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• Zeny Naranjo

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DISTILLATION SAMPLE PROBLEMS

(i) % A in D 38.3 / 60 x 100

(ii) %A in B

Sample Problem No. 1: An equimolal mixture of benzene and toluene is subjected to a simple batch distillation at atmospheric pressure. For the purpose of this problem, assume α = 2.55.

11.7 / 40 x 100

(iii) For DA / A1

38.3 / 50 x 100

a. If the distillation is discontinued when the mols of distillate amount to 60% of the mols charged, calculate:

= 63.9%

= 29.3%

= 76.6%

i. The concentration of the distillate. ii. The concentration of the liquid left in the still. iii. The amount of benzene in the distillate, expressed as percentage of the amount of benzene in the charge. b. If the distillation be discontinued when 60% of the original is in the distillate, calculate: i. The concentration of the distillate. ii. The concentration of the liquid left in the still. iii. The mols of distillate, expressed as percentage of the mols of the charge.

DA = 50 x 0.60 = 30 mol A2 = 50 - 30

= 20 mol

log 50 = 2.55 log 50 20 B2 = 34.90

B2

W = A2 + B2 = 20 + 34.90 = 54.90 mol

Solution: (a)

(b)

A1 = 50 mol

B1 = 50 mol

D = 100 x 0.6 = 60 mol

B = F - D = 100 - 60 = 40 mol

D = 100 - 54.90 = 45.1 mol (i) % A in D 30 / 45.1 x 100

= 66.6%

A2 + B2 = 40 A2 = 40 - B2

(ii) %A in B 20 / 54.9 x 100

log A1 = αAB log B1 log

A2

50

= 36.42%

B2

= 2.55 log 50

40 – B2

B2 = 28.3

A2 = 40 - 28.3 = 11.7

DA = 50 - 11.7 = 38.3 DB = 50 - 28.3 = 21.7

B2

(iii) For D / F 45.1 / 100 x 100

= 45.1%

Sample Problem No. 2: From a still containing 156 lbs of benzene and 736 lbs of toluene, distillation is carried out until the boiling point of the residue has risen to 106 0C. Calculate the pounds of benzene and toluene in the distillate and residue.

At 1060C: ``

x2 =

A2

= 0.09

A2 + B2

A2 = 0.09 A2 + 0.09 B2

Solution:

B2 = 10.11 A2

lbmol C6H6 = 156 / 78 = 2 lbmol C7H8 = 736 / 92 = 8

log 2 = 2.57 log

F = 2 + 8 = 10

A2 = 0.44

A2

8

10.11A2

B2 = 10.11 x 0.44 = 4.45

Feed Composition: xA = 2 / 10 = 0.2

Residue:

xB = 8 / 10 = 0.8

lbmol C6H6 = 0.44 x 78

= 34.32 lb

lbmol C7H8 = 4.45 x 92

= 409.4 lb

Using Temperature-Concentration Diagram: At xA = 0.2

Boiling point = 102 C 0

Residue: At 1020C: yA = 0.38 yB = 0.62

αAB1 = yA xB = 0.38 x 0.60 = 2.45 yB xA

lbmol C6H6 = 156 - 34.32

= 121.68 lb

lbmol C7H8 = 736 - 409.4

= 326.6 lb

0.62 x 0.20

At 1060C: xA = 0.09

xB = 0.91

yA = 0.21

yB = 0.79

αAB1 = yA xB = 0.21 x 0.91 = 2.65 yB xA

0.79 x 0.09

αAB = 2.45 + 2.65 = 2.57 2

Sample Problem No. 3: Glycerin is steam distilled at 182 0C under a 26 inch vacuum. A test shows a steam consumption 1 lb/lb of glycerine distilled. What percentage excess steam referred to that theoretically needed is actually used? Data: Vapor pressure of glycerine at 1820F is 21 mmHg. Solution: mw of glycerine, C3H8O3 = 92 P = 26 inHg vac P = (29.92 - 26) = 3.92 in Hg = 99.57 mmHg

log A1 = αAB log B1 A2

B2

PB0 = 21 mmHg

PS = 99.57 - 21 = 78.57

QUESTIONS AND PROBLEMS

WS = PS x mwS = 78.57 x 18 = 0.7320 WB

PB0 x mwB

21 x 92

1.

% excess = 1 - 0.7320 x 100

In _distillation the vapor generated by boiling the liquid withdrawn from contact with liquid and condensed as fast as it is formed.

0.7320 % excess = 36.6% 2.

Sample Problem No. 4: The HETP of a certain packed tower may be taken as 8 inches. A binary mixture with a constant relative volatility of 1.120 is to be separated in this unit. The tower is used as an enriching section, and the liquid concentration of the more volatile component in the still pot is maintained at a mole fraction of 0.15. If the tower is packed to a height of 15 ft, what is the maximum composition of distillate obtainable under any conditions?

3.

a. multi-staged

c. fractional

b. differential

d. flash

In binary distillation, the first component to condense in the distillate flask will be a. the one with the lower melting point

c. the one with the higher melting point

b. the one with the lower boiling point

d. the one with the lower boiling point

A distillation column separates 10000 kg/hr of a benzene-toluene mixture as shown in the figure below. In the figure xF, xD and xW represent the weight fraction of benzene in the feed, distillate and residue respectively. The reflux ratio is a. 0.5

b. 1.0

Solution:

c. 0.6 d.2.0

HETP = 8 inches = 0.6667 ft N =

z HETP

=

15

= 22.5

0.6667

Using Frenske Equation: N = log

xD x (1 – xW)

xW x (1 – xD) logαAVE

= log

xD x (1 – 0.15)

= 22.5

0.15 x (1 – xD) log 1.12

xD = 0.71

4.

5.

When the feed to the rectifying column is a saturated liquid, the feed line is a. Vertical

c. Horizontal

b. Inclined to the left

d. Inclined to the right

It separates volatile compounds from non-volatile compounds or volatiles with boiling points that are greater than 25 OC apart a. Simple Distillation

c. Fractional Distillation

b. Vacuum Distillation

d. Steam Distillation

6.

A liquid mixture containing 30.0 mole% benzene (B), 25.0% toluene (T), and the balance xylene (X) is fed to a

13. A mixture containing 0.53 mole fraction A and 0.47 mole fraction B is subjected to a simple batch distillation

distillation column. The bottom product contains 98.0 mole% X and no B, and 96.0% of the X in the feed is

until instantaneous composition of the vapors leaving becomes 0.50 mole fraction A. If the relative volatility of

recovered in this stream. The overhead product is fed to a second distillation column. The overhead product

A with respect to B is 3.2, what is the average composition of the total distillate collected?

from the second column contains 97.0% of the B in the feed to this column. The composition of this stream is

a. 0.78

c. 0.24

94.0 mole% B and the balance T. What will be the percent recovery B?

b. 0.34

d. 0.68

a. 97%

c. 87%

b. 89%

d. 50%

14. Overall efficiency of the distillation column is a. the ratio of number of actual plates to ideal plates.

7.

Fractional distillation gives a better separation that simple distillation because _.

b. always more than the point efficiency.

a. more fractionating column used in fractional distillation contains more theoretical plates

c. the ratio of number of ideal plates to actual plates.

b. more frationating column used in fractional distillation contains less theoretical plates

d. same as the Murphree efficiency.

c. does not require as much as better because heat as simple distillation d. simple distillation is better because it requires less glassware. 8.

9.

For distillation purposes it is more convenient to plot y against x at a _, a. constant temperature

c. constant pressure

b. constant enthalpy

d. constant reaction rate

Is the separation and purification of liquid substances utilizing differences in boiling point a. centrifugation

c. distillation

b. sedimentation

d. screening

15. Frenske equation determines the a. maximum number of ideal plates.

c. height of the distillation column.

b. minimum number of theoretical plates.

d. optimum reflux ratio.

16. Total reflux in a distillation operation requires minimum a. reboiler load

c. condenser load

b. number of plates

d. all (a), (b) and (c)

For numbers 17 to 18: A liquid under pressure containing 50 mole percent benzene and 50 mole percent toluene is continuously

10. Distillation works by the application and removal of heat to exploit differences in,

throttled to a pressure of 1 atm. The temperature after throttling is found to be 96.5 0F. The average molal heat

a. density

c. vapor pressure

capacity of the liquid is 36 g-cal/mmol- 0C and the latent heat of vaporization of the liquid at 96.6 0C may be

b. viscosity

d. relative volatility

taken as 7100 g-cal/mmol. Assume adiabatic operation of the throttling valve, and that no heat is conducted across the valve. Neglect kinetic energy changes.

11. In distillation column design, the McCabe-Thiele procedure is inadequate and a Ponchon-Savarit procedure is needed when,

17. What percent of the mixture is vapour after the throttle valve?

a. Saturated feed is not used

a. 53%

c. 61%

b. A total condenser is used

b. 72%

d. 58%

c. The latent heats of vaporization of the more and less volatile components are greatly different d. An azeotrope forms

18. If the pressure before throttling was sufficiently high so that no vapour was present, what was the temperature of this liquid before throttling?

12. For a fixed number of ideal stages in a distillation column, as the reflux ratio is increased, the difference in composition between the top and bottom product streams, a. increases

c. remains unaffected

b. decreases

d. passes through a maximum

a. 2450C

c. 2300C

b. 216 C

d. 2510C

0

19. Calculate the composition of the vapor in equilibrium with a liquid mixture of benzene, toluene, and water at

26. For a binary mixture distillation process, the degree of freedom is 2. However, if the pressure is fixed in this

83.2 C and absolute pressure of 1 atm. Assume that Dalton’s law applies to the benzene and toluene and that

process, the number of independent variables in this process will be

these compounds are insoluble in water.

a. 1

c. 0

a. H2O – 53.2%, C6H6 – 7.25% and C7H8 – 39.55%

b. 2

d. 3

0

b. H2O – 7.25%, C6H6 – 53.2% and C7H8 – 39.55% c. H2O – 53.2%, C6H6 – 39.55% and C7H8 – 7.25%

27. A 100 API of 500 molecular weight is being withdrawn from the bottom of a still, where it is being stripped

d. H2O – 7.25%, C6H6 – 39.55% and C7H8 – 53.2%

with a steam at atmospheric pressure. The charge to this still contains 1% by liquid volume of a light hydrocarbon, which may be assumed to be n-heptane. The stripped product contains 0.1% by liquid volume of

For numbers 20 to 23:

the light hydrocarbon. The steam is admitted through a spider, which is located below the surface of the

An equimolal mixture of ethyl benzene and water exists in the vapor phase at 80 C and 200 mmHg absolute

liquid. The vapor pressure of the liquid phase in the still is entirely the result of the light hydrocarbon. The

in a closed vessel. Assume isothermal conditions are maintained while mixture is being compressed by means

distillation is carried out at 450 0F. How much steam in pound per hour is required if 2000 bbl/day of stripped

of a suitable piston, and that any liquid formed is well mixed with the remaining vapor. If ethyl benzene and

product is eliminated?

water are essentially immiscible with each other

a. 120

c. 680

b. 460

d. 540

0

20. The pressure at which condensation begins. a. 292 mmHg

c. 250 mmHg

b. 235 mmHg

d. 246 mmHg

For numbers 28 to 29: 100 gal/hr turpentine are to be steam distilled at 96 0F at atmospheric pressure. The latent heat of vaporization of turpentine is 74 cal/g. Its specific gravity is 0.865. No external heat is supplied.

21. The composition of the first vapor drop of condensate is a. 0 % ethyl benzene

c. 90% ethyl benzene

b. 50% ethyl benzene

d. 100% ethyl benzene

28. Calculate the amount of carrier steam per turpentine distilled a. 0.50

c. 0.80

b. 0.65

d. 0.75

22. The composition of the vapor if 30% is condensed is a. 25.7% ethyl benzene

c. 28.6% ethyl benzene

b. 74.3% ethyl benzene

d. 71.4% ethyl benzene

23. The composition of the last drop of liquid condensed is a. 25.7% ethyl benzene

c. 28.6% ethyl benzene

b. 74.3% ethyl benzene

d. 71.4% ethyl benzene

24. Nitrobenzene (boiling point = 210.6°C) is steam distilled at 1 atm pressure. Nitrobenzene will distill off _ °C. a. at < 100

c. at > 210.6

b. between 100 and 210

d. one of these

25. In a binary distillation column, if the feed contains 40 mole % vapor, the q line will have a slope of a.1.5

c.-0.6

b. -1.5

d.0.6

29. How much steam at 5 psig will be used per hour? Neglect heat required to heat up the charge, and heat lost by radiation? a. 198.5 lb/hr

c. 632.5 lb/hr

b. 337.5 lb/hr

d. 486.5 lb/hr

30. For a binary mixture with low relative volatility, a. use steam distillation.

c. use molecular distillation.

b. use high pressure distillation.

d. an azeotrope may be formed during distillation.

ANSWERS

ADDITIONAL PROBLEMS

1.

b

16. b

2.

b

17. c

3.

c

18. b

4.

a

19. a

5.

a

20. d

6.

a

21. d

7.

a

22. c

8.

c

23. a

9.

c

24. a

10. d

25. b

11. c

26. a

12. a

27. d

13. d

28. d

14. c

29. c

15. b

30. d

For numbers 1 to 3: A mixture of 100 kg mol which contains 60 mol% n-pentane (A) and 40 mol% n-heptane (B) is vaporized at 101.32 kPa pressure under differential conditions until 40 kg mol are distilled. 1.

2.

3.

What is the average composition of the total vapor distilled? a. 0.501

c. 0.510

b. 0.450

d. 0.540

What is the composition of the remaining liquid? a. 0.501

c. 0.510

b. 0.892

d. 0.829

If the same vaporization is done in an equilibrium or flash distillation and 40 kg mol are distilled, what is the composition of the vapor distilled? a. 0.405

c. 0.430

b. 0.450

d. 0.403

For numbers 4 to 5: Four hundred and fifty lbmol/h (204 kmol/h) of a mixture of 60mol % benzene (LK) and 40 mol% toluene (HK) is to be separated into a liquid distillate and a liquid bottoms of 95 mol% and 5 mol% benzene, respectively. The feed enters the column with a molar percent vaporization equal to the distillate to feed ratio. 1 atm (101.3 kPa) 4.

5.

6.

What will be the Nmin? a. 6.7

c. 7.2

b. 5.6

d. 7.6

What will be the Rmin? a. 3.24

c. 2.35

b. 1.22

d. 7.89

A mixture of water and ethyl alcohol containing 0.16 mole fraction alcohol is continuously distilled in a plate fractionating column to give a product containing 0.77 mole fraction alcohol and a waste of 0.02 mole fraction alcohol. It is proposed to withdraw 25 per cent of the alcohol in the entering stream as a side stream containing 0.50 mole fraction of alcohol. Determine the number of theoretical plates required. a. 5 plates

c. 7 plates

b. 8 plates

d. plates

7.

A batch fractionation is carried out in a small column which has the separating power of 6 theoretical plates. The mixture consists of benzene and toluene containing 0.60 mole fraction of benzene. A distillate is required, of constant composition, of 0.98 mole fraction benzene, and the operation is discontinued when 83 per cent of the benzene charged has been removed as distillate. Estimate the reflux ratio needed at the start and finish of the distillation, if the relative volatility of benzene to toluene is 2.46. a. 1.3; 30

c. 1.5; 31

b. 1.7; 32

d. 1.9; 33

For number 8 to 10: Methyl and ethyl alcohols form substantially ideal liquid solutions. The normal boiling point of methanol is 64.7°C and for ethanol is 78.4°C. At 70°C, the vapor pressure of methanol is 1.22 atm and the vapor pressure of ethanol is 542.5 mmHg. 8.

What is the mole fraction y of the volatile component in the vapor phase when liquid-vapor mixture of these two compounds are in equilibrium at 70°C?

9.

a. 0.456

c. 0.565

b. 0.621

d. 0.689

What is the relative volatility of more volatile component in a two-component ideal system in terms of the vapor pressure of the components? a. 1.04

c. 1.71

b. 1.77

d. 1.81

10. What is the relative volatility of methanol with ethanol at 64.7 0C? a. 1.04

c. 1.71

b. 1.77

d. 1.81