Unformatted text preview: = V/F =1, and Eq. (1), combined with (4), becomes:
f{xA, xE, T} = zA P
P
− 1 + zE
−1 = 0
s
γ A {xA , xE } PA {T}
γ E {xA , xE } PEs {T} where because yA = zA = 0.8 and yE = zE = 0.2, xA , and xE =(1  xA) are left as unknowns. The
liquid phase mole fractions are from Eq. (3), xi = zi /Ki . Solving these equations by trial and
error with a spread sheet, starting from T = 70oC, xA = 0.8 and xE = 0.2, quickly leads to a dewpoint temperature of 74.3oC. The Kvalues at the dew point are computed to be KA = 0.922 and
KE = 1.508, with xA = 0.8674 and xE = 0.1326.
(c) To determine the existence of an azeotrope, where yi = xi , a series of bubblepoint
calculations can be made, using the procedure in part (a), starting from say, xA = 0.05 in
increments of 0.05. If, in the range of xA from 0.05 to 0.95, the Kvalue of A switches from more
than 1 to less than 1, then an azeotrope exists in this range. The calculations can then be refined.
The result from a spreadsheet is a minimumboiling azeotrope at 72.46oC with a composition of
54.4 mol% A and 45.6 mol% B. This compares to experimental values from Perry's Handbooof
71.8oC at a composition of 54 mol% A. Exercise 4.36
Subject: Bubble point, dew point, and azeotrope of a water (W)  formic acid (F) mixture.
Given: Liquid mixture of 50 mol% W  50 mol% F at 107oC. Liquidphase activity
coefficients for W and F as a function of liquidphase mole fractions from the van Laar
equations.
Assumptions: Modified Raoult's law, Eq. (272) applies.
Find: (a) Bubblepoint pressure. (b) Dew point pressure. (c) Azeotropic pressure and
composition at 107oC.
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 Ps
Ki = iL i
(4)
P
Antoine vapor pressure (in torr) equations are obtained from Section 13 of Perry's Handbook:
xi = 1730.630
T ( C ) + 233.426
1295.260
log PFs = 6.94459 − o
T ( C ) + 218.00
s
log PW = 8.07131 − (5) o (6) The van Laar equations, Table 2.9, with the given constants are:
ln γ W = ln γ F = −0.2935
( −0.2935) xA
1+
( −0.2757) xE
−0.2757
( −0.2757) xE
1+
( −0.2935) xA (7) (8) Exercise 4.36 (continued)
Analysis: (continued)
(a) Since T = 107oC and the normal boiling points of water and formic acid are 100oC
and 100.8oC, respectively, it might be expected that the bubble and dew point pressures of the
mixture would be in the vicinity of 1 atm, 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 lie between 0.7
and 1.0 At the bubble point, Ψ = V/F = 0, and Eq. (1), combined with (4), becomes: f { P} = zW 1 − s
γ W PW {107 O C}
γ P s {107 O C}
+ zF 1 − F F
=0
P
P (9) Exercise 4.36 (continued)
Analysis: (continued)
Also, at the bubble p...
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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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