11_562ln08

11_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms

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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 #11: INTERNAL DEGREES OF FREEDOM FOR ATOMS AND DIATOMIC MOLECULES Readings: Hill, pp. 147-159; Maczek pp. 42-53 Pages 11-1, 11-2 and 11-3 are a review of Lecture #10. ATOMS have one internal degree of freedom ELECTRONIC degree of freedom MOLECULES — have other degrees of freedom ELECTRONIC, VIBRATION, AND ROTATION which each contribute to total energy and to other macroscopic properties. Nuclear hyperfine? [Nuclear spin degeneracy factors. LATER.] Internal energy adds to translational energy to get total energy ε = ε trans + ε int quantum #'s internal quantum #'s N,M,L where ε int = energy from internal degrees of freedom q = e −ε i kT = g( ε )e − ε ( trans + ε int ) kT i ε all molecular all molecular states energies We do not have to start from the beginning. q trans and q int appear as separate multiplicative factors. q = e −ε trans kT e −ε int kT translational internal states states q = q trans q int INTERNAL MOLECULAR PARTITION FUNCTION (q trans q int ) N N! q N trans N! Q = = q int N
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5.62 Spring 2008 Lecture 11, Page 2 NOTE: N! is included with q trans . This is because it's the translational motion that causes the positions of identical particles to be interchanged (thus rendering them indistinguishable), requiring the factor of N! The internal motions do not interchange particles. Q = Q trans Q int Q trans = q trans N N! Q int = q int N CANONICAL PARTITION FUNCTION CANONICAL TRANSLATIONAL PARTITION FUNCTION CANONICAL INTERNAL PARTITION FUNCTION Classically Q cl = Q trans,cl Q int,cl Q trans,cl = q trans,cl N N! = e −ε trans /kT d p 3 d q N!h 3N 3 N Q int,cl = q int N = dp 3N dq 3N e −ε int /kT CONTRIBUTION OF INTERNAL DEGREES OF FREEDOM TO MACROSCOPIC PROPERTIES E = kT 2 ⎛ ∂ lnQ = kT 2 ⎛ ∂ lnQ trans Q int T N,V T N,V ⎛ ∂ lnQ trans ⎛ ∂ lnQ int E = kT 2 T N,V + kT 2 T N,V E = E trans + E int revised 1/10/08 12:44 PM
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5.62 Spring 2008 Lecture 11, Page 3 A = –kT ln Q = –kT ln Q trans Q int = –kT ln Q trans + –kT ln Q int = A trans + A int Likewise: S = S trans + S int because A = E TS S = E / T A / T = E / T kTlnQ / T But: p = kT lnQ V N,T for internal coordinates INTERNAL DEGREE OF FREEDOM OF AN ATOM Electronic Excitation: promotion of an electron to a higher energy orbital. He
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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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11_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms

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