# 5.10: Untitled Page 108

- Page ID
- 18241

## Chapter 5

### Special Condition:

( *x *)

0

(5‐75)

*A * o

so that Eq. 5‐74 takes the form

( *x *) *M*

( *y *) *M*

( *y *) *M*

(5‐76)

*A * 2

*A * 1

*A * 3

At this point our objective is to determine ( *y *) in terms of ( *y *) , and we begin *A * 1

*A * 3

*Figure 5‐12*. Two‐unit extraction process

by arranging this result in the form

( *y *) ( *x *)

*M*

*M*

( *y *)

(5‐77)

*A * 1

*A * 2

*A * 3

Here we note that the process equilibrium relation is given by Process equilibrium relation:

( *y *)

*K*

( *x *)

(5‐78)

*A * 2

*eq,A*

*A * 2

and use of this result allows us to simplify the mole balance for species *A* to ( *y *) ( *y *)

*M*

*M*

*K*

( *y *)

(5‐79)

*A * 1

*A * 2

*eq,A *

*A * 3

We now use Eq. 5‐73 to determine ( *y *) so that Eq. 5‐79 provides the following *A * 2

result

( *y *) ( *y *) *A * 1 *A * ( *y *) (5‐80)

*A * 1

*A * 1

*A * 3

which can be solved for ( *y *) to obtain

*A * 1

( *y *)

Two Equilibrium Stages:

*A * 3

( *y *)

(5‐81)

*A * 1

2

1 *A * *A*

*Two‐Phase Systems* & *Equilibrium Stages *

197

We are now ready to determine ( *y *) when three equilibrium stages are *A * 1

employed as illustrated in Figure 5‐13.

*Figure 5‐13*. Three‐unit extraction process

In this case the molar balance for species *A* can be expressed as ( *x *) *M*

( *y *) *M*

( *x *) *M*

( *y *) *M*

(5‐82)

*A * 3

*A * 1

*A * o

*A*

4

*molar flow of species A*

*molar flow of species A*

*out of the control volume*

*into the control volume*

and we continue to impose the condition

Special Condition:

( *x *)

0

(5‐83)

*A * o

so that Eq. 5‐82 takes the form

( *x *) *M*

( *y *) *M*

( *y *) *M *

(5‐84)

*A * 3

*A * 1

*A * 4

At this point our objective is to determine ( *y *) as a function of ( *y *) , and we *A * 1

*A * 4

begin by arranging this result in the form

( *y *) ( *x *)

*M*

*M*

( *y *)

(5‐85)

*A * 1

*A * 3

*A * 4

Here we note that the process equilibrium relation is given by Process equilibrium relation:

( *y *)

*K*

( *x *)

(5‐86)

*A * 3

*eq,A*

*A * 3

and use of this result allows us to simplify the mole balance for species *A* to ( *y *) ( *y *)

*M*

*M*

*K*

( *y *)

(5‐87)

*A * 1

*A * 3

*eq,A *

*A * 4