1(5)
.
The equation of state of a material
is given by
2
0
V
Va
Pb
T
=−
+
, where
V
0
,
a
, and
b
are constants. Derive the equation for the change of the chemical potential of this
material,
0
(,) ( ,)
PT
P T
µµ
−
, when its pressure is raised from
P
0
to
P
.
0
3
3
00
0
0
(
)
(
) (/
3
)
(
)
P
P
VdP
V bT P P
a
P
P
−=
=
+
−
−
−
∫
2(10)
. Obtaining very high vacuum inside an aluminum container is ultimately limited by
the fact that some of the atoms of Al escape the bulk of the metal and form the vapor
phase. Calculate the pressure of aluminum vapor that is in equilibrium with Al(s) at
T=298K using the value
(Al(g))
f
G
∆
=285.7 kJ/mol for Al(g) at P=1atm and T=298K. To
simplify your calculations, neglect the pressure dependence of the chemical potential of
Al(s) .
The equilibrium pressure is determined by the condition
(,)
gs
=
We can write this as
0
0
0
l
n
(/ )
(,) (
)
s
s
PT RT PP
PT V P P
µ
+≈
+
−
≈
,
where P
0
=1atm. This gives
0
/
51
exp
8.3 10
f
GPTR
T
sg
PP
P
e
a
t
m
RT
−∆
−
−
==
≈
×
The equation
0
f
G PT
∆
for Al(g) is obtained the same way we
have found heats of reaction from formation enthalpies in thermochemistry (this can be
done for any quantity that is a function of state).
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 Spring '08
 LIM
 Physical chemistry, Thermodynamics, pH, P0, Cp dT

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