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Chemistry 391
Fall 2007
Problem Set 5
(Due, Monday October 8)
1. The Gibbs differentials imply that
pV
GA
S
TT
∂∂
⎞
⎞
=−
⎟⎟
⎠
⎠
. This is a remarkable result. Prove it from the defining relation
()
(
)
,,
,
)
,
GTp ATVTp
pVTp
=+
.
2. You have containers of pure H
2
and He at 298 K and 1 atm pressure. Calculate
mixing
mixing
GT
S
Δ=
−
Δ
relative to the unmixed gases of
a. a mixture of 10 mol of H
2
and 10 mol of He
b. a mixture of 10 mol of H
2
and 20 mol of He
c. For what composition (proportion of the two gases) does
mixing
G
Δ
have its minimum
value? Explain physically and show it with calculus.
3. Show that
P
p
V
dH
C dT
V T
dp
T
⎡⎤
∂
⎛⎞
−
⎢⎥
⎜⎟
∂
⎝⎠
⎣⎦
. (These are all easily measurable properties
for a gas and are useful for e.g. JouleThompson calculations). HINT – It will prove
useful to consider
GHT
S
and what this produces for
T
G
p
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 Fall '08
 Cuckier

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