CL 351                                   Homework # 1

 

Due date: 4 August, 2005

 

Shell mass balances and diffusion coefficients

 

1.       A spherical ball of solid, nonporous naphthalene, a “moth ball,” is suspended in still air.  The ball slowly sublimes, releasing the naphthalene into the surrounding air by molecular diffusion.  Estimate the time required to reduce the diameter from 2 cm to 0.5 cm when the surrounding air is at 347 K and 1 atm.  Naphthalene has a molecular weight of 128 g/mole, a solid density of 1.145 g/cm3, a diffusivity of 8.19 x 10-6 m2/s, and exerts a vapour pressure of 5 torr at 347 K.

 

1.       Tubular membranes of silicone rubber can be used for bubbleless aeration of water.  Pure and pressurized oxygen is passed inside a silicone rubber tubing of inner diameter 12.7 mm and wall thickness 3.2 mm.  The tubing is immersed in a large volume of an aqueous solution.  Silicone rubber is permeable to oxygen gas but not to water.  The oxygen gas dissolves into silicone, diffuses through it and then dissolves into water.  This process is use to deliver oxygen to aqueous suspensions of fragile microorganisms that could be damaged by the fluid forces associated with vigorous bubble aeration.  If pure oxygen at a pressure of 2 atm is passed in the tube and the dissolved oxygen concentration in the aqueous solution is 0.05 mole O2/m3, what is the flux of oxygen to the outer surface of the tube?  Diffusivity of O2 in silicone is 1 x 10-11 m2/s at 298 K.  The partition constant for dissolution of O2 gas within the silicone is 3.16 mole/(m3 atm) at 298 K.  Concentration of dissolved O2 gas in the silicone is 2.5 times the concentration of dissolved O2 gas in water.

 

2.       For a binary mixture of A and B, prove that DAB = DBA if partial molal volumes are constant and the fluxes are expressed relative to volume average velocity.

 

3.       In one microelectronics application, a depression of 5 x 10-3 cm is filled with gallium arsenide and, the top surface is coated with zinc.  Researchers have found that a slight scratch on the surface of gallium arsenide causes a zinc dopant to diffuse into the arsenide.  When these devices at later baked at 850oC, zinc diffuses into the gallium arsenide.  If it spreads enough to increase the zinc concentration to ten percent of the maximum at 4 x 10-4 cm, the device is ruined.  If the diffusion coefficient of zinc is 10-11 cm2/s, how long can we bake the device?

 

4.       Estimate the diffusion at 25oC for oxygen in dissolved water using Wilke-Change correlation.  Compare your results with the experimental value of 1.80 x 10-5 cm2/s.