PRACTICAL 10: Steady state 1-d mass transfer in absence of chemical reactions
1. In an oxygen-nitrogen gas mixture at 1 atm pressure, 25 oC, the concentration of oxygen at two planes 2 mm apart are 10 and 20 vol% respectively. Calculate the flux of diffusion of the oxygen assuming:
1. the N2 is non-diffusing (stagnant)
1. there is equimolar counter diffusion of the two gases
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2. Two very large tanks, maintained at 323 K and 1 atm total system pressure, are connected by a 0.1 m diameter circular duct which is 5 m in length. Tank 1 contains a uniform gas of 60 mol% acetone and 40 mol% air, whereas Tank 2 contains a uniform gas of 10 mol% acetone and 90 mol% air. Determine the initial rate of acetone transfer between the two tanks. The gas diffusivity of acetone in air at 298 K and 1 atm is 0.093 cm2 s-1.
3. (an exercise for week 12) Consider a 3 m by 8 m shaded concrete patio which has just been hosed down. It has a 2 mm thick film of water uniformly covering the surface. If air above the concrete is 27 oC, with no breeze and relative humidity of 30 %, determine the following:
1. The concentration of water vapour in the gas phase, at the interface between the wet concrete and the overlying air.
1. The concentration of water in the air far from the water surface.
1. The mass transfer coefficient for transfer of water from the concrete to the air
1. The rate of water evaporated from the concrete (kg s-1)
1. The rate of heat removed due to evaporation of the water
1. How long will it for the concrete to dry under these conditions?
1. Explain how a breeze blowing over the patio, direct sunshine on the concrete, or a change in relative humidity would affect mass transfer and hence the time taken for the concrete to dry.
1. Comment on any limitations to your calculations
4. The dissolution of lead-soldered joints in household piping is a possible health hazard. If the water flowing through the pipe is mildly acidic, then some of the lead will dissolve from the inner surface of the lead-soldered pipe section into the water. At present, water flows at 18oC through a 0.025 m ID pipe at a bulk velocity of 0.2 ms-1. The diffusivity of soluble lead in water at 18oC is 1 x 10-9 m2s-1.
0. What is the mass transfer coefficient kc for transfer of lead from the pipe wall through the water?
0. Extension question: Develop an expression for the concentration of Pb in the water at distance L along the soluble joint
0. Extension questions: Drinking water requirements stipulate that soluble lead (Pb) concentration levels should not exceed 0.015 gm-3. The water chemistry results in a soluble lead concentration of 10 gm-3 at the surface of the soldered pipe section. What length of lead-soldered joints in this system would lead to Pb concentrations in the water above drinking water guidelines of 0.015 gm-3?
5. You have just started work at a brewery, and you notice that the green (newly fermented) beer is held in open tanks. It is a warm day, and there is a strong smell of beer in the air. You boss tells you that the loss of beer through evaporation is negligible, but you are concerned, and decide to apply your mass transfer knowledge to reassure yourself. The air temperature is 25oC, air pressure is 1 atm, and you have determined that the partial pressure of ethanol is 10 kPa at the surface of the beer, but tank falls to zero 5 mm above the surface. The density of ethanol at 25 oC is 785 kgm-3. Determine the following for a tank (5 m in diameter),filled to a depth of 4 m with beer (5 % ethanol, 95 % water by volume):
1. What is the molar fraction of ethanol in the beer?
1. What is the molar fraction of ethanol in the air at the beer surface?
1. What is the diffusivity for ethanol in air under these conditions?
1. Calculate the molar diffusive flux of ethanol through the air film on the surface of the beer, using Fick’s law
1. Calculate the absolute flux of ethanol through the air film on the surface of the beer, accounting for mass flows.
1. What is the mass of ethanol lost from the tank per hour under these conditions?
1. What proportion of the volume of beer in the tank will be lost in the next hour?
1. How will this affect the concentration of the beer remaining? Was your boss correct? Why?
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