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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Cuckier
 Derivative, Trigraph, James Clerk Maxwell, ∂V ⎠T

Click to edit the document details