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(c) αA,B and Kvalues plotted against temperature.
(d) xy plot based on the average αA,B.
(e) Comparison of xy and Txy plots with experimental data.
Analysis: (a) To calculate yx and Txy curves from vapor pressure data, using Raoult's and
Dalton's laws. Eq. (244 ) 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 nheptane (A) in terms of the Kvalues:
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
nheptane 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 xy plot is given below.
(b) From the above table, a Txy plot is given below. The xcurve is the bubblepoint curve,
while the ycurve is the dewpoint curve.
(c) A graph of relative volatility and Kvalues 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 KValues For a constant relative volatility, Eq. (48) 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)
yx Plot for an average relative volatility
1 Mole fraction nheptane 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 nheptane 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.
 Spring '11
 Levicky
 The Land

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