# 5.20: Untitled Page 117

## Chapter 5

Section 5.5

5‐20. Demonstrate that if the batch process illustrated in Figure 5‐4 is repeated N

times, the concentration of species A in the organic phase is given by N

( c

)

 ( c )

1  A

(1)

AN

A o

in which A is the absorption factor defined by

A V

V

(2)

eq,A

Here V represents the original volume of the organic phase, and V represents

the volume of the aqueous phase used in each of the N steps in the process.

5‐21. The result indicated by Eq. 1 in Problem 5‐20 is based on the condition that the concentration of species A is zero in the aqueous phase used in the extraction process. Repeat the analysis of the batch extraction process assuming that the concentration of species A in the original aqueous phase is ( c

)

A

.

o

5‐22. In the analysis of the batch liquid‐liquid extraction process illustrated in Figure 5‐4 the equilibrium relation was given as

Equilibrium relation:

c

 

( c

)

(1)

A

eq,A

A

Illustrate how 

is related to the Henry’s law equilibrium coefficient given by eq,A

K

in Eq. 5‐31. Use y

eq,A

A to represent the mole fraction of species A in the organic phase and xA to represent the mole fraction of species A in the aqueous phase.

5‐23. In order to justify the simplification indicated by Eq. 5‐54 we need estimates of M

  M and M  M . If we let species B represent the organic phase (the 1

4

2

3

phase ), and we assume that none of this species is transferred to the aqueous phase (the  phase ), a mole balance for species B takes the form Species B:

 ( y ) M  ( y ) M

 0

(1)

B 2

2

B 3

3

Use this species mole balance along with the definition

( y )

 ( y )  ( y )

(2)

B 3

B 2

B Two‐Phase Systems & Equilibrium Stages

215

to obtain an estimate of M

  M . Use this estimate to identify the conditions 2

3

that are required in order that the molar flow rates of the  phase are constrained by M

M

M

2

3

3

5‐24. Small amounts of an inorganic salt contained in an organic fluid stream can be removed by contacting the stream with pure water as illustrated in Figure 5.24. The process requires that the organic and aqueous streams Figure 5.24. Liquid‐liquid extraction

be contacted in a mixer that provides a large surface area for mass transfer, and then separated in a settler. If the mixer is efficient, the two phases will be in equilibrium as they leave the settler and you are to assume that this is the case for this problem. You are given the following information:

a) Organic stream flow rate: 1000 lbm/min

b) Specific gravity of the organic fluid: 

/

 0 8

. 7

org

H2O

c) Salt concentration in the organic stream entering the mixer: ( c )

= 0.0005 mol/L

A org

d) Equilibrium relation for the inorganic salt: ( c )

 

( c )

A org

eq,A

A aq

where 

 1 / 60

eq,A

Here ( c ) represents the salt concentration in the aqueous phase that is in A aq

equilibrium with the salt concentration in the organic phase, ( c )

. In this

A org

problem you are asked to determine the mass flow rates of the water stream that 216