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Sept_29_12_08_PM_KS_HW4_solutions

Sept_29_12_08_PM_KS_HW4_solutions - Chemical Engineering...

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Page 1 of 1 Chemical Engineering 150B- Fall 2005 Problem Set #4 Solutions Problem 1. (15 points) Consider liquid A evaporating into initially pure gaseous B in a closed vessel shown below: This vessel initially has 0.4 liter of A with 75 cm 2 of surface area in a total volume of 20 liters. After 4 minutes, B is five percent saturated with A. (a) What is the mass transfer coefficient of A? Note that the vessel is isothermal at 298 K, and the equilibrium vapor pressure of A at 298K is 24 torr. Both A and B are ideal in the gas phase. The flux at 4 minutes can be found directly from the values given: ( )( ) ( )( ) 1 vapor concentration air volume N liquid area time = ( ) ( ) ( ) 2 1 2 1 24 273 0 05 19 6 760 22 4 298 75 240 mol . . . L N mol / cm s cm sec = = -8 7.0 x 10 The concentration difference is that at the interface between A and B minus that in the solution. That at the surface is the value at saturation; that in the bulk at short times is essentially zero. Thus, ( ) 1 A,i A N k c c = 2 3 3 1 24 273 0 760 298 22 4 10 mol mol / cm s k . * cm k = = -8 7.0 x 10 0.054 cm/s This value is lower than that commonly found for transfer in gases. (b) How long will it take to reach ninety percent saturation of A in B? The time required for 90 percent saturation can be found from a mass balance: accumulation in gas phase = evaporation rate B ( g ) A ( l ) 2 pt 2 pt 3 pt
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