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ChE 359 Homework #6
due Thursday, March 25, 2010 at 2:30 pm
Prepared by Chris Singer
1.
(35 points) Intermolecular interactions are
often
described
by
the
LennardJones
potential
u(r)
,
which
gives
the
internal
energy of interaction between two molecules
as a function of intermolecular separation:
u r
( )
=
4
ε
σ
r
Λ
Ν
Μ
Ξ
Π
Ο
12
−
r
Λ
Ν
Μ
Ξ
Π
Ο
6
Ρ
Σ
Τ
Φ
Υ
where
and
are characteristic energy and
bond length parameters.
a.
(5
points)
At
low
temperatures,
entropy is relatively unimportant, and
the free energy is minimized at the intermolecular separation of the
molecules at which the potential energy is minimized.
At what separation
r*
does that occur?
What is the energy
u(r*)
of that state?
Minimization occurs at the zero of the potential energy derivative
du
dr
r
=
r
*
( ) =
0
=
4
−
12
12
r
*
13
+
6
6
r
*
7
Ρ
Σ
Τ
Φ
Υ
=
24
r
*
r
*
Λ
Ν
Μ
Ξ
Π
Ο
6
−
2
r
*
Λ
Ν
Μ
Ξ
Π
Ο
12
Ρ
Σ
Τ
Φ
Υ
⇒
r
*
=
2
1/ 6
The energy at this distance is
u
(
r
=
r
*)
=
u
(
r
=
2
1/ 6
)
=
4
1
2
1/ 6
Λ
Ν
Μ
Ξ
Π
Ο
12
−
1
2
1/ 6
Λ
Ν
Μ
Ξ
Π
Ο
6
Ρ
Σ
Τ
Φ
Υ
=
−
b.
(5 points) What is the physical meaning of
and
?

ε
is the minimum energy which corresponds to the bond energy.
σ
is the interatomic distance at which the potential is equal to zero. Note: this
is not the distance where attractive and repulsive forces are equal. You can
check this by evaluating F = (dU/dr) at r =
σ
.
c.
(5
points)
The
constants
for
several
compounds are given in the table to the
right
(Source:
Atkins
and
de
Paula,
Physical
Chemistry,
7
th
edition,
W.
H.
Freeman and Company, New York, 2002).
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What physical properties of these systems can you deduce?
ε
gives information on the bonding strengths. From this you can deduce trends
in boiling and melting points and the corresponding heats of such phase
changes.
σ
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This note was uploaded on 02/09/2011 for the course CHE 359 taught by Professor Cynthialo during the Spring '10 term at Washington University in St. Louis.
 Spring '10
 CynthiaLo
 Mole, Kinetics

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