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Unformatted text preview: achfordRice equation to be satisfied.
Given: Eq. (3), Table 4.4, which is the RachfordRice equation.
Find: Conditions under which the equation can be satisfied for 0 ≤ V
≤ 1.
F Analysis: A necessary, but not sufficient, condition is that at least one Kvalue is < 1 and at
least one Kvalue is > 1. If all Kvalues are > 1, the sum:
zi 1 − Ki
will be negative and can not be zero.
i =1 1 + Ψ Ki − 1
C If all Kvalues are < 1, the numerator in the sum will be positive for each term. With Ψ between
0 and 1, the term Ψ(Ki  1) will always be < 1. Therefore, the denominator will be positive also
and the sum will be positive and can not be zero. Exercise 4.19
Subject: Flash vaporization of a benzene (A)  toluene (B) mixture for αAB = 2.3.
Given: Feed is 40 mol% A and 60 mol% B.
Find: Percent of A in the equilibrium vapor if 90% of the toluene leaves in the liquid by
graphical means.
α A,B xA
Analysis: For constant relative volatility, Eq. (48) applies,
yA =
1+ xA α A,B − 1
Solving this equation for yA as a function of xA ,
xA
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 yA
0.2035
0.3651
0.4964
0.6053
0.6970
0.7753
0.8429
0.9020
0.9539 A plot of the calculated equilibrium curve is given below. To use this plot for a graphical
solution of the equilibrium, draw a qline, using the following equation above Eq. (46), for an
assumed value of Ψ = V/F and check the resulting % recovery of toluene in the liquid. Vary Ψ
until the % recovery = 90%. Then compute, for the corresponding Ψ , the % recovery of
benzene in the vapor.
yA = Ψ −1
1
Ψ −1
1
xA +
zA =
xA +
0.40
Ψ
Ψ
Ψ
Ψ (1) Analysis: (continued) Exercise 4.19 (continued) Basis: F = 100 moles, 60 moles toluene (B). Want 0.9(60) = 54 moles B in liquid. Therefore,
60  54 = 6 moles B in vapor. Therefore, want (nB)V = yBV = (1  yA)100Ψ = 6. Then compute %
recovery of benzene in vapor = (nA)V/40 x 100% = yAV/40 x 100% = 2.5 yAΨ x 100%. The
following are typical values for the trial and error procedure, with the final result at the bottom.
Assumed Ψ yA 0.3
0.2
0.15
0.142 0.54
0.56
0.575
0.58 xA (nB)V ,
moles
0.35
13.8
0.36
8.8
0.37
6.4
0.375
6.0 % recovery
of A in vapor
40.5
28.0
21.6
20.6 Exercise 4.20
Subject: Flash vaporization of a benzene (A)  toluene (B) mixture.
Given: Feed is 40 mol% A and 60 mol% B. Vapor pressure data.
Assumptions: Raoult's law (ideal solutions). Pressure = 1 atm.
Find: Percent of A in the equilibrium vapor if 90% of the toluene leaves in the liquid.
Analysis: Basis: F = 100 mole with 60 moles B and 40 moles A. Want 0.9(60) = 54 moles B
in liquid. Therefore, 60  54 = 6 moles B in vapor. Therefore, want (nB)V = yBV = (1 yA)100Ψ = 6. Then compute % recovery of benzene in vapor = (nA)V/40 x 100% = yAV/40 x
100% = 2.5 yAΨ x 100%. The following trial and error procedure can be used, based on material
balance and equilibrium equations:
(1) Guess a temperature. (2) Read vapor pressures from Fig. 2.4 and compute Kvalues from
Raoult's law (Eq. (3), Table 2.3), Ki = Pi s / P . (3) Solve for Ψ = V/F using the fifth equation in
Exercise 4.17,
zA KA − KB / 1 − KB − 1 0.40 KA − KB / 1 − KB − 1
Ψ=
=...
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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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