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Van Voorhis, Troy, 5.62 Physical Chemistry II, Spring 2008. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

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.


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.



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


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


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.


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.


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


Homework (8 problem sets) 25%
Three midterm exams (15% each) 45%
Final exam 30%


1 Review of thermodynamics  
2 E, A, and S: macroscopic properties for microscopic probabilities {Pi}  
3 Canonical partition function: replace {Pi} by Q  
4 Microcanonical ensemble: replace {Pi} 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: qtrans  

Quantum vs. classical qtrans Equipartition Internal degrees of freedom

11 Internal degrees of freedom for atoms and diatomic molecules Problem set 3 due

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 qrot and qvib  
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

Transition state theory II Kinetic isotope effect

35 Statistical mechanics for photons  
36 Rates of unimolecular reactions: RRKM  
Final exam   Tell A Friend