Mass Transfer

1. What are the advantages of distillation over absorption?

2. Define the term relative volatility

3. State Henry's law

4. What is Murphree tray efficiency?

5. What is meant by equilibrium distillation?

6. What is absorption factor?

7. What is molecular distillation?

8. Sketch the operating line and equilibrium curve for an absorber and stripper

9. What is meant by minimum liquid gas ratio?

10. What is plait point?

11. Explain percolation method of leaching?

12. Define distribution coefficient and state its importance

13. What is electrodialysis?

14. What are the properties of solvent for extraction?

15. What is ion retardation?

16. Mention few industrial adsorbents

17. What is adsorption hysteresis?

18. Write the principle of ion-exchange

19. What is meant by constant molal over flow?

20. What is the role of Raoult's law in distillation?

Part B

21. (a) Write short notes on:

(i) Azeotropic distillation

(ii) Extractive distillation

(iii) Rayleigh's equation

Or

(b) A binary mixture of benzene and toluene containing 40% of benzene is to be distilled at 1 atm pressure to recover 95% of the benzene. Estimate the molal percent of mixture to be distilled and the composition of the distillate obtained if distillation is carried out by

(i) Equilibrium distillation

(ii) Differential distillation, collecting all the distillate together.

The average relative volatility of benzene to toluene is 2.5.

22. (a) Explain in detail, the method of estimation of number of stages by Mc Cabe - Thiele method.

Or

(b) A continuous fractionator is to be designed for separating a feed mixture containing equimolar amounts of CCl₄ and CS₂ to get a top product containing 95% CS₂ and bottom product containing 6% CS₂ at 1 atm pressure. The feed is saturated vapor and fed at the rate of 5000 kg/hr. A total condenser is used and reflux is returned to the top plate as a saturated liquid. The equilibrium data is given below:

x	0.06	0.11	0.26	0.39	0.53	0.66	0.76	0.86	1
y	0.16	0.27	0.50	0.63	0.75	0.83	0.88	0.93	1

(i) Determine the flow rate of top and bottom product

(ii) Calculate the theoretical number of trays required if a reflux ratio of 2 times Rm is used.

(iii) Locate the feed tray.

23. (a) Derive an expression for the number of plates in terms of absorption factor.

Or

(b) The experimental data given below are obtained for the absorption of ammonia from air into water using a 2.5 cm diameter Rasching rings packed in a 25 cm diameter up to 2 m. The total pressure is 1 atm and the average temperature is 20^oC. Air flow rate excluding ammonia is 105 m³/hr and the water flow rate is 400 kg/hr. Ammonia concentration in the gas inlet is 7% and in the outlet is 0.314%. The interfacial area of packing is 185 m²/m³. Partial pressure of ammonia at equilibrium with the solution at the bottom is 0.011 atm and at the top is zero/since pure water is used. Assuming that both equilibrium and operating line are straight, calculate:

(i) Overall mass transfer coefficient for the system.

(ii) The number of overall gas phase transfer unit.

(iii) The height of overall gas phase transfer unit.

24. (a) With neat sketch, explain the working of Bollman extractor.

Or

(b) An aqueous solution of solute C is to be extracted with pure solvent B to recover the solute. The equilibrium data in terms of weight % of solute in the two layers are given below:

Aqueous layer	2	8	15	20
Solvent layer	8	22	35	45

A feed 20% by weight of solute is to be treated in two consecutive cross current cascades using aqueous solution to solvent ratio of 1.8. Calculate:

(i) Concentration of final raffinate

(ii) Amount of raffinate

(iii) % recovery of solute

(iv) Amount of solvent to be used for a single stage extraction to obtain the same final concentration.

Water and solvent are immiscible with each other.

25. (a) Write short notes on:

(i) Electrodialysis

(ii) Ultrafiltration

(iii) Reverse osmosis

Or

(b) The equilibrium absorption of acetone vapor on activated carbon at 30^oC is given below:

Acetone partial pressure, in mm Hg	2	12	42	92
Gram acetone/Gram carbon	0.1	0.2	0.3	0.35

The vapor pressure of acetone at 30^oC is 283 mm Hg. A one litre flask containing air and acetone mixture at 1 atm is fed with 2 gram of activated carbon and then sealed. Compute the final vapor concentration and the final pressure. Neglect the adsorption of air.

Mass Transfer - GATE problems

1. (a) Simplify the Fick's law of mass diffusion for equimolar counter diffusion for a binary system.

(b) In a gas mixture of hydrogen and oxygen, steady state equimolar counter diffusion is occuring at a total pressure of 100 kPa and temperature of 20^oC. If the partial pressures of oxygen at two planes 0.01m apart, and perpendicular to the direction of diffusion are 15 kPa and 5 kPa, respectively and the mass diffusion flux of oxygen in the mixture is 1.6 x 10^-5 kmole/(m².sec), Calculate the molecular diffusivity for the system.

2. Carbon disulfide is to be absorbed from a dilute gas mixture of CS₂ - N₂ into a pure nonvolatile oil at atmospheric pressure in a counter current absorber. The molefraction of CS₂ in inlet gas stream is 0.05 and the flow rate of gas stream, G is 1500 kmol/hr. The equilibrium relation is given by:
y = 0.5x
where x is the molefraction of CS₂ in liquid stream. It is desired to reduce the mole fraction of CS₂ in the exit gas stream to 0.005.
(a) Calculate the minimum value of L/G where L is the liquid flow rate in kmol/hr.
(b) Derive the equation for the operating line if L/G is equal to 1.5 times the minimum value.

3. A liquid mixture containing 50 mole % each of benzene and toluene at 40^oC is to be continuously flash vaporized to vaporize 60 mole % of the feed. The residual liquid product contains 35 mole % benzene. If the enthalpies per mole of feed, the liquid product and the vapor product are respectively 2,5 and 30 kJ/mole,

(a) calculate the heat added in kJ per mole of vapor product

(b) represent the process on a H-x-y diagram

4. 160 kg of wet solid is to be dried from an initial moisture content of 25% to a final value of 6%. Drying test shows that the rate of drying is constant at 3 x 10^-4 kg H₂O / m².s in the region 0.2 - 0.4 ⁴ kg H₂O / kg solid. The drying rate falls linearly in the range 0.01 - 0.2 kg H₂O / kg solid. If the equilibrium moisture content is 0.01 kg H₂O / kg solid, calculate the time of drying. The drying surface is 1 m² / 30 kg dry weight.

5. A material having a critical moisture content of 24% is dried under constant drying conditions in slabs of dimensions 20cm x 20cm x 2cm from a moisture content of 40% to 25% in 8 hours. Drying takes place from the two larger surfaces only. The same material is dried in slabs of 40cm x 40cm x 4cm under similar drying conditions from 50% to 25% moisture content. All moisture content are on wet basis. If the critical moisture content and other physical properties remain unchanged, how long will the drying take?

6. In a laboratory drying test with a solid material the following relation for the falling rate period was obtained,

dX/dq = -0.8 (X - 0.05)

where X is the moisture content on dry basis and q is the time in hours. The critical moisture content is 1.4 kg moisture per kg of dry material. Calculate:

a. the time required for drying the material from X₁ = 4.0 to X₂ = 0.1

b. the equilibrium moisture content.

7.Drying of a food product is carried out in an insulated tray. The drying air has a partial pressure of water equal to 2360 Pa and a wet bulb temperature of 30^oC. The product has a drying surface of 0.05 m²/kg dry solid. The material has a critical moisture content of 0.12 (dry basis) and negligible equilibrium moisture content. The drying rate in the falling rate period is proportional to the moisture content and the mass transfer coefficient is 5.34 x 10^-4 kg/m²hrPa. Calculate:

a.the drying rate in the constant rate period in kg/m²hr

b. the time required to dry the material from a moisture of 0.22 to 0.06 (both on dry basis).

Vapor pressure of water at 30^oC = 4232 Pa.

1. Derive from first principles an expression for steady state diffusion of a liquid species A through a stagnant liquid species B.
2. Explain the psychrometric chart with the help of a neat sketch. Also indicate the method of obtaining the various characteristic curves for a given gas-solvent vapor system.
3. Discuss the significance and application of psychrometric charts in simultaneous heat/mass transfer operations.
4. Explain the two film theory of interphase mass transfer. Discuss the reasons for modifying this theory later, by Higle and Dauckwefts.
5. Discuss the need for defining the interphase mass transfer resistance in terms of overall coefficients. How they are related to individual coefficients?
6. Define J factors for heat and mass transfer. State its applications and limitations.
7. Find an expression for obtaining the total drying time for the drying of a wet solid material under constant drying conditions of to a final moisture content well below the critical moisture content.
8. Discuss in detail each one of the following processes separately giving an example.

1. Direct fractional crystallization
2. Extractive fractional crystallization
3. Adductive fractional crystallization

1. Discuss the theory of wet-bulb thermometry. Under what conditions the wet-bulb temperature and adiabatic saturation temperature will be identical.
2. Discuss the steady state diffusion of A through a non-diffusing B and show how the diffusion rate will be modified when component B is counter diffusing.
3. State Higbie's theory for mass transfer and the assumptions made in deriving the expression for mass transfer coefficient.
4. Discuss the Reynolds analogy of heat and momentum transport. How they are rectified by Prandtl and Von Karman in their analogies?
5. Discuss in detail the design of a cooling tower based on enthalpy transfer unit concept. State the important assumptions made and the limitations in application.
6. Discuss the concept of the transfer units used in mass transfer problems. How is overall height of a transfer unit related to the individual heights of transfer unit.
7. How does the super-saturation theory explain the phenomenon of crystallization?
8. What is DL law? How is crystal growth controlled in continuous crystallizers?
9. Describe a method to estimate the diffusivity of a volatile solvent into air.
10. Discuss Penetration theory of mass transfer giving its application.
11. Describe the method of obtaining the length and diameter of a rotary dryer.
12. Describe the various types of cooling towers employed in cooling hot water from process plants.
13. State and derive Lewis relationship. What are its applications and limitations?
14. What is psychrometric ratio? Indicate the methods by which the mass transfer coefficient and heat transfer coefficient are obtained when Lewis relationship fails.
15. List and explain the different ways in which the drying rate of a given substance in the constant rate period may be increased.
16. Giving reasons, indicate the type of dryer that can be used for the following purpose:

1. Removal of the last 6 percent moisture from salt
2. Drying of cakes of soap
3. Drying of heat sensitive materials like pharmaceuticals
4. Drying of paddy

1. Explain the meaning of gas-film controlled and liquid-film controlled mass transfer processes with suitable examples.

1. The following data were obtained during a test run of a packed cooling tower of 0.4 m dia and 1 m packed height, operating at atmospheric pressure. Calculate the humidity of the exit air by means of an enthalpy balance. Average temperature of entering and leaving air is 38^oC and 39^oC respectively. Average temperature of water entering and leaving is 46^oC and 35^oC respectively.

Rate of entering air = 13.6 m³/min

Rate of entering water = 1000 kg/hr

Humidity of entering air = 0.0175 kg water vapor / kg dry air

Latent heat of evaporation of water = 589 kcal/kg

Specific heat of air = 0.245 kcal/kg^oC

Specific heat of water vapor = 0.45 kcal/kg^oC

2. A wet solid material is dried from 0.7 kg water/kg dry solid to 0.08 kg water/kg dry solid in a continuous counter-current drier from which the product flows out at the rate of 500 kg/hr. The inlet air to the drier is at 54^oC with an initial humidity of 0.015 kg water/kg of dry air and the exit air is at 32.2^oC with 80% saturated humidity. Calculate the inlet air rate in m³/hr and the heat supplied by the preheater if the atmospheric temperature is 24^oC.

Data:

Saturated humidity at 32.2^oC = 0.025 kg water/kg dry air

Specific volume of dry air at 54^oC = 0.925 m³/kg

Saturated volume = 1.09 m³/kg

Humid heat 0.015 humidity = 0.243 cal/gm^oC

Humid heat at 32.2^oC and at 80% saturated humidity = 0.250 cal/gm^oC

3. For a drying process, air is required at 38^oC with a dew point of 21^oC. To make this air at 15^oC and 40 percent relative humidity is first heated and passed through an adiabatic humidifier until the required conditions are obtained. Estimate the temperature to which air is to be heated first. Vapor pressure of water: 12.8 mm Hg at 15^oC and 18.7 mm Hg at 21^oC. Latent heat of vaporization at 38^oC = 576 cal/gm. Specific heat of dry air = 0.24 and that of water vapor = 0.48
4. A continuous counter-current drier is to be used to dry 10000 kg per hour of wet solid containing 5% water (wet basis) to a water content of 0.1% (wet basis). Ambient air at 27^oC and a humidity of 0.0075 will be heated to 150^oC and the heated air is passed through the drier. The air leaving the drier is at 70^oC with a percentage humidity of 10 percent. Calculate the air required and the heat supplied in the preheater.

Saturation humidity at 70^oC = 0.299

Humid heat of inlet air = 0.243 cal/gmol^oK

5. Conditioned air at 24^oC and 40% saturation is to be supplied to a laboratory room of size 4 X 20 X 6 meters, with no facility for recirculation. The air-conditioner takes outside air with 90% relative humidity at 38^oC which it refrigerates and separates out the condensed water and then reheats it in a heat exchanger using condensing steam at 1 atm pressure. Determine the following:
1. The volume of outside air at entry conditions, and the temperature to which it must be cooled.
2. The tonnes refrigeration required and the kg of saturated steam required per hour.
6. A mixture of oxygen and acetone vapor at a total pressure of 1050 mm Hg at 25^oC has a percentage saturation of 75%. Calculate:
1. The molal humidity
2. Absolute humidity
3. Relative humidity
4. Volume percent acetone
5. Molal humid volume and
6. Molal humid heat.

The saturation vapor pressure of acetone at 25^oC is 290 mm Hg and the specific heats of oxygen and acetone vapor are 0.25 and 0.35 kcal/kg^oC respectively.

7. The air supply to a rotary drier has a dry bulb at 32.5^oC and a wet bulb of 25^oC. the air is heated by steam coils to 95^oC before it enters the drier. In passing through the drier, the air cools along adiabatic cooling line and finally leaves the drier at 90% saturation.
1. Estimate the temperature of exit air
2. Calculate the diameter of the drier if it is to handle 10 tones per hour of a salt with 10% moisture on wet basis. Air mass velocity is given as 5000 kg per hour per sq.ft. and the salt is to be dried to 2% moisture content.
8. A mechanical draft cooling tower is to be designed to cool 75000 kg/hr of water from 45^oC using 62500 kg of dry air per hour. 24^oC is suggested as the design air wet bulb temperature. Calculate the number of transfer units and hence the height of the packed section if the height of a transfer unit for the condition stated above is 4 m. It may be assumed that the liquid phase resistance to heat transfer is negligible. Temperature t ^oC - saturated enthalpy in kcal/kg dry air (H) data is as follows:

t ^oC	24	29	32.5	38	43.5
H	20	25	28	36	46

9. A horizontal spray chamber with recirculated water is to be used for the adiabatic humidification and cooling of air. The active part of the chamber is 1.5 m long and a cross section of 6 m with the nozzle arrangements provided and when operated with water circulation rate recommended by the nozzle manufacturer, the coefficient of heat transfer is expected to be h_Ga = 1600 kcal/hr.cm.^oC. An amount of 200 cc/min of air at 65^oC, Y' = 0.017 kg water / kg dry air, is to be blown through the spray. Determine
1. What exit temperature and humidity can be expected from the air
2. Express the performance in terms of k_ya, N_tOG, and H_G and stage efficiency

Note: For air water system C_S (humid heat) = 0.24 + 0.45 Y'

10. The air supply to a drier has a dry bulb temperature of 21^oC and wet bulb temperature of 15^oC. It is heated to 90^oC by heating coils and introduced into the drier. In the drier it cools along adiabatic cooling line and leaves the drier fully saturated.
1. What is the dew point of the initial air?
2. What is its humidity?
3. How much water will be evaporated per 100 cubic meters of entering air?
4. How much heat is needed to heat 100 cubic meters to 90^oC?
5. At what temperature does the air leave the drier?

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