# 4.5: Untitled Page 60

## Chapter 4

Figure 4‐2. Mixing process

If we designate the mass of species A as mA and the volume of the uniform mixture as V, the species mass density can be expressed as

A

mA V

(4‐24)

For the mixing process illustrated in Figure 4‐2, we are given the density, o

A ,

and the volume,

, and this allows us to determine the mass of species A as A

V

(4‐25)

From this we can determine the species mass density,  A , in the mixture according to

(4‐26)

This type of calculation can be carried our for species B and C in order to determine  and 

B

C .

Multicomponent systems

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The total mass density is simply the sum of all the species mass densities and is defined by

(4‐27)

The total mass density can be determined experimentally by measuring the mass, m, and the volume, V, of a mixture. For any a particular mixture, it is difficult to measure directly the species mass density; however, one can prepare a mixture in which the species mass densities can be determined as we have suggested in Figure 4‐2. When working with molar forms, we often need the total molar concentration and this is defined by

(4‐28)

in which cA is determined by Eq. 4‐13.

4.2.1 Mass fraction and mole fraction

For solid and liquid systems it is sometimes convenient to use the mass fraction as a measure of concentration. The mass fraction of species A can be expressed in words as

(4‐29)

and in precise mathematical form we have

(4‐30)

Note that the indicator, G, is often referred to as a dummy indicator since any letter would suffice to denote the summation over all species in the mixture. In this particular case, we would not want to use A as the dummy indicator since this could lead to confusion.

The mole fraction is analogous to the mass fraction and is defined by

105