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Unformatted text preview: preadsheet. Curved (instead of
straight) lines connecting the points would be a good improvement.
(a) For a benzene mole fraction of 0.25, a vertical line from M intersects the liquid line at
N at 69.4oC, which is the bubble point.
(b) The benzene mole fraction in the vapor at 69.4oC, obtained from the leftmost vapor
line at P, is 0.56.
(c) To find the benzene mole fraction in the liquid at 25 mol% vaporization, extend a
dashed, vertical line upward from the bubble point at N, as shown in the figure on the next 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 benzene mole fraction in the equilibrium liquid at
point A is 0.175 at a temperature of 71.2oC.
(d) To find the benzene mole fraction in the liquid at 90 mol% vaporization, extend a
dashed, vertical line upward from the bubble point, as shown in the figure on the next page, until
point Eis reached. At this point, using the inverse leverarm rule, the ratio of the DE line length
to the EF line length is 90/10. The benzene mole fraction in the equilibrium liquid at point D is
0.045 at a temperature of 75.1oC.
(e) To find the benzene mole fraction in the liquid when the liquid from part (c) is
removed from the vapor and further vaporized, proceed as follows. If we start with 100 moles,
then the liquid at 25 mol% vaporized is 75 moles with a benzene mole fraction of 0.17. If an
additional 35 mol% is vaporized, we will have 35 moles of vapor in equilibrium with 40 moles
of liquid. Therefore, extend a dashed, vertical line upward from point A, as shown in the figure
on the next page, until point H is reached. At this point, using the inverse leverarm rule, the
ratio of the GH line length to the HI line length is 35/40. The benzene mole fraction in the liquid
at G is 0.05 at a temperature of 74.9oC. Exercise 4.6 (continued)
Analysis: (f) Extending parts (c) and (e) to other percent vaporizations, the following data are
obtained, where for the extension of part (e), the first 25 mol% of vapor is removed in each case.
Mol% vaporization
0
25
50
75
100 (g)
Thus, Part (c) temperature, oC
69.4
71.2
72.9
74.3
75.3 Part (e) temperature, oC
69.4
71.2
73.8
75.5
76.3 To calculate 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.
letting A = benzene and B = ethyl alcohol,
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 4.6 (continued)
Analysis: (g) (continued)
Equations (1) to (4) can be reduced to the following equations for the mole
fractions of benzene in terms of the Kvalues:
xA = 1 − KB
KA − KB , y A = KA x A (5, 6) If the given vapor pressure data are fitted to Antoine equations, we obtain: PAs = exp 15.5645 − 2602.34
T + 211.271 (7) 505106
.
(8)
T + 272.702
Where vapor pressure is in torr and temperature is in oC. Solving, Eqs. (1) to (8),
PBs...
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 Spring '11
 Levicky
 The Land

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