Polycomponent Systems

Eqs. (12) to (14) are readily obtained by taking as the generalized expressions for the entropy and heat of mixing in a polycomponent system... 

Corresponding parameter for the interaction of component i with j in a polycomponent system. 

Until recently, most of the physicochemical data on molten oxides have been directly obtained from the industrial slags and glasses. These are mainly based on highly complex polycomponent systems and hence not usually amenable to basic interpretation. In the last two decades, however, the increasing interest in high temperature chemistry and the advances in... 

The adsorption mechanism discussed in previous chapters dealt only with a monocomponent system mineral - surfactant, as a result of an adsorption equilibrium related to appropriate PDI. Since a real flotation system consists of two or more mineral components it is necessary to mention conditions of the selective surfactant adsorption in such a system. In monocomponent systems the adsorption is controlled by the character of PDI with respect to the chemical composition of the polar heads of the surfactant. However, this rule is not valid in polycomponent systems containing both kinds of PDI. Generally and under simplifying circumstances, it is possible to classify the adsorption systems according to the role played by the PDI and the kind of the mineral. 

In contrast to their general use, the isotherms describing phase separation are not indicative of the existence of a real equilibrium between the phases they only indicate incipient phase-separation at zero time. Although neither of the starch fractions separately studied was subfractionated (and, therefore, each represents in itself a polycomponent system), they will be treated as if they were pure, single components. Likewise, magnesium sulfate will be considered to be a pure single component. The system is, then, one con-... 

As we said above, in exact science there is no place for a priori predilection for one of the components of a polycomponent system, they all being quite as important or unimportant initially. 

Nonideal behaviors are also expected for rare earth metals that are alloyed with the two divalent lanthanide metals europium and ytterbium. Cerium and samarium may also be anomalous because these two metals have a tendency to exhibit other valence states rather than the normal 3 state (2" for Sm and 4" for Ce). However, the mischmetal study reported by Palmer et al. (1982) did not indicate any anomalous behavior for cerium in this polycomponent system. 

Polycomponent Catalytic Systems Based on Amphiphiles and Polymers... 

To proceed further, we need to know the variations of the chemical potentials of the different components and the quantities of those components. Two cases need to be considered. In the first case, component A, is pure in its condensed phase. In the second case, component A, is either a pure gas or it belongs to a polycomponent phase of the system. 

If the component added is gaseous or belongs to one of the polycomponent phases of the system, the application of relation [2.8] to inequality [2.1] depends on the variations of the chemical potentials with the quantity of the added component, i.e. definitively of the law of variation of the activities of the components belonging to the same phase as that which has been added. We know that there is no general law. The laws issuing from the different models of solution can be applied, but the result will depend on the model chosen. 

It is possible to plot diagrams for equilibria involving a polycomponent phase with four components of the reaction. The system contains three independent components. These diagrams are square. To demonstrate their representation and their operation, we shall consider the reduction of carbon dioxide by hydrogen, in accordance with ... 

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