Sepa

LEACHING

per kg of inert solid. The extract quantity obtained in kg

1. During the obtainment of soluble coffee, the soluble

was therefore

solids are extracted with water in a solid liquid extraction.

6. In a determination of the solution retention data, the

This extraction is performed in a multistage system that

mass fraction of the solute in the extract was determined

operates counter currently, where 3000 kg/h of roasted

to be 0.6. The corresponding underflow analysis showed

and ground coffee contains 24% in weight of soluble solids,

retention of 0.6 kg solvent per kg of inert solid. The mass

while the moisture content is negligible. Five percent of

fraction of solute in the underflow is most likely

the soluble solids contained in the food appear in the final

7. Barium carbonate is to be made by reacting sodium

underflow stream, while the overflow stream contains

carbonate and barium sulfide. The quantities fed to the

35% in weight of such solids. From the previous laboratory

reaction agitators per 24 hours are 20 Mg of barium sulfide

experiments, it was obtained that the amount of solution

dissolved in 60 Mg of water, together with the

retained by inert solids is 1.6 kg solution per kg inert solids.

theoretically necessary amount of sodium carbonate.

Calculate the number of stages needed if the global

Three thickeners in series are run on a countercurrent

efficiency of the system is 75%.

decantation system. Overflow from the second thickener

2. Cod liver oil is obtained from crushed livers by extraction

goes to the agitators, and overflow from the first thickener

with an organic solvent. A sample that contains 0.335 kg of

is to contain 10% sodium sulfide. Sludge from all

oil per each kg of exhausted liver is fed into a multistage

thickeners contains two parts water to one-part barium

extractor that operates under countercurrent, where pure

carbonate by mass. How much sodium sulfide will remain

organic solvent is employed. It is desired to recover 90% of

dried barium carbonate precipitate?

the oil in the final overflow, with a composition 60% in

8. Aluminum sulfate, Al 2 (SO4)3, is to be produced by the

weight of oil. If retention of the solution is 2 kg per each

action of sulfuric acid, H2 SO4, ob bauxite in a series of

3.2 kg of insoluble solids, calculate the number of ideal

agitators, with a cascade of continuous thickeners to wash

stages required to carry out the desired extraction.

the insoluble mud free of aluminum sulfate.

Calculations are made assuming that 100 kg of food is introduced into the extractor. 3. It is desired to recover precipitated chalk from the causticizing of soda ash. After decanting the liquor from the precipitators the sludge has the composition 5 per cent CaCO3, 0.1 percent NaOH and the balance water. 1000 Mg/day of this sludge is fed to two thickeners where it is washed with 200 Mg/day of neutral water. The pulp removed from the bottom of the thickeners contains 4 kg of water/kg of chalk. The pulp from the last thickener is taken to a rotary filter and concentrated to 50 per cent solids and the filtrate is returned to the system as wash water. Calculate the net percentage of CaCO 3 in the product after drying. 4. Powdered limestone (CaCO 3) containing 10000 ppm NaOH is to be washed in a two-step continuous counter current washing system to remove most of the NaOH. Two cells and 100000 L of water per 10 MT/day of limestone feed are used. The slurry discharged and removed from the underflow contains 0.091 MT of water per MT CaCO 3. Assuming complete mixing and washing, calculate the NaOH content of the washed and dried limestone in ppm. 5. Ten kg of a solid containing 45% of soluble material were treated with 15 kg of a solvent containing the same solute at 2% concentration in a vessel under constant agitation. After a long time, the solution and the solid were separated by pressing. The solid analyzed 0.8 kg of solvent

Al 2 O3 + 3H2SO4  Al 2(SO4) 3 + 3H2O The reaction agitators are fed with 25 tons bauxite/day, containing 50% Al 2O3 and the rest insoluble; the theoretical quantity of aqueous acid containing 60% H2SO4 ; and the overflow from the second thickener. Assume the reaction is complete. The strong product solution is to contain 22% Al 2(SO4) 3, and no more than 2% of the Al 2 (SO4) 3 produced is to be lost in the washed mud. The last thickener is to be fed with pure wash water. The underflow from each thickener will contain 4 kg liquid / kg insoluble solid, and the concentration of soluble in the liquid of the underflow from each thickener may be assumed to be the same as that in the overflow. Calculate the number of thickeners required and the amount of wash water required per day. 9. One hundred kg of a solid containing 40% solute A and 60% inert B is treated with solvent C in a single stage single contact extraction. The extracted solids are then screw pressed. The pressed solids contain 1.2 kg solution per kg of inert. Entrainment of solids in the extract may be neglected. (a) The mass fraction of the solute in the extract if 90% of the solute in the feed is to be recovered in a single stage contact is

(b) The percent recovery of the solute if the extraction is

3. The ratio of the solubility of stearic acid per unit volume

carried out in two crosscurrent stages if 50% of the solvent

of n-heptane to that in 97.5% acetic acid is 4.95. How many

amount in problem no. 2 is used in each stage is

extractions of a 10 ml solution of stearic acid in 97.5%

10. How many stages and how much water is needed for

acetic acid with successive 10 ml portions of n-heptane are

the countercurrent extraction of NaOH from a feed

needed to reduce the residual stearic acid content of the

consisting 80 lb of NaOH, 400 lb water and 100 lb CaCO 3.

acetic acid layer to less than 0.5% of its original value?

The final extract solution will contain 10% NaOH with the

4. To plan a liquid–liquid extraction we need to know the

recovery of 95% NaOH. We shall set the underflow at a

solute’s distribution ratio between the two phases. One

constant 3 lb solution per lb CaCO 3?

approach is to carry out the extraction on a solution

11. A multiple contact extraction is to treat 1.25 tons per

containing a known amount of solute. After extracting the

hour of dry black ash containing 40% Na 2CO3 and 60%

solution, we isolate the organic phase and allow it to

insoluble matter with 30 gpm of water. If 5% of the Na 2 CO3

evaporate, leaving behind the solute. In one such

remains unextracted, calculate the number of ideal stages

experiment, 1.235 g of a solute with a molar mass of 117.3

by absorption factor method. The mass ratio of insoluble

g/mol is dissolved in 10.00 mL of water. After extracting

matter to solvent in the underflow from the stage is 1:2.

with 5.00 mL of toluene, 0.889 g of the solute is recovered

12. A mineral containing 20% elemental sulfur is to be

in the organic phase. How many extractions will we need

leached with hot gas oil in which sulfur is soluble to the

to recover 99.9% of the solute?

extent of 10 parts in 100 parts of oil by weight. The oil is

5. The distribution equilibrium for A between an extract

recycled over the over the batch of ground mineral until

solvent S and a raffinate solvent B is given Y=2X where

no farther dissolution of sulfur takes place. On drainage,

Y=mass of A per unit mass of S, X=mass of A per unit mass

the solid minerals retain the solution to the extent of one-

of B. The extract and raffinate solvents are immiscible with

tenth the weight of not dissolved solid (sulfur and gangue).

each other at all concentrations of A. From these data,

No preferential absorption takes place. Calculate the

calculate the amount of extract solvent needed per 100 kg

equilibrium compositions and quantities of the solid and

solution containing 30% A in B in 95% of A is to be removed

liquid phases if 50 kg of oil is used for leaching 100 kg of

for each of the following arrangements:

fresh mineral.

(a) Single stage contact (b) Three-stage batch contact, one third of the solvent will be used in each contact

LIQUID-LIQUID EXTRACTION 1. Carbon disulfide is used to extract iodine from its saturated aqueous solution. The distribution of iodine between carbon disulfide and water at equilibrium may be expresses as K = Y*/X = 588.2 where: Y* = g iodine / L of carbon disulfide X = g iodine /L of water Calculate the concentration of iodine in the aqueous phase when 1 L of a saturated solution at 200C containing 0.3 g of iodine per 1 L of water is stirred with 50 ml of carbon disulfide. Repeat for two ideal extractions using 25 ml of solvent each time.

(c) Three-stage countercurrent operation 6. (a) The solubility of iodine per unit volume is 200 times greater in ether than in water at a particular temperature. If an aqueous solution of iodine, 30 ml in volume and containing 2 mg of iodine is shaken with 30 ml of ether and the ether is allowed to separate, what quantity of iodine remains in the water layer? (b) What quantity of iodine remains in the water layer if only 3 ml of ether is used? (c) How much iodine is left in the water layer if the extraction in (b) is followed by a second extraction, again using 3 ml of ether? (d) Which method is more efficient, a single large washing or repeated small washing?

2. A solution that contains a valuable material M in water

7. In order to extract acetic acid from dilute aqueous

is recovered from the solution using solvent S. If 9 kg is

solution with isopropyl ether, the two immiscible phases

used per kg of solution and the distribution equilibrium is

are passed counter currently through a packed column 3

X/Z = 3, where X = kg M per kg water and Z = kg M per kg

m in length and 75 mm in diameter.

S. Calculate the % M that will remain in the solution after

It is found that, if 0.5 kg/m2 s of the pure ether is used to

solvent extraction using

extract 0.25 kg/m2s of 4.0 percent acid by mass, then the

(a) single batch equilibrium stage

ether phase leaves the column with a concentration of 1.0

(b) two successive batch equilibrium stage using fresh

percent acid by mass.

solvent for each step

The equilibrium relationship is given by:

(kg acid/kg isopropyl ether) = 0.3 (kg acid/kg water). Calculate: (a) The log mean driving force (b) The number of overall transfer units based on the raffinate phase (c) The overall extraction coefficient based on the raffinate phase 8. 30 kg benzoic acid in 100 L of water is extracted with 35 liters of toluene. If a 3-stage counter current extraction

Calculate the product flow rate ES and the composition

system is used, calculate the weight of solute that will

YOUT.

remain in the raffinate. The distribution coefficient, K is 4.

12. An aqueous solution containing 1.5 kmol X / m 3 is fed

9. A liquid mixture of acetaldehyde and toluene contains 8

at 36 ml/s to the top of the column of height 1.60 m and

lb of acetaldehyde and 90 lb of toluene. Part of the

cross sectional area of 0.0045 m 2 and it leaves at the

acetaldehyde in this solution is to be extracted using pure

bottom with 1.4 kmol / m3. An organic solvent containing

water as the extracting agent. The extraction is to be

0.006 kmol X / m3 flows counter to the aqueous phase at 9

performed in two stages, using 25 lb of fresh water for

ml/s. The equilibrium relationship is given by: C X organic =

each stage. The raffinate layer from the first stage is

0.3 CX aqueous. Calculate:

treated by fresh water in the second stage. The extraction

(a) The log mean concentration difference for the transfer.

takes place at 170C and the equilibrium equation Y=2.2X

(b) the overall volumetric transfer coefficient based on the

may be employed. Assuming toluene and water is

organic phase.

immiscible, what would be the weight percent of

(c) the height of transfer unit.

acetaldehyde in a mixture of the extracts from both stage if each of the extraction were theoretically perfect?

DISTILLATION

10. To plan a liquid–liquid extraction we need to know the

1. Determine the mass percentage of carbon tetrachloride

solute’s distribution ratio between the two phases. One

(P0 = 114.5 torr) in the vapor phase at equilibrium in a 1:1

approach is to carry out the extraction on a solution

mole ideal solution with trichloromethane (P 0 = 199.1 torr)

containing a known amount of solute. After extracting the

at 25 0C.

solution, we isolate the organic phase and allow it to

2. A 537 kg solution of 50% wt heptane and 50% wt octane

evaporate, leaving behind the solute. In one such

is batch-distilled until only 4.74 lbmols remain in the still.

experiment, 1.235 g of a solute with a molar mass of 117.3

Assuming α=2.0, what will be the octane concentration of

g/mol is dissolved in 10.00 mL of water. After extracting

the residue by weight?

with 5.00 mL of toluene, 0.889 g of the solute is recovered

3. Determine the relative volatility of n-butane/n-pentane

in the organic phase. How many extractions will we need

mixture at 300C and 1 atm abs .

to recover 99.9% of the solute?

4. One hundred mols of 15% by mole n-butane/n-pentane

11. A feed (F) containing a solute is contacted with a

mixture is distilled until the residual liquid contains 45.5

solvent (S) in an ideal stage shown in the diagram below.

mols. Using the value of the relative volatility obtained in

Only the soluble transfers into the solvent. The flow rates

problem no. 3, find the average concentration of the

of all the streams are shown on a solute free basis and

distillate in mol% butane.

indicated by the subscript S. The compositions of the

5. A mixture of 60 mole % A and 40 mol % B is subject to

streams are expressed on a mole ratio basis. The extract

flash distillation at a separator pressure of 1 atm. The

leaving the contactor is divided into two equal parts, one

relative volatility of A with respect to B is constant 3. What

part is collected as the product and the other stream is

fraction of the feed must be vaporized to have the

recycled to join the solvent. The equilibrium relationship is

composition of the vapor leaving the separator be 75 mol

Y*=2X.

% A? 6. A liquid mixture containing 55% benzene and 45% toluene by weight is fed to a fractionating column at a rate of 1000 kg/h. The concentration of benzene in the distillate and the bottoms are 92% and 6% by weight, respectively. (a) If the reflux ratio is 2, determine the amount of vapor in the top section of the column.

(b) What percentage of toluene from the feed goes to the bottoms product? (c) If the relative volatility between benzene and toluene is assumed to be constant at α = 3, what is the minimum number of stages required to achieve the desired separation? 7. It is desired to produce an overhead product containing 80 mol% benzene from a feed mixture of 68 mol% benzene and 32 mol% toluene. If the mixture is subjected to equilibrium distillation at 1 atm, what is the fraction of the liquid that is vaporized? 8. Calculate the composition of the vapor in equilibrium with a liquid mixture of benzene, toluene, and water at 83.2 0C and absolute pressure of 1 atm. Assume that Dalton’s law applies to the benzene and toluene and that these compounds are insoluble in water. 9. A vessel contains a liquid mixture of 50% benzene and 50% toluene by weight at 1000 C. Calculate the average molecular weight of the vapor in contact with the solution. 10. A mixture containing 60 mol% benzene and 40 mol% toluene is fed to a distillation column at its dew point in order to be separated into a liquid distillate and a liquid bottoms product of 95 mol% and 5 mol% benzene, respectively. The distillation is operated at a pressure P where the relative volatility can be assumed at a value of 2.48. If the McCabe-Thiele assumptions can be applied for the system, determine the reflux ratio for the infinite number of stages.