Physical Chemistry (I)
Quiz 04
Nov. 22, 2007
1. (20%) For a Bertholet equation,
2
m
m
RT
a
P
V
b
TV
=


, expand this expression in a
Taylor series.
(a)
Based on a Taylor series expansion for the low density condition to obtain
2
m
RT
a
V
b
P
RT
≈
+

. (10%)
(b)
Find an expression for the Boyle temperature in terms of
a
,
b
, and
R
. (10%)
2.
(20%) The experimental critical constants of H
2
O are
T
c
= 647.14 K,
P
c
= 220.64
bar, and
V
c
= 55.95 × 10
–3
L.
(a)
Predict the density of water vapor at
T
= 700 K and
P
= 300 atm. (6%)
(b)
If one measured the density of H
2
O at 1200 bar and 800 K to be 537 g L
–1
,
calculate
z
and
V
m
based on the above information. (6%)
(c)
Following (b), calculate the relative error if the law of corresponding states is
applied. (8%)
3. (20%) The fugacity
f
can be viewed as the effective pressure that a real gas exerts.
(a)
Derive an expression for
f
as a function of
z
and
P
.
(10%)
(b)
Following (a), find the fugacity coefficient for a hardsphere gas (the van der
Waals gas with the
a
parameter set to zero). (5%)
(c)
Following (b), find the expression for
f
as a function of
z
and
P
at the low
density condition. (5%)
4.
(15%) The vapor pressure of methanol (
l
) is given by
3
3.6791 10
ln
23.593
Pa
31.317
K
P
T
×
=


.
(a)
Calculate the standard boiling temperature. (5%)
(b)
Calculate
Δ
H
vaporization
by the vapor pressures at 298 K and at the standard
boiling temperature. (10%)
5.
(10%) The densities of a given solid and liquid of molecular weight 122.5 at its
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 Winter '06
 pathievan
 Physical chemistry, pH, Vapor pressure, Water vapor, rt rt rt

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