Practice Exam 2

# Practice Exam 2 - Problem 1 When considering mass transfer...

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increasing time c f A c f A final membrane concentration c A > c f A Problem 1 When considering mass transfer across different phases , the relevant variable is the difference in chemical potentials and not the difference in concentrations. Although the concentration of A is the same in both the fluid phase and the membrane, this does not necessarily imply that no mass transfer will occur. A difference in the chemical potential of A within the fluid phase and the membrane may still exist, and if so, species A will be transferred from the region with a higher chemical potential to a region with a lower chemical potential. In fact, we are told that experiments indicate that A is more soluble in the membrane than in the fluid. So, if allowed to reach its final equilibrium state, the concentration of A within the membrane will exceed the concentration of A in the fluid. Or, starting from the same concentration in both phases, the chemical potential of A in the fluid is greater than the chemical potential of A in the membrane. Hence, A will flow into the membrane. Mass transfer will cease when the chemical potentials are equal, which corresponds to a final concentration of A within the membrane that is greater than the concentration of A in the fluid. Hence, Proposal I is incorrect. Although, Proposal II does account for the higher final concentration of A within the membrane (as compared to the surrounding fluid), the variation of A throughout the membrane as a function of time is not properly sketched. By having the center of the membrane become more concentrated with time, as compared to the sides, Proposal II requires A to diffuse “uphill”. In other words, A is being transported in the direction with the same sign as the concentration gradient, i.e., from lower to higher concentrations. Within a given phase, however, mass transfer should satisfy Fick’s law, in that matter flows in the direction opposite to the sign of the concentration gradient (i.e., matter is transferred from regions with high concentrations to regions

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## This note was uploaded on 11/02/2009 for the course CHEM 378 taught by Professor Corti during the Spring '09 term at Purdue.

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Practice Exam 2 - Problem 1 When considering mass transfer...

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