hw1_solutions_9sept05

hw1_solutions_9sept05 - Chemical Engineering 150B- Fall...

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1 Chemical Engineering 150B- Fall 2005 Problem Set #1 Solutions Problem 1. (10 points) For a binary mixture with species A and B, are the following relations either "always true," "always false," or "sometimes true"? Please briefly justify your answer. a) J A + J B = 0 Always true. Note: Credit will also be given to "sometime true," since there was some confusion at office hours between N , which includes convective terms, and J, which has no convective terms. Also, if A and B are in different phases, the this statement need not be true. For Example 6 in lecture with waste, "A," and biofilm, "B," the biofilm is considered to be in a different phase from A, which does not have spatial concentration gradients, while the waste does have concentration gradients, and thus a non-zero diffusive flux. The answer above is a subtle point, but definitely rigorously true as proven above. b) N A + N B = c V Always true. This is the definition of the total flux, as shown below. 2 pt for justification 3 pt 2 pt for justification 3 pt 2 Problem 2. (15 points) An absorption tower is proposed to remove selectively two pollutants, hydrogen sulfide (H 2 S) and sulfur dioxide (SO 2 ), from an exhaust gas stream containing H 2 S 3 vol% SO 2 5 vol% N 2 92 vol% Estimate the diffusivity of hydrogen sulfide in the gas mixture at 350 K and 1.013 x 10 5 Pa. Use Hirschfelder's equation for the diffusion coefficient of pairs of gaseous nonpolar, nonreacting molecules. The critical temperature (T C ) of H 2 S is 373.2 K and the critical volume (V C ) of H 2 S is 98.5 cm 3 /mole. 3 pt 2 pt 2 pt 3 pt 5 pt
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3 Problem 3. (15 points) The liquid phase diffusivity of carbon tetrachloride (CCl 4 ) in methanol was reported by Reid, Prausnitz, and Sherwood to be 1.7 x 10 -9 m 2 /s at 288 K. (a) Use this experimental value to evaluate the association parameter, φ Β , of methanol. The viscosity of methanol at 288 K is 0.62 centipoise. (b) Compare this experimental value to the diffusion coefficient estimated using the Scheibel correlation. 5 pt 2 pt 3 pt 5 pt 4 Problem 4. (20 points) Solute A is diffusing through a cylinder shown below. Inside and outside the cylinder the solute A is held a constant concentration such that the interior and outside wall concentrations are constants, c Ai and c Ao respectively. Note that the cylinder has a very thin wall (i.e., the gap between R i and R o is much, much smaller than R i ). r=R o i c Ai c Ao (a) Start with a mole balance in cylindrical shell and derive the concentration profile in the cylindrical wall at steady state. State all your assumptions. Hint: Do you really need to use cylindrical coordinates for this problem considering that the cylinder wall thickness is much smaller than the inner diameter? Is the cross-sectional area changing significantly through the diffusion path in this situation? There are two approaches to this problem. The first is to treat the problem in Cartesian coordinates and the second is to treat the problem in cylindrical coordinates (like the problem in the discussion session). We will give both results here (you get credit for either) and compare the result in part (b).
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hw1_solutions_9sept05 - Chemical Engineering 150B- Fall...

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