1.
Faculty of Chemical Engineering CPE553 Chemical Engineering Thermodynamics
Semester March-July 2013 9 May 2013
ASSIGNMENT 2
*Individual assignment. You are allowed to use Microsoft Excel for calculations. Graphs must be
plotted manually except question 3.
1. The excess Gibbs energy of a binary liquid mixture at T and P is given by:
1 2 1 20.8815 1.2251
E
G
x x x x
RT
(a) Find expressions for ln 1 and ln 2 at T and P by using partial properties relation.
Hint: The summability relation for the excess Gibbs energy is
ln 11.99
E
i i
i
G
x
RT
(b) Show that expressions in (a) satisfy the Gibbs/Duhem equation.
(c) Plot GE
/RT, ln 1 and ln 2 as calculated by the given equation for GE
/RT and by the equations
developed in (a) vs. x1. Label points ln 1
andln 2
and show their values on the plot.
(Show table of calculated values and a sample of calculation for GE
/RT, ln 1 and ln 2 at x1 =
0.3)
2. Assuming that eq. (11.68) is valid for vapor phase and eq. (11.44) is fugacity for liquid phase
where the molar volume of saturated liquid is given by eq. (3.72), determine the fugacity and
fugacity coefficient for chloroform at 200o
C (473.15K) and pressure range from 0 to 40 bar. Plot
the results as function of pressure on a single graph. At 200o
C (473.15K) the vapor pressure of
chloroform is 22.27 bar.
2/7
0 1
0
1.6
1
4.2
1
exp 11.68
0.422
0.083 3.65
0.172
0.139 3.66
exp 11.44
3.72
r
r
r
r
r
sat sat
isat sat
i i i
Tsat
c c
P
B B
T
where B
T
B
T
V P P
f P
RT
where V V Z
(Show table of calculated values and a sample of calculation for fugacity and fugacity coefficient
at P = 15 bar, 22.27 bar and 40 bar)
3. The following table is a set of VLE data for the system methanol(1)/water(2) at 60o
C (333.15K).
(a) Prepare a P-x1-y1 diagram that compares the experimental data with values calculated from
Wilson and NRTL equations.
(b) Prepare diagrams that show the residuals P and y1 plotted vs. x1 for both models.
2.
Faculty of Chemical Engineering CPE553 Chemical Engineering Thermodynamics
Semester March-July 2013 9 May 2013
exp
exp
1 1 1calc
calcP P P
y y y
(Show table of calculated values and a sample of calculation in part (a) and (b) for each
model.)
P (kPa) x1 y1
19.953 0.0000 0.0000
39.223 0.1686 0.5714
42.984 0.2167 0.6268
48.852 0.3039 0.6943
52.784 0.3681 0.7345
56.652 0.4461 0.7742
60.614 0.5282 0.8085
63.998 0.6044 0.8383
67.924 0.6804 0.8733
70.229 0.7255 0.8922
72.832 0.7776 0.9141
84.562 1.0000 1.0000
(Source: K.Kurihara et al., J.Chem. Eng. Data, vol. 40, pp. 679-684, 1995)
Date of submission: 22nd
May 2013 before 5pm
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