Chem 350: Statistical Mechanics and Chemical Kinetics. Spring Preface. Introduction 2

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2 Preface Introduction 2

3 Statistical Mechanics and Chemical Kinetics: Syllabus Textbook: Thermodynamics, Statistical Thermodynamics and Kinetics 3 rd 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 3

4 Introduction Physical chemistry is divided into: Microscopic laws of physics - Electromagnetism - Quantum Mechanics - (quantum field theory) For Quantum Mechanics: Schrodinger s equation : Ĥ E i Hˆ t x, x, x... x and Ĥ is the Hamiltionian The wave function of every particle, where operator Hˆ 2 P qq i i j 2m r 4 i i ij o QM is our most detailed description of the world (for a chemist). Everything else would/should follow First Principle theory. Inputs : e 1, Z, m 1 1, m 2, 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 T, P, V, which are all measurable o very few variables to describe system experimentally (useful) o In thermodynamics lots of experimental data is used such as H o f 298 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 4

5 It uses microscopic (often quantum) input to provide absolute values for thermodynamic quantities S, A, G,, CV, CP,,. Similar principles can be used to describe rates of elementary reactions which forms the basic inputs for kinetics. 23 Underlying principle: Use statistical averages that involve huge numbers ( 10 ), 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 ( CO2, H2O, NH 3 ). 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 5

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 Statistical Mechanics bridges the two Macroscopic Physics Physical Chemistry change?) Quantum Mechanics Thermodynamics (equilibrium) Kinetics (how fast? How does it Transport properties (diffusion, heat) Introduction 6