Practice Problems: Mass Transfer
Question 1
A chemical engineer is designing an absorption column to remove sulfur dioxide from a gas stream using water as the solvent. The column operates at 25°C and 1 atm. Given the following information:
Gas flow rate: 100 kmol/h
Inlet SO₂ concentration (mole fraction): 0.05
Outlet SO₂ concentration (mole fraction): 0.005
Liquid flow rate: 500 kmol/h
Henry's law constant for SO₂ in water at 25°C: 40 atm/(mole fraction)
What is the mole fraction of SO₂ in the exiting liquid stream, assuming equilibrium is achieved at the column exit?
(a) 0.00010
(b) 0.00013
(c) 0.00090
(d) 0.00125
Question 2
A process engineer is evaluating a distillation column separating benzene and toluene. The column operates at 1 atm with the following conditions:
Feed flow rate: 1000 kg/h
Feed composition: 40% benzene by mass
Distillate composition: 95% benzene by mass
Bottoms composition: 5% benzene by mass
Average relative volatility (α): 2.5
Using the Fenske equation, how many minimum theoretical stages are required?
(a) 5.2 stages
(b) 6.8 stages
(c) 7.4 stages
(d) 8.1 stages
Question 3
An environmental engineer is designing a packed tower for air stripping of trichloroethylene (TCE) from contaminated groundwater. Given:
Water flow rate: 50 gpm
Tower diameter: 2 ft
Packing: 1-inch Pall rings
Liquid mass velocity: 1500 lb/(h·ft²)
Gas mass velocity: 400 lb/(h·ft²)
Packing factor (Fp): 56 ft⁻¹
What is the approximate flooding percentage at which the tower is operating if the flooding gas velocity correlation gives a flooding factor of 0.20?
(a) 45%
(b) 58%
(c) 67%
(d) 72%
Question 4
A chemical engineer is designing a wetted-wall column to measure mass transfer coefficients. The following data is available:
Column height: 1.5 m
Column diameter: 0.05 m
Liquid flow rate: 0.002 kg/s
Liquid viscosity: 0.001 Pa·s
Liquid density: 1000 kg/m³
Diffusivity of solute in liquid: 2 × 10⁻⁹ m²/s
Calculate the Reynolds number for the liquid film.
(a) 51
(b) 127
(c) 255
(d) 318
Question 5
A petroleum engineer is analyzing gas absorption in a natural gas sweetening unit using methyldiethanolamine (MDEA) to remove H₂S. Given:
Operating temperature: 40°C
Operating pressure: 800 kPa
Gas feed rate: 1000 kmol/h (99% CH₄, 1% H₂S)
Required H₂S removal: 98%
MDEA solution flow rate: 150 kmol/h
Equilibrium relationship: y = 0.8x
What is the minimum liquid-to-gas ratio (L/G)min on a molar basis?
(a) 0.123
(b) 0.245
(c) 0.490
(d) 0.612
Question 6
A process engineer is evaluating a cooling tower where water is cooled from 45°C to 30°C. The following data is available:
Water flow rate: 50 kg/s
Inlet air dry-bulb temperature: 25°C
Inlet air wet-bulb temperature: 20°C
Exit air temperature: 38°C
Tower height: 8 m
Tower cross-sectional area: 25 m²
What is the volumetric mass transfer coefficient (KGa) if the number of transfer units (NTU) is 2.5?
(a) 0.83 kmol/(m³·s)
(b) 1.25 kmol/(m³·s)
(c) 2.08 kmol/(m³·s)
(d) 3.12 kmol/(m³·s)
Question 7
A chemical engineer is designing an extraction column to separate acetic acid from water using ethyl acetate as the solvent. Given:
Feed flow rate: 100 kg/h
Feed concentration: 30% acetic acid by mass
Solvent flow rate: 80 kg/h
Equilibrium data: y = 1.5x (mass fraction basis)
Desired raffinate concentration: 5% acetic acid
Number of equilibrium stages: 4
What is the acetic acid concentration in the exit extract stream?
(a) 0.285
(b) 0.356
(c) 0.412
(d) 0.469
Question 8
A process engineer is analyzing a binary distillation column separating methanol and water. The column operates with:
Feed composition: 0.40 mole fraction methanol
Feed condition: saturated liquid (q = 1)
Distillate composition: 0.95 mole fraction methanol
Bottoms composition: 0.05 mole fraction methanol
Reflux ratio: 2.0
Equilibrium data at x = 0.40: y* = 0.73
What is the slope of the rectifying section operating line?
(a) 0.500
(b) 0.667
(c) 0.750
(d) 0.833
Question 9
An environmental engineer is designing a stripping column to remove ammonia from wastewater using air. Given:
Liquid flow rate: 200 L/min
Inlet ammonia concentration: 100 mg/L
Outlet ammonia concentration: 5 mg/L
Air flow rate: 500 L/min (at standard conditions)
Henry's law constant: H = 0.95 (dimensionless, y/x)
Operating temperature: 20°C
What is the stripping factor (S) for this system?
(a) 1.58
(b) 2.38
(c) 3.16
(d) 4.12
Question 10
A chemical engineer is analyzing diffusion through a stagnant gas film. Carbon dioxide diffuses through nitrogen at 25°C and 1 atm. Given:
Film thickness: 2 mm
CO₂ partial pressure at surface 1: 0.20 atm
CO₂ partial pressure at surface 2: 0.05 atm
Diffusivity of CO₂ in N₂: 0.16 cm²/s
Total pressure: 1 atm
What is the molar flux of CO₂ through the film in mol/(cm²·s)?
(a) 4.8 × 10⁻⁶
(b) 6.2 × 10⁻⁶
(c) 7.9 × 10⁻⁶
(d) 9.1 × 10⁻⁶
Question 11
A process engineer is evaluating the performance of a spray dryer. Moisture is being removed from a slurry droplet. Given:
Initial droplet diameter: 100 μm
Ambient temperature: 200°C
Droplet surface temperature: 60°C
Mass transfer coefficient: 0.15 m/s
Vapor pressure at droplet surface: 20 kPa
Partial pressure in bulk air: 2 kPa
Gas constant: 8.314 J/(mol·K)
What is the evaporation flux in kg/(m²·s)?
(a) 0.0078
(b) 0.0121
(c) 0.0165
(d) 0.0203
Question 12
A chemical engineer is designing a membrane separator for hydrogen recovery from a refinery off-gas stream. Given:
Membrane area: 100 m²
Membrane thickness: 50 μm
Feed pressure: 3000 kPa
Permeate pressure: 100 kPa
H₂ permeability: 50 × 10⁻¹⁰ mol/(m·s·Pa)
Feed H₂ partial pressure: 1500 kPa
What is the hydrogen flux through the membrane in mol/(m²·s)?
(a) 1.05
(b) 1.40
(c) 1.75
(d) 2.10
Question 13
A process engineer is analyzing a liquid-liquid extraction process for removing phenol from wastewater using benzene. Given:
Wastewater flow rate: 1000 kg/h
Initial phenol concentration: 5% by mass
Benzene flow rate: 600 kg/h
Distribution coefficient (K = y/x): 2.0
Number of theoretical stages: 3
Assuming countercurrent operation, what is the final phenol concentration in the raffinate phase?
(a) 0.85%
(b) 1.12%
(c) 1.47%
(d) 1.89%
Question 14
A chemical engineer is designing a packed absorption column for removing acetone from air using water. Given:
Tower diameter: 1.2 m
Packing: 25 mm ceramic Raschig rings
Height of packing: 6 m
Gas flow rate: 2000 kg/h
Liquid flow rate: 4000 kg/h
Height of transfer unit (HOG): 0.75 m
What is the number of transfer units (NOG) for this column?
(a) 6.0
(b) 7.0
(c) 8.0
(d) 9.0
Question 15
A process engineer is evaluating a crystallizer where sodium chloride is being crystallized from an aqueous solution. Given:
Feed solution flow rate: 5000 kg/h
Feed concentration: 28% NaCl by mass
Feed temperature: 90°C
Crystallizer temperature: 20°C
Solubility at 20°C: 26.4 g NaCl/100 g water
What is the production rate of NaCl crystals in kg/h?
(a) 352
(b) 428
(c) 516
(d) 624
Question 16
An environmental engineer is designing an adsorption column for removing volatile organic compounds (VOCs) from air using activated carbon. Given:
Air flow rate: 1000 m³/h (at standard conditions)
Inlet VOC concentration: 500 ppm
Outlet VOC concentration: 10 ppm
Carbon bulk density: 450 kg/m³
Adsorption capacity: 0.25 kg VOC/kg carbon
Breakthrough time required: 8 hours
What is the minimum required mass of activated carbon in kg?
(a) 145
(b) 198
(c) 256
(d) 312
Question 17
A chemical engineer is analyzing mass transfer in a falling film absorber where ammonia is being absorbed from air into water. Given:
Film thickness: 0.5 mm
Film velocity: 0.2 m/s
Schmidt number (Sc): 500
Diffusivity of NH₃ in water: 2.0 × 10⁻⁹ m²/s
Film length: 2.0 m
What is the average Sherwood number for mass transfer in this system?
(a) 245
(b) 316
(c) 387
(d) 452
Question 18
A process engineer is designing a steam stripper to remove dissolved oxygen from boiler feedwater. Given:
Water flow rate: 50,000 kg/h
Inlet O₂ concentration: 8 ppm
Outlet O₂ concentration: 0.007 ppm (7 ppb)
Steam flow rate: 500 kg/h
Operating pressure: 150 kPa
Henry's constant for O₂: 4.4 × 10⁴ atm
What is the required number of theoretical stages using the Kremser equation if the stripping factor is 12?
(a) 4.2
(b) 5.1
(c) 5.8
(d) 6.5
Question 19
A chemical engineer is evaluating an evaporator system concentrating a sugar solution. Given:
Feed flow rate: 10,000 kg/h
Feed concentration: 15% sugar by mass
Product concentration: 60% sugar by mass
Feed temperature: 25°C
Evaporator pressure: 20 kPa (absolute)
Boiling point elevation: 8°C
Specific heat of feed: 3.9 kJ/(kg·K)
Latent heat of vaporization: 2250 kJ/kg
What is the rate of water evaporation in kg/h?
(a) 6250
(b) 7500
(c) 8750
(d) 9150
Question 20
A process engineer is analyzing molecular diffusion in a liquid phase. Ethanol is diffusing through a stagnant water layer at 25°C. Given:
Diffusion path length: 5 mm
Ethanol concentration at point 1: 10 mol/m³
Ethanol concentration at point 2: 2 mol/m³
Diffusivity of ethanol in water: 1.24 × 10⁻⁹ m²/s
Total molar concentration: 55,000 mol/m³
What is the molar flux of ethanol in mol/(m²·s)?
(a) 1.59 × 10⁻⁶
(b) 1.98 × 10⁻⁶
(c) 2.36 × 10⁻⁶
(d) 2.84 × 10⁻⁶
