mse103-spring02-mt2-Glaeser-soln

# mse103-spring02-mt2-Glaeser-soln - MSE 103 Exam #2 A.M....

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MSE 103 Exam #2 A.M. Glaeser ! 2 ! In this exam we are interested in an A-B system. The material is subjected to a series of processes in which the chemistry, chemical distribution or phase content is changed. a) It is desired to add component B to pure A by allowing a gaseous form of component B to dissolve in A. The gas is in the form B 2 , but dissolves in the material in monatomic form. As a result, the dissolution reaction can be written: B 2 ( g ) = 2B ( ss ) Experiments at 1000K show that when the pressure of B 2 gas is 1 atmosphere, the resulting mole fraction of B dissolved (in monatomic form) in A is 0.01. In applications, the desired level of B in A ranges from a mole fraction of 0.005 to 0.015. If we assume that B is Henrian in this concentration range, please determine 1) the Sievert’s law coefficient and 2) the range of B 2 pressure that will produce the desired range of X B at 1000K. Show your work and explain your reasoning. ( 15 points ) work space: Sievert’s Law: X B = kp B n For a diatomic gas dissolving in a solid in monotomic form: X B = B 2 k = X B p B 2 ± = 0.01 ² (1atm) ± = 0.01atm ± If the solution is Henrian, a B = ± B X B , and the activities and partial pressures are proportiaonal to the mole fraction. To define the range of pressures: p B 2 = X B k ± ² ³ ´ µ 2 p B 2 = 0.005 0.01atm · ± ² ³ ´ µ 2 = 0.25atm p B 2 = 0.015 0.01atm · ± ² ³ ´ µ 2 = 2.25atm The range of pressure that will produce the desired concentration in the solid is 0.25-2.25 atm.

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MSE 103 Exam #2 A.M. Glaeser ! 3 ! b) A rod of pure A with a tapered cross section as shown below separates gaseous B 2 at pressures P 1 and 2 . The gases establish uniform surface concentrations C 1 at x = , and C 2 x=x . At steady state, the concentration varies linearly with position as shown. (The rod can be assumed to extend infinitely in the direction normal to the plane of the paper.) 1 2 At the same temperature as above, the same pressures P 1 and P 2 now established on two sides of a plate with no taper. If the system reaches steady state, please show what the concentration profile would look like on the figure on the next page. At steady state, what would be the ratio of the concentration gradients at 2 and 1 ? Show your work, and explain your reasoning. ( 20 points ) work space: At steady state the total flux anywhere in the plate must equal the total flux at any other point: J X 1 = J X 2 ± J X 1 A X 1 = J X 2 A X 2 From the diagram, one can see that the area at x 1 is twice the area at x 2 . A X 1 = 2A X 2 ± J X 1 = 1 2 J X 2 The linear concentration gradient implies: ± C () X 1 = ± C X 2 From Fick’s First law: J X 1 = ± D X 1 ² C X 1 and J X 2 = ± D X 2 ² C X 2 Solving for the diffusivity at x 1 in terms of the diffusivity at x 2 yields:
MSE 103 Exam #2 A.M. Glaeser ! 4 !

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## mse103-spring02-mt2-Glaeser-soln - MSE 103 Exam #2 A.M....

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