CL 319 [S1]
Homework 1
Due date: 11-Aug-2022
Fundamentals of Interfacial Mass Transfer
1. Write the driving forces for the following cases for interfacial mass transfer. Also, define the
terms in the driving force. Working need not be shown.
System and direction of mass transfer
Driving force
Gas to liquid
Liquid to gas
Solid to gas
Solid to liquid
2. Calculate the driving forces for the following cases and write the values for them with correct
units. Working need not be shown. Note: some information needed for calculations is to be
obtained from relevant sources.
System
Driving force
Sugar crystals dissolving in water when it is
50 % saturated with sugar
In units of g/cc:
Oxygen dissolving in water from air under
ambient conditions when water is 75 %
saturated with oxygen
In units of mol/litre:
Water evaporating from a wet cloth hung for
drying at 28 oC and 90 % relative humidity
In units of mm Hg:
A small disk of benzoic acid is kept in a room
at 25 oC. Benzoic acid sublimates into air in
the room.
In units of Pascal (Pa):
A small amount of toluene spilled on the floor
of a room at 35 oC. The spilled toluene
evaporates into the room air.
In units of bar:
3. Write the interfacial area for mass transfer for the below cases. Working need not be shown.
System
Interfacial area (cm2)
1. A 1-cm oxygen bubble rising up in water
2. A 1.5-cm sugar cube suspended in water
3. 50 % of a vessel is filled with water containing
oxygen. Oxygen hold-up is 30 %. That is, the
ratio of volume of oxygen to the total fluid volume
is 0.3. Vessel diameter = 23.3 cm, its height =
46.6 cm, average diameter of oxygen bubble in
water = 5 mm.
4. A cylinder is filled with packing whose interfacial
area is reported by the manufacturer as 3
cm2/cm3. The diameter of the cylinder is 50 cm
and its height is 2.5 m. 90 % of the cylinder is
filled with the packing material.
4. The mass transfer coefficient for dissolution of oxygen in water from air is 1.8 x 10-3 cm/s.
Calculate the mass transfer flux of oxygen at the instant air is brought into contact with water.
Henry’s law constant for oxygen is 43,000 atm. Show your working. Report your answer in
mol/(cm2 sec)
5. The gas phase mass transfer coefficient of ammonia to a catalyst surface is 2.3 cm/s. Ammonia
transfers from the bulk to the surface of catalyst where it reacts instantaneously. That is, the
concentration of ammonia on the catalyst surface is zero. What is the mass transfer flux of
ammonia if gas contains 10 % (vol/vol) ammonia, pressure is 5 atm and temperature is 900 oC.
Show your working.
6. A 1-cm diameter disk of benzoic acid in placed in 100-cc of water and stirred. Calculate the
time required, in hours, to reach 50 % saturation if the mass transfer coefficient is 1.5 x 10-3
cm/sec. After very long time, benzoic acid concentration in water is 3.4 x 10-3 g/cc. Adopted
from Cussler’s text book.
7. Pure oxygen is being bubbled into a tank containing 5 litres of water. Average diameter of the
bubbles in water is 4 mm. Experiments indicate that the total bubble volume is 1.5 litres.
Experimental measurements of oxygen concentration in the water are tabulated below. Find the
volumetric mass transfer coefficient, 𝑘𝑎, in units of sec-1. 𝑎 is interfacial area, cm2 per cm3 of
water volume. Show your working. Use MS Excel for fitting purposes.
Time, min
0
1
2
3
5
10
20
40
Concentration, ppm 0 0.7 1.3 1.6 2.6 4.8 7.5 9.7
Long time
10
Homework 1
Fundamentals of Interfacial Mass Transfer
1. Write the driving forces for the following cases for interfacial mass transfer. Also, define the terms in
the driving force. Working need not be shown.
System and direction of mass transfer
Driving force
Gas to liquid
Csat - C
Liquid to gas
Psat – P or Csat - C
Solid to gas
Psat – P or Csat - C
Csat - C
Solid to liquid
2. Calculate the driving forces for the following cases and write the values for them with correct units.
Working need not be shown. Note: some information needed for calculations is to be obtained from
relevant sources
System
Driving force
Sugar crystals dissolving in water when it is
50 % saturated with sugar
In units of g/cc: 0.67 at 25 oC
Oxygen dissolving in water from air under
ambient conditions when water is 75 %
saturated with oxygen
In units of mol/litre: 6.7 x 10-5
Water evaporating from a wet cloth hung for
drying at 28 oC and 90 % relative humidity
In units of mm Hg: 2.8
A small disk of benzoic acid is kept in a room
at 25 oC. Benzoic acid sublimates into air in
the room.
Toluene spilled on the floor of a room at 35
o
C. The spilled evaporates into the air in the
room.
In units of Pascal (Pa): 40
In units of bar: 0.06
3. Write the interfacial area for mass transfer for the below cases. Working need not be shown.
System
Interfacial area (cm2)
3.14
A 1-cm oxygen bubble rising up in water
13.5
A 1.5-cm sugar cube suspended in water
35766
50 % of a vessel filled with water and oxygen containing.
Oxygen hold-up is 30 %. That is, volume of oxygen to
total fluid volume is 30 %. Vessel dimensions: diameter
= 23.3 cm and height = 46.6 cm. Average diameter of
oxygen bubble in water is 5 mm.
1.33 x 106
A cylinder is filled with packing whose interfacial area is
reported by the manufacturer as 3 cm2/cm3. The
diameter of the cylinder is 50 cm and its height is 2.5 m.
90 % of the cylinder is filled with the packing material.
4. The mass transfer coefficient for dissolution of oxygen in water from air is 1.8 x 10-3 cm/s. Calculate
the mass transfer flux of oxygen at the instant air is brought into contact with water. Henry’s law
constant for oxygen is 43,000 atm. Show your working. Report your answer in mol/(cm2 sec)
Answer: 4.8 x 10-10
5. The gas phase mass transfer coefficient of ammonia to a catalyst surface is 2.3 cm/s. What is the
mass transfer flux of ammonia if gas contains 10 % (vol/vol) ammonia, pressure is 5 atm and
temperature is 900 oC. Show your working.
Answer: 1.2 x 10-5 mol/(cm2 sec)
6. A 1-cm diameter disk of benzoic acid in placed in 100-cc of water and stirred. Calculate the time
required, in hours, to reach 50 % saturation if the mass transfer coefficient is 1.5 x 10-3 cm/sec. After
very long time, benzoic acid concentration in water is 3.4 x 10-3 g/cc. Adopted from Cussler’s text
book.
Answer: 16.3 hours, only surface was considered for area; if two surfaces are taken, time would be less
than 16.3 hours
7. Pure oxygen is being bubbled into a tank containing 5 litres of water. Average diameter of the bubbles
in water is 4 mm. Experiments indicate that the total bubble volume is 1.5 litres. Experimental
measurements of oxygen concentration in the water are tabulated below. Find the volumetric mass
transfer coefficient, , in units of sec-1. is interfacial area, cm2 per cm3 of water volume. Show your
working. Use MS Excel for fitting purposes.
Time, min
0
1
2
3
5
10
20
40
Concentration, ppm 0 0.7 1.3 1.6 2.6 4.8 7.5 9.7
Answer: 1.38 x 10-3 sec-1
Long time
10
CL 319 [S1]
Homework 2
Due date: 18 Aug 2022
1. Air containing small quantities of sulphur dioxide (SO2) is in contact with pure water.
SO2 dissolves in water through the interface between air and water. The partial
pressure of SO2 at the interface on the air side is 10 mm Hg. What is the molar flux
of SO2 when its transfer just begins? Henry’s law constant for the system is 840 (atm
cc/mol) and the liquid side mass transfer coefficient is 1.5 x 10-3 cm/sec. Report your
answer in mol/ (cm2 sec)
2. Air is flowing into a small vessel filled with some packing. Pure water is passed
through the vessel. What is the mass transfer coefficient for the dissolution of
oxygen in water? The contents of the vessel are well mixed such that the
concentration of oxygen in water inside the vessel and at the outlet are same. Flow
rate of water is 1 litre per minute; concentration of oxygen in water at the outlet is 1.1
x 10-4 molar; Henry’s law constant for air water system is 43,800 atm; the interfacial
area offered by the packing is 2 cm2/cm3 of packing; volume of packing in the vessel
is 2 liters
3. Water is flowing through a 1-cm diameter tube at 5 cm/s. The walls of the tube are
coated with a thin layer of benzoic acid. As the water flows from inlet to the outlet of
the tube, benzoic acid dissolves into it. What is the percent saturation of water with
benzoic acid after 1 m tube length? Mass transfer coefficient of benzoic acid in water
is 1.2 x 10-3 cm/s.
4. A wet T-shirt hung on hanger has a surface area of 0.6 m2. It loses water as follows:
Time, pm
3:15
3:20
3:38
4:00
.
Weight (g)
661
640
580
553
The saturation vapour pressure of water at the room temperature is 20 mm Hg. The
relative humidity is 20%. Find the mass transfer coefficient of water in air for the
above information.
5. As part of the manufacture of microelectronic circuits, silicon wafers are partially
coated with a 5,400-A˚ film of a polymerized organic film called a photoresist. The
density of this polymer is 0.96 g/cm3. After the wafers are etched, this photoresist
must be removed. To do so, the wafers are placed in groups of twenty in an inert ‘
“boat,’’ which in turn is immersed in strong organic solvent. The solubility of the
photoresist in the solvent is 2.23 x 10-3 g/cm3. If the photoresist dissolves in 10
minutes, what is its mass transfer coefficient?
CL 319 [S1]
Homework 2
Due date: 18 Aug 2022
1. Air containing small quantities of sulphur dioxide (SO2) is in contact with pure water.
SO2 dissolves in water through the interface between air and water. The partial
pressure of SO2 at the interface on the air side is 10 mm Hg. What is the molar flux
of SO2 when its transfer just begins? Henry’s law constant for the system is 840 (atm
cc/mol) and the liquid side mass transfer coefficient is 1.5 x 10-3 cm/sec. Report your
answer in mol/ (cm2 sec)
ANSWER: 2.8 x 10-10 mol/(cm2 sec)
2. Air is flowing into a small vessel filled with some packing. Pure water is passed
through the vessel. What is the mass transfer coefficient for the dissolution of
oxygen in water? The contents of the vessel are well mixed such that the
concentration of oxygen in water inside the vessel and at the outlet are same. Flow
rate of water is 1 litre per minute; concentration of oxygen in water at the outlet is 1.1
x 10-4 molar; Henry’s law constant for air water system is 43,800 atm; the interfacial
area offered by the packing is 2 cm2/cm3 of packing; volume of packing in the vessel
is 2 liters
ANSWER: 3 x 10-3 cm/sec
3. Water is flowing through a 1-cm diameter tube at 5 cm/s. The walls of the tube are
coated with a thin layer of benzoic acid. As the water flows from inlet to the outlet of
the tube, benzoic acid dissolves into it. What is the percent saturation of water with
benzoic acid after 1 m tube length? Mass transfer coefficient of benzoic acid in water
is 1.2 x 10-3 cm/s.
ANSWER: 9.2%
4. A wet T-shirt hung on hanger has a surface area of 0.6 m2. It loses water as follows:
Time, pm
3:15
3:20
3:38
4:00
.
Weight (g)
661
640
580
553
The saturation vapour pressure of water at the room temperature is 20 mm Hg. The
relative humidity is 20%. Find the mass transfer coefficient of water in air for the
above information.
ANSWER: 0.53 cm/sec or 4 x 10-4 g/(cm2 sec atm)
5. As part of the manufacture of microelectronic circuits, silicon wafers are partially
coated with a 5,400-A˚ film of a polymerized organic film called a photoresist. The
density of this polymer is 0.96 g/cm3. After the wafers are etched, this photoresist
must be removed. To do so, the wafers are placed in groups of twenty in an inert ‘
“boat,’’ which in turn is immersed in strong organic solvent. The solubility of the
photoresist in the solvent is 2.23 x 10-3 g/cm3. If the photoresist dissolves in 10
minutes, what is its mass transfer coefficient?
ANSWER: 3.8 x 10-5 cm/sec
CL 319 [S1]
Homework 3
Due date: 25-Aug-2022
1. [Cussler] You need to estimate an overall mass transfer coefficient for solute
adsorption from an aqueous solution of density 1.3 g/cm3 into hydrogel beads 0.03
cm in diameter.
The mass transfer coefficient, 𝑘𝑠 , in the solution is 10-3 cm/sec; that within the beads
is given by
𝑘𝐵 = 6
2.
3.
4.
5.
6.
7.
𝐷
𝑑
where 𝑑 is the particle diameter and 𝐷 is the diffusion coefficient, equal here to 3 x
10-6 cm2/sec. Because the beads are of hydrogel, the partition coefficient is one.
Estimate the overall mass transfer coefficient based on solution side and beads side.
Sketch concentration profile of the solute in the solution side and the beads side. Be
neat.
A carcinogen present in water at 500 parts per million (kg per million kg of water) is to
be removed by blowing air through it. What is the driving force for mass transfer
based on overall mass transfer coefficient on air side at the beginning of the removal
process? The equilibrium relation for the carcinogen is 𝑦 = 150𝑥, where 𝑦 and 𝑥 are
mass fractions in air and water phases.
A fermentation beer (essentially water) contains 66 mg/L of an enzyme. This
enzyme is to be extracted into propylene glycol, which is immiscible with the beer.
When the concentration of the enzyme in the glycol is 0.5 mg/L, what is the
concentration driving force for the enzyme transfer based on a overall mass transfer
coefficient on beer side? The partition coefficient for the enzyme, relating its
concentration in beer [mg/L] to its concentration in the glycol [mg/L], is 103 in favour
of glycol.
Case 1: Ammonia dissolution in dilute sulphuric acid is controlled by gas phase
resistance
Case 2: Methane dissolution in water is completely dominated by liquid side
resistance
For these two cases, sketch and label concentration profiles for mass transfer. Be
neat.
Calculate the percentage resistance offered by the air and water phase to the
transfer of chloroform. The mass transfer coefficients of chloroform in air is 0.16
cm/s and in water it is 8.2 x 10-3 cm/s. The equilibrium relation is 𝑦 = 170𝑥 where
𝑥 𝑎𝑛𝑑 𝑦 are the mole fractions in the water and air phases. Pressure is 2.2 atm and
temperature is 30 oC.
For problem 5, does the mass transfer of chloroform occur from air phase to water
phase or other way round, if the concentration of chloroform in both phases is 5
milligram per liter?
In which direction does oxygen transfer? Nitrogen to water or water to nitrogen?
Oxygen concentration in water is 6.25 x 10-5 molar, nitrogen contains 1% (vol/vol)
oxygen, total pressure is 3 atm, temperature is 25 oC, Henry’s law constant is 43,000
atm.
CL 319 [S1]
Homework 3
Due date: 25-Aug-2022
1. [Cussler] You need to estimate an overall mass transfer coefficient for solute
adsorption from an aqueous solution of density 1.3 g/cm3 into hydrogel beads 0.03
cm in diameter.
The mass transfer coefficient, 𝑘𝑠, in the solution is 10-3 cm/sec; that within the beads
is given by
𝐷
𝑘𝐵 = 6
𝑑
where 𝑑 is the particle diameter and 𝐷 is the diffusion coefficient, equal here to 3 x
10-6 cm2/sec. Because the beads are of hydrogel, the partition coefficient is one.
Estimate the overall mass transfer coefficient based on solution side and beads side.
Sketch concentration profile of the solute in the solution side and the beads side. Be
neat.
Answer: Overall mass transfer coefficient based on solution side = Overall mass
transfer coefficient based on beads side = 3.75 x 10-4 cm/s
Cs
Csi
Cbi
Cb
2. A carcinogen present in water at 500 parts per million (kg per million kg of water) is to
be removed by blowing air through it. What is the driving force for mass transfer
based on overall mass transfer coefficient on air side at the beginning of the removal
process? The equilibrium relation for the carcinogen is 𝑦 = 150𝑥, where 𝑦 and 𝑥 are
mass fractions in air and water phases.
Answer: 0.075
3. A fermentation beer (essentially water) contains 66 mg/L of an enzyme. This
enzyme is to be extracted into propylene glycol, which is immiscible with the beer.
When the concentration of the enzyme in the glycol is 0.5 mg/L, what is the
concentration driving force for the enzyme transfer based on a overall mass transfer
coefficient on beer side? The partition coefficient for the enzyme, relating its
concentration in beer [mg/L] to its concentration in the glycol [mg/L], is 103 in favour
of glycol.
Answer: -66 mg/L or 66 mg/L
4. Case 1: Ammonia dissolution in dilute sulphuric acid is controlled by gas phase
resistance
Case 2: Methane dissolution in water is completely dominated by liquid side
resistance
For these two cases, sketch and label concentration profiles for mass transfer. Be
neat.
Answer:
Case 1
P1i
Liquid
phase
P1
P1
Gas
phase
Case 2
P
C1i 1
interfacei
Liquid
phase
P1
C1
C1i
Gas
phase
C1
interface
5. Calculate the percentage resistance offered by the air and water phase to the
transfer of chloroform. The mass transfer coefficients of chloroform in air is 0.16
cm/s and in water it is 8.2 x 10-3 cm/s. The equilibrium relation is 𝑦 = 170𝑥 where
𝑥 𝑎𝑛𝑑 𝑦 are the mole fractions in the water and air phases. Pressure is 2.2 atm and
temperature is 30 oC.
Answer: Percentage resistance offered by air = 16.3%; Percentage resistance
offered by water = 83.7%;
6. For problem 5, does the mass transfer of chloroform occur from air phase to water
phase or other way round, if the concentration of chloroform in both phases is 5
milligram per liter?
Answer: Transfer occurs from the air phase to water phase
7. In which direction does oxygen transfer? Nitrogen to water or water to nitrogen?
Oxygen concentration in water is 6.25 x 10-5 molar, nitrogen contains 1% (vol/vol)
oxygen, total pressure is 3 atm, temperature is 25 oC, Henry’s law constant is 43,000
atm.
Answer: Oxygen transfers from the water phase to nitrogen phase.
CL 319 [S1]
Homework 4
Due date: 01-Sep-2022
1. 450 litres per hour of fermentation broth containing 260 milligrams per litre of
actinomycin is contacted with 370 litres per hour of butyl acetate phase. We wish to
extract 90% of the actinomycin present in the broth into butyl acetate. The mass
transfer coefficients of actinomycin in broth and butyl acetate phases are is 1.2 x 10-3
cm/s and 8 x 10-4 cm/s. Actinomycin is 55 times more soluble in butyl acetate than in
broth. Use units of milligrams per cc to relate the equilibrium concentrations. These
phases are mixed vigorously in a mixer such that the interfacial area is 3 cm2/cm3 of
the volume of broth and acetate phases together. Determine this volume in litres.
Hint: find rate of transfer of actinomycin into butyl acetate phase from mass balances;
equate this rate to the rate described by an overall mass transfer coefficient
2. Carbon dioxide is being scrubbed out of a gas using water flowing through a packed
bed. The carbon dioxide is absorbed at a rate of 2.3 x 10–6 mol/(cm2 sec) when its
concentration in the bulk is zero. The carbon dioxide is present at a partial pressure
of 10 atm, the Henry’s law coefficient is 600 atm, and the diffusion coefficient of
carbon dioxide in water is 1.9 x 10–5 cm2/sec. Find the liquid film thickness.
3. Ammonia is dissolving into an aqueous solution from a gas phase at 1.1 atm and 25
o
C. Find the overall mass transfer coefficient and the percentage resistance offered
by the two phases, for the following information: gas film thickness is 0.1 cm, liquid
film thickness is 0.01 cm, diffusivities of ammonia in gas and water are 0.15 cm2/sec
and 1.2 x 10-5 cm2/sec, and equilibrium relation is 𝑦 = 0.85𝑥, where 𝑥 and 𝑦 are mole
fractions of ammonia in gas and liquid phases, respectively.
4. 20 cc of an ether is contacted with 100 cc of water phase in a small vessel. The
phases are separated by an interface with an area of 12.2 cm2. An iodine-like solute
is originally present in both phases at 3 x 10–3 molar. However, it is 700 times more
soluble in ether than in water. The solute transfers to the ether phase and the
interface remains undisturbed during the transfer. Diffusion coefficients in both
phases are around 10–5 cm2/sec; resistance to mass transfer in both phases is
across a 10–2 cm film. What is the solute concentration in the ether phase after 20
minutes? Hint: find overall mass transfer coefficient and then write a mass balance of
the solute in the ether phase.
CL 319 [S1]
Homework 4
Due date: 01-Sep-2022
1. 450 litres per hour of fermentation broth containing 260 milligrams per litre of
actinomycin is contacted with 370 litres per hour of butyl acetate phase. We wish to
extract 90% of the actinomycin present in the broth into butyl acetate. The mass
transfer coefficients of actinomycin in broth and butyl acetate phases are is 1.2 x 10-3
cm/s and 8 x 10-4 cm/s. Actinomycin is 55 times more soluble in butyl acetate than in
broth. Use units of milligrams per cc to relate the equilibrium concentrations. These
phases are mixed vigorously in a mixer such that the interfacial area is 3 cm2/cm3 of
the volume of broth and acetate phases together. Determine this volume in litres.
Hint: find rate of transfer of actinomycin into butyl acetate phase from mass balances;
equate this rate to the rate described by an overall mass transfer coefficient
Answer: 400 liters
2. Carbon dioxide is being scrubbed out of a gas using water flowing through a packed
bed. The carbon dioxide is absorbed at a rate of 2.3 x 10–6 mol/(cm2 sec) when its
concentration in the bulk is zero. The carbon dioxide is present at a partial pressure
of 10 atm, the Henry’s law coefficient is 600 atm, and the diffusion coefficient of
carbon dioxide in water is 1.9 x 10–5 cm2/sec. Find the liquid film thickness.
Answer:76 microns
3. Ammonia is dissolving into an aqueous solution from a gas phase at 1.1 atm and 25
o
C. Find the overall mass transfer coefficient and the percentage resistance offered
by the two phases, for the following information: gas film thickness is 0.1 cm, liquid
film thickness is 0.01 cm, diffusivities of ammonia in gas and water are 0.15 cm 2/sec
and 1.2 x 10-5 cm2/sec, and equilibrium relation is 𝑦 = 0.85𝑥, where 𝑥 and 𝑦 are mole
fractions of ammonia in gas and liquid phases, respectively.
Answer: Overall mass transfer coefficient based on gas side is 0.8 cm/sec;
percentage resistance offered by gas side is 53%; percentage resistance offered by
liquid side is 47%.
4. 20 cc of an ether is contacted with 100 cc of water phase in a small vessel. The
phases are separated by an interface with an area of 12.2 cm2. An iodine-like solute
is originally present in both phases at 3 x 10–3 molar. However, it is 700 times more
soluble in ether than in water. The solute transfers to the ether phase and the
interface remains undisturbed during the transfer. Diffusion coefficients in both
phases are around 10–5 cm2/sec; resistance to mass transfer in both phases is
across a 10–2 cm film. What is the solute concentration in the ether phase after 20
minutes? Hint: find overall mass transfer coefficient and then write a mass balance of
the solute in the ether phase.
Answer: 5 x 10-3 molar
CL 319 [S1]
Homework 5
Due date: 08-Sep-2022
1. Blood oxygenator is a machine that is used to replicate the function of lungs during
open heart surgery. During the surgery, blood is made to flow through this machine
in which oxygen is supplied to the blood and carbon dioxide is removed from it. The
oxygenated blood is supplied to the body and this process continues until the surgery
is completed. In one type of a blood oxygenator, blood is made to flow through the
inside of fibres; concentrated oxygen gas flows outside the fibres. The oxygen
transfers through the walls of fibres and from there to blood. Estimate the mass
transfer coefficient of oxygen transfer into blood for the following information:
diameter of fibre is 400 microns, blood velocity through the fibres is 1 cm/sec,
diffusivity of oxygen in blood is 1.4 x 10-5 cm2/sec, and the length of the fibres is 30
cm, kinematic viscosity of blood is 0.025 cm2/sec. Also, estimate the mass transfer
coefficient if the blood is made to flow outside and perpendicular to the fibres. In this
case, air flows inside the fibres.
2. Non-porous pharmaceutical granules containing 18 % (w/w) water are to be dried in
a fluidized bed drier at a low temperature. The air temperature inside the drier is 12
o
C, pressure is 1.1 atm, and the relative humidity is 85% for the entire duration of
drying. The size of granule sis 2 mm and their density is 0.64 grams per cc. The air
velocity in the drier is 0.8 m/sec. The kinematic viscosity of air is 0.018 cP and the
diffusivity of water in air can be assumed to be 0.1 cm2/sec. The vapour pressure of
water at 12 oC is 10.5 mm Hg. Find the time taken to remove 99% of the water from
the granules, in hours.
3. A liquid is in turbulent flow in a pipe coated with benzoic acid. What is the
percentage increase or decrease in mass transfer coefficient if: a) the velocity is
doubled and b) viscosity of the liquid doubled? If film theory is used to describe the
interfacial mass transfer, what is the percentage change in the liquid film thickness
for parts a and b.
4. A packed tower is to be designed to remove benzene from N2 gas. Kerosene is the
liquid into which benzene is absorbed. The gas flows into the tower at 1.5 m3/s at 25
o
C and 1.1 x 105 N/m2. The diameter of the tower is 76 cm. Kerosene flows in at 4
kg/s, its density is 800 kg/m3, viscosity is 2.3 cP. 2-inch metal Pall rings are used as
packing material in the tower and they offer a surface area of about 1 cm2/cm3. The
equilibrium relation is given by y = 0.05x where x and y are mole fractions of
benzene in the kerosene phase and nitrogen phase, respectively. Molecular weight
of kerosene is 170 g/mol. Kinematic viscosities of kerosene and nitrogen are 0.029
cm2/sec and 0.15 cm2/sec. Diffusivities of benzene in kerosene and nitrogen are 8 x
10-6 cm2/sec and 0.08 cm2/sec, respectively. Use appropriate correlations to find the
mass transfer coefficients of benzene in the kerosene and nitrogen phases. Then,
find the overall mass transfer coefficient based on the nitrogen phase. Also,
determine the percentage resistances offered by the kerosene and nitrogen phases.
CL 319 [S1]
Homework 6
Due date: 6 Oct 2022
1. As a result of extraction in a chemical plant, a 62,000 mol/hr of water containing 0.2
mol % of butanol is generated. This is contacted with 63,000 mol/hr of air, at 30 oC
and 1.3 atm, in a packed tower to strip of the butanol; this air is used in a power plant
to burn the butanol. Find the diameter of the tower if it is packed with 2-inch Berl
saddles and the pressure drop is to be 0.5 inch water per foot of the tower. Also,
what is the diameter if the tower is operated at 60 % flooding?
2. A packed tower is used to scrub NH3 from a gas stream flowing into it at 0.93 kg/sec
at 30 oC and 1,100 mm Hg. The liquid is water flowing at 6.7 kg/sec at 30 oC. The
tower diameter is 50-cm and it is packed with ½-inch Raschig rings. The gas enters
the tower with 3% NH3 and leaves the tower with 2.2 x 10-6 % NH3. The tower is 4.3
meters tall. The Henry’s law constant under the conditions in the tower is 𝑦 = 0.85𝑥.
What is the mass transfer coefficient KG (cm/s) in this tower?
3. Chlorinating drinking water kills microbes but produces trace amounts of chloroform.
You want to remove this chloroform by air stripping, that is, by blowing air through the
water to remove the chloroform as vapor. Such a process is the opposite of gas
absorption. You know the equilibrium line is 𝑦 = 170𝑥. The tower is at 25 oC and 1
atm. You know that the mass transfer coefficients in the vapor and the liquid in your
equipment are 0.16 cm/sec and 8.2 x 10-3 cm/sec. You also know the gas velocity is
16 cm/sec and the packing has interfacial area of 6.6 cm2/cm3. (a) Sketch typical
equilibrium and operating lines for this process. (b) Find the HTU based on an overall
gas-phase driving force.
4. A fragrance is stripped out of flowers using 5 mol of air. This fragrance is to be
recovered with 1 mol of oil, which is initially fragrance free. The equilibrium for the
fragrance between the air and oil is given by y* = 0.2 x. You want to evaluate two
possible separations. (a) First, imagine that you mix air and oil in a stirred tank. At
equilibrium, what percentage of fragrance is in the oil? (b) Now imagine that air and
oil are contacted countercurrently in a packed tower at 0.5 mol air/hr and 0.1 mol
oil/hr. Draw operating and equilibrium lines, and label the slopes. (c) If the tower and
the mass transfer coefficient give six transfer units (NTU), what percentage of the
fragrance is now in the oil?
5. You have successfully developed a small column which removes 99% of the H2S in
an effluent stream. The HTU in this tower is around 1.2 m; the gas enters with 630
ppm H2S. The absorbing liquid enters pure. The gas flux per liquid flux G/L is 0.025.
While this tower is running well, you now need to remove 99.9% of the H2S to meet
governmental requirements. To do so, you plan to use a new absorbing liquid which
reacts instantaneously with the H2S, reducing the liquid-side mass transfer resistance
by 90%; this liquid-side resistance had been 80% of the total. The new equilibrium
line with this reactive liquid is 𝑦 = 𝑥. (a) What is the new HTU? b) Assume the tower
is 8 m high. What flow of gas per reactive liquid G/L will be required now?
CL 319 [S1]
Homework 6
Due date: 6 Oct 2022
1. As a result of extraction in a chemical plant, a 62,000 mol/hr of water containing 0.2
mol % of butanol is generated. This is contacted with 63,000 mol/hr of air, at 30 oC
and 1.3 atm, in a packed tower to strip of the butanol; this air is used in a power plant
to burn the butanol. Find the diameter of the tower if it is packed with 2-inch Berl
saddles and the pressure drop is to be 0.5 inch water per foot of the tower. Also,
what is the diameter if the tower is operated at 60 % flooding?
Answer: 66 cm for pressure drop is to be 0.5 inch water per foot of the tower; 50 cm
for 60% flooding
2. A packed tower is used to scrub NH3 from a gas stream flowing into it at 0.93 kg/sec
at 30 oC and 1,100 mm Hg. The liquid is water flowing at 6.7 kg/sec at 30 oC. The
tower diameter is 50-cm and it is packed with ½-inch Raschig rings. The gas enters
the tower with 3% NH3 and leaves the tower with 2.2 x 10-6 % NH3. The tower is 4.3
meters tall. The Henry’s law constant under the conditions in the tower is 𝑦 = 0.85𝑥.
What is the mass transfer coefficient KG (cm/s) in this tower?
Answer: 2.4 cm/sec
3. Chlorinating drinking water kills microbes but produces trace amounts of chloroform.
You want to remove this chloroform by air stripping, that is, by blowing air through the
water to remove the chloroform as vapor. Such a process is the opposite of gas
absorption. You know the equilibrium line is 𝑦 = 170𝑥. The tower is at 25 oC and 1
atm. You know that the mass transfer coefficients in the vapor and the liquid in your
equipment are 0.16 cm/sec and 8.2 x 10-3 cm/sec. You also know the gas velocity is
16 cm/sec and the packing has interfacial area of 6.6 cm2/cm3. (a) Sketch typical
equilibrium and operating lines for this process. (b) Find the HTU based on an overall
gas-phase driving force.
Answer: 50 cm
4. A fragrance is stripped out of flowers using 5 mol of air. This fragrance is to be
recovered with 1 mol of oil, which is initially fragrance free. The equilibrium for the
fragrance between the air and oil is given by y* = 0.2 x. You want to evaluate two
possible separations. (a) First, imagine that you mix air and oil in a stirred tank. At
equilibrium, what percentage of fragrance is in the oil? (b) Now imagine that air and
oil are contacted countercurrently in a packed tower at 0.5 mol air/hr and 0.1 mol
oil/hr. Draw operating and equilibrium lines, and label the slopes. (c) If the tower and
the mass transfer coefficient give six transfer units (NTU), what percentage of the
fragrance is now in the oil?
Answer: a) 50%, c) 86%
5. You have successfully developed a small column which removes 99% of the H2S in
an effluent stream. The HTU in this tower is around 1.2 m; the gas enters with 630
ppm H2S. The absorbing liquid enters pure. The gas flux per liquid flux G/L is 0.025.
While this tower is running well, you now need to remove 99.9% of the H2S to meet
governmental requirements. To do so, you plan to use a new absorbing liquid which
reacts instantaneously with the H2S, reducing the liquid-side mass transfer resistance
by 90%; this liquid-side resistance had been 80% of the total. The new equilibrium
line with this reactive liquid is 𝑦 = 𝑥. (a) What is the new HTU? b) Assume the tower
is 8 m high. What flow of gas per reactive liquid G/L will be required now?
Answer: a) 0.22 m, b) 0.87
CL 319 [S1]
Homework 7
Due date: 13-Oct-2022
1. A chemical plant produces 68 tons per day of sulphuric acid. It is produced by
several steps occurring in sequence: first, sulphur is burned with air to make
sulphur dioxide (SO2); second, SO2 is oxidized with air to produce sulphur trioxide
(SO3); finally, SO3 is absorbed in water to produce sulphuric acid. The plant
achieves 95 % conversion of SO2 to SO3. The concentration of SO2 in the gas
leaving the final step, absorber, must be below 350 parts per million (ppm) on a
volume basis.
a. Check if the concentration of SO2 in the gas released from the absorber exceeds
the pollution norms.
b. A packed tower is to be designed to remove SO2 in the gas leaving the absorber
to levels below the norms. If pure water is used for absorbing SO2, find the
height of the tower if its diameter is 1 meter. Henry’s law constant is 840 (atm
cc/mol). Take gas-side mass transfer coefficient, 𝑘𝑔 𝑎 as 1.7 (sec-1) and liquid
mass transfer coefficients, 𝑘𝑐𝑜 𝑎 as 3.8 x 10-3 (sec-1). The operating water flow is
50 % more than the minimum needed to operate the absorber.
c. Find the height of the tower if NaOH is added to water entering the tower. Adjust
the concentration of NaOH in water such that the overall mass transfer coefficient
with chemical reaction is maximized and remains constant at this maximum value
throughout the tower. Confirm with calculations that the above condition is
satisfied.
2. A process gas containing 4% chlorine (average molecular weight 30) is being
scrubbed at a rate of 14 kg per minute in a 13.2 meters tall packed tower 60-cm
in diameter with aqueous sodium carbonate (average molecular weight 18). 94%
of the chlorine is removed. The flow of this aqueous solution is 20% more than
the minimum required for the removal process. The Henry’s law for this system
is 𝑦 = 94𝑥, where 𝑥 and 𝑦 are mole fractions of chlorine in aqueous and gas
phases. The temperature is 10 oC, pressure is 1.2 atm and the packing has a
surface area of 82 m2/m3.
a. Find the overall mass transfer coefficient, KG (cm/sec)
b. Assume that this coefficient results from two thin films of equal thickness, one
on the gas side and one on the liquid. Assuming that the diffusion coefficients
in the gas and in the liquid are 0.1 cm2/sec and 10-5 cm2/sec, respectively,
find this thickness.
c. Which phase controls mass transfer?
CL 319 [S1]
Homework 8
Due date: 18 Oct 2022
1. A mixture of methane and n-octane is flashed at 323 K and 12 bar. The feed is 30
mol % methane and has a total flowrate of 100 kmol/h. What is the composition and
flowrate of the exit streams? 𝐾𝑚𝑒𝑡ℎ𝑎𝑛𝑒 = 24 and 𝐾𝑜𝑐𝑡𝑎𝑛𝑒 = 0.009.
2. A stream containing 45 kmol/h hydrogen (component 1) and 70 kmol/h n-hexane
(component 2) is flashed at 311 K and 40 bar. Find the flowrate and composition of
the exit streams. Also, calculate the component flows in the exit streams. Use the
experimental VLE data given below to estimate K-values for the mixture.
T (K)
310.93
310.93
310.93
310.93
P (bar)
34.473
68.947
103.420
137.894
x1
0.031
0.059
0.084
0.108
y1
0.986
0.992
0.994
0.995
3. A four component mixture of hydrogen (1) – benzene (2) – cyclohexane (3) – nhexane (4) is fed to a flash separator at 200 oF and 520 psia. The feed contains 10
mol % hydrogen, 10 mol % benzene, 60 mol % cyclohexane and 20 mol % n-hexane,
at a total flow of 80 kmol/h. At this temperature and pressure, the experimentally
measured K-value are: 𝐾1 = 38.16, 𝐾2 = 0.0684, 𝐾3 = 0.0609 and 𝐾4 = 0.0825.
Calculate the total flowrate, the component flowrates, and the composition of the exit
streams. Use Goal Seek feature of MS Excel to solve the polynomial generated by
the Rachford-Rice equation.
4. In the manufacture of polysilicon, the reactor effluent is an equimolar mixture of HCl
(component 1) and trichlorosilane (component 2) with a total flowrate of 100 kmol/h.
The objectives of the flash separation are to achieve high fractional recovery of
trichlorosilane (more than 0.98) in the liquid stream and to obtain high purity HCl
(upwards of 0.975) in the vapour. Solve the flash problem at the following conditions
and assess if the objectives are improved or not in each case.
a. Flash temperature = −40 oC, pressure = 2 atm.
b. Flash temperature = −30 oC, pressure = 1 atm.
c. Flash temperature = −80 oC, pressure = 2 atm.
𝐵
Antoine equation: log10 Psat = 𝐴 − 𝑇+𝐶 T is temperature in oC.
Substance
Trichlorosilane
Hydrogen chloride
A
6.95524
7.44899
B
1102.9
868.358
1/2
C
238.865
274.904
5. A stream containing 80 kmol/h of 1,3 butadiene (component 1) and 20 kmol/h styrene
(component 2) is to be flashed at 20 oC and 1 atm. Calculate the flows and
compositions of vapour and liquid streams exiting the flash separator. The system is
non-ideal liquid in equilibrium with a perfect gas. Vapour-liquid equilibrium can be
calculated using the widely used Wilson’s model.
This problem requires trial and error computations, which can be effectively done
using MS Excel Goal Seek feature.
The equilibrium relation for non-ideal liquid mixture in contact with a perfect gas can
found from the following relation:
Equilibrium relation:
𝑃𝑦𝑖 = 𝑃 𝑠𝑎𝑡 𝛾𝑖 𝑥𝑖
𝐵
Antoine equation: log 𝑃 𝑠𝑎𝑡 = 𝐴 − 𝑇+𝐶 𝑃 𝑠𝑎𝑡 in mm Hg, 𝑇 in oC
Substance
1,3 butadiene
Styrene
A
6.85364
7.50233
B
C
933.586
239.511
1819.810 248.662
Wilson’s equation for calculating activity coefficients:
Λ12
Λ21
ln 𝛾1 = −𝑙𝑛 (𝑥1 + Λ12 𝑥2 ) + 𝑥2 (
−
)
𝑥1 + Λ12 𝑥2 𝑥2 + Λ21 𝑥1
Λ12
Λ21
ln 𝛾2 = −𝑙𝑛 (𝑥2 + Λ21 𝑥1 ) + 𝑥1 (
−
)
𝑥1 + Λ12 𝑥2 𝑥2 + Λ21 𝑥1
𝑣
Λ12 = 𝑣2𝐿 𝑒𝑥𝑝 (−
1𝐿
𝑣1𝐿
𝐴12⁄
𝐴21⁄
𝑅𝑇) and Λ21 = 𝑣2𝐿 𝑒𝑥𝑝 (−
𝑅𝑇)
𝐴12 = 1100.1231 and 𝐴21 = −417.8319 in units of cal/gmol
𝑣1𝐿 = 87.09 and 𝑣2𝐿 = 115.57 in units of cm3/gmol
2/2
Homework 9
Column Distillation
1. Consider the separation of a 100 kmol/hour of a saturated liquid feed mixture of 50
mole % acetone (the light component) and 50 mole % propyl acetate, in a column
operated at 1 atm. The distillate should contain 95 % acetone and the bottoms
should contain 5 % acetone. Assume that constant molar overflow applies and that
𝛼𝑥
the equilibrium diagram can be represented by 𝑦 = 1+(𝛼−1)𝑥 where 𝛼 = 4.74. You
need to generate y versus x equilibrium diagram from the given equation. Use the
graphical McCabe-Thiele method to find:
a. The minimum number of equilibrium stages required to achieve the separation.
b. The minimum reflux and reboil ratios
c. The actual number of equilibrium stages required to achieve the separation at a
reflux ratio of 1.5 𝑟𝑚𝑖𝑛
d. The optimum feed location for part c
e. The composition of acetone in the liquid leaving top stage
f. The composition of vapour and liquid leaving feed stage
g. Temperature of the feed stage. Hint: solve for dew point temperature of the
vapour leaving this stage or bubble point temperature of liquid leaving this stage.
Use Goal Seek feature of MS Excel
h. Condenser and reboiler duties in kJ/hour
i. For the reboiler duty in part g, determine the steam flow needed in the reboiler in
kg/hour, if the steam is saturated at a temperature 15 oC above the reboiler
temperature
Note: Some of the data needed for solving parts f, g and h are not given. You need
to get this data from an authentic source.
2. For each of the following feed qualities, draw feed line for the system given in
problem 1.
a) Saturated vapour feed
b) 25 % vapour and 75 % liquid
c) Feed enters as a sub-cooled liquid at a temperature 30 oC below the saturation
temperature of feed stage. Average specific heat of liquid is about 140 J/(mol K)
and average latent heat of the components is about 34,000 J/mol.
d) Feed enters as a superheated vapour at a temperature 30 oC above the
saturation temperature of feed stage. Average specific heat of vapour is about
84 J/(mol K) and average latent heat of the components is about 34,000 J/mol.
For parts c and d, do an energy balance around the feed stage to determine q.
1/3
3. Distillation is being carried out in a packed column to produce 99.9% benzene from a
feed of 99% benzene and 1% toluene fed directly to the reboiler. The equilibrium line
over this concentration range is 𝑦 ∗ = 0.58 + 0.42𝑥. The feed is 100 mol/hr, and the
bottoms is 16 mol/hr. The condenser is not total, but produces equal amounts of a
product and a liquid returned to the top of the tower. These streams are
approximately in equilibrium. (a) How much distillate is produced? (b) What is the
reflux ratio? (c) What is the vapor concentration coming out of the top of the tower?
(d) What is the vapor concentration going into the bottom of the tower? (e) What
number of transfer units (NTU) is involved?
4. A 100 kmol/hr saturated liquid feed containing 40 mol % methanol and 60 mol %
water is to be separated in an atmospheric distillation column to give 95 mol %
methanol in the distillate and 5 mol % methanol in the bottoms. The column operates
at a reflux ratio of 1.5. A side stream is drawn from the liquid leaving the fourth stage
at a rate of 10 kmol/hr. Find the number of equilibrium stages needed in the column.
Generate equilibrium x-y diagram for methanol-water system from the equation, 𝑦 =
7.15𝑥
1+6.15𝑥
− 0.33𝑥(1 − 𝑥)
5. As part of applying paint, you produce a large amount of methanol vapor. You
recover the methanol by absorbing the vapor in water, and then distilling the water–
methanol mixture in an old six-stage column plus reboiler. You have an old
description of the column, which says that the Murphree efficiency of the top three
stages is 50 % but that of the bottom three and the reboiler is 100 %. The man who
wrote the report died last year, only eleven months after retiring. Company policy
dictates a reflux of 1.5 times the minimum. You need to process 1200 kg/hr of a 32
mol % methanol feed. You want a distillate that is 90 mol % methanol. What is the
concentration of the bottoms product? Generate equilibrium x-y diagram for
7.15𝑥
methanol-water system from the equation, 𝑦 = 1+6.15𝑥 − 0.33𝑥(1 − 𝑥)
2/3