Lecture2 - Macroscopic versus microscopic Ficks laws...

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1 Physical Chemistry Lecture 2 Random walks; microscopic theory of diffusion Macroscopic versus microscopic Fick’s laws describe time evolution macroscopically Do not specifically consider a single molecule (although we discussed them in that manner) Focus on the tendency to eliminate density gradients Can be explained by ad hoc appeal to kinetic theory Diffusion can be understood in terms of a microscopic process – the random walk Uses probability concepts Implies randomness in a system with many molecules Time development occurs in a “natural” way Random motion of a single molecule is the underlying driving force described by diffusion. Probability of event Random events Each event is considered equally likely unless other information is known Can only discuss likelihood of an event, p n = number of possible results Only applies to a “large sample” Examples Coin flips (n=2) Throws of dice (n=6) For events that are not equally likely, one must know (by some external means) the probability, , of each event n p 1 Probability of a sequence Probability of a sequence, P , is product of the probabilities of the elementary events that make up each sequence When the probabilities of the elementary events are the same, this equation simplifies Example: tossing a coin four times or tossing four coins at the same time Since h = t = ½, each sequence has a likelihood of happening = (½) 4 16 possible sequences, so the probability of any one sequence is 1/16 (= (½) 4 ) n p p p p p P 4 3 2 1
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2 Probability of a configuration Often concerned only with the number of elementary outcomes in a sequence, not order Example of tossing a coin: probability of getting 3 heads when tossing a coin four times Four different sequences have three heads P ‘ = 4(1/6) = 1/4 ) ( ' sequences all for P P if P n P P i sequences e appropriat i sequences e appropri at all over Numbers of configurations
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This note was uploaded on 02/02/2012 for the course CHEM 419 taught by Professor Staff during the Fall '10 term at University of Delaware.

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Lecture2 - Macroscopic versus microscopic Ficks laws...

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