Mass Transfer II - Problems

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Absorption

  1. 5000 kg/hr of a SO2 - air mixture 5% by volume SO2 is to be scrubbed with 2,00,000 kg/hr of water in a packed tower. The exist concentration of SO2 is reduced to 0.15%. The tower operates at 1 atmosphere. The equilibrium relationship is given by Y = 30 X

    2. where Y = mole SO2 / mole air;

    X = mole SO2 / mole water

    If the packed height of the tower is 420 cm, estimate the height of transfer unit (H.T.U).

  2. An acetone-air mixture containing 0.015 mole fraction of acetone has the mole fraction reduced to one-hundredth of this value by counter-current absorption with water in a packed tower. The gas flow rate is 4000 kg/hr.sqm of air and the water entering is 6250 kg/hr.sqm. For this system, Henry's law holds good and y = 1.75 x, where y is the mole fraction of acetone in the gas in equilibrium with a mole fraction x in the liquid. How many overall transfer units are required?

  3. An oil containing 2.55 mole % of a hydrocarbon is stripped by running to oil down a column up which live steam is passed, so that 4 moles of steam are used per 100 moles of oil stripped. Determine the number of theoretical plates required to reduce to hydrocarbon content of 0.05 mole % assuming the oil is non-volatile. The vapor liquid relation of the hydrocarbon in the oil is given by y = 33 x, where y is the mole fraction in the vapor and x is the mole fraction in the liquid. The temperature is maintained by interval heating.

  4. A waste water stream contains 0.1 mole % ammonia which is to be removed in an air-stripping operation. Ammonia free air saturated with water will be fed to a tower which should serve to reduce the ammonia content of water stream to 0.002 mole %. The tower will operate isothermally at 27oC and 1 atm where the equilibrium relation may be represented as y = 1.414 x. Compute the air requirement (moles per mole of water) if the tower is a packed tower providing 3 overall gas-phase transfer units. Will the requirement be different if it is a plate tower providing 3 equilibrium stages?

  5. It is desired to absorb 95% of the acetone in a 2 mole percent mixture of acetone in air in a continuous counter-current absorption tower, using water at a rate of 1750 lb/hr.ft2. Pure water is introduced at the top of the tower and the gas mixture is blown into the bottom of the tower at a rate of 1000 lb/hr. The tower is packed with 1.0 inch Rasching rings and the HL and HG are known for this system as 1.06 ft and 1.78 ft. Assuming the tower operates isothermally at atmospheric pressure, the equilibrium relation is y = 2.53 x where the concentrations are given in mole fraction. Calculate the height of the tower to effect this separation.

  6. A soluble gas is absorbed in water, using a packed tower. The equilibrium relationship may be taken as Ye = 0.06 Xe, where Ye and Xe are ratios of moles of solute to moles of inert component. The terminal conditions are
    7.  

    Top

    Bottom

    X

    0.0

    0.08

    Y

    0.001

    0.009

    If the individual heights of transfer units based on liquid and gas phases respectively are Hx = 0.24 m and Hy = 0.36 m, what is the height of the packed section?

  7. Carbon disulfide used as a solvent in a chemical plant is evaporated from the product in a drier into an inert gas essentially nitrogen in order to avoid an explosion hazard. The vapor-nitrogen mixture is to be scrubbed with an absorbed hydrocarbon oil, which will be subsequently steam stripped to recover the CS2. The CS2-N2 mixture has a partial pressure of CS2 equal to 50 mm Hg at 23oC and is to be blown into the absorber at essentially atmospheric pressure at the rate of 1400 m3/hr. The vapor content of the gas is to be reduced to 0.5%. The absorption oil has an average molecular weight of 180, viscosity 2 centipoises, and specific gravity of 0.81at 24oC. The oil enters to absorber essentially stripped of all CS2 and solutions of oil and CS2 are ideal. The vapor pressure of CS2 at 24oC = 346 mm Hg. Assume isothermal operation.
      1. Determine the minimum liquid / gas ratio.
      2. For a liquid / gas ratio of 1.5 times the minimum determine the weight of oil per hour to enter the absorber.
      3. Determine the number of theoretical trays required analytically.

  8. An effluent gas containing 12% benzene is to be scrubbed in a packed column continuously, operating in counter-current manner at 43oC and 1 atm pressure. The column is to be designed for treating 15 m3 of entering gas per hour per square meter of the column cross section, such that the exit gas will contain 1% benzene. The solvent for scrubbing is mineral oil which will enter the top of the column at a rate of 28 kmol/hr.m2 and a benzene content of 1%. Determine the height of the column assuming height of transfer unit to be 0.75 m. The equilibrium concentration at the operating conditions may be estimated as y* = 0.263 x.

    9. Extraction

  9. A 4% acetaldehyde solution in toluene is to be extracted with water in 4 stage cross-current unit. If 30 kg of water are used per stage for 100 kg of feed, find the amount of acetaldehyde extracted and the final concentration. The equilibrium relation is given by y = 2.2x, where y = kg acetaldehyde per kg water and x = kg acetaldehyde per kg toluene.

  10. Nicotine in water solution containing 1% nicotine is to be extracted with kerosene at 20oC. Kerosene and water are insoluble. Determine the percentage of extraction if 100 milligram of feed solution is extracted once with 150 milligram of solvent. What will be the extraction if three ideal stages are used with 50 kg solvent in each stage?

    11. Equilibrium data:

    X'

    0

    0.00101

    0.00246

    0.00502

    0.00751

    0.00998

    0.0204

    Y'

    0

    0.00081

    0.001962

    0.00456

    0.00686

    0.00913

    0.0197

    Where X' is kg nicotine / kg water and Y' is kg nicotine / kg kerosene.

  11. 2000 kg/hr of an acetic acid - water solution containing 30% acid is to be counter-currently extracted with isopropyl ether to reduce the acid concentration to 2% in the solvent free raffinate product.
      1. Determine the minimum amount of solvent required for this extraction.
      2. Determine the number of theoretical stage if 5000 kg/hr of solvent is used.

    The equilibrium data are:

    Water layer

    Ether layer

    100xc

    Water

    Ether

    100yc

    Water

    Ether

    0.69

    98.1

    1.2

    0.18

    0.5

    99.3

    1.41

    97.1

    1.5

    0.37

    0.7

    98.9

    2.89

    95.5

    1.6

    0.79

    0.8

    98.4

    6.42

    91.7

    1.9

    1.93

    1.0

    97.1

    13.30

    84.4

    2.3

    4.82

    1.9

    93.3

    25.50

    71.1

    3.4

    11.40

    3.9

    84.7

    36.70

    59.9

    4.4

    21.60

    6.9

    71.5

    44.30

    45.1

    10.6

    31.10

    10.8

    58.1

    46.40

    37.1

    16.5

    36.20

    15.1

    48.7

    Adsorption

  12. The equilibrium relation for adsorption of colour from a carrier is given by y = 0.57 x0.5 where y is gram colour removed per gram adsorbent and x is gram colour per 100 gram of carrier. If 100 kg of the above carrier containing 1 part of colour per 3 parts of carrier is contacted with 25 kg of adsorbent, calculate the percentage of colour removed by (i) single contact and (ii) two stage cross-current contact dividing the adsorbent equally per contact.

  13. The equilibrium data for adsorption of ethylene from acetylene and ethylene mixtures on silica gel at 1 atm, 25oC are given below:
    14.

    Mole fraction of ethylene in adsorbate

    Mole fraction of ethylene in gas at equilibrium

    Mg moles mixture adsorbed per g adsorbent

    0.0686

    0.2422

    1.622

    0.292

    0.562

    1.397

    0.458

    0.714

    1.298

    0.592

    0.814

    1.193

    0.630

    0.838

    1.170

    0.864

    0.932

    1.078

    A gas containing equimolar amounts of acetylene and ethylene is to be fractionated in a continuous counter-current adsorber, to yield products containing 98 and 2% acetylene by volume. Assuming the temperature to remain constant at 25oC and the pressure to be 1 atm, calculate the number of transfer units and the gel circulation rate per 1000 cuft of feed gas, using 1.2 times the minimum gel circulation rate.

  14. A counter-current adsorber uses silica gel for adsorbing NO2 from a dilute mixture with air. Gas enters the adsorber at the rate of 1000 lb/hr containing 1.5% NO2 by volume and 90% of NO2 is removed. The entering gel will be free from NO2. Calculate the minimum weight of the gel required per hour. The following equilibrium data is given:
    15.

    Partial pressure of NO2 mm Hg

    0

    2

    4

    6

    8

    10

    12

    gm NO2 / 100 gm gel

    0

    0.4

    0.9

    1.65

    2.00

    3.65

    4.85

    Distillation

  15. Methanol and ethanol form an ideal solution. Compute vapor-liquid equilibrium data and prepare plots of x-y and T-x-y at 1 atm pressure. The following pure component vapor pressure data is given:
    16.

    Vapor pressure, mm Hg

    200

    400

    760

    1520

    Temperature oC for ethanol

    48.4

    62.5

    78.4

    97.5

    Temperature oC for methanol

    34.8

    49.9

    64.7

    84

    What value of relative volatility will you recommend for this system?

  16. A liquid mixture containing 45 mole % n-heptane (A) and 55 mole % n-octane (B) at 30oC is to be continuously flash vaporized at 1 std atmospheric pressure to vaporize 60 mole % of the feed. What will be the composition of the vapor and the liquid and the temperature in the separator for an equilibrium stage?

    17. Equilibrium data:

    Temperature oC

    98.4

    105

    110

    115

    120

    125.6

    Vap.pr.of n-heptane, mmHg

    760

    940

    1050

    1200

    1350

    1540

    Vap.pr.of n-octane, mmHg

    333

    417

    484

    561

    650

    760

  17. Vapor pressures of chlorobenzene and water are given below:
    18.

    Pressure, mm Hg

    100

    50

    30

    26

    Temperature oC, Chlorobenzene

    70.4

    53.7

    42.7

    34.5

    Temperature oC, Water

    51.7

    38.5

    29.9

    22.5

    If steam is blown into the still containing a mixture of these two components and the total pressure is 130 mm Hg, estimate the temperature of boiling and the composition of the distillate. The two components are immiscible in the liquid state.

  18. A liquid feed consisting of 1200 gmoles of mixture containing 30% naphthalene and 70% dipropylene glycol is differentially distilled at 100 mm Hg pressure and final distillate contains 55% of naphthalene. The VLE data are
    19.

    x

    8.4

    11.6

    28.0

    50.6

    68.7

    80.6

    88

    y

    22.3

    41.1

    62.9

    74.8

    80.2

    84.4

    88
    1. determine the amount of distillate
    2. determine the concentration of naphthalene in residue and distillate

  19. A feed of 50 mole % hexane and 50 mole % octane is fed into a pipe still through a pressure reducing valve and then into a flash disengaging chamber. The vapor and liquid leaving the chamber are assumed to be in equilibrium. If the fraction of the feed converted to the vapor is 0.5, find the compositions of the top and bottom products. the following table gives the equilibrium data for this system.
    20.

    Mole fractions of hexane in liquid x

    1.00

    0.69

    0.40

    0.192

    0.045

    0.00

    Mole fractions of hexane in vapor y

    1.00

    0.932

    0.78

    0.538

    0.1775

    0.00

  20. A continuous fractionating column is to be designed for separating 10,000 kg per hour of a liquid mixture containing 40 mole percent methanol and 60 mole percent water into an overhead product containing 97 mole percent methanol and a bottom product having 98 mole percent water. A mole reflux ratio of 3 is used. Calculate (i) moles of overhead product obtained per hour and (ii) number of ideal plates and location of the feed plate if the feed is at its bubble point.

    21. Equilibrium data:

    x

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0.9

    y

    0.417

    0.579

    0.669

    0.729

    0.78

    0.825

    0.871

    0.915

    0.959

    Where x = mole fraction of methanol in liquid

    And y = mole fraction of methanol in vapor.

  21. A mixture of benzene and toluene containing 40 mole % of benzene is to be separated to give a product of 90 mole % of benzene at the top and bottom product with not more than 10 mole % of benzene. Using an average value of 2.4 for the volatility of benzene relative to toluene, calculate the number of theoretical plates required at total reflux. Also calculate the minimum reflux ratio, if the feed is liquid and at its boiling point.

  22. 1000 kg/hr of a mixture containing 42 mole percent heptane and 58 mole percent ethyl benzene is to be fractionated to a distillate containing 97 mole percent heptane and a residue containing 99 mole percent ethyl benzene using a total condenser and feed at its saturated liquid condition. The enthalpy-concentration data for the heptane-ethyl benzene at 1 atm pressure are as follows:
    23.

    xheptane

    0

    0.08

    0.18

    0.25

    0.49

    0.65

    0.79

    0.91

    1.0

    yheptane

    0

    0.28

    0.43

    0.51

    0.73

    0.83

    0.90

    0.96

    1.0

    Hl 10-3 x kJ/kmol

    24.3

    24.1

    23.2

    22.8

    22.05

    21.75

    21.7

    21.6

    21.4

    Hv 10-3 x kJ/kmol

    61.2

    59.6

    58.5

    58.1

    56.5

    55.2

    54.4

    53.8

    53.3

    Calculate the following:
    1. Minimum reflux ratio
    2. Minimum number of stages at total reflux
    3. Number of stages at reflux ratio of 2.5
    4. Condenser duty
    5. Reboiler duty
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    Last Modified on: 04-Feb-2022

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