Physical Chemistry II

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Physical Chemistry II posted by member7_php on 2/16/2009

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Physical Chemistry II

Spring 2008

Three-dimensional random walk. (Figure courtesy of Ziad Ganim.)

Course Description

This course covers elementary statistical mechanics, transport properties, kinetic theory, solid state, reaction rate theory, and chemical reaction dynamics.

Acknowledgements

The staff for this course would like to acknowledge that these course materials include contributions from past instructors, textbooks, and other members of the MIT Chemistry Department affiliated with course #5.62. Since the following works have evolved over a period of many years, no single source can be attributed.

Syllabus

Overview

This course will cover the following three major areas:

Principles of Statistical Mechanics

Ensembles and partition functions: canonical and microcanonical
Atomic and molecular degrees of freedom: translation, rotation, vibration, electronic, and nuclear spin
Chemical equilibrium and thermodynamic properties: entropy, enthalpy, free energy, chemical potential
Intermolecular potentials, equations of state

Solid State Chemistry

Models for solids: Einstein, Debye, metals, semiconductors

Kinetics

Kinetic theory of gases: pressure, effusion, transport
Rate theory: collision theory, transition state theory

Textbook

Hill, Terrill L. An Introduction to Statistical Thermodynamics. New York, NY: Dover, 1987. ISBN: 9780486652429.

Reading Assignments

Readings of relevant pages in several standard texts are listed per lecture. No single textbook is satisfactory for the topics covered (and the level at which they are covered) in 5.62. It is expected that you will spend 5-10 minutes previewing each day's lecture notes before class.

Homework

Problem sets will be assigned weekly. The problem sets will be due in class. Lat problem sets will not be accepted, although adjustments for missed homework due to prearranged absences will be made in the final grades.

Exams

There will be three hour-long midterm exams and a three hour final exam.

Grading

Grading criteria.
ACTIVITIES	PERCENTAGES
Homework (8 problem sets)	25%
Three midterm exams (15% each)	45%
Final exam	30%

Calendar

Course calendar.
LEC #	TOPICS	KEY DATES
1	Review of thermodynamics
2	E, A, and S: macroscopic properties for microscopic probabilities {P_i}
3	Canonical partition function: replace {P_i} by Q
4	Microcanonical ensemble: replace {P_i} by Ω, Q vs. Ω
5	Molecular partition function: replace E (assembly) by ε (molecule)	Problem set 1 due
6	Q corrected for molecular indistinguishability
7	Translational part of Boltzmann partition function
8	Boltzmann, Fermi-Dirac, and Bose-Einstein statistics	Problem set 2 due
9	Calculation of macroscopic properties from microscopic energy levels: q_trans
10	Quantum vs. classical q_transEquipartition Internal degrees of freedom
11	Internal degrees of freedom for atoms and diatomic molecules	Problem set 3 due
12	Rotational partition function Equipartition
First hour exam
13	Nuclear spin statistics: symmetry number, σ Low temperature limit for rotational partition function
14	Low and high-T limits for q_rot and q_vib
15	Polyatomic molecules: rotation and vibration
16	Chemical equilibrium I
17	Chemical equilibrium II	Problem set 4 due
18	Model intermolecular potentials
19	Configurational integral: cluster expansion
20	Virial equation of state	Problem set 5 due
21	Thermodynamics of solid: Einstein and Debye models
Second hour exam
22	Einstein and Debye solids
23	Phonons: 1-D linear chain of atoms
24	Free electron theory of a metal
25	Heat capacity in metals
26	Band theory of solids	Problem set 6 due
27	Crystal phase equilibria
28	Kinetic theory of gases: Maxwell-Boltzmann distribution
29	Kinetic theory of gases: effusion and collisions
30	Kinetic theory of gases: collision dynamics and scattering	Problem set 7 due
31	Kinetic theory of gases: mean free path and transport
Third hour exam
32	Kinetic theory of gases: transport coefficients
33	Transition state theory I	Problem set 8 due
34	Transition state theory II Kinetic isotope effect
35	Statistical mechanics for photons
36	Rates of unimolecular reactions: RRKM
Final exam

Readings

A session wise schedule of readings is provided in the table below.

Textbook

Hill, Terrill L. An Introduction to Statistical Thermodynamics. New York, NY: Dover, 1987. ISBN: 9780486652429.

Other Resources

Knox, J. H. Molecular Thermodynamics. New York, NY: John Wiley & Sons, 1971. ISBN: 9780471495901.

Andrews, F. C. Equilibrium Statistical Mechanics. New York, NY: John Wiley & Sons, 1975. ISBN: 9780471031239.

Silbey, R., R. Alberty, and M. Bawendi. Physical Chemistry. 4th ed. New York, NY: John Wiley & Sons, 2004. ISBN: 9780471215042.

McQuarrie, D., and J. Simon. Physical Chemistry: A Molecular Approach. University Science, 1997. ISBN: 9780935702996.

Metiu, H. Physical Chemistry: Statistical Mechanics. Taylor & Francis, 2006. ISBN: 9780815340850.

Maczek, A. Statistical Thermodynamics. New York, NY: Oxford University Press, 1998. ISBN: 9780198559115.

Nash, L. Elements of Statistical Thermodynamics. 2nd ed. New York, NY: Dover, 2006. ISBN: 9780486449784.

Callen, H. Thermodynamics and an Introduction to Thermostatistics. 2nd ed. New York, NY: John Wiley & Sons, 1985. ISBN: 9780471862567.

Widom, B. Statistical Mechanics: A Concise Introduction for Chemists. Cambridge, UK: Cambridge University Press, 2002. ISBN: 9780521811194.

McQuarrie, D. Statistical Mechanics. 2nd ed. University Science Books, 2000. ISBN: 9781891389153.

Reif, F. Fundamentals of Statistical and Thermal Physics. New York, NY: McGraw-Hill, 1965. ISBN: 9780070518001.

Kittel, C. Introduction to Solid State Physics. New York, NY: John Wiley & Sons, 1986. ISBN: 9780471874744.

Mayer, J., and M. Mayer. Statistical Mechanics. New York, NY: John Wiley & Sons, 1966.

Sachs, M. Solid State Theory. New York, NY: McGraw-Hill, 1963.

Bube, R. Electrons in Solids. Burlington, MA: Academic Press, 1992. ISBN: 9780121385538.

Ibach, H., and H. Lüth. Solid State Physics. New York, NY: Springer-Verlag, 2003. ISBN: 9783540438700.

Ashcroft, N. W., and, N. D. Mermin. Solid State Physics. Saunders College, 1976. ISBN: 9780030839931.

Kauzmann, W. Kinetic Theory of Gases. Benjamin, 1966.

Houston, P. Chemical Kinetics and Reaction Dynamics. New York, NY: Dover, 2006. ISBN: 9780486453347.

Readings Text Legend

H = Hill
Mac = Maczek
Met = Metiu

Course readings.
LEC #	TOPICS	READINGS
1	Review of thermodynamics	H: 1-6
2	E, A, and S: macroscopic properties for microscopic probabilities {P_i}	H: 6-20
3	Canonical partition function: replace {P_i} by Q	H: 12-13 and 18-20
4	Microcanonical ensemble: replace {P_i} by Ω, Q vs. Ω	H: 26-30 and 33-38
5	Molecular partition function: replace E (assembly) by ε (molecule)	H: 59-70 Mac: 16-19 Met: 49-55
6	Q corrected for molecular indistinguishability	H: 68-70
7	Translational part of Boltzmann partition function	H: 74-77
8	Boltzmann, Fermi-Dirac, and Bose-Einstein statistics	H: 59-72
9	Calculation of macroscopic properties from microscopic energy levels: q_trans	H: 74-81
10	Quantum vs. classical q_trans Equipartition Internal degrees of freedom	H: 82-85 and 112-115
11	Internal degrees of freedom for atoms and diatomic molecules	H: 147-158 Mac: 42-53
12	Rotational partition function Equipartition	H: 153-159 Mac: 47-53 Met: 131-142
13	Nuclear spin statistics: symmetry number, σ Low temperature limit for rotational partition function	H: 153-159 and 466-472 Mac: 54-57
14	Low and high-T limits for q_rot and q_vib	H: 153-159 Mac: 51-53
15	Polyatomic molecules: rotation and vibration	H: 151-153 Mac: 53 and 58-63
16	Chemical equilibrium I	H: 177-182 Mac: 77-83 Met: 179-191
17	Chemical equilibrium II	H: 182-187 Mac: 83-92 Met: 191-196
18	Model intermolecular potentials	H: 261-274
21	Thermodynamics of solid: Einstein and Debye models	H: 86-98
22	Einstein and Debye solids	H: 98-105 and 490-495
24	Free electron theory of a metal	H: 441-444