31
Chapter 3: The Importance of State Functions: Internal
Energy and Enthalpy
Problem numbers in italics indicate that the solution is included in the
Student’s Solutions Manual.
Questions on Concepts
Q3.1)
Why is
C
P,m
a function of temperature for ethane, but not for argon?
Argon has only translational degrees of freedom, which are fully excited at very
low temperatures because
,
∆<
<
translational
Ek
T
where
translational
E
∆
is the spacing
between translational levels. The translational degrees of freedom for ethane are
also fully excited at 298 K.
This condition is not fulfilled for the spacing between
vibrational levels for ethane, and
C
P,m
increases with temperature as the
vibrational degrees of freedom become excited.
Q3.2)
Why is
q
V
=
∆
U
only for a constant volume process?
Is this formula valid if work
other than
P–V
work is possible?
Because
∆
U
=
q
+
w
,
q
V
=
∆
U
only if
w
is zero. Therefore, the formula is not valid
if work other than
P–V
work is possible.
Q3.3)
Refer to Figure 1.6 and explain why
T
U
V
∂
∂
is generally small for a real gas.
The depth of the minimum in the potential is generally very small.
Therefore, it
takes very little energy to separate the atoms or molecules that make up the gas.
Q3.4)
Explain without using equations why
T
H
P
∂
∂
is generally small for a real gas.
The variation of
H
with
P
is a measure of how the energy of a gas changes with
the spacing between the molecules of the gas. Because the depth of the minimum
in the potential in Figure 1.6 is generally very small, it takes very little energy to
separate the atoms or molecules that make up the gas.
Q3.5)
Why is it reasonable to write
P
dH
C dT
VdP
≈+
for a liquid or solid sample?
This approximation is valid because
T
U
TV
V
∂
<<
∂
for a liquid or solid.
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The Importance of State Functions: Internal Energy and Enthalpy
32
Q3.6)
Why is the equation
() ()
,
ff
ii
TT
PP
m
HC
T
d
T
n
C
T
d
T
∆=
=
∫∫
valid for an ideal gas
even if
P
is not constant in the process?
Is this equation also valid for a real gas?
Why or
why not?
It is valid because for an ideal gas,
H
is a function of
T
only, and is not a function
of
V
or
P
.
The formula is not accurate for a real gas, because
H
is a weak
function of
V
and
P
.
Q3.7)
Heat capacity
C
P,m
is less than
C
V,m
for H
2
O(
l
) between 4º and 5ºC.
Explain this
result.
This unusual behavior occurs because the density of water decreases with
temperature in this range.
Therefore, work is done by the surroundings on the
system as water is heated at constant
P
between 4ºC and 5ºC.
Q3.8)
What is the physical basis for the experimental result that
U
is a function of
V
at
constant
T
for a real gas?
Under what conditions will
U
decrease as
V
increases?
U
is a function of
V
for a real gas because of the interaction potential between gas
molecules.
U
decreases as
V
increases if the density is such that the gas is
dominated by the repulsive part of the potential.
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 Fall '09
 Goux
 Physical chemistry, Enthalpy, pH, Equation of state

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