07_562ln08

07_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 #7: Translational Part of Boltzmann Partition Function CANONICAL PARTITION FUNCTION FOR INDEPENDENT, INDISTINGUISHABLE MOLECULES Q(N,V,T) = q N /N! approximation valid for q N, not assured to be always valid “corrected Boltzmann statistics” where q = e −ε i /kT molecular partition function i sum over states of one of the molecules GOAL: to determine for what systems q N is valid. PROCEDURE: 1) develop a (simplified) physical picture for q 2) calculate a value for q 1) PROPERTIES OF q q is a measure of the total number of molecular states available to one molecule at some temperature. ε i /kT e proportional to population in state i at T q total # of states accessible at T ( kT q ) population in single-particle state i in N atom system: N e −ε i where the term in parentheses is the probability of finding any single particle in state i. Consider molecules A and B with energy levels sketched below.
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5.62 Spring 2008 Lecture 7, Page 2 state of energy ε i 1. Molecule A has more states because they are more closely spaced in energy. 2. The total number of thermally accessible states in molecule A is larger because there are more states with ε i less than or comparable to kT. Contribution of each state to the sum in the definition of q depends on its energy relative to kT. (kT is an energy) (k = 1.38 × 10 –23 J/K) Therefore q A > q B So, q plays an essential role in determining the probability that a molecule is in state i.
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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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07_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62...

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