Lectures_part1 - Chemistry 163C Roger Anderson 2011...

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Chemistry 163C Lectures 1 © Roger Anderson 2011 Course Outline Statistical Mechanics to calculate thermodynamic properties Foundations of Statistical Mechanics: Quantum mechanics Ensemble averages and fluctuations Microcanonical ensemble Canonical ensemble -- partition function Boltzmann statistics Fermi statistics (Fermions) Bose statistics (Bosons) Applications: Calculate translational, rotational, electronic, and vibrational contributions to partition functions. Use to calculate for Ideal Gases Pressure, P Energy, U or E Enthalpy, H Heat capacities, C v and C p Entropy, S Helmholtz free energy, A Gibbs free energy, G, and equilibrium constants Non Ideal Gases Bose-Einstein Condensation Ortho and Para Hydrogen Kinetic Gas Theory Velocity distributions and moments Calculation of pressure and effusion rates Collision rates, cross sections, and mean free path Collisions with molecular interactions: Impact parameter Deflection function Differential cross section Rainbow and Glory scattering Inelastic scattering (energy transfer) Transport Phenomenological kinetics Chemical Reaction Rate Theory Potential energy surfaces
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Chemistry 163C Lectures 2 © Roger Anderson 2011 Collision theory Opacity function, integral cross sections, k(T) Classical trajectory calculations Transition state theory Tunneling, isotope effects Estimates of pre-exponential factors Molecular beam experiments Photochemistry Lasers Diffusion controlled reactions Relaxation kinetics Acid-Base catalysis Primary salt effect Enzyme catalysis Magnetic Resonance Spectroscopy Electric and Magnetic Properties Solid State Structure
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Chemistry 163C Lectures 3 © Roger Anderson 2011 Foundations of Statistical Mechanics Consider a system with N molecules: Use quantum mechanics to attempt to specify this system: { } ( { } ( , , H r R E r R Ψ = Ψ ɶɶ ɶɶ where { } , r R ɶɶ represents the electronic and nuclear coordinates for each of the N molecules. For a mole, this is a very large set of coordinates. Separate wave function: Product of wave functions for individual molecules Energy: 1 i N i i E = = = where i is the energy of the i th molecule. Additional separation of energy of each molecule into translational, rotational, vibrational, and electronic energies. t r v e i i i i i ∈ =∈ + ∈ + ∈ + ∈ These contributions can be further split into translational energy in x,y, and z directions, two or three rotations, and zero or more vibrations. Is { } ( , r R Ψ ɶɶ the correct way to express the state of the system? No coherences! Correct way is to use a density matrix formulation: Only populations (occupancy number) in each molecular state matter. Distinction between states and energy levels. Ensembles Microcanonical Ensemble: N particles in a volume V that are completely isolated from the rest of the world. The equilibrium state is described by N , V , and E . E is constant.
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Chemistry 163C Lectures 4 © Roger Anderson 2011 Canonical Ensemble: N particles in a volume V that are in thermal contact with a large heat reservoir at temperature T . Now the equilibrium state is characterized by N , V , and T .
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