Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# Solving eqs 1 to 8 analysis a continued exercise

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Unformatted text preview: plot. (c) αA,B and K-values plotted against temperature. (d) x-y plot based on the average αA,B. (e) Comparison of x-y and T-x-y plots with experimental data. Analysis: (a) To calculate y-x and T-x-y curves from vapor pressure data, using Raoult's and Dalton's laws. Eq. (2-44 ) applies, as well as the sum of the mole fractions in the phases in equilibrium. Thus, s yA PA T KA = = xA P , yA + y B = 1 s yB PB T KB = = xB P (1, 2) , xA + x B = 1 (3, 4) Equations (1) to (4) can be reduced to the following equations for the mole fractions of n-heptane (A) in terms of the K-values: xA = 1 − KB KA − KB , y A = KA x A (5, 6) If the given vapor pressure data in Exercise 4.8 for toluene, and this exercise for n-heptane are fitted to Antoine equations, we obtain: PAs = exp 15.7831 − 2855.27 T + 213.64 (7) PBs = exp 17.2741 − 3896.3 T + 255.67 (8) Where vapor pressure is in torr and temperature is in oC. Solving, Eqs. (1) to (8), Analysis: (a) (continued) Exercise 4.9 (continued) T, oC Ps of A, torr Ps of B, torr 98.4 99.0 100.0 101.0 102.0 103.0 104.0 105.0 106.0 107.0 108.0 109.0 110.0 110.5 760.0 773.0 795.9 819.2 843.1 867.6 892.6 918.1 944.2 970.9 998.1 1026.0 1054.4 1068.9 528.7 538.3 555.2 572.5 590.2 608.4 627.1 646.2 665.8 685.9 706.5 727.5 749.1 760.1 KA KB xA 1.0000 1.0172 1.0472 1.0780 1.1094 1.1415 1.1744 1.2080 1.2424 1.2775 1.3133 1.3500 1.3874 1.4064 0.6956 0.7083 0.7305 0.7533 0.7766 0.8006 0.8251 0.8503 0.8761 0.9025 0.9296 0.9573 0.9856 1.0001 1.000 0.944 0.851 0.760 0.671 0.585 0.501 0.418 0.338 0.260 0.184 0.109 0.036 0.000 yA αA,B 1.000 1.438 0.961 1.436 0.891 1.434 0.819 1.431 0.745 1.428 0.668 1.426 0.588 . 1.423 0.506 1.421 0.420 1.418 0.332 1.415 0.241 1.413 0.147 1.410 0.050 1.408 0.000 1.406 From this table, an x-y plot is given below. (b) From the above table, a T-x-y plot is given below. The x-curve is the bubble-point curve, while the y-curve is the dew-point curve. (c) A graph of relative volatility and K-values as a function of temperature is given on the next page. (d) From the above table, the arithmetic average relative volatility, using the extreme values is:(αA,B)avg = (1.438 + 1.406)/2 = 1.422 Analysis: (a) (continued) Exercise 4.9 (continued) Exercise 4.9 (continued) Analysis: (c) and (d) (continued) Relative Volatility and K-Values For a constant relative volatility, Eq. (4-8) applies. For αA,B = 1.422, α A,B xA 1.422 xA yA = = 1 + xA α A,B − 1 1 + 0.422 xA Solving this equation for values of xA = 0 to 1.0 gives the following: xA yA 0 0.0000 0.1 0.1364 0.2 0.2623 0.3 0.3787 0.4 0.4867 0.5 0.5871 0.6 0.6808 0.7 0.7684 0.8 0.8505 0.9 0.9275 1 1.0000 Exercise 4.9 (continued) Analysis: (c) and (d) (continued) y-x Plot for an average relative volatility 1 Mole fraction n-heptane in vapor 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole fraction n-heptane in liquid (e) Raoult’s law calculations compared to experimental are as follows: T, o C 110.75 106.80 104.50 102.95 101.35 99.7...
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## This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.

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