34_562ln08

34_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 Spring 2008 Lecture #34 Page 1 Transition State Theory. II. E vs. E a . Kinetic Isotope Effect. Want to get k TST into Arrhenius form k TST = ! kT h K " but K " = e # G RT $ % $ # RTlnK = G so k TST = ! kT h e # G /RT = ! kT h e S /R e # H /RT because G = H # TS NOW: H = E + nRT where n = (# molecules in TS) – (molecularity of reaction) (molecularity: e.g., unimolecular, bimolecular, etc.) e.g. n = 1 –2 = –1 So: k TST = ! kT h e S R e 1 e " E RT k TST # BT m e " E RT where m = 1 Surprisingly, theory predicts a temperature dependence to the pre-exponential factor. This T-dependence is difficult to observe experimentally unless the rate constant is measured over a wide temperature range (at least a factor of 5) Now: d ln k TST dT = d ln ! k h e S / R e 1 " # $ % + ln T + e ( E ) * + , - . dT = 1 T + E RT 2 (TST) Contrast this to Arrhenius model: d ln k dT = E a RT 2 revised 4/24/08 11:34 AM
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5.62 Spring 2008 Lecture #34 Page 2 dlnk dT = dlnk TST dT E a RT 2 = 1 T + E RT 2 ! E a = RT + E Again, the experimental E a is larger than E because E a is a difference between the average energy of molecules in the pot and the average energy of molecules that react,
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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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34_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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