Chem 331, Homework #8 (Real Gases, Phase Stability)
(Due Mon., Nov. 5th, 2007 at beginning of class)
(1)
At 25ºC the 2nd virial coefficients (
B
) for CH
4
and
n
C
4
H
10
are –42 cm
3
/mol and –732
cm
3
/mol, respectively. For a mixture of 0.0300 mol of CH
4
and 0.0700 mol of
n
C
4
H
10
at 25ºC
in a 1.000 L vessel, calculate the pressure using the virial equation and
(a)
the approximation
B
12
!
1
2
B
1
+
B
2
(
)
(b)
the fact that for this mixture
B
12
= –180 cm
3
/mol.
Compare these results with the ideal gas equation result.
(2)
Use the virial equation (in terms of the pressure) to show that
(a)
μ
JT
=
RT
2
C
P
d
!
B
dT
+
d
!
C
dT
P
+
d
!
D
dT
P
2
+
!
"
#
$
%
&
’
(b)
!
U
!
V
"
#
$
%
&
’
T
(
0
as
P
→
0
Remember that
!
H
!
P
"
#
$
%
&
’
T
=
(
μ
JT
C
P
=
V
1
(
T
)
(
)
and
!
U
!
V
"
#
$
%
&
’
T
=
(
)
T
*
P
(3)
For CH
4
at –50ºC, measured
V
values as a function of
P
are
V
(in cm
3
/mol)
18224
1743
828
366
P (in atm)
1
10
20
40
V
(in cm
3
/mol)
207
128.7
91.4
76.3
P (in atm)
60
80
100
120
Find the fugacity and fugacity coefficient of CH
4
at –50ºC and 120 atm (Hint: use the above data in
a polynomial fit of (Z–1)/P ). Please show all work (including plots).
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 Spring '08
 PRESTONSNEE
 Thermodynamics, pH, cm /mol

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