Lecture notes for Lecture #7, November 4, 2010
Definitions
Bond Energy:
a measure of the bond strength for a particular bond. Bond strength (energy) can
be directly related to the bond length or bond distance. At equilibrium this bond length is r
0
.
For large, realistic samples, in which the number of moles is easily determined, the bond energy
can be found from using
Total bond energy =  ½ (nearest neighbor bonds/atom)*N
A
*
ε
Monotomic Gas:
a gas in which atoms are not bound to each other, and there are no interatomic
bonds. At STP all of the noble gases are monatomic
Diatomic Gas
: a gas in which
the molecules are composed only of two atoms of either the same
or different chemical element. Diatomic gasses have internal atomic structure, linking the atoms so
that the gas comes in pairs, like O
2
, N
2
, etc
Avogadro constant
6.02214179(30)×10
23
mol
−
1
Equipartition:
the equipartition theorem is a general formula that relates the temperature of a
system with its thermal energy, E
th
. The equipartition theorem states that energy is shared equally
among all of its various forms; or modes. This can be written in equation form as:
E
th
/mode = ½ k
B
T
So that the total thermal energy, found from considering the energy in all modes is given by
E
th
= (total # of modes) ½ k
B
T
Calculating Bond Energies
In today
’s lecture
we took a closer look at calculating the bond energy of any given atomic
configuration.
We looked at a few different situations over the course of the last few DLs and
lectures as follows:
i)
A small configuration of three or four or maybe five atoms.
ii)
A larger configuration of 20, 40 or even 60 atoms
iii)
A very large, realistic configuration of atoms, say a mole
(or Avoragadro’s number
of atoms)
For the small configuration of atoms, we found, as we did many times in DL and in doing the
FNTs, that the necessary criteria for determining the bond energy is simply determining the
number of significant bonds.
For small configurations,
nearest neighbor bonds contribute the
most
to the overall bond energy, but next
nearest neighbor bonds, because of the small
configuration and the relatively small differences between all the bond lengths, do contribute a
significant amount
, even though that amount might be small compared to the nearest neighbor
bond length; so it must be considered in the overall bond energy.
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View Full DocumentWe can consider the following cases below to calculate the total bond energy; a triad of atoms, the
linear triatomic molecule, (both done in DL) and a more complicated structure requiring the use of
the Pythagorean theorem to get a good measure of the next nearest neighbor bonds.
The triad structure, that is, three atoms whose centers are all equidistance from each other is the
easiest to evaluate. In this configuration there are NO next nearest neighbor bonds, so all that we
need to do is add up the nearest neighbor bonds.
Since the molecule is sitting at equilibrium, each
bond is a length, r
0
. And as we know, r
0
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 Fall '08
 PARDINI
 Physics, Atom, Energy, Kinetic Energy, Chemical bond, Monotomic Gas, nearest neighbor bonds

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