were assigned the values recommended by Chang et al. (4.). 

Liquid Solution Behavior. The component activity coefficients in the liquid phase can be addressed separately from those in the solid solution by direct experimental determination or by analysis of the binary limits, since y p = 1. Because of the large amount of experimental effort required to study a ternary composition field and the high vapor pressures encountered in the arsenide and phosphide melts, a direct experimental determination of ternary activity coefficients has been reported only for the Ga-In-Sb system (26). Typically, the available binary liquidus data have been used to fix the adjustable parameters in a solution model with 0,p determined by Equation 7. The solution model expression for the activity coefficient has been used not only to represent the component activities along the liquidus curve, but also the stoichiometric liquid activities needed in Equation 7. The ternary melt solution behavior is then obtained by extending the binary models to describe a ternary mixture without additional adjustable parameters. In general, interactions between atoms in different groups exhibit negative deviations from ideal behavior... 

Four different methods were presented to determine the reduced standard state chemical potential change and applied to the Ga-Sb system. It is common practice to use Equation 7 and a solution model representing the stoichiometric liquid activities to determine 0. The solution model parameters are then estimated from a fit of the binary phase diagram. It has been shown that this procedure can lead to large errors in the value of 0. The use of Equation 9, however, gave the correct temperature dependence of 0 and the inclusion of activity measurements in the data base replicated the recommended values of 0Tp. 

Abstract The term Lewis acid catalysts generally refers to metal salts like aluminium chloride, titanium chloride and zinc chloride. Their application in asymmetric catalysis can be achieved by the addition of enantiopure ligands to these salts. However, not only metal centers can function as Lewis acids. Compounds containing carbenium, silyl or phosphonium cations display Lewis acid catalytic activity. In addition, hypervalent compounds based on phosphorus and silicon, inherit Lewis acidity. Furthermore, ionic liquids, organic salts with a melting point below 100 °C, have revealed the ability to catalyze a range of reactions either in substoichiometric amount or, if used as the reaction medium, in stoichiometric or even larger quantities. The ionic liquids can often be efficiently recovered. The catalytic activity of the ionic liquid is explained by the Lewis acidic nature of then-cations. This review covers the survey of known classes of metal-free Lewis acids and their application in catalysis. 

The choice of an ionic liquid was shown to be critical in experiments with [NBuJBr (TBAB, m.p. 110°C) as a catalyst carrier to isolate a cyclometallated complex homogeneous catalyst, tra .s-di(ri-acetato)-bis[o-(di-o-tolylphosphino) benzyl] dipalladium (II) (Scheme 26), which was used for the Heck reaction of styrene with aryl bromides and electron-deficient aryl chlorides. The [NBu4]Br displayed excellent stability for the reaction. The recycling of 1 mol% of palladium in [NBu4]Br after the reaction of bromobenzene with styrene was achieved by distillation of the reactants and products from the solvent and catalyst in vacuo. Sodium bromide, a stoichiometric salt byproduct, was left in the solvent-catalyst system. High catalytic activity was maintained even after the formation of visible palladium black after a fourth run and after the catalyst phase had turned more viscous after the sixth run. The decomposition of the catalyst and the formation of palladium... 

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