# Anna University Mass Transfer and Separation Model Paper

(V Semester) Mass Transfer and separation

**PART A Answer all the questions 10 X 2 = 20 marks**

1. Write down the Ficks first law of diffusion

2. Predict diffusivity of ovalbumin at 298 ^{o}K in water as a dilute solution. Molecular weight of Ovalbumin is 44,000 Kg/Kgmol and viscosity at 25 ^{o}C = 0.8937 X 10^{-3 }Pa.s.

3. Define Schimdt number

4. A strain of B.sphaericus is grown in 10 m^{3} fermenter. The maximum cell concentration achieved in the fermenter is 10 g/l. An improvement is made in the medium by precursor addition due to which the oxygen uptake rate of the organism is doubled. Determine the maximum cell concentration that can be achieved in the fermenter in the new medium. Assume the k_{L}a and oxygen solubility is not changing due to the precursor addition.

5. Define relative volatility of vapor liquid system

6. Explain Pressure Swing cycle in Adsorption

7. Explain weeping and flooding in tray towers

8. A polyethylene film 0.00015m thick is being considered for use in packaging a pharmaceutical product at 30 C. If the partial pressure of oxygen outside is 0.21 atms and inside the package is 0.01 atms. Calculate the diffusionflux of oxygen at steady state. Permeability of film=4.17 X 10-12m^{3}O_{2}/s.m^{2}.(atm/m)

9. What is meant by constant molal outflow in distillation.

10. Explain minimum boiling azeotroph mixture. Give an example.

**Part B Question no 11 is compulsory 5 X 16 = 80 marks**

*11. Aspergillus niger.* is used to produce citric acid in the 30 kl fermenter. The total fermentation time is 168 hrs. *Aspergillus niger* mycelia will form pellets during the growth phase and the size of the pellet will be 4-6 mm. The amount of citric acid produced by the culture largely depend on the effective oxygen transfer from the medium to A*.niger* pellets. Explain different resistances acting in the transfer of oxygen from gas bubble to *A.niger *pellets. State which step is rate limiting step after the formation of pellet.

12. An ion exchange column containing 99.3 g of amberlite ion-exchange resin was used to remove Cu2+ from a solution where Co = 0.18 M CuSO4. The tower height = 30.5 cm and the diameter 2.59 cm. the flow rate was 1.37 cm3 solution/s to the tower. The breakthrough data are shown below

t (S) | 420 | 480 | 510 | 540 | 600 | 660 |

C (gmol Cu/l) | 0 | 0.0033 | 0.0075 | 0.0157 | 0.0527 | 0.1063 |

t (S) | 720 | 780 | 810 | 870 | 900 | |

C (gmol Cu/l) | 0.1433 | 0.1634 | 0.1722 | 0.1763 | 0.180 |

The concentration desired at the breakpoint is c/co = 0.010. Determine the break point time, fraction of total capacity used upto the breakpoint and length of unused bed.

**(OR)**

13. A rectification column is fed 100 Kg mol /hr of a mixture of 50 mol% benzene and 50 mol% toluene. The feed is saturated vapor at dew point. The distillate is to contain 90 mol% benzene and the bottoms 10 mol% benzene. Calculate the Kg mol /h distillate & bottoms, minimum reflux ratio (Rm) and theoretical number of trays at an operating reflux ratio of 1.5 Rm. Equilibrium data are given below for the mole fraction Benzene

x | 1.000 | 0.780 | 0.581 | 0.411 | 0.258 | 0.130 | 0 |

y | 1.000 | 0.900 | 0.777 | 0.632 | 0.456 | 0.261 | 0 |

14. Derive the flux equation for gas liquid mass transfer in aerobic fermentations. State how the flux equation will vary for highly soluble and poorly soluble solute.

**(OR)**

15. Calculate the maximum rate of absorption of oxygen in a fermenter from air bubbles at 1 atms pressure having diameters of 100 µm at 37 ^{o}C into water having zero concentration of dissolved oxygen. The solubility of oxygen from air in water at 37 ^{o}C is 2.26 X 10^{-4} Kg mole O_{2}/m^{3}. The viscosity and density of water are 6.947 X 10^{-4} Pa.s and 994 Kg/m^{3}. The density of air is 1.13 Kg/m^{3}. The Schmidt number for the system is 215. Agitation is used to produce the air bubbles.

16. Experiments are being conducted to determine the suitability of a cellophane membrane 0.029 thick for use in an artificial kidney device. In an experiment at 37^{o}C using NaCl as the diffusing solute, the membrane separates two components containing stirred aqueous solutions of NaCl, where c_{1}=1.0X10^{-4} g.mol/cm^{3} and c_{2}=5.0 X 10^{-7} g.mol/cm^{3}. The mass transfer coefficients on either side of the membrane have been estimated as equal and its value is 5.24 X 10^{-5} m/s. Experimental data obtained gave a flux 8.11 X 10^{-4} g.mol NaCl/s.m^{2} at pseudo steady state conditions.

a) Explain different type of resistances and derive the equation for flux with series resistances in this membrane process.

b) Calculate the permeability p_{M} in m/s and D_{AB}.K’ in m^{2}/s

c) Calculate the percent resistance to diffusion in the liquid films.

**(OR)**

17. Derive the basic equations for the complete mixing model used for design of gas separation by membranes and the solution of equations for the calculating y_{p}, q, and A_{m} while all the other variables are known.

18. A drop of liquid toluene is kept at a uniform temperature of 25.9 ^{o}C and is suspended in air by a fine wire. The initial radius r1= 2.00 mm. The vapour pressure of toluene at 25.9^{o}C is p_{A1}= 3.84 kPa and r_{A} = 866 Kg/m^{3} , P = 101.325 kPa , R=8314 m^{3}.Pa/Kg mol. K , Molecular weight of toluene is 92.13 Kg/Kg mol , D_{AB} = 0.086 X 10^{-4} m^{2}/sec

a) Derive the equation to calculate the complete time taken for evaporation of the liquid

b) Calculate the time in secs for complete evaporation.

**(OR)**

19. a) Derive the equation for the experimental determination of diffusivity of gas by two bulb method.

b) Write the equation for converting k_{L} to k_{x} and k_{c}’ to k_{y}