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090123_Lecture5 - Physical Chemistry I for Biochemists...

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1 Physical Chemistry I for Biochemists Chem340 Lecture 5 (1/23/09) Yoshitaka Ishii Kinetic Theory of Gas Intro of Ch. 2 HW2 Announcement 82 are registered now! 81 submitted HW1. Thanks! If you did not submit HW1, please come to me after the class. We will have the first discussion section today from 3 pm.
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2 Boltzmann Distribution Summary Z T k E j p B j / ) / exp( ) ( = Z T k x E x p B / } / ) ( exp{ ) ( = = = N m B m T k E Z 1 ) / exp( Discrete Energy Level / } / ) ( exp{ T k x E dx Z B = X= v, z, E etc Continuous Energy Level Kinetic Energy of Gas • v 2 = v x 2 + v y 2 + v z 2 The probability of finding a molecule flying at v x is p(v x ) = exp(-mv x 2 /2k B T)/Z, where Z = {2 π k B T/m} 1/2 and a = m/2k B T. The expected kinetic energy due to v x 2 4 2 2 2 2 2 2 2 2 2 2 / ) / exp( ) ( ) ( T k a aZ m dv T k mv v Z m dv v p v m dv v p mv mv B x B x x x x x x x x x = = = = >= < π 2 2 2 2 2 2 2 / / / / T k mv mv mv B Z Y X >= >=< >=< < 2 3 2 2 / / T k mv E B trans >= >=< < V = (v x , v y , v z )
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