Day19 - CE 561 Lecture Notes Fall 2009 Day 19: Review for...

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CE 561 Lecture Notes Fall 2009 p. 1 of 6 Day 19: Review for 1 st Exam Here, I will attempt to outline what we have covered during the first half of the course. This completes the portion of the course devoted to reaction kinetics. After the exam, we will begin the reactor and reaction engineering portion of the course. What did we learn so far? Introduction and review: Definitions of: reaction rate, rate coefficient, reaction order, molecularity, elementary reaction, law of mass action, reactive intermediates, unimolecular reaction, bimolecular reaction, termolecular reaction, molecularity of a reaction, principle of microscopic reversibility, Arrhenius equation, reaction mechanism . How to write rate equations and how to analytically integrate simple rate expressions for a single reaction (0 th order, 1 st order, 2 nd order, etc.). How to use integrated rate expressions to determine the reaction order and find the rate constant for a single reaction given concentration vs. time data. How to make an Arrhenius plot and extract rate parameters from it. How and when to use classical analytical approximations made in analyzing reaction mechanisms: the partial equilibrium approximation and the pseudo-steady-state approximation. Matrix Methods and Notation Writing reactions in matrix notation 1 0, 1, N ij j j A iM α = = = ( α ij <0 for reactants, >0 for products), or 0 A = Writing rate equations in matrix notation T dC r dt = and MC dt = Finding a set of linearly independent reactions by finding the rank of the stoichiometric matrix. General solution of linear 1 st order ODE’s (rate equations) in matrix form:
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CE 561 Lecture Notes Fall 2009 p. 2 of 6 ( ) exp( ) o C t Mt C = , which becomes -1 ( ) ( exp( ) ) o Ct T t T C = Λ using eigenvalues and eigenvectors of M . This includes understanding the definitions of eigenvalues and eigenvectors and how they are calculated. Solution of linear ODE’s using Laplace transform methods. Stochastic methods for analyzing chemical reaction processes Definition and use of the conditional probability of having a particular state of a system given after some time given the state of the system at some earlier time Basic algorithm for kinetic Monte Carlo simulation of a reacting system
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Day19 - CE 561 Lecture Notes Fall 2009 Day 19: Review for...

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