# 5.3: Untitled Page 101

- Page ID
- 18234

## Chapter 5

*M* *M*

*A *

(5‐61)

*Keq,A*

Use of this expression in Eq. 5‐60 and solving for ( *y *) leads to the following *A * 3

expression for the mole fraction of species *A* in the organic stream (‐phase) leaving the settler illustrated in Figure 5‐6.

( *y *)

*A*

*A * 2

( *y *)

*K*

( *x *)

(5‐62)

*A * 3

*eq,A A * 1

1 *A*

1 *A*

This allows us to express two important limiting cases given by *A * 0 *, *

( *y *) ( *y *) *, *

no change occurs

(5‐63a)

*A * 3

*A * 2

*A * *, *

( *y *) *K*

( *x *) *, *

maximum change occurs

(5‐63b)

*A * 3

*eq,A*

*A * 1

In order to design a mixer‐settler to achieve a specified mole fraction of species *A* in Stream #3, one needs only to specify the absorption factor.

In the previous paragraphs, we examined a purification process from the point of view of an *equilibrium* *stage*, i.e., we assumed that the organic and aqueous streams leaving the settler are in equilibrium. The true state of equilibrium will never be achieved in a dynamic system such as the mixer‐settler illustrated in Figure 5‐6. However, the assumption of equilibrium is often a reasonable approximation and when that is the case, various mass transfer systems can be successfully designed and analyzed using the concept of an equilibrium stage.

If we are confronted with the problem of species *A* being transferred between a gas stream and a liquid stream, we require a contacting device that is quite different from that shown in Figure 5‐6. In this case we employ a gas‐liquid contacting device of the type illustrated in Figure 5‐7. Here a gas is forced through a perforated plate and then up through a liquid stream that flows across the plate. If the gas bubbles are *small enough* and if the liquid is *deep enough* and *completely mixed*, the gas will be in equilibrium with the liquid as it leaves the control volume. When this is the case, we can treat the system illustrated in Figure 5‐7 as an *equilibrium stage*. When the analysis is restricted to dilute solutions, one can usually employ a linear equilibrium relation, thus the mole fractions of species *A* in the exiting gas and liquid streams are related by Process equilibrium relation:

( *y *)

*K*

( *x *)

(5‐64)

*A * 3

*eq,A*

*A * 4

*Two‐Phase Systems* & *Equilibrium Stages *

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Under these circumstances the analysis of this system is identical to the analysis of the liquid‐liquid extraction process illustrated in Figure 5‐6.

*Figure 5‐7*. Gas‐liquid contacting device.

When the process equilibrium relation given by Eq. 5‐64 is *not valid*, the simplification of an *equilibrium stage* can no longer be applied and one must move to a smaller length scale to analyze the mass transfer process. This situation is illustrated in Figure 5‐8 where we have indicated that the mass transfer process *Figure 5‐8*. Gas‐liquid mass transfer

must be studied at a smaller scale. The analysis of mass transfer at this scale will occur in a subsequent chemical engineering course where the equilibrium

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