Unformatted text preview: = zi /Ki . Solving these equations by trial and
error with a spread sheet, starting from T = 105oC, x1 = 0.2 and x2 = 0.8, quickly leads to a dewpoint temperature of 109.7oC. The Kvalues at the dew point are computed to be K1 = 1.793 and
K2 = 0.772, with x1 = 0.2231 and x2 = 0.7769.
The equilibrium flash calculation is carried out at T = (109.7 + 106.9)/2 = 108.3oC. In
this case, the values of Ψ, x1, and x2 are computed from Eqs. (1) and (3), where the vapor
pressures are computed from Eqs. (5) and (6) to be 714 torr for 1 and 539 torr for 2. Values of y1
and y2 are obtained from Eq. (2). Using, again, a spreadsheet with a trial and error procedure,
the following result is quickly obtained:
V/F = 0.604 x1 = 0.2949 x2 = 0.7051 y1 = 0.4689 y2 = 0.5311 Exercise 4.35
Subject: Bubble point, dew point, and azeotrope of an ethyl acetate (A)  ethyl alcohol (E)
mixture.
Given: Liquid mixture of 80 mol% A  20 mol% E at 101.3 kPa (1 atm). Liquidphase activity
coefficients for A and E as a function of liquidphase mole fractions from the van Laar
equations.
Assumptions: Modified Raoult's law, Eq. (272) applies.
Find: (a) Bubblepoint temperature and vapor composition. (b) Dew point. (c) Temperature
and composition of possible azeotrope.
Analysis: The RachfordRice flash equations can be used from Table 4.4:
f {Ψ} = yi = zi 1 − Ki
=0
i =1 1 + Ψ Ki − 1
C (1) zi Ki
1 + Ψ Ki − 1 (2) zi
(3)
1 + Ψ Ki − 1
The modified Raoult's law from Eq. (272) is:
γ iL Pi s
Ki =
(4)
P
Antoine vapor pressure (in torr) equations are obtained from Section 13 of Perry's Handbook:
xi = 1244.951
T ( C ) + 217.881
1281590
.
log PEs = 7.58670 − o
T ( C ) + 193.768 log PAs = 7.10179 − o The van Laar equations, Table 2.9, with the given constants are:
ln γ A = ln γ E = 0.855
0.855xA
1+
0.753xE
0.753
0.753xE
1+
0.855xA (7) (8) (5)
(6) Exercise 4.35 (continued)
Analysis: (continued)
(a) Since P = 1 atm and the normal boiling points of ethyl acetate and ethyl alcohol are
o
77.1 C and 78.4oC, respectively, it might be expected that the bubble and dew points of the
mixture would be in the vicinity of 70oC, unless the liquidphase activity coefficients are much
different from 1. To check this, activity coefficients are computed from Eqs. (7) and (8), with a
spread sheet, with the following result as a plot. It is seen that the coefficients are not large, but
are as high as 2.35. At the bubble point, Ψ = V/F = 0, and Eq. (1), combined with (4), becomes: f {T} = zA 1 − γ A PAs {T}
γ P s {T}
+ zE 1 − E E
=0
P
P (9) Exercise 4.35 (continued)
Analysis: (continued)
Also, at the bubble point, xA = zA = 0.8 and xE = zE = 0.2. Then, the only unknown in Eq.
(9) is T. Solving nonlinear Eq. (9), by trial and error with a spreadsheet, starting from a guess of
T = 70oC, quickly leads to a bubblepoint temperature of 73.5oC. The composition of the vapor
bubble is obtained from Eq. (2), which at the bubble point reduces to yi = xiKi = ziKi.. The Kvalues at the bubble point are computed to be KA = 0.913 and KE = 1.350, giving yA = 0.730 and
yE = 0.270.
(b) At the dew point, Ψ...
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 Spring '11
 Levicky
 The Land

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