# Lecture32A - Going Beyond Initial Rates(28.5-8) Before we...

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Lecture 32 1 Going Beyond Initial Rates (28.5-8) Before we explore how rate laws can be deduced, we will examine the variation in rate laws with longer times and temperature. Implicitly we know that reactions must “end”. For a large set of reactions, reactants and products can come into equilibrium or at least a quasi-equilibrium where A B B In a general sense, this reaction is “reversible” (reactant to product and vice versa), but not in a thermodynamic sense. If we initially start with A, such that [ ] [ ] , f d A A B k A dt B - = (we’re assuming 1 st order kinetics, k f =forward rxn rate const.) As the concentration of B builds up, the rate will slow as the reverse reaction A B occurs. i.e. B “back reacts” to form A so [ ] [ ] [ ] r k reverse rate constant f r d A k A k B dt - = - =

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Lecture 32 2 ( 29 1 1 note the text has f r k k k k A B A B - I A I A [ ] [ ] At some point, the net consumption of A stops, i.e. 0 Also 0 and the system is in dynamic equilibrium. d A dt d B dt - = = [ ] [ ] Now at equilibrium we know but from our rate law, we have: eq c eq B K A = [ ] [ ] [ ] [ ] [ ] [ ] 0 so f r eq eq eq f c r eq d A d B k A k B dt dt B k K A k - = = = - = =
Lecture 32 3 [ ] [ ] [ ] [ ] [ ] [ ] 0 0 If at time 0 and 0, then at any time, t, t A A B B A A = = = = - [ ] [ ] [ ] [ ] [ ] [ ] { } ( 29 [ ] [ ] 0 0 f r f r f r r d A k A k B k A k A A k k A k A dt - = - = - - = + - [ ] ( 29 [ ] [ ] 0 (see HW problem 28-32) f r r d A dt k k A k A = - + - [ ] [ ] [ ] ( 29 ( 29 [ ] [ ] [ ] 0 where A at equilibrium f r k k t eq eq eq A A A e A A - + = - + = [ ] [ ] ( 29 [ ] [ ] ( 29 ( 29 0 ln ln f r eq eq A A A A k k t - = - - + Plot has slope of –(k f +k r ) Fig 28.5 This shows the time dependence of [A] and [B].

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Lecture 32 4 What if the reaction is really fast with respect to mixing, so we can’t do
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## This note was uploaded on 04/13/2008 for the course CHEM 444 taught by Professor Jameslis during the Spring '08 term at University of Illinois at Urbana–Champaign.

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Lecture32A - Going Beyond Initial Rates(28.5-8) Before we...

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