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Analysis: (continued) 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,
KA = s
yA PA T
=
xA
P yA + y B = 1 s
yB PB T
=
xB
P , KB = , xA + x B = 1 (1, 2)
(3, 4) Exercise 4.8 (continued)
Analysis: (continued)
Equations (1) to (4) can be reduced to the following equations for the mole
fractions of benzene (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 4.6 for benzene, and this exercise for toluene are
fitted to Antoine equations, we obtain:
PAs = exp 15.5645 − 2602.34
T + 211.271 (7) 3896.3
(8)
T + 255.67
Where vapor pressure is in torr and temperature is in oC. Solving, Eqs. (1) to (8),
PBs = exp 17.2741 − T, oC Ps of A, torr Ps of B, torr 80.1
82.5
85.0
87.5
90.0
92.5
95.0
97.5
100.0
102.5
105.0
107.5
110.0
110.5 759.9
817.4
880.8
948.0
1019.1
1094.1
1173.4
1256.9
1345.0
1437.6
1535.0
1637.3
1744.7
1766.8 290.0
314.9
342.7
372.5
404.4
438.5
474.9
513.7
555.2
599.3
646.2
696.1
749.1
760.1 KA KB xA yA 0.9998
1.0755
1.1590
1.2474
1.3409
1.4396
1.5439
1.6539
1.7697
1.8916
2.0198
2.1544
2.2957
2.3248 0.3816
0.4144
0.4510
0.4901
0.5321
0.5769
0.6249
0.6760
0.7305
0.7885
0.8503
0.9159
0.9856
1.0001 1.000
0.886
0.775
0.673
0.579
0.490
0.408
0.331
0.259
0.192
0.128
0.068
0.011
0.000 1.000
0.953
0.899
0.840
0.776
0.706
0.630
0.548
0.459
0.363
0.259
0.146
0.025
0.000 Plots of yx and Txy based on the above table from Raoult's law calculations are shown on the
next page. When the yx plot is compared to the previous yx plot based on a constant relative
volatility, it is seen that, for a given value of x for benzene, the values of y for benzene are in
fairly close agreement. From the above table, the Raoult's law αA,B = PAs / PBs ranges from 2.62
at 80.1oC to 2.32 at 110.5oC. Analysis: (continued) Exercise 4.8 (continued) Exercise 4.8 (continued)
Analysis: (continued)
(a) To find the temperature at 25 mol% vaporization, starting with a liquid
mixture of 70 mol% benzene and 30 mol% toluene, extend a dashed, vertical line upward from
point M on the Tyx diagram on the previous page until point B is reached. At this point, using
the inverse leverarm rule, the ratio of the AB line length to the BC line length is 25/75. The
temperature is 88oC. The benzene mole fraction of the equilibrium vapor when condensed is the
same as the equilibrium vapor at point C or 0.88. The benzene mole fraction in the residue liquid
is the same as the equilibrium liquid at point A or 0.65.
(b) The Raoult's law Kvalues are included in the above table, and are plotted
below. Exercise 4.9
Subject: Vaporliquid equilibrium for nheptane (A)  toluene (B) system at 1 atm
Given: Vapor pressure data for nheptane and toluene, and experimental Tyx data.
Assumptions: Raoult's and Dalton's laws
Find: (a) xy plot based on nheptane, the most volatile component.
(b) Tx bubblepoint...
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 Spring '11
 Levicky
 The Land

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