## PREGATE-4

1. A gas mixture of 100 kmol consists of carbon dioxide, oxygen, water vapour, and nitrogen at 500 K and 110 kPa. In a sample of the gas the molar fractions of CO2 and O2 are 12% and 6%, respectively. The weight fraction of H2O in the gas is 6.17%. Estimate the density of this gas at the said temperature and pressure. (Ans: 0.772 kg/m3)

2. A liquefied gas mixture has the following molar composition: 93.5% CH4, 4.6% C2H6, 1.2% C3H8, and 0.7% CO2. Calculate:

2. A liquefied gas mixture has the following molar composition: 93.5% CH4, 4.6% C2H6, 1.2% C3H8, and 0.7% CO2. Calculate:

(a) Average molecular weight of the LNG mixture (Ans: 0.017 kg/mol)

(b) Weight fraction of CH4 in the mixture (Ans: 0.871).

(c) The gas mixture is heated to 300 K and 150 kPa, and vaporise completely. Estimate the density of the gas mixture under these conditions (Ans: 1.022 kg/m3)

3. A gas stored in a 30 m3 container at 340 K and 101.3 kPa is saturated with water vapour. Partial pressure of water vapour is 27.35 kPa. Determine the following of the gas mixture:

a) Mole fraction of water vapour (Ans: 0.27).

b) Average molecular weight of the mixture (Ans: 0.026 kg/mol). c) Total mass contained in the tank (27.985 kg).

d) Mass of water vapour in the tank (5.224 kg).

4. NH3 is being absorbed from an NH3 (A)-air (B) mixture in H2SO4. The concentration of NH3 in the air, 10 mm from the acid surface is 40% by volume and that at the acid surface is negligible. The total pressure in the system is 400 mm Hg and temperature is 270C. Calculate (a) the rate of absorption of NH3 across 0.1 m2 gas liquid contact area, (b) the partial pressure gradient of NH3 at 4 mm from the acid surface, (c) the rate of mass transfer of NH3 by molecular transport and that by bulk flow at the acid side end of the film, and (d) the rate of mass transfer of NH3 by molecular transport and that by bulk flow at the gas side end of the film. Given: (DAB×P)/T1.5=Constant; DAB of NH3 at 1 atm. and 600C is 2.53×10-5 m2/s. Ans: (a) 4.486×10-6 kmol/s; (b) 21.92 atm/m; (c) 4.486×10-5 kmol/ m2s; and 0 (d) 2.69×10-5 kmol/m2s and 1.79×10-5 kmol/m2s

5. Equimolar counter-diffusion of A and B occurs between points 1 (yA1=0.3) and 2 (yA2=0.1) through a distance of 1 cm. Total pressure is 1 atm, temperature is 250C and diffusivity is 0.2 cm2/s. What is the “diffusion velocity” of „A‟ halfway in the diffusion path? Ans: 2 mm/s

6. A mixture of C6H6 (A) and C6H5Cl (B) is being separated by fractional distillation. If molar latent heats of vaporization are 94.0 and 78.0 K Cal/kg, respectively, for C6H6 and C6H5Cl, value of NA/NB is ______ across the vapor film. Ans: -0.83

7. Ammonia is absorbed into water from an air- ammonia mixture at 300 K and 1 atm. The individual film coefficients are kL = 6.3 cm/hr and kG = 1.17 kmol/m2-hr-atm. The equilibrium relationship for very dilute solutions of ammonia in water at 300 K and 1 atm is 1.64. Determine: a) ky and kx c) Ky. Ans: a) 3.25 10-4 kmole/m2s, b) 9.722 10-4 kmole/m2s, c) 0.21 kmole/m2s.

8. An ethanol (A)-water (B) solution in the form of a stagnant film 2.0 mm thick at 293 K is in contact at one surface with an organic solvent in which ethanol is soluble and water is insoluble. Hence NB = 0. At point 1, the concentration of ethanol is 16.8 wt% and the solution density is 972.8 kg/m3. At point 2, the concentration of ethanol is 6.8 wt% and density is 988.1 kg/m3.The diffusivity of ethanol is 0.740 × 10-9 m2/s. Calculate the steady state flux NA.

9. In an experimentation, dry air flows upward through the core of a wetted column where water flows down the inside wall. The wetted column is a 25-mm ID and 1 m long. Dry air enters at the rate of 7 kg/m2-s. The air is controlled everywhere at its average conditions of 309 K and 1 atm, the water at 294 K, and the mass-transfer coefficient constant. Estimate the average partial pressure of water in the air leaving. Ans: 1.578 kPa.

4. NH3 is being absorbed from an NH3 (A)-air (B) mixture in H2SO4. The concentration of NH3 in the air, 10 mm from the acid surface is 40% by volume and that at the acid surface is negligible. The total pressure in the system is 400 mm Hg and temperature is 270C. Calculate (a) the rate of absorption of NH3 across 0.1 m2 gas liquid contact area, (b) the partial pressure gradient of NH3 at 4 mm from the acid surface, (c) the rate of mass transfer of NH3 by molecular transport and that by bulk flow at the acid side end of the film, and (d) the rate of mass transfer of NH3 by molecular transport and that by bulk flow at the gas side end of the film. Given: (DAB×P)/T1.5=Constant; DAB of NH3 at 1 atm. and 600C is 2.53×10-5 m2/s. Ans: (a) 4.486×10-6 kmol/s; (b) 21.92 atm/m; (c) 4.486×10-5 kmol/ m2s; and 0 (d) 2.69×10-5 kmol/m2s and 1.79×10-5 kmol/m2s

5. Equimolar counter-diffusion of A and B occurs between points 1 (yA1=0.3) and 2 (yA2=0.1) through a distance of 1 cm. Total pressure is 1 atm, temperature is 250C and diffusivity is 0.2 cm2/s. What is the “diffusion velocity” of „A‟ halfway in the diffusion path? Ans: 2 mm/s

6. A mixture of C6H6 (A) and C6H5Cl (B) is being separated by fractional distillation. If molar latent heats of vaporization are 94.0 and 78.0 K Cal/kg, respectively, for C6H6 and C6H5Cl, value of NA/NB is ______ across the vapor film. Ans: -0.83

7. Ammonia is absorbed into water from an air- ammonia mixture at 300 K and 1 atm. The individual film coefficients are kL = 6.3 cm/hr and kG = 1.17 kmol/m2-hr-atm. The equilibrium relationship for very dilute solutions of ammonia in water at 300 K and 1 atm is 1.64. Determine: a) ky and kx c) Ky. Ans: a) 3.25 10-4 kmole/m2s, b) 9.722 10-4 kmole/m2s, c) 0.21 kmole/m2s.

8. An ethanol (A)-water (B) solution in the form of a stagnant film 2.0 mm thick at 293 K is in contact at one surface with an organic solvent in which ethanol is soluble and water is insoluble. Hence NB = 0. At point 1, the concentration of ethanol is 16.8 wt% and the solution density is 972.8 kg/m3. At point 2, the concentration of ethanol is 6.8 wt% and density is 988.1 kg/m3.The diffusivity of ethanol is 0.740 × 10-9 m2/s. Calculate the steady state flux NA.

9. In an experimentation, dry air flows upward through the core of a wetted column where water flows down the inside wall. The wetted column is a 25-mm ID and 1 m long. Dry air enters at the rate of 7 kg/m2-s. The air is controlled everywhere at its average conditions of 309 K and 1 atm, the water at 294 K, and the mass-transfer coefficient constant. Estimate the average partial pressure of water in the air leaving. Ans: 1.578 kPa.

10. For a system in which component A is transferring from the gas phase to the liquid phase, the equilibrium relation is given by PA,i = 0.8XAi where PA,i is the equilibrium partial pressure in atm. and XA,i is the equilibrium liquid concentration in molar fraction. At one point in the apparatus, the liquid stream contains 4.5 mole % and the gas stream contains 9.0 mole % A. The total pressure is 1 atm. The individual gas-film coefficient at this point is kG = 3.0 mole/m2-s-atm. Fifty per cent of the overall resistance to mass transfer is known to be encountered in the gas phase. Evaluate

a) The overall mass-transfer coefficient and individual liquid-film coefficient

b) The molar flux of A

c) The interfacial concentrations of A.

Ans: a) ky = 3.0 mole/m2/s, Ky = 1.5 mole/m2/s, kx = 2.4 mole/m2/s; b) 0.081 mole/m2/s; c) xAi = 0.079, yAi = 0.0632

11. Nicotine is to be extracted from a liquor using a solvent in a three-stage crosscurrent device. The feed rate is 2000 kg/hr, containing 10 mass % nicotine. 95% of the solute has to be recovered. The solvent has 0.001 kg nicotine/kg pure solvent. The equilibrium in the system can be expressed as Wl=0.85 Ws, where, Wl is kg nicotine/kg nicotine-free feed and Ws is kg is the nicotine/kg nicotine free solvent. If equal amounts of solvent are used in the stages, calculate the total solvent requirement Ans. 8541 kg

11. Nicotine is to be extracted from a liquor using a solvent in a three-stage crosscurrent device. The feed rate is 2000 kg/hr, containing 10 mass % nicotine. 95% of the solute has to be recovered. The solvent has 0.001 kg nicotine/kg pure solvent. The equilibrium in the system can be expressed as Wl=0.85 Ws, where, Wl is kg nicotine/kg nicotine-free feed and Ws is kg is the nicotine/kg nicotine free solvent. If equal amounts of solvent are used in the stages, calculate the total solvent requirement Ans. 8541 kg

12. A gas stream comprising of air and vapor of an organic compound is to be scrubbed in an absorption tower for separation of organic compound by absorption in oil. The operation is countercurrent.

Given: Mol. wt. of oil: 250 kg/kmol; Inlet concentration of vapor of organic compound in gas stream: 5% (by volume); Targeted (or desired) removal of organic vapor: 95%; Flow rate of gas stream: 1000 m3/h at 1.2 bar and 30oC; Mol wt of organic vapor: 80 kg/kmol and vapor pressure of organic vapor at 30oC: 0.125 bar. You can assume that the system obeys Raoult’s law. If the inlet oil to the absorption column does not contain any trace of organic vapor initially, answer the following:

(A) Calculate the minimum flow rate of oil to the column for desired removal of organic vapor.

(B) Calculate the number of theoretical stages using Kremser’s equation if the absorption factor A = L/mG = 1.4.

If the inlet oil to the absorption column contains 0.5% by mass of organic compound initially, answer the following:

(C) Calculate the number of theoretical stages of the absorption factor L/mG = 1.4. Ans. (a) Lmin=943 kg/hr; (b) 6; (c) 9.

13. A gas flows at the rate of 15 kmol/s at 298 K and 1 atm with a H2S content of 0.10 mol%. Ninety five percent of the hydrogen sulfide is to be removed by absorption with a pure liquid at 298 K. The design liquid flow rate will be 30% higher than the minimum. Under these conditions, The equilibrium line is Y = 10X/(1- 9X) based on solute free basis.

(a) Calculate the operating flow rate of the liquid and the H2S concentration in the liquid leaving the absorber

(b) Calculate the number of ideal stages required for the specified flow rates and %H2S removal.( a) 185.0453 kmol/s, 7.70×10-05 (b) 7.25

14. Determine the following psychrometric properties of a moist air sample having a dry-bulb temperature 270C and a humidity of 0.015 kg/kg dry air, using the psychrometric chart and/or the vapor pressure equation for water: (a) Relative humidity (b) Dew point (c) Adiabatic saturation temperature (d) Wet-bulb temperature (e) Enthalpy (f) Humid volume (g) Humid heat. Antoine Equation: ln PAV (bar)=11.96481-3984.923/(T-39.724). Total pressure is 1 atm. Ans: (a) 66.8%; (b) 20.30C; (c) 22.50C; (d) 22.50C; (e) 64.7, 65.6, 64 kJ/kg dry air; (f) 0.87, 0.88, 0.873 m3/kg dry air; (g) 1.033 kJ/kg dry air. 0C

15. A sample of air has a dry-bulb temperature of 330C and wet-bulb temperature of 230C. The total pressure is atmospheric. (a) Determine the following psychrometric properties – humidity; enthalpy; dew point; humid volume and humid heat. (b) If the sample air is heated to 500C, what will be its wet-bulb temperature? (c) How much heat is rejected if 1 kg of air (dry basis) is cooled down from 330C to 150C? (d) If the air sample is heated to 500C and its pressure is doubled (2 atm.), what would be its relative humidity and dew point? Antoine Equation: ln PAV (bar)=11.96481-3984.923/(T-39.724). Ans : (a) Humidity, Y/=0.014 kg/kg dry air; Enthalpy, H/=69.03 KJ/kg dry air; Dew point, Td=19.95 C; Humid volume, vH=0.0886 m3/kg dry air; Humid heat, cH=1.031 KJ/(kg dry air). C; (b) Twb=27oC; (c) H=28.558 KJ/kg dry air; (d) R.H.=37.77% and Td=31oC

14. Determine the following psychrometric properties of a moist air sample having a dry-bulb temperature 270C and a humidity of 0.015 kg/kg dry air, using the psychrometric chart and/or the vapor pressure equation for water: (a) Relative humidity (b) Dew point (c) Adiabatic saturation temperature (d) Wet-bulb temperature (e) Enthalpy (f) Humid volume (g) Humid heat. Antoine Equation: ln PAV (bar)=11.96481-3984.923/(T-39.724). Total pressure is 1 atm. Ans: (a) 66.8%; (b) 20.30C; (c) 22.50C; (d) 22.50C; (e) 64.7, 65.6, 64 kJ/kg dry air; (f) 0.87, 0.88, 0.873 m3/kg dry air; (g) 1.033 kJ/kg dry air. 0C

15. A sample of air has a dry-bulb temperature of 330C and wet-bulb temperature of 230C. The total pressure is atmospheric. (a) Determine the following psychrometric properties – humidity; enthalpy; dew point; humid volume and humid heat. (b) If the sample air is heated to 500C, what will be its wet-bulb temperature? (c) How much heat is rejected if 1 kg of air (dry basis) is cooled down from 330C to 150C? (d) If the air sample is heated to 500C and its pressure is doubled (2 atm.), what would be its relative humidity and dew point? Antoine Equation: ln PAV (bar)=11.96481-3984.923/(T-39.724). Ans : (a) Humidity, Y/=0.014 kg/kg dry air; Enthalpy, H/=69.03 KJ/kg dry air; Dew point, Td=19.95 C; Humid volume, vH=0.0886 m3/kg dry air; Humid heat, cH=1.031 KJ/(kg dry air). C; (b) Twb=27oC; (c) H=28.558 KJ/kg dry air; (d) R.H.=37.77% and Td=31oC

16. Determine the adiabatic saturation temperature and wet-bulb temperature of air-ethanol system. The temperature of air is 300C and it does not contain any ethanol.

Given: Diffusivity of ethanol in air, DAB=0.145 cm2/s at 313K and 1 atm; the vapor pressure equation of ethanol is lnPV=12.05896-3667.705/(T-46.966), T in K, take other properties of air from literature. Ans: 276.2K, 275.2K

17. The vapor pressure of an alcohol is 10.0 torr at 14.7 °C. Calculate the vapor pressure at 52.8 °C if its vaporization is 47.2 kJ/mol. (Ans: 100.2 torr)

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17. The vapor pressure of an alcohol is 10.0 torr at 14.7 °C. Calculate the vapor pressure at 52.8 °C if its vaporization is 47.2 kJ/mol. (Ans: 100.2 torr)

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