DISTILLATION
(b)
SAMPLE PROBLEMS
DA = 50 x 0.60 = 30 mol
A2 = 50 - 30 = 20 mol
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.
log 50 = 2.55 log 50
20
B2
B2 = 34.90
a. If the distillation is discontinued when the mols of distillate amount to 60% of the mols charged,
calculate:
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.
W = A2 + B2 = 20 + 34.90 = 54.90 mol
D = 100 - 54.90 = 45.1 mol
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.
Solution:
(a)
A1 = 50 mol
B1 = 50 mol
D = 100 x 0.6 = 60 mol
B = F - D = 100 - 60 = 40 mol
A2 + B2 = 40
A2 = 40 - B2
log A1 = αAB log B1
A2
B2
log
50
= 2.55 log 50
40 – B2
B2
B2 = 28.3
A2 = 40 - 28.3 = 11.7
DA = 50 - 11.7 = 38.3
DB = 50 - 28.3 = 21.7
(i) % A in D
38.3 / 60 x 100
(ii) %A in B
11.7 / 40 x 100
(iii) For DA / A1
38.3 / 50 x 100
(i) % A in D
30 / 45.1 x 100
(ii) %A in B
20 / 54.9 x 100
(iii) For D / F
45.1 / 100 x 100
= 66.6%
=
36.42%
= 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.
Solution:
lbmol C6H6 = 156 / 78 = 2
lbmol C7H8 = 736 / 92 = 8
F = 2 + 8 = 10
Feed Composition:
xA = 2 / 10 = 0.2
xB = 8 / 10 = 0.8
= 63.9%
Using Temperature-Concentration Diagram:
At xA = 0.2
Boiling point = 1020C
= 29.3%
At 1020C:
yA = 0.38
yB = 0.62
= 76.6%
αAB1
= yA xB
yB xA
= 0.38 x 0.60 = 2.45
0.62 x 0.20
At 1060C:
xA = 0.09
yA = 0.21
αAB1
= yA xB
yB xA
PB0 = 21 mmHg
PS = 99.57 - 21 = 78.57
WS = PS x mwS = 78.57 x 18 = 0.7320
WB
PB0 x mwB
21 x 92
xB = 0.91
yB = 0.79
% excess = 1 - 0.7320 x 100
0.7320
= 0.21 x 0.91 = 2.65
0.79 x 0.09
% excess = 36.6%
αAB
=
2.45 + 2.65 = 2.57
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?
log A1 = αAB log B1
A2
B2
At 1060C:
x2 =
A2
= 0.09
``
A 2 + B2
A2 = 0.09 A2 + 0.09 B2
B2 = 10.11 A2
Solution:
HETP = 8 inches = 0.6667 ft
N = z
=
15
= 22.5
HETP 0.6667
log 2 = 2.57 log 8
A2
10.11A2
A2 = 0.44
B2 = 10.11 x 0.44 = 4.45
Residue:
lbmol C6H6 = 0.44 x 78
Using Frenske Equation:
N = log
xD x (1 – xW)
xW x (1 – xD)
logαAVE
= log
xD x (1 – 0.15)
0.15 x (1 – xD)
log 1.12
= 22.5
= 34.32 lb
xD = 0.71
lbmol C7H8 = 4.45 x 92
= 409.4 lb
Residue:
lbmol C6H6 = 156 - 34.32
lbmol C7H8 = 736 - 409.4
= 121.68 lb
= 326.6 lb
Sample Problem No. 3:
Glycerin is steam distilled at 1820C 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.
QUESTIONS AND PROBLEMS
1.
In _distillation the vapor generated by boiling the liquid withdrawn from contact with liquid and
condensed as fast as it is formed.
a. multi-staged
c. fractional
b. differential
d. flash
2.
In binary distillation, the first component to condense in the distillate flask will be
Solution:
mw of glycerine, C3H8O3 = 92
P = 26 inHg vac
P = (29.92 - 26) = 3.92 in Hg = 99.57 mmHg
a. the one with the lower melting point
b. the one with the lower boiling point
3.
c. the one with the higher melting 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
c. 0.6
b. 1.0
d.2.0
b. sedimentation
d. screening
10. Distillation works by the application and removal of heat to exploit differences in,
a. density
c. vapor pressure
b. viscosity
d. relative volatility
11. In distillation column design, the McCabe-Thiele procedure is inadequate and a Ponchon-Savarit
procedure is needed when,
a. Saturated feed is not used
b. A total condenser is used
c. The latent heats of vaporization of the more and less volatile components are greatly different
d. An azeotrope forms
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
4.
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
5.
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
A liquid mixture containing 30.0 mole% benzene (B), 25.0% toluene (T), and the balance xylene (X) is
fed to a distillation column. The bottom product contains 98.0 mole% X and no B, and 96.0% of the X
in the feed is recovered in this stream. The overhead product is fed to a second distillation column.
The overhead product from the second column contains 97.0% of the B in the feed to this column.
The composition of this stream is 94.0 mole% B and the balance T. What will be the percent recovery
B?
a. 97%
c. 87%
b. 89%
d. 50%
6.
7.
Fractional distillation gives a better separation that simple distillation because _.
a. more fractionating column used in fractional distillation contains more theoretical plates
b. more frationating column used in fractional distillation contains less theoretical plates
c. does not require as much as better because heat as simple distillation
d. simple distillation is better because it requires less glassware.
8.
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
9.
Is the separation and purification of liquid substances utilizing differences in boiling point
a. centrifugation
c. distillation
13. A mixture containing 0.53 mole fraction A and 0.47 mole fraction B is subjected to a simple batch
distillation until instantaneous composition of the vapors leaving becomes 0.50 mole fraction A. If the
relative volatility of A with respect to B is 3.2, what is the average composition of the total distillate
collected?
a. 0.78
c. 0.24
b. 0.34
d. 0.68
14. Overall efficiency of the distillation column is
a. the ratio of number of actual plates to ideal plates.
b. always more than the point efficiency.
c. the ratio of number of ideal plates to actual plates.
d. same as the Murphree efficiency.
15. Frenske equation determines the
a. maximum number of ideal plates.
b. minimum number of theoretical plates.
c. height of the distillation column.
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 throttled to a pressure of 1 atm. The temperature after throttling is found to be 96.5 0F.
The average molal heat 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 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.
17. What percent of the mixture is vapour after the throttle valve?
a. 53%
c. 61%
b. 72%
d. 58%
18. If the pressure before throttling was sufficiently high so that no vapour was present, what was the
temperature of this liquid before throttling?
a. 2450C
c. 2300C
0
b. 216 C
d. 2510C
19. 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.
a. H2O – 53.2%, C6H6 – 7.25% and C7H8 – 39.55%
b. H2O – 7.25%, C6H6 – 53.2% and C7H8 – 39.55%
c. H2O – 53.2%, C6H6 – 39.55% and C7H8 – 7.25%
d. H2O – 7.25%, C6H6 – 39.55% and C7H8 – 53.2%
For numbers 20 to 23:
An equimolal mixture of ethyl benzene and water exists in the vapor phase at 80 0C and 200 mmHg
absolute in a closed vessel. Assume isothermal conditions are maintained while mixture is being
compressed by means of a suitable piston, and that any liquid formed is well mixed with the remaining
vapor. If ethyl benzene and water are essentially immiscible with each other
20. The pressure at which condensation begins.
a. 292 mmHg
b. 235 mmHg
c. 250 mmHg
d. 246 mmHg
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
22. The composition of the vapor if 30% is condensed is
a. 25.7% ethyl benzene
b. 74.3% ethyl benzene
27. A 100 API of 500 molecular weight is being withdrawn from the bottom of a still, where it is being
stripped 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 the light hydrocarbon. The steam is admitted through a spider, which is located below
the surface of the liquid. The vapor pressure of the liquid phase in the still is entirely the result of the
light hydrocarbon. The distillation is carried out at 450 0F. How much steam in pound per hour is
required if 2000 bbl/day of stripped product is eliminated?
a. 120
c. 680
b. 460
d. 540
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.
28. Calculate the amount of carrier steam per turpentine distilled
a. 0.50
c. 0.80
b. 0.65
d. 0.75
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.
c. 28.6% 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
26. For a binary mixture distillation process, the degree of freedom is 2. However, if the pressure is fixed
in this process, the number of independent variables in this process will be
a. 1
c. 0
b. 2
d. 3
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
b
b
c
a
a
a
a
c
c
d
c
a
d
c
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
b
c
b
a
d
d
c
a
a
b
a
d
d
c
15. b
30. d
a. 3.24
b. 1.22
6.
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.
ADDITIONAL PROBLEMS
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.
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
3.
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.
What will be the Nmin?
a. 6.7
b. 5.6
What will be the Rmin?
c. 2.35
d. 7.89
c. 7.2
d. 7.6
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?
a. 0.456
c. 0.565
b. 0.621
d. 0.689
9.
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 64.70C?
a. 1.04
c. 1.71
b. 1.77
d. 1.81