prob set _12. 08

prob set _12. 08 - Chemical Engineering 140 November 12,...

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Unformatted text preview: Chemical Engineering 140 November 12, 2008 Problem Set #12 51. 17.18 52. 18.19 53. 18.26 54. 19.21 55. 6.41 FR 56. from Midterm 3, 2004 A liquid mixture initially containing 60.0 moles of n-pentane and 40.0 moles of n-heptane and initially at 53oC is partially vaporized at P = 1 atm in a batch still, as illustrated in Figure 2. A constant heating rate is applied to vaporize the liquid at a & rate nv (mol/s). The vapor product and remaining liquid are always in equilibrium with each other. The relationship between the liquid and vapor mole fractions of 1 2ax . Assume that a and b are x b constant across the practical range of interest. N (the total moles of liquid in the still), pentane, x and y, respectively, is given by y & x, y, and nv (the vaporization rate) all change with time. y, heat Figure 1: Schematic of a batch still to separate a binary liquid mixture (a) Derive the relationship between a and b in the vapor-liquid equilibrium expression. From this result, find the expression for the K factor of pentane only in terms of the parameter a (and the independent variable x). (b) Write the differential equation describing the change of total moles in the still over time. Now write a species balance for pentane. The final form of your pentane balance & should be simplified to include only the following terms: dx/dt, N, a, nv , and x. Specify the initial condition for each differential equation. Be sure to indicate the control volume you used for each balance! (c) Simplify the pentane balance when the pentane liquid mole fraction does not change with time. Solve for the mole fraction of pentane in the liquid phase in this situation. What is the physical significance of your answer? (d) Qualitatively sketch the liquid mole fractions and vapor mole fractions for pentane and heptane on the same plot as a function of time. Clearly label each mole fraction on the sketch! Describe what happens to the composition of the vapor product and residual liquid over time. 2 ...
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