05_562ln08

05_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.62 Lecture #5: Molecular Partition Function: Replace E(assembly) by ε (molecule) Readings: Hill, pp. 59-70; Maczek, pp. 16-19; Metiu pp. 49-55 Overview: We've learned to calculate thermodynamic (macroscopic) properties of a system from the partition function. However, the partition function, as it is presently written, depends on the energy levels available to the entire many-particle system . We still need to input an understanding of the energy levels of a single molecule (microscopic) into a description of the energy levels of the entire many-particle system (= assembly). Today we will do this, using statistics (combinatorics). Goal: Reformulate Q as a function of the energies, ε i , of states of individual molecules rather than the energies E j of an assembly of molecules. Procedure: Change labeling of states from " α -type" (assembly centered) description to an occupation number, n i , (molecule centered) n-type description. α -type assembly description (list of the state of each molecule in assembly) m 1x m 1y m 1z m 2x m 2y m 2z m 3x m 3y m 3z m 4x m 4y m 4z m 5x m 5y m 5z 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1 molecule 1 molecule 2 molecule 3 molecule 4 molecule 5 state #1 state #2 state #1 state #3 state #2 energy ε 1 energy ε 2 energy ε 1 energy ε 3 energy
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

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05_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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