090121_Lecture4

090121_Lecture4 - 1 Physical Chemistry I for Biochemists...

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Unformatted text preview: 1 Physical Chemistry I for Biochemists Chem340 Lecture 4 (1/21/09) Yoshitaka Ishii • Boltzmann Distribution • Kinetic Theory of Gas • Intro of Ch. 2 of the text Boltzmann Distribution Population at energy level j: E 2 E 1 ) / exp( ) ( kT E A j p j − = ∑ = − = N j j kT E A 1 1 ) / exp( / 2 Boltzmann Distribution When E j is in molar energy: E 2 E 1 ) / exp( ) ( RT E A j p j − = ∑ = − = N j j RT E A 1 1 ) / exp( / Boltzmann Distribution ∑ = − − = N m m j kT E kT E j p 1 ) / exp( / ) / exp( ) ( ∑ = − − = N m molar m molar j RT E RT E j p 1 ) / exp( / ) / exp( ) ( _ _ [ ] kT E E kT E kT E m p j p m j m j / ) ( exp ) / exp( / ) / exp( ) ( / ) ( − − = − − = Molar Energy 3 [ ] kT E E m p j p m j / ) ( exp ) ( / ) ( − − = E j E m If (E j – E m ) >> kT Æ p(j) = 0. kT E j E m kT If (E j – E m ) << kT Æ p(j) ~ p(m). Population and Transition Energy Thermal Excitation Continuous Potential • The potential energy of a gas molecule with mass m at a height z E(z) is given by E( z ) = mg z • What is the probability of finding the molecule at h ? p(z) = Aexp(-mgz/kT) = Aexp(-Mgz/RT) • What is A for this case? Mg RT dz RT Mgz A dz z p / ) / exp( / ) ( = − = = ∫ ∫ ∞ ∞ 1 1 Since the population of the gas molecule n/V is proportional to the pressure Æ P(z) = P(0)exp(-Mgz/RT) 4 Probablity of Having Speed C, P(C) for O2 in Gas 0.00E+00 1.00E-03 2.00E-03 3.00E-03 500 1000 1500 2000 Speed (C) (m/s) P(C) Q. The data show temperature dependence of speed distribution of O 2 molecules....
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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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090121_Lecture4 - 1 Physical Chemistry I for Biochemists...

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