Unit Operations 1 – Diffusion, Distillation, Gas Absorption, Humidification, and Drying

What will be the diffusivity of methanol in water at 20°C if the experimental value is 1.26 x 10^-9 m²/s measured at 15°C?

It is desired to produce an overhead product containing 80 mole% benzene from a feed mixture of 68 mole % benzene and 32 mole % toluene. If the mixture is subjected to equilibrium distillation at 1 atm, calculate the number of moles vaporized per 100 mols of feed.

A vertical tube with 0.775 sq. in cross-section is filled with water at the bottom. The distance from the water surface to the open end of the tube is 2.527 in. A flow of perfectly dried air is blown over the open end. The tube is held at a constant temperature of 87.5°F. The water evaporated is measured by weighing and is found to be 5.165 x 10^-5 lb/hr. Determine the diffusion coefficient of water vapor in air in ft²/hr.

Naphthalene is to be open-steam distilled at 200°C and 1 atm. How many pounds of steam will be required to collect 1 lb mole of pure naphthalene? The vapor pressure of naphthalene at 200°C is 496.235 mmHg.

An equimolal mixture of benzene and toluene is subjected to a simple batch distillation at 1 atm. If the distillation is discontinued when the mols of distillate amount to 40 % of the mols charged, what should be the concentration of the distillate in mol % of benzene? Assume the relative volatility is 2.55.

A tower packed with 1-inch ceramic Intalox saddles (F_P = 92, English units) is to be built to treat 25,000 ft³ of NH₃-air mixture per hour. The ammonia content of the entering gas is 2% by volume T = 20°C and P = 1 atm. The solvent used is pure water. The ratio of liquid flow to gas flow is 1.0 pound liquid per pound of gas. Estimate the flooding velocity in ft/s obtained using Figure 14-55, 8th Edition of Perry’s handbook.

Air from a solvent plant contains 2 % n-pentane by volume. The pentane concentration is to be reduced to 0.1 % by contacting the gas at 27°C and 10 atm, with 6950 lb/hr of oil that contains 0.05 % of n-pentane by weight; 100,000 ft³ of gas measured at 60°F and 1 atm is handled per hour. M of oil = 220. The vapor pressure of pentane at 27°C is 530 mm Hg. Assume Raoult’s law applies. Estimate the number of theoretical plates assuming both E.C. and O.L. are linear within limits.

A mixture containing 50 mols of benzene and 50 mols of toluene is fractionated in a plate tower at 1 atm. The overhead product must contain at least 98 % by mol of benzene. The feed is saturated liquid. The maximum vaporization capacity of the reboiler is 120 mols per hour. If the reflux ratio is 1.74, how many mols of the bottoms are obtained?

Soap (wet density=60 lb/ft³) 2 ft square by 1.0 inch thick is dried on both sides from 30 % moisture (wb) to 6% moisture (wb) in a batch drier with air at 180°F and 20 % RH flowing parallel to the surface at 3 ft/s. If Wc=0.15 (wb) and X*=0.037 (db) determine the drying time in hours. The heat transfer coefficient may be determined using, hc = 0.0128 G^0.8

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The estimated mass transfer coefficient for a single dissolving solute of spherical shape in water with negligible forced convective effects is _____m²/s if the diffusivity is 0.25 m²/s and the diameter of the sphere is 2.5 cm.

A mixture containing 15 lb mol n-butane and 85 lb mol n-pentane is subjected to a simple batch distillation at 1atm. If 90% of the butane is removed, determine the composition of the residue in mol fraction. Assume an average relative volatility of 3.4.

When a wet granular solid material is placed in a metal tray and subjected to direct drying, the mechanism of heat transfer is by

An equimolal mixture of benzene and toluene is subjected to flash distillation at a separator pressure of 1 atm. If 60% of the charge is vaporized, what is the concentration of the distillate in mol % benzene?

The molecular diffusion flux of A is 4.0 x 10^-7 g-mol/s-cm² at 298 K and 1 atm. What will be the bulk velocity in cm/s if the diffusion flux relative to a stationary observer is 5.35 x 10^-7 g-mol/s-cm² and the mole fraction of the diffusing A in B is 0.015?

How many design variables are to be specified (degrees of freedom) for a feed stage in a rectification operation if there are 3 components involved in the process

The analogy between molecular heat and molecular mass transport may not be considered similar because of

A binary solution where A is the low boiler, exhibiting a maximum boiling point, is subjected to fractional distillation using finite number of stages. If the feed has a concentration in A higher than the azeotropic point, the concentration of the distillate will be

In measuring the wet bulb temperature of ambient air using a sling psychrometer, the effect of radiation in the reading is minimized by

A continuous rectifying column handles a mixture containing 40 % benzene by mass and 60 % toluene by mass at the rate of 4 kg/s, and separates it into a product containing 97 % benzene by mass and a liquid containing 98 % toluene by mass. The feed is saturated liquid. If the reflux ratio is 3.5, and the overall efficiency is 60 %, determine the actual number of plates in the rectifying section. A total condenser is used. The equilibrium data for benzene-toluene in mass fraction is given below:

If the operating pressure of a gas-absorption column is increase, all other conditions remaining the same, the height of the column will

A continuous countercurrent adiabatic dryer is being designed to produce 500 lb/hr of a product containing 2 % moisture from a feed containing 30 % moisture. The air entering the dryer is at a dry bulb temperature of 230°F and wet bulb temperature of 102°F It leaves at 115°F. Because of the small size of the crystals being dried, the highest allowable air velocity should be 10 lb of dry air per minute per square foot of cross-section. What should be the cross-sectional area of the dryer in ft²?

Estimate the relative volatility of n-heptane/ n-octane mixture at 110°C and 2 atm?

A gas absorption packed column containing 1-inch ceramic Raschig rings is to recover 99% of NH₃ in air. The ammonia stream fed to the absorber uses water as the absorbing liquid. The ammonia content of the air is 30 m-%. The total gas flow rate is 300 lb moles/hr. The absorber temperature is to be kept at 40°C by cooling coils. The cross-sectional area of the tower is 1.5 ft² and it is estimated that the over-all mass transfer coefficient, K’_Ga = 70 lb moles/hr-ft³-atm. If the water flow rate used is 969 lb moles/hr, estimate the height of the packed column.

A room 20 ft x 20 ft x 10 ft is charged with air every 8 minutes at 70°F dry bulb and 65°F wet bulb by cooling outside air available at 120°F dry bulb and 100°F wet bulb. Estimate the tons of refrigeration needed to cool the air.

A mixture of ethanol vapor and nitrogen has a dry bulb temperature of 122°F and wet-bulb temperature of 68°F at 1 atm. Latent heat of evaporation for ethanol is 16,910 Btu/lb mole. Diffusivity of ethanol in nitrogen is 0.44 ft²/hr. Vapor pressure of ethanol at 68°F is 43.6 mmHg and at 122°F is 229 mmHg. For nitrogen-ethanol vapor mixture, h_G/k_y = 0.379 Btu/lb-°F. Determine the percentage humidity, also called percentage saturation.

In gas absorption, when the number of transfer units in the gas phase is equal to unity, it means that

Air enters a cooling tower at a d.b temperature of 77°F and a w.b. temperature of 62°F. Water enters counter-currently at 110°F and leaves at 85°F. What is the minimum air flow rate in lb dry air per hour expected if water entering the tower is 1000 gal/min.

Benzene in an air/benzene mixture is to be removed in a plate gas absorber using hydrocarbon oil (M=200). The absorber operates at constant temperature of 80°F and at 1 atm. The mixture enters the bottom of the tower at a rate of 600 lb mols/hr containing 5% benzene by volume. Assuming Raoult’s law applies, determine the minimum liquid flow rate in lb/hr to recover 90% of the entering benzene. Assume the vapor pressure of benzene at 80°F is 103 mmHg.

In dehumidification of air-water vapor mixture, the temperature of the contacting liquid must be

A wet solid is dried in a batch drier under constant drying conditions from 40% db to 8% db in 20 hours. The critical moisture content is 15% db and the equilibrium moisture content is 4% db. How long should it take to dry the solid from 40% db to 5% db under the same drying conditions?

If 400 pounds of moist air at 56°F dry bulb and 50°F wet bulb are mixed with 855 pounds of moist air at 82°F dry bulb and 60°F wet bulb, what will be the wet bulb temperature of the mixture in °F.

Wet solid is fed to a dryer at the rate of 0.3 kg/s and the moisture removed is 35 % of the wet charge. The feedstock enters and leaves the dryer at 324 K. The air enters the dryer countercurrently at a dry bulb temperature of 341 K and absolute humidity of 0.01 kg water/kg dry air, and it leaves at a dry bulb temperature of 310 K and H = 0.02 kg water/kg dry air. Determine the heat loss to the surroundings in kW.

A simplified equimolal MTC is estimated to be 4.00 x 10^-5 kg-mol/s-m². If the same system is to be processed in a wetted-wall column where the concentrations of the transferring components in the gas-phase entering and leaving are y_A1 = 0.26 and y_A2 = 0.01 mole fraction, respectively, what mass transfer coefficient will be applied in kg-mol/s-m²?

A rotary countercurrent dryer is fed with ammonium nitrate crystals containing 5 % moisture at the rate of 1.5 kg/s, and discharges the nitrate with 0.2 % moisture. The air enters at 405 K and leaves at 355 K; the humidity of the entering air being 0.007 kg moisture/kg dry air. The nitrate enters at 294 K and leaves at 339 K. Neglect radiation losses. Latent heat of water at 294 K is 2450 kJ/kg. Specific heat capacity of ammonium nitrate is 1.88 kJ/kg-K. Specific heat capacity of dry air is 0.99 kJ/kg-K. Specific heat capacity of water vapor is 2.01 kJ/kg-K. Estimate the mass flow rate of dry air in kg/s.

This is the moisture in the solid that exerts a vapor pressure less than that of a pure liquid at the prevailing conditions

An adiabatic tunnel drier is to be designed to handle 1200 lb per hour of wet crystals from a moisture content of 30% to 5% wb. It has been found that the drying times in Zone I and Zone II of the dryer are 4.56 hr and 1.461 hr, respectively. What will be the length of the dryer if it can hold 50 lb of dry material per foot of dryer.

It has been determined that the equivalent HTU and NTU of a packed absorption tower are 1.6 ft and 21, respectively. If the same separation can be done in a 15-plate absorption tower whose over-all plate efficiency is 78 %, then the HETP is

A condo unit has a floor area of 40 m² and a height of 3 m. The temperature and the relative humidity in the unit are to be maintained at 24°C and 80%, respectively. The closed-loop air-conditioning unit installed for the purpose has an air handling capacity to change the air in the room, of which 80% is void space, every 10 min. The air leaving the condenser of the A/C unit has a temperature of 18°C. Assume the air leaving the A/C unit is saturated. What should be the kilowatt rating of the A/C?

If drying occurs at a linear falling rate period initially at its critical moisture content, doubling the drying time will reduce the moisture content by _______% compared to the initial moisture content.

The air in a room 35 ft x 60 ft x 12 ft is to be changed every 2 minutes and is to be supplied to the room at 70°F and 40% relative humidity. The worst winter conditions outside will be 0°F and zero humidity. The operation is to consist only of preheating and then humidifying adiabatically to the desired condition. What will be the volume of the spray chamber used in humidifying the preheated air if the overall heat transfer coefficient is 90 Btu/(hr-ft³-°F)?