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1
Chemistry 391
Fall 2007
PS5 KEY
1. Write the differential
VT
AA
dA
dT
dV
TV
∂∂
⎛⎞
=+
⎜⎟
⎝⎠
Take its derivative with respect to
T
at fixed
p
:
pVT
p
AAA
V
TTV
T
∂∂∂
∂
⎛⎞⎛⎞
⎜⎟⎜⎟
∂
⎝⎠⎝⎠
Combine with
()
( )
( )
,,
,
)
,
GTp
ATVTp
pVTp
to get
p
p
GAA
V
V
p
T
T
∂
∂
∂
+
∂
∂
Now use the definition
T
A
p
V
∂
=−
∂
to obtain the desired result
pV
GA
S
TT
−=
=
.
2.
mixing
mixing
GT
S
Δ=
−
Δ
=
nRT
(
x
1
ln
x
1
+
x
2
ln
x
2
)
1
1
1
1
1111
a)
20 mol 8.314 J K mol
298 K
ln
ln
34.4 kJ
2222
1122
b)
30 mol 8.314 J K mol
298 K
ln
ln
47.3 kJ
3333
mixing
mixing
G
G
×
××
+
=
−
×
+
=
−
c) Physically, you should expect equal amounts of the two gases,
x
1
=
x
2
=1/2, to produce
the lowest
mixing
G
Δ
because it will produce the largest
mixing
S
Δ
. The largest
mixing
S
Δ
because there is the greatest expansion of each gas for the amount of gases you have. If
you plot
mixing
G
Δ
for a few
x
1
values you will see that it is the case. To prove it, call
12
;1
x
xx
x
==
−
and take the derivative of
mixing
G
Δ
with respect to
x
to get
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This note was uploaded on 07/25/2008 for the course CEM 391 taught by Professor Cuckier during the Fall '08 term at Michigan State University.
 Fall '08
 Cuckier

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