# 4.4: Untitled Page 59

## Chapter 4

Figure 4‐1. Chemical production system

It is important to note that in Figure 4‐1 we have suggested the stoichiometry of the reactions taking place while the actual chemical kinetic processes taking place may be much more complicated. The subject of local and global stoichiometry is discussed in detail in Chapter 6. There we make use of the concept that atomic species are conserved in order to develop constraints on the local and global net rates of production. In Chapter 9 we introduce the concept of reaction kinetics and elementary stoichiometry. There we begin to explore the actual chemical kinetic processes that are the origin of the net rate of production of carbon dioxide and other molecular species.

4.1.2 Moving control volumes

In Sec. 3.3 we developed the macroscopic mass balance for a single component system in terms of an arbitrary moving control volume, ( ) . The

a

V t

speed of displacement of the surface of a moving control volume is given by w n, and the flux of species A that crosses this moving surface is given by the normal component of the relative velocity for species A, i.e.,

. On the

basis of this concept, we can express the first axiom for the mass of species A in the form

Axiom I:

(4‐20)

When it is convenient to work with molar quantities, we divide this result by the molecular mass of species A in order to obtain the form for an arbitrary moving control volume form given by

Multicomponent systems

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Axiom I:

(4‐21)

The volume associated with a specific moving control volume will be designated by V( t) while the volume associated with a fixed control volume will be designated by V . Throughout this chapter, we will restrict our studies to fixed control volumes in order to focus our attention on the new concepts associated with multicomponent systems. However, the world of chemical engineering is filled with moving, dynamic systems and the analysis of those systems will require the use of Eqs. 4‐20 and 4‐21.

4.2 Species Mass Density

The mass of species A per unit volume in a mixture of several components is known as the species mass density, and it is represented by  A . The species mass density can range from zero, when no species A is present in the mixture, to the density of pure species A, when no other species are present. In order to understand what is meant by the species mass density, we consider a mixing process in which three pure species are combined to create a uniform mixture of species A, B, and C. This mixing process is illustrated in Figure 4‐2 where we have indicated that three pure species are combined to create a uniform mixture having a measured volume of 45 cm3. The total volume of the three pure species is 50 cm3, thus there is a change of volume upon mixing as is usually the case with liquids. We denote this change of volume upon mixing by mix

V

, and for the

process illustrated in Figure 4‐2 we express this quantity as (4‐22)

The densities of the pure species have been denoted by a superscript zero, thus o

A

represents the mass density of pure species A. The species mass density of species A is defined by

(4‐23)

and this definition applies to mixtures in which species A is present as well as to the case of pure species A.

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