Chemical Engineering 150B Fall 2005
Problem Set #6 Solutions
Problem 1.
(15 points) Consider an isothermal, isobaric ideal binary gas mixture of A and B being
separated below into k streams:
where n is the molar flow rate.
Derive an expression for the minimum (reversible) work of separation in terms of gas constant,
R, temperature T
o
, and mole fractions of A and B. [Hint: Try reading Seader, Chapter 1 and
using Tables 2.1/2.4.]
From Table 2.1 you can use the expression (4) to calculate the minimum work of separation:
Since the temperature is constant, the enthalpy change is zero.
Now use Table 2.4 to get the
s
in
terms of mole fractions, where
s
for an ideal gas solution at constant temperature and pressure
reduces to:
1
C
ii
i
sR
y
l
n
y
=
=−
∑
Combining the above two equations, we arrive at the final answer:
[]
1
k
min
o
k
k,A
k,B
o in
A
A
B
B
k
W
R
T nyl
n
y yl
n
y
R
T
ny
l
n
y y
l
n
y
=
=+
−
+
⎡⎤
⎣⎦
∑
Through complicated mathematics, we can show that regardless of values for y between 0 and 1,
W
min
is always positive.
Since W
min
is independent of the process, this implies that the
separation of a mixture into essentially pure species, or other mixtures of differing compositions,
always require the transfer of energy to the mixture or a degradation of its energy.
y
A
y
B
y
1,A
y
1,B
.
.
.
y
2,A
y
2,B
y
k,A
y
k,B
n
in
n
1
n
2
n
k
4 pt
8 pt
3 pt
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View Full DocumentProblem 2.
(30 Points)
In petroleum refineries, a mixture of paraffins and cycloparaffins is
commonly reformed in a fixedbed catalytic reactor to produce blending stocks for gasoline and
aromatic precursors for making petrochemicals.
A typical multicomponent product from
catalytic reforming is a mixture of ethylbenzene with the three xylene isomers.
If this mixture is
separated, these four chemicals can be subsequently processed to make styrene, phthalic
anhydride, isophthalic acid, and terephthalix acid.
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 Spring '08
 Bell
 WMIN, dry air, Huntsville

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