Multicomponent mixtures discrete description

By discrete description, we mean a description of multicomponent mixtures where the number of components considered, though possibly very large, is finite. Consider a mixture containing N (< >) components A/, 7=1,2,.. ., N. Given any physical property / of the components (such as concentration and chemical potential), its value for the 7th component is indicated by// the N ordered values of// constitute an A-dimensional vector f. The usual scalar product can be defined for vectors f we introduce the somewhat unusual notation for the scalar product, for reasons that soon become apparent (the <, > scalar product is reserved to A-dimensional vectors we also need vectors of different dimensionality). The notation <, > is also used more generally for sums over the range of the 7 index. 

In this section, we attack the problem of kinetics in multicomponent mixtures, and we dedicate attention mostly to the case where one is only interested in, or may only be able to determine experimentally, some overall concentration of species of a certain class, such as sulfurated compounds in an oil cut during a hydrodesulfurization process. The presentation is given in terms of a continuous description special cases of the corresponding discrete description are discussed as the need arises. Instead of working with the masses of individual species, we will work with their mass concentration distribution c x). In the case of a batch reactor, the distinction is irrelevant, but in the case of a plug flow reactor the concentration-based description is clearly preferable. The discussion is presented in purely kinetic terms for, say, a batch reactor. 

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