090123_Lecture5

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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3 Integrals of exp(-ax 2 ) (correction) (from appendix A-10 of the text) 2 0 2 3 0 2 2 0 2 0 2 2 1 4 1 2 1 4 A dx Ax x A A dx Ax x A dx Ax x A dx Ax = = = = ) exp( ) exp( ) exp( ) exp( π a Z a Z dv av Z dv av Z dv v p Z x x x x x x 1 4 2 2 1 1 1 0 2 2 0 = = = = = ) exp( ) exp( ) ( Æ Z = a HW2 5. Calculate the average translational energy of (a) one Ar molecule and (b) one mole of Ar assuming that it is an ideal gas. What kind of equations should you use for (a) and (b)?
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4 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0 500 1000 1500 2000 2500 C (m/s) Population P(C) Å O 2 at 300K O 2 MW ~32 Which molecules represent the red line ?
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This note was uploaded on 10/11/2009 for the course CHEM 340 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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090123_Lecture5 - Physical Chemistry I for Biochemists...

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