chem 350: statistical mechanics and chemical...

Spring 2012 Chem 350: Statistical Mechanics and Chemical Kinetics

Introduction 2

Preface


Introduction 3

Statistical Mechanics and Chemical Kinetics: Syllabus

Textbook: Thermodynamics, Statistical Thermodynamics and Kinetics 3rd ed

by Thomas Engel and Philip Reid Additional Resource (very good): Physical Chemistry: Statistical Mechanics

By Horia Metiu Grading:

- Biweekly Assignments (4 in total) = 40%

o Assignments will use computers extensively (Matlab) o Okay to collaborate with one another

- Midterm (focus on Stat Mech) = 30%

- Final Exam = 30%

Lectures: Monday, Wednesday, Friday from 10:30 – 11:30 Tutorial Session: On some Mondays, tutorial will be held instead of lectures at

the Freisen Lab (C2-160). These tutorials will be used to work on assignments or to demonstrate concepts discussed in class.


Introduction 4

Introduction Physical chemistry is divided into:

Microscopic laws of physics

- Electromagnetism - Quantum Mechanics - (quantum field theory)

For Quantum Mechanics: Schrodinger’s equation : H E ˆi Ht

The wave function of every particle, where 231 2 3 10, , ....x x x x and H is the Hamiltionian

operator 2

ˆ2 4

i ji

i i ij o

q qPH

m r

QM is our most detailed description of the world (for a chemist). Everything else would/should follow

First Principle theory. Inputs : 1e , 1

Z, 1m , 2m ,

Imagine “Ultimate Google” from QM. world describes everything that can (physically) exist. Use a Google search machine to zoom in on the events that interest you. This is fantasy, but it also captures out scientific view of the world.

Macroscopic Laws of Physics

i) Thermodynamics (Thermostatics, although it’s no longer heat related.) describes systems in equilibrium or shifting from one equilibrium to another

o very few variables to describe system , , ,T P V which are all measurable

experimentally (useful)

o In thermodynamics lots of experimental data is used such as 298

o

f H

o Something else, special about thermodynamics, is that it can only calculate changes in thermodynamic quantities , ,U S H etc..

ii) Chemical Kinetics: addresses the question of how fast processes or chemical reactions proceed

o By monitoring concentrations over time (concentration profiles), plus kinetic models (theory + simulation) we can understand reaction mechanisms

o Catalysis, enzymatic catalysis o Long term limits chemical equilibrium thermodynamics o Use experimental data: elementary rates of reaction, functions of T

Statistical Mechanics : provides the bridge to connect the microscopic (QM) world to the macroscopic description


Introduction 5

It uses microscopic (often quantum) input to provide absolute values for thermodynamic quantities

, , , , , , ,V PS A G C C . Similar principles can be used to describe rates of elementary reactions which

forms the basic inputs for kinetics.

Underlying principle: Use statistical averages that involve huge numbers ( 2310 ), more or less independent or weakly interacting entities. With such large numbers statistics becomes “certainty” since the fluctuations become very small. - non equilibrium statistical mechanics: A difficult topic that describes behavior of macroscopic systems as they change in time.

Eg. Reactions in a flow reactor, reactions where energy is fed in. Transport properties are the simplest examples.

Founding fathers of Stat-Mech: Maxwell: kinetic theory of gases Boltzmann: microscopic definition of entropy Gibbs: ensembles and classical mechanics Bose-Einstein, Fermi Dirac: particle statistics Ehrenfest: concepts in stat-mech Just some remarks

1) System are almost never in a state of fully stable equilibrium. If there were a fully stable

equilibrium, it would be very “boring”, only low energy molecules would exist ( 2 2 3, ,CO H O NH ).

Most of the equilibriums we talk about are metastable states (relatively stable but degrade after a while), a local but not global equilibrium. The barriers (kinetical hump) are too high to allow reaching of a global equilibrium This is a fundamental feature of all systems.

- In statistical mechanics, we speak of “accessible” states

2) Quantum Mechanics in practice is:

- good for molecules in gas phase (especially non-interacting)


Introduction 6

- good for solid state periodic crystals

- Quantum gets more complicated for: liquids, large floppy molecules (like proteins, conformations etc..) for these there isn’t quite a Quantum Mechanical method yet, classical mechanics still predominates.

Microscopic Physics Chemical Physics Quantum Mechanics Statistical Mechanics bridges the two Thermodynamics (equilibrium) Macroscopic Physics Physical Chemistry Kinetics (how fast? How does it change?) Transport properties (diffusion, heat)

chem 350: statistical mechanics and chemical...

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