Multiple-component systems

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

This statistical analysis can be easily extended to a multiple-component system. For an /V-component system with fraction abundances/ ,, . . ., /v, one has... 

Betalains, the pigments of the red beet, have found increased use as food colorants. This unit describes a multiple-component system using visible spectrophotometry to determine the concentration of the pigment components (i.e., betacyanins and betaxanthins) calculated in terms of betanin and vulgaxanthin-I, respectively (see Basic Protocol 1). The total pigment content (betalain) is expressed as the sum of betacyanins and betaxanthins. 

Efficiency in multiple component systems is far more complex. Every component may have a different efficiency at each stage. Components may interact and composition profiles may even reverse. The equilibrium slope for each component depends on many coupling and interaction effects. Therefore, overall efficiency cannot be easily derived from Murphree tray efficiencies. Most designs for both binary and multiple component systems use overall efficiency values based on operating data or test systems. 

The second consideration is that thermal methods are extremely versatile, allowing useful characterization of almost any sample. Indeed, the methods may be used to study single or multiple component systems such as finished dosage forms, although care is required in the interpretation of data from the latter. Finally, these methods tend to be simple to use, inexpensive, and operator friendly. This is a highly pertinent practical consideration, as methods whereby absolute specialization is required may be extremely useful but are less likely to have widespread application. 

Covering chemical phenomena of 1,2, 3, 4, and multiple component systems, this standard work on the subject (Nature, London), has been completely revised and brought up to date by A. N. Campbell and N. O. Smith. Brand new material has been added on such matters as binary, tertiary liquid equilibria, solid solutions in ternary systems, quinary systems of salts and water. Completely revised to triangular coordinates in ternary systems, clarified graphic representation, solid models, etc. gth revised edition. Author, subject indexes. 236 figures. 505 footnotes, mostly bibliographic, xii -f- 494pp. 536 x 8. 

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