Lecture34A - Mechanisms to Rate Laws(29.4-6 Today we will...

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Lecture 34 1 Mechanisms to Rate Laws (29.4-6) Today we will cover 3 important concepts in deriving rate equations from elementary reaction steps: the steady state approximation; pre- equilibrium; and the Lindemann-Hinshelwood Mechanism for unimolecular dissociation. Recall from last lecture our two step mechanism: [ ] [ ] [ ] [ ] 1 2 0 0 0 at 0 0 k k A I P t A A I P = = = = We solved for [A], [I], and [P] under general conditions and limiting cases where k 1 <<k 2 and k 2 <<k 1 . Fig 29.1 ( 29 [ ] [ ] [ ] 1 2 1 2 a) 10 This case had A disappearing at a faster rate than P forming. The reason: a substantial buildup of I . k k k k = ( 29 [ ] 2 1 2 1 b) 10 This case has I low and nearly constant for most times. k k k k =
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Lecture 34 2 [ ] The latter case (b) suggests 0 for most times, t. d I dt 2245 [ ] [ ] [ ] 1 2 From our elementary reaction steps: d I k A k I dt = - [ ] [ ] [ ] [ ] 1 2 Assuming I remains constant and low, the steady state approximation gives 0 ss ss d I k A k I dt = = - [ ] [ ] [ ] 1 1 1 0 2 2 So I k t ss k k A A e k k - = = [ ] [ ] Note that I is time-dependent. So what is ? ss ss d I dt [ ] [ ] 1 2 1 0 2 which we expect to be 0. k t ss d I k A e dt k - = - 2245 [ ] 2 1 0 2 2 1 Indeed this will be true when is very small. Since , this is a good approximation. k A k k k
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Lecture 34 3 Fig 29.2 The steady state approximations are the solid lines for k 2 =10k 1 . In the last lecture I mentioned that the simple reaction: ( 29 ( 29 3 2 2 3 O g O g [ ] [ ] [ ] [ ] 2 3 3 2 3 1 had a rather nasty rate law equation: 2 ' '' d O k O dt k O k O - = + The proposed mechanism is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 2 3 2 3 2 2 k k k O g M g O g O g M g O g O g O g - + + + + Note: M activates the decomposition of O 3 by collision, but is not a reactant.
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