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Separation Process Principles

J. D. Seader, Ernest J. Henley

Chapter 7

Distillation of Binary Mixtures - all with Video Answers

Educators

Chapter Questions

01:38

Problem 1

List as many differences between absorption and distillation
as you can. List as many differences between stripping and distillation as you can

Adriano Chikande
Adriano Chikande
Numerade Educator
02:32

Problem 2

Prior to the 1980s, packed columns were rarely used for distillation unless column diameter was less than 2.5 ft. Explain why,
in recent years, some existing trayed towers are being retrofitted
With packing and some new large-diameter columns are being
designed for packing rather than trays.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
01:18

Problem 3

A mixture of methane and ethane is to be separated by distillation. Explain why water cannot be used as the coolant in the
condenser. What would you choose as the coolant?

Will Li
Will Li
Numerade Educator
01:46

Problem 4

A mixture of ethylene and ethane is to be separated by distillation. Determine the maximum operating pressure of the column.
What operating pressure would you suggest? Why?

Eileen Sullivan
Eileen Sullivan
Numerade Educator
02:44

Problem 5

Under what circumstances would it be advisable to conduct
laboratory or pilot-plant tests of a proposed distillation separation?

AM
Andrew Macphail
Numerade Educator
02:04

Problem 6

Explain why an economic tradeoff exists between the number
of trays and the reflux ratio.

Daniel Cisneros
Daniel Cisneros
Numerade Educator
07:29

Problem 7

Following the development by Sore1 in 1894 of a mathematical model for continuous, steady-state, equilibrium-stage distillation, a number of methods were proposed for solving the
equations graphically or algebraically during an 18-year period
from 1920 to 1938, prior to the availability of digital computers.
Today, the only method from that era that remains in widespread
use is the McCabe-Thiele method. What are the attributes of this
method that are responsible for its continuing popularity?

Chareen Guzman
Chareen Guzman
Numerade Educator
04:14

Problem 8

(a) For the cascade shown in Figure 7.39a, calculate the compositions of streams V4 and L1. Assume atmospheric pressure, saturated liquid and vapor feeds, and the vapor-liquid equilibrium data
given below. Compositions are in mole percent.
(b) Given the feed compositions in cascade (a), how many equilibrium stages are required to produce a V4 containing 85 mol%
alcohol?
(c) For the cascade configuration shown in Figure 7.39b, with
D = 50 mol, what are the compositions of D and L,?
(d) For the configuration of cascade (b), how many equilibrium
stages are required to produce a D of 50 mol% alcohol?
EQUILIBRIUM DATA, MOLE-FRACTION ALCOHOL
x 0.1 0.3 0.5 0.7 0.9
y 0.2 0.5 0.68 0.82 0.94

Ronald Prasad
Ronald Prasad
Numerade Educator
02:47

Problem 9

Liquid air is fed to the top of a perforated-tray reboiled stripper operated at substantially atmospheric pressure. Sixty percent of
the oxygen in the feed is to be drawn off in the bottoms vapor product from the still. This product is to contain 0.2 mol% nitrogen.
Based on the assumptions and data given below, calculate:
(a) The mole percent of nitrogen in the vapor leaving the top plate.
(b) The moles of vapor generated in the still per 100 mol of feed.
(c) The number of theoretical plates required.
Notes: To simplify the problem, assume constant molar overflow equal to the moles of feed. Liquid air contains 20.9 mol%
of oxygen and 79.1 mol% of nitrogen. The equilibrium data [Chem.
Met. Eng., 35,622 (1928)l at atmospheric pressure are
Temperature, Mole-Percent N2 Mole-Percent N2
K in Liquid in Vapor
77.35 100.00 100.00
77.98 90.00 97.17
78.73 79.00 93.62
Temperature,
K
79.44
80.33
81.35
82.54
83.94
85.62
87.67
90.17
Mole-Percent Nz
in Liquid
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Mole-Percent Nz
in Vapor
90.31
85.91
80.46
73.50
64.05
50.81
3 1 .OO
0.00

Lottie Adams
Lottie Adams
Numerade Educator
06:33

Problem 10

A mixture of A (more volatile) and B is being separated in
plate distillation column. In two separate tests run with a saturate(
liquid feed of 40 mol% A, the following compositions, in mol% i
were obtained for samples of liquid and vapor streams from the
consecutive stages between the feed and total coildenser at the to1
Mol% A
Test 1 Test 2
Stage Vapor Liquid Vapor Liquid
M + 2 79.5 68.0 75.0 68.0
M+l 74.0 60.0 68.0 60.5
M 67.9 51.0 60.5 53.0
Determine the reflux ratio and overhead composition in

Lottie Adams
Lottie Adams
Numerade Educator
03:01

Problem 11

A saturated-liquid mixture containing 70 mol% benzene an
30 mol% toluene is to be distilled at atmospheric pressure to prc
duce a distillate of 80 mol% benzene. Five procedures, describe
below, are under consideration. For each of the procedures, calci
late and tabulate:
(a) Moles of distillate per 100 moles of feed,
(b) Moles of total vapor generated per mole of distillate,
(c) Mole percent benzene in the residue, and
(d) For each part, construct a y-x diagram. On this, indicate th
compositions of the overhead product, the reflux, and the composj
tion of the residue.
(e) If the objective is to maximize total benzene recovery, which, i
any, of these procedures is preferred?
Note: Assume that the relative volatility equals 2.5.
The procedures are as follows:
1. Continuous distillation followed by partial condensatior
The feed is sent to the direct-heated still pot, from which th
residue is continuously withdrawn. The vapors enter the to
of a helically coiled partial condenser that discharges intl
a trap. The liquid is returned (refluxed) to the still, whil
the residual vapor is condensed as a product containin,
80 mol% benzene. The molar ratio of reflux to product is 0.5
2. Continuous distillation in a column containing one equilib
rium plate. The feed is sent to the direct-heated still, fron
which residue is withdrawn continuously. The vapors fron
the plate enter the top of a helically coiled partial condense
that discharges into a trap. The liquid from the trap is re
turned to the plate, while the uncondensed vapor is con
densed to form a distillate containing 80 mol% benzene
The molar ratio of reflux to product is 0.5.
3. Continuous distillation in a column containing the equivalen
of two equilibrium plates. The feed is sent to the direct-heate(
still, from which residue is withdrawn continuously. The vapors from the top plate enter the top of a helically coiled
partial condenser that discharges into a trap. The liquid from
the trap is returned to the top plate (refluxed) while the uncondensed vapor is condensed to form a distillate containing 80
mol% benzene. The molar ratio of reflux to product is 0.5.
4. The operation is the same as that described for Procedure 3
with the exception that the liquid from the trap is retumed to
the bottom plate.
5. Continuous distillation in a column containing the equivalent of one equilibrium plate. The feed at its boiling point is
illtroduced on the plate. The residue is withdrawn continuously from the direct-heated still pot. The vapors from the
plate enter the top of a helically coiled partial condenser that
discharges into a trap. The liquid from the trap is returned to
the plate while the uncondensed vapor is condensed to form
a distillate containing 80 mol% benzene. The molar ratio of
reflux to product is 0.5.

Grigoriy Sereda
Grigoriy Sereda
Numerade Educator
01:23

Problem 12

A saturated-liquid mixture of benzene and toluene containing 50 mol% benzene is distillated in an apparatus consisting of a
still pot, one theoretical plate, and a total condenser. The still pot is
equivalent to one equilibrium stage, and the pressure is 101 kPa.
The still is supposed to produce a distillate containing 75 mol%
benzene. For each of the following procedures, calculate, if possible, the number of moles of distillate per 100 moles of feed.
Assume a relative volatility of 2.5.
(a) No reflux with feed to the still pot.
4: (b) Feed to the still pot, reflux ratio LID = 3. ' (c) Feed to the plate with a reflux ratio of 3.
(d) Feed to the plate with a reflux ratio of 3. However, in this case,
a partial condenser is employed.
(e) Part (b) using minimum reflux.
R (f) Part (b) using total reflux

Aadit Sharma
Aadit Sharma
Numerade Educator
02:50

Problem 13

A fractionation column operating at 101 kPa is to separate 30 kgh of a solution of benzene and toluene containing ' 0.6 mass-fraction toluene into an overhead product containing 0.97 mass-fraction benzene and a bottoms product containing " 0.98 mass-fraction toluene. A reflux ratio of 3.5 is to be used. The
r feed is liquid at its boiling point, feed is to the optimal tray, and
the reflux is at saturation temperature.
I (a) Determine the quantity of top and bottom products
(b) Determine the number of stages required.

Lottie Adams
Lottie Adams
Numerade Educator
04:10

Problem 14

A mixture of 54.5 mol% benzene in chlorobenzene at its
bubble point is fed continuously to the bottom plate of a column
containing two theoretical plates. The column is equipped with a
partial reboiler and a total condenser. Sufficient heat is supplied to
the reboiler to give V/F = 0.855, and the reflux ratio LIV in the
top of the column is kept constant at 0.50. Under these conditions,
what quality of product and bottoms (xD, xB) can be expected?
EQUILIBRIUM DATA AT COLUMN PRESSURE,
MOLE-FRACTION BENZENE
x 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800
Y 0.314 0.508 0.640 0.734 0.806 0.862 0.905 0.943

Mukesh Devi
Mukesh Devi
Numerade Educator
16:21

Problem 15

A continuous distillation operation with a reflux ratio (LID)
of 3.5 yields a distillate containing 97 wt% B (benzene) and
bottoms containing 98 wt% T (toluene). Due to weld failures, the
10 plates in the bottom section of the column are ruined, but the
14 upper plates are intact. It is suggested that the column still be
used, with the feed (F) as saturated vapor at the dew point, with
F = 13,600 kgh containing 40 wt% B and 60 wt% T. Assuming
that the plate efficiency remains unchanged at 50%: (a) Can this
column still yield a distillate containing 97 wt% B, (b) How much
distillate can we get, and (c) What will the composition of the
residue be in mole percent?
For vapor-liquid equilibrium data, see Exercise 7.13.

Chareen Guzman
Chareen Guzman
Numerade Educator
16:21

Problem 16

A distillation column having eight theoretical stages (seven
in the column + partial reboiler + total condenser) is being used to
separate 100 krnollh of a saturated-liquid feed containing 50 mol%
A into a product stream containing 90 mol% A. The liquid-to-vapor
molar ratio at the top plate is 0.75. The saturated-liquid feed is
introduced on plate 5 from the top. Determine: (a) The composition
of the bottoms, (b) The L/V ratio in the stripping section, and
(c) The moles of bottoms per hour.
Unbeknown to the operators, the bolts holding plates 5, 6, and 7
rust through, and the plates fall into the still pot. If no adjustments
are made, what is the new bottoms composition?
It is suggested that, instead of returning reflux to the top plate,
an equivalent amount of liquid product from another column be
used as reflux. If this product contains 80 mol% A, what now is the
composition of: (a) The distillate, and (b) The bottoms.
EQUILIBRIUM DATA, MOLE FRACTION OF A
y 0.19 0.37 0.5 0.62 0.71 0.78 0.84 0.9 0.96
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Chareen Guzman
Chareen Guzman
Numerade Educator
06:31

Problem 17

A distillation unit consists of a partial reboiler, a column with
seven equilibrium plates, and a total condenser. The feed consists of
a 50 mol% mixture of benzene in toluene. It is desired to produce a
distillate containing 96 mol% benzene, when operating at 101 kPa.
(a) With saturated-liquid feed fed to the fifth plate from the top,
calculate: (1) Minimum reflux ratio (LR/D),i,, (2) The bottoms
composition, using a reflux ratio (LR/D) of twice the nlinimuni, and
(3) Moles of product per 100 moles of feed.
(b) Repeat part (a) for a saturated-vapor feed fed to the fifth plate
from the top.
(c) With saturated-vapor feed fed to the reboiler and a reflux ratio
(LIV) of 0.9, calculate: (1) Bottoms composition, (2) Moles of
product per 100 mole of feed.
Equilibrium data are given in Exercise 7.13

Shazia Naz
Shazia Naz
Numerade Educator
06:33

Problem 18

A valve-tray fractionating column containing eight theoretical plates, a partial reboiler equivalent to one theoretical plate,
and a total condenser is in operation separating a benzene-toluene
mixture containing 36 mol% benzene at 101 kPa. Under normal
operating conditions, the reboiler generates 100 krnol of vapor per
hour. A request has been made for very pure toluene, and it is proposed to operate this column as a stripper, introducing the feed on
the top plate as a saturated liquid, employing the same boilup at the
still, and returning no reflux to the column. Equilibrium data are
given in Exercise 7.13.
(a) What is the minimum feed rate under the proposed conditions,
and what is the corresponding composition of the liquid in the
reboiler at the minimum feed?(b) At a feed rate 25% above the minimum, what is the rate of production of toluene, and what are the compositions in mole percent
of the product and distillate?

Lottie Adams
Lottie Adams
Numerade Educator
02:47

Problem 19

9 A solution of methanol and water at 101 kPa containing
50 mol% methanol is continuously rectified in a seven-theoreticalplate, perforated-tray column, equipped with a total condenser and
a partial reboiler heated by steam.
During normal operation, 100 kmoVh of feed is introduced on
the third plate from the bottom. The overhead product contains
90 mol% methanol, and the bottoms product contains 5 mol%
methanol. One mole of liquid reflux is returned to the column for
each mole of overhead product.
Recently it has been impossible to maintain the product purity
in spite of an increase in the reflux ratio. The following test data
were obtained:
I Stream kmoVh mol%alcohol
I Feed 100 51
I Waste 62 12
I
I Product 53 80
I Reflux 94 -
1,
What is the most probable cause of this poor performance?
I
; I What further tests would you make to establ~sh definitely the
I reason for the trouble? Could some 90% product be obtained by I further increasing the reflux ratlo, while keeping the vapor rate
I
I constant?
I I; Vapor-liquid equilibrium data at 1 atm [Chem. Eng. Prog. 48,
I 192 (1952)l in mole-fraction methanol

Lottie Adams
Lottie Adams
Numerade Educator
06:33

Problem 20

0 A fractionating column equipped with a partial reboiler
heated with steam, as shown in Figure 7.40, and with a total condenser, is operated continuously to separate a mixture of 50 mol%
A and 50 mol% B into an overhead product containing 90 mol% A
and a bottoms product containing 20 mol% A. The column has
three theoretical plates, and the reboiler is equivalent to one theoretical plate. When the system is operated at an LIV = 0.75 withthe feed as a saturated liquid to the bottom plate of the column, the 'desired products can be obtained. The system is instrumented as
shown. The steam to the reboiler is controlled by a flow controll
so that it remains constant. The reflux to the column is also on
flow controller so that the quantity of reflux is constant. The fee
to the column is normally 100 kmolth, but it was inadvertently c
back to 25 krnol/h. What would be the composition of the reflu
and what would be the composition of the vapor leaving th
reboiler under these new conditions? Assume that the vapor leavin
the reboiler is not superheated. Relative volatility for the syste
is 3.0.

Lottie Adams
Lottie Adams
Numerade Educator
03:24

Problem 21

A saturated-vapor mixture of maleic anhydride and ben
acid containing 10 mol% acid is a by-product of the manufac
of phthalic anhydride. This mixture is distilled continuou
13.3 kPa to give a product of 99.5 mol% maleic anhydride
bottoms of 0.5 mol% anhydride. Using the data below, calculate th
number of theoretical plates needed using an LID of 1.6 times t
minimum.
VAPOR PRESSURE, TORR: 4Temperature, "C: 10 50 100 200 400
Maleic anhydride 78.7 116.8 135.8 155.9 179.5
Benzoic acid 131.6 167.8 185.0 205.8 227

Crystal Wang
Crystal Wang
Numerade Educator
03:15

Problem 22

A bubble-point binary mixture containing 5 mol% A in B is
to be distilled to give a distillate containing 35 mol% A and a bottoms product containing 0.2 mol% A. If the relative volatility is
constant at a value of 6, calculate the following algebraically,
assuming that the column will be equipped with a partial reboiler
and a partial condenser.
(a) The minimum number of equilibrium stages
(b) The minimum boilup ratio V/B leaving the reboiler (c) The actual number of equilibrium stages for a boilup ratio
equal to 1.2 times the minimum value

Lottie Adams
Lottie Adams
Numerade Educator
04:05

Problem 23

Methanol (M) is to be separated from water (W) by distillation as shown in Figure 7.41. The feed is subcooled such that
q = 1.12. Determine the feed-stage location and the number of theoretical stages required. Vapor-liquid equilibrium data are given in
Exercise 7.19.

Md Mohibullah
Md Mohibullah
Auburn University Main Campus
07:54

Problem 24

A saturated-liquid mixture of 69.4 mol% benzene (B) in
toluene (T) is to be contilluously distilled at atmospheric pressure
to a distillate containing 90 mol% benzene, with a yield
of 25 moles of distillate per 100 moles of feed. The feed is sent to
, steamheated still (reboiler), where residue is to be withdrawn
continu~~~ly. The vapors from the still pass directly to a partial
condenser. From a liquid separator following the condenser, reflux
is returned to the still. Vapors from the separator, which are in equilibrium with the liquid reflux, are sent to a total condenser and are
continu~~~ly withdrawn as distillate. At equilibrium the mole ratio
ofB to T in the vapor may be taken as 2.5 times the mole ratio of B
to T in the liquid. Calculate analytically and graphically the total
moles of vapor generated in the still per 100 mol of feed.

Bhumika Jayee
Bhumika Jayee
Numerade Educator
06:33

Problem 25

A plant has a batch of 100 kmol of a liquid mixture containing 20 mol% benzene and 80 mol% chlorobenzene. It is desired
to rectify this mixture at 1 atm to obtain bottoms containing only
0.1 mol% benzene. The relative volatility may be assumed constant
at 4.13. There are available a suitable still to vaporize the feed, a
column containing the equivalent of four theoretical plates, a total
condenser, and a reflux drum to collect the condensed overhead.
The run is to be made at total reflux. While the steady state is being
approached, a finite amount of distillate is held in a reflux trap.
When the steady state is reached, the bottoms contain 0.1 mol%
benzene. With this apparatus, what yield of bottoms can be obtained? The liquid holdup in the column is negligible compared to
that in the still and in the reflux drum

Lottie Adams
Lottie Adams
Numerade Educator
01:18

Problem 26

A mixture of acetone and isopropanol containing 50 mol%
acetone is to be distilled continuously to produce an overhead product containing 80 mol% acetone and a bottoms containing 25 mol%
acetone. If a saturated-liquid feed is employed, if the column is
operated with a reflux ratio of 0.5, and if the Murphree vapor efficiency is 50%, how many trays will be required? Assume a total
condenser, partial reboiler, saturated-liquid reflux, and optimal feed
stage. The vapor-liquid equilibrium data for this system are
EQUILIBRIUM DATA, MOLE-PERCENT ACETONE
Liquid 0 2.6 5.4 11.7 20.7 29.7 34.1 44.0 52.0
Vapor 0 8.9 17.4 31.5 45.6 55.7 60.1 68.7 74.3
Liquid 63.9 74.6 80.3 86.5 90.2 92.5 95.7 100.0
Vapor 81.5 87.0 89.4 92.3 94.2 95.5 97.4 100.0

Aadit Sharma
Aadit Sharma
Numerade Educator
01:18

Problem 27

A mixture of 40 mol% carbon disulfide (CS2) in carbon
tetrachloride (CC4) is continuously distilled The feed is 50%
vaporized (q = 0.5). The top product from a total condenser is
95 mol% CS2, and the bottoms product from a partial reboiler is a
liquid of 5 mol% CS2.
The column operates with a reflux ratio, LID, of 4 to 1. The
Murphree vapor efficiency is 80%.
(a) Calculate graphically the minimum reflux, the minimum boilup
ratio from the reboiler, V/B, and the minimum number of stages
(including reboiler).
(b) How many trays are required for the actual column at 80% efficiency by the McCabe-Thiele method.
The vapor-liquid equilibrium data at column pressure for this
mixture in terms of CS2 mole fraction are
X0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Y 0.135 0.245 0.42 0.545 0.64 0.725 0.79 0.85 0.905 0.955

Aadit Sharma
Aadit Sharma
Numerade Educator
16:21

Problem 28

A distillation unit consists of a partial reboiler, a bubble-cap
column, and a total condenser. The overall plate efficiency is 65%.The feed is a liquid mixture, at its bubble point, consisting of
50 mol% benzene in toluene. This liquid is fed to the optimal plate.
The column is to produce a distillate containing 95 mol% benzene
and a bottoms of 95 mol% toluene. Calculate for an operating pressure of 1 atm: (a) Minimum reflux ratio (LID),,,, (b) Minimum
number of actual plates to carry out the desired separation,
(c) Using a reflux ratio (LID) of 50% more than the minimum, the
number of actual plates needed, (d) The kilograms per hour of
product and residue, if the feed is 907.3 kgh, (e) The saturated
steam at 273.7 kPa required in kilograms per hour for heat to the
reboiler using enthalpy data below and any assumptions necessary,
and (f) A rigorous enthalpy balance on the reboiler, using the
enthalpy data, tabulated below and assuming ideal solutions.
Enthalpies in Btu/lbmol at reboiler temperature:
h~ h v
benzene 4,900 18,130
toluene 8,080 21,830
Vapor-liquid equilibrium data are given in Exercise 7.13.

Chareen Guzman
Chareen Guzman
Numerade Educator
16:21

Problem 29

A continuous distillation unit, consisting of a perforated-tray
column together with a partial reboiler and a total condenser, is to
be designed to operate at atmospheric pressure to separate ethanol
and water. The feed, which is introduced into the column as liquid
at its bubble point, contains 20 mol% alcohol. The distillate is to
contain 85 mol% alcohol, and the alcohol recovery is to be 97%.
(a) What is the molar concentration of the bottoms?
(b) What is the minimum value of:
(1) The reflux ratio LlV?
(2) The reflux ratio LID?
(3) The boilup ratio V/B from the reboiler?
(c) What is the minimum number of theoretical stages and the
corresponding number of actual plates if the overall plate efficiency
is 55%?
(d) If the reflux ratio LlVused is 0.80, how many actual plates will
be required?
Vapor-liquid equilibrium for ethanol-water at 1 atm in terms of
mole fractions of ethanol are [Ind. Eng. Chem., 24, 881 (1932)

Chareen Guzman
Chareen Guzman
Numerade Educator
01:18

Problem 30

A solvent A is to be recovered by distillation from its water
solution. It is necessary to produce an overhead product containing
95 mol% A and to recover 95% of the A in the feed. The feed is
available at the plant site in two streams, one containing 40 mol%
A and the other 60 mol% A. Each stream will provide 50 kmollh of
component A, and each will be fed into the column as saturated liquid. Since the less volatile component is water, it has been proposed
to supply the necessary heat in the form of open steam. For the preliminary design, it has been suggested that the operating reflux
ratio, LID, be 1.33 times the minimum value. A total condenser will
be employed. For this system, it is estimated that the overall plateefficiency will be 70%. How many plates will be required, and
what will be the bottoms composition? The relative volatility may
be assumed to be constant at 3.0. Determine analytically the points
necessary to locate the operating lines. Each feed should enter the
column at its optimal location.

Aadit Sharma
Aadit Sharma
Numerade Educator
06:33

Problem 31

A saturated-liquid feed stream containing 40 mol% nhexane (H) and 60 mol% n-octane is fed to a plate column. A reflux
ratio LID equal to 0.5 is maintained at the top of the column. An
overhead product of 0.95 mole fraction H is required, and the column bottoms is to be 0.05 mole fraction H. A cooling coil submerged in the liquid of the second plate from the top removes sufficient heat to condense 50 mol% of the vapor rising from the third
plate down from the top.
(a) Derive the equations needed to locate the operating line.
(b) Locate the operating lines and determine the required number
of theoretical plates if the optimal feed plate location is used.

Lottie Adams
Lottie Adams
Numerade Educator
05:02

Problem 32

One hundred kilogram-moles per hour of a saturated liquid
mixture of 12 mol% ethyl alcohol in water is distilled continuously
by direct steam at 1 atm introduced directly to the bottom plate. The
dislillate required is 85 mol% alcohol, representing 90% recovery
of the alcohol in the feed. The reflux is saturated liquid with
LID = 3. Feed is on the optimal stage. Vapor-liquid equilibrium
data are given in Exercise 7.29. Calculate:
(a) Steam requirement, kmollh
(b) Number of theoretical stages
(c) The feed stage (optimal)
(d) Minimum reflux ratio, (L/D)min

Ronald Prasad
Ronald Prasad
Numerade Educator
06:20

Problem 33

A water-isopropanol mixture at its bubble point containing
10 mol% isopropanol is to be continuously rectified at atmospheric
pressure to produce a distillate containing 67.5 mol% isopropanol.
Ninety-eight percent of the isopropanol in the feed must be recovered. If a reflux ratio LID of 1.5 times the minimum is used, how
many theoretical stages will be required: (a) If a partial reboiler is
used? (b) If no reboiler is used and saturated steam at 101 kPa is introduced below the bottom plate? (c) How many stages are required
at total reflux?
Vapor-liquid equilibrium data in mole fraction of isopropanol at
101 kPa are
I; "C 93.00 84.02 82.12 81.25 80.62 80.16 80.28 81.51
y 0.2195 0.4620 0.5242 0.5686 0.5926 0.6821 0.7421 0.9160
x 0.0118 0.0841 0.1978 0.3496 0.4525 0.6794 0.7693 0.9442
Notes: Composition of the azeotrope is x = y = 0.6854. Boiling
point of azeotrope = 80.22"C

Chareen Guzman
Chareen Guzman
Numerade Educator
01:18

Problem 34

An aqueous solution containing 10 mol% isopropanol is fed
at its bubble point to the top of a continuous stripping column,
operated at atmospheric pressure, to produce a vapor containing
40 mol% isopropanol. Two procedures are under consideration,
both involving the same heat expenditure with V/F (moles of vapor
generatedlmole of feed) = 0.246 in each case. Scheme 1 uses a
partial reboiler at the bottom of a plate-type stripping column, generating vapor by the use of steam condensing inside a closed coil.
In Scheme 2, the reboiler is omitted and live steam is injected
directly below the bottom plate. Determine the number of stages
required in each case.
Equilibrium data for the system isopropanol-water are given in
Exercise 7.33. The usual simplifying assumptions may be made

Aadit Sharma
Aadit Sharma
Numerade Educator
04:02

Problem 35

Determine the optimal-stage location for each feed and the
number of theoretical stages required for the distillation separation
shown in Figure 7.42 using the following equilibrium data in mole
fractions.

David Collins
David Collins
Numerade Educator
01:38

Problem 36

Determine the number of theoretical stages required and the
optimal-stage locations for the feed and liquid side stream for the
distillation process shown in Figure 7.43 assuming that methanol (M)
and ethanol (E) form an ideal solution.

Nidhi Singhi
Nidhi Singhi
Numerade Educator
01:18

Problem 37

A mixture of n-heptane (H) and toluene (T) is separated by
extractive distillation with phenol (P). Distillation is then used to
recover the phenol for recycle as shown in Figure 7.44a, where the
small amount of n-heptane in the feed is ignored. For the conditions
shown in Figure 7.44a, determine the number of theoretical stages required. Note that heat will have to be supplied to the reboiler at a
high temperature because of the high boiling point of phenol.
Therefore, consider the alternative scheme in Figure 7.44b, where
an interreboiler, located midway between the bottom plate and
the feed stage, is used to provide 50% of the boilup used in Figure 7.44a. The remainder of the boilup is provided by the reboiler.
Determine the number of theoretical stages required for the case
with the interreboiler and the temperature of the interreboiler stage.
Unsmoothed vapor-liquid equilibrium data at 1 atm are [Trans.
AIChE, 41,555 (1945)l:

Aadit Sharma
Aadit Sharma
Numerade Educator
00:00

Problem 38

A distillation column for the separation of n-butane from
n-pentane was recently put into operation in a petroleum refinery.
Apparently, an error was made in the design because the column
fails to make the desired separation as shown in the following table
[Chem. Eng. Prog., 61 (8), 79 (1965)l:
Design Actual
Specification Operation
Mol% nCs in distillate 0.26 13.49
Mol% nC4 in bottoms 0.16 4.28
In order to correct the situation, it is proposed to add an intercondenser in the rectifying section to generate more reflux and an
interreboiler in the stripping section to produce additional boilup.
Show by use of a McCabe-Thiele diagram how such a proposed
change can improve the operation.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
06:33

Problem 39

9 In the production of chlorobenzenes by chlorination of benzene, two close-boiling isomers, para-dichlorobenzene (P) and
ortho-dichlorobenzene (O), are separated by distillation. The feed
to the column consists of 62 mol% of the para isomer and 38 mol%
of the ortho isomer. Assume that the pressures at the bottom and top
of the column are 20 psia (137.9 kPa) and 15 psia (103.4 kPa),
respectively. The distillate is a liquid containing 98 mol% para
isomer. The bottoms product is to contain 96 mol% ortho isomer.
At column pressure, the feed is slightly vaporized with q = 0.9.
Calculate the number of theoretical stages required for a reflux ratio
equal to 1.15 times the minimum-reflux ratio. Base your calculations on a constant relative volatility obtained as the arithmetic
average between the column top and column bottom using appropriate vapor pressure data and the assumption of Raoult's and
Dalton's laws. The McCabe-Thiele construction should be supplemented at the two ends by use of the Kremser equations as illustrated in Example 7.4.

Lottie Adams
Lottie Adams
Numerade Educator
06:33

Problem 40

Relatively pure oxygen and nitrogen can be obtained by the
distillation of air using the Linde double column, which, as shown
in Figure 7.45, consists of a lower column operating at elevated
pressure surmounted by an atmospheric-pressure column. The
boiler of the upper column is at the same time the reflux condenser
for both columns. Gaseous air plus enough liquid to take care of
heat leak into the column (more liquid, of course, if liquid-oxygen
product is withdrawn) enters the exchanger at the base of the lower
column and condenses, giving up heat to the boiling liquid and thus
supplying the vapor flow for this column. The liquid air enters an
intermediate point in this column, as shown in Figure 7.45. The
vapors rising in this col~~rnn are partially condensed to form the
reflux, and the uncondensed vapor passes to an outer row of tubes
and is totally condensed, the liquid nitrogen collecting in an annulus, as shown. By operating this column at 4 to 5 atm, the liquid
oxygen boiling at 1 atm is cold enough to condense pure nitrogen.
The liquid that collects in the bottom of the lower column contains
about 45 mol% O2 and forms the feed for the upper column. Such a
double column can produce very pure oxygen with high oxygen
recovery, and relatively pure nitrogen. On a single McCabe-Thiele
diagram-using equilibrium lines, operating lines, q-lines, 45"line,
stepped-off stages, and other illustrative aids-show qualitatively
how the stage requirements of the double column can be computed.

Lottie Adams
Lottie Adams
Numerade Educator
06:33

Problem 41

The following performance data have been obtained for a distillation tower separating a 50/50 by weight percent mixture of methanol and water: Feed rate = 45,438 lbh, Feed condition = bubble-point liquid at feed-tray pressure, Wt% methanol in distillate = 95.04, and Wt% methanol in bottoms = 1 .OO Reflux ratio = 0.947; Reflux condition = saturated liquid Boilup ratio = 1.138; Pressure in reflux drum = 14.7 psia Type condenser = total; Type reboiler = partial Condenser pressure drop = 0.0 psi; Tower pressure drop = 0.8 psi Trays above feed tray = 5; Trays below feed tray = 6 Total trays = 12; Tray diameter = 6 ft Type tray = single-pass sieve tray; Flow path length = 50.5 in Weir length = 42.5 in.; Hole area = 10%; Hole size = 3/16 in Weir height = 2 in.; Tray spacing = 24 in. Viscosity of feed = 0.34 cP Surface tension of distillate = 20 dynelcm; Surface tension of bottoms = 58 dynelcm Temperature of top tray = 154°F; Temperature of bottom
I tray = 207OF
I
I Vapor-liquid equilibrium data at column pressure in mole fraction
I
I
of methanol are
I y 0.0412 0.156 0.379 0.578 0.675 0.729 0.792 0.915
I x 0.00565 0.0246 0.0854 0.205 0.315 0.398 0.518 0.793
I
I Based on the above data:
I
I (a) Determine the overall tray efficiency from the data, assuming
I that the reboiler is the equivalent of a theoretical stage.
I (b) Estimate the overall tray efficiency from the DrickamerI Bradford correlation.
I
I (c) Estimate the overall tray efficiency from the O'Connell correI lation, accounting for length of flow path.
I (d) Estimate the Murphree vapor tray efficiency by the method of
I Chan and Fair.

Lottie Adams
Lottie Adams
Numerade Educator
01:01

Problem 42

For the conditions of Exercise 7.41, a laboratory Oldershaw
I
I
I
column measures an average Murphree vapor-point efficiency of
65%. Estimate EM" and E,.

Carson Merrill
Carson Merrill
Numerade Educator
01:26

Problem 43

Conditions for the top tray of a distillation column are as
I Throttle valve shown in Figure 7.46. Determine the column diameter correspondI t: ing to 85% of flooding if a valve tray is used. Make whatever as-
!ji.:.
, :,, sumptions necessary

Ranjeet Singh
Ranjeet Singh
Numerade Educator
10:22

Problem 44

A separation of propylene from propane is achieved by distillation as shown in Figure $7.47$, where two columns in series are used because a single column would be too tall. The tray numbers refer to equilibrium stages. Determine the column diameters, tray efficiency using the O'Connell correlation, number of actual trays, and column heights if perforated trays are used.

Chareen Guzman
Chareen Guzman
Numerade Educator
01:00

Problem 45

Determine the height and diameter of a vertical flash drum for the conditions shown in Figure $7.48$.

Kimberly Waterbury
Kimberly Waterbury
Numerade Educator
02:40

Problem 46

Determine the length and diameter of a horizontal reflux drum for the conditions shown in Figure $7.49$.

Chai Santi
Chai Santi
Numerade Educator
09:04

Problem 47

Results of design calculations for a methanol-water distillation operation are given in Figure 7.50.
(a) Calculate the column diameter at the top tray and at the bottom tray for sieve trays. Should the column be swaged?
(b) Calculate the length and diameter of the horizontal reflux drum.

Jake Rempel
Jake Rempel
Numerade Educator
03:10

Problem 48

For the conditions given in Exercise 7.41, estimate for the top tray and the bottom tray: (a) Percent of flooding, (b) Tray pressure drop in psi, (c) Whether weeping will occur, (d) Entrainment rate, and (e) Froth height in the downcomer.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
03:08

Problem 49

If the feed rate to the tower of Exercise $7.41$ is increased by $30 \%$ with all other conditions except for tower pressure drop remaining the same, estimate for the top and bottom trays: (a) Per-Figure

Paul Gabriel
Paul Gabriel
Numerade Educator
04:44

Problem 50

Data for Exercise 7.47.
Data for $x-y$ at 1 atm (in benzene mole fractions) are
$\begin{array}{llllllllll}x & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \\ y & 0.11 & 0.22 & 0.325 & 0.426 & 0.526 & 0.625 & 0.720 & 0.815 & 0.91\end{array}$

Rashmi Sinha
Rashmi Sinha
Numerade Educator
16:21

Problem 51

Consider a distillation column for separating ethanol from water at $1 \mathrm{~atm}$. The following specifications are set:
Feed: $10 \mathrm{~mol} \%$ ethanol (bubble-point liquid)
Bottoms: $1 \mathrm{~mol} \%$ ethanol
Distillate: $80 \mathrm{~mol} \%$ ethanol (saturated liquid)
Reflux ratio: $1.5$ times the minimum
Constant molar overflow may be assumed and vapor-liquid equilibrium data are given in Exercise 7.29.
(a) How many theoretical plates are required above and below the feed if a plate column is used?
(b) How many transfer units are required above and below the feed if a packed column is used?
(c) Assuming that the plate efficiency is approximately $80 \%$ and the plate spacing is 18 in., how high is the plate column?
(d) Using an $H_{O G}$ value of $1.2 \mathrm{ft}$., how high is the packed column?
(e) Assuming that you had HTU data available only on the benzenetoluene system, how would you go about applying the data to obtain the HTU for the ethanol-water system?

Chareen Guzman
Chareen Guzman
Numerade Educator
16:21

Problem 52

7.52 Plant capacity for the methanol-water distillation of Exercise $7.41$ is to be doubled. Rather than installing a second trayed tower identical to the one in operation, a packed column is to be considered for the new installation. This column will have a feed location identical to the present trayed tower and will be expected to achieve the same product puritics with the same top pressure and reflux ratio. Two packings are being considered:
1. $50-\mathrm{mm}$ plastic NOR PAC rings (a random packing)
2. Montz metal B 1-300 (a structured packing)
For each of these two packings, design a packed column to operate at $70 \%$ of flooding by calculating for each section: (a) Liquid holdup, (b) Column diameter, (c) Hogi (d) Packed height, (e) Pressure drop. What are the advantages, if any, of each of the packed-column designs over a second trayed tower? Which packing, if either, is preferable?

Chareen Guzman
Chareen Guzman
Numerade Educator
03:40

Problem 53

For the specifications of Example 7.1, design a packed column using 50 -mm metal Hiflow rings and operating at 705 of flooding by calculating for each section: (a) Liquid holdup, (b) Column diameter, (c) $H_{O G}$, (d) Packed height, and (e) Pressure drop.

What are the advantages and disadvantages of a packed column as compared to a trayed tower for this service?
Section 7.6

Alexander Allen
Alexander Allen
Numerade Educator
02:50

Problem 54

An enthalpy-concentration diagram is given in Figure $7.37$ for a mixture of $n$-hexane (H), and $n$-octane (O) at $101 \mathrm{kPa}$. Using this diagram, determine the following:
(a) The mole-fraction composition of the vapor when a liquid containing $30 \mathrm{~mol}$ S $\mathrm{H}$ is heated from point $\mathrm{A}$ to the bubble-point temperature at point B.
(b) The energy required to vaporize 60 mol\% of a mixture initially at $100^{\circ} \mathrm{F}$ and containing $20 \mathrm{~mol} \% \mathrm{H}$ (point $\mathrm{G}$ ).
(c) The compositions of the equilibrium vapor and liquid resulting from part (b).

Lottie Adams
Lottie Adams
Numerade Educator
04:28

Problem 55

Using the enthalpy-concentration diagram of Figure 7.37, determine the following for a mixture of $n$-hexane (H) and $n$-octane (O) at $1 \mathrm{~atm}$ :
(a) The temperature and compositions of equilibrium liquid and vapor resulting from adiabatic mixing of $950 \mathrm{lb} / \mathrm{h}$ of a mixture of $30 \mathrm{~mol} \% \mathrm{H}$ in $\mathrm{O}$ at $180^{\circ} \mathrm{F}$ with $1,125 \mathrm{lb} / \mathrm{h}$ of a mixture of $80 \mathrm{~mol} \%$ $\mathrm{H}$ in $\mathrm{O}$ at $240^{\circ} \mathrm{F}$.
(b) The energy required to partially condense, by cooling, a mixture of $60 \mathrm{~mol} \% \mathrm{H}$ in $\mathrm{O}$ from an initial temperature of $260^{\circ} \mathrm{F}$ to $200^{\circ} \mathrm{F}$. What are the compositions and amounts of the resulting vapor and liquid phases per pound-mole of original mixture?
(c) If the equilibrium vapor from part (b) is further cooled to $180^{\circ} \mathrm{F}$, determine the compositions and relative amounts of the resulting vapor and liquid.

Aadit Sharma
Aadit Sharma
Numerade Educator
06:29

Problem 56

One hundred pound-moles per hour of a mixture of $60 \mathrm{~mol} \%$ methanol in water at $30^{\circ} \mathrm{C}$ and 1 atm is to be separated by distillation at the same pressure into a liquid distillate containing $98 \mathrm{~mol} \%$ methanol and a bottoms liquid product containing $96 \mathrm{~mol}_{8}$ water. Enthalpy and equilibrium data for the mixture at 1 atm are given in Table 7.8. The enthalpy of the feed mixture is $765 \mathrm{Btu} / \mathrm{lbmol}$.
(a) Using the given data, plot an enthalpy-concentration diagram.
(b) Devise a procedure to determine, from the diagram of part (a), the minimum number of equilibrium stages for the condition of total reflux and the required separation.
(c) From the procedure developed in part (b), determine $N_{\min }$. Why is the value independent of the feed condition?
(d) What are the temperatures of the distillate and the bottoms?

Banhishikha Sinha
Banhishikha Sinha
Numerade Educator