# 5.10: Untitled Page 108

## 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

198