lecturenotes_nov42010 - Lecture notes for Lecture#7...

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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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We 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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lecturenotes_nov42010 - Lecture notes for Lecture#7...

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