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Using this probability and the energy dependence of Z AB

Using this probability and the energy dependence of Z AB derived from the Boltzmann distribution, the reaction rate can be obtained. The result is:. Where Z AB = ( AB ) 2 < u rel > (N A /V)(N B /V). R= { ( AB ) 2 < u rel > e -E A /RT } (N A /V)(N B /V).

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Using this probability and the energy dependence of Z AB

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  1. Using this probability and the energy dependence of ZAB derived from the Boltzmann distribution, the reaction rate can be obtained. The result is: Where ZAB = (AB)2<urel> (NA/V)(NB/V)

  2. R= {(AB)2 <urel> e -EA/RT} (NA/V)(NB/V) Often kR is written kR=A e -EA/RT Since <urel>=(8kT/)1/2, A increases linearly with square root of T.

  3. Temperature Dependence of kR There are two places where T comes into the expression for kR

  4. Orientation Effects: The Steric Factor We have left out one consideration in our model for R, the reaction rate. For example, in the reaction of NO+O2 to form NO2, the one O from O2 must attach to the N in NO, not the O in NO! Might expect collisions between NO and O2 that occur at the nitrogen end of NO will be more effective in producing NO2 than collisions at the O end of NO!

  5. Cl Cl Cl Cl Cl Cl O O O N N N N N N O O O No reaction + ClNO + ClNO  Cl2 + 2 NO + + + Steric Effects on Chemical Reactions

  6. Bonus * Bonus * Bonus * Bonus * Bonus * Bonus Units (cgs) and typical numbers:

  7. Chemical Kinetics: Laboratory Measurements We now have a model for chemical reactions (Binary Collision Model) and need to deal with practical issue of how to make observations in the laboratory. This will involve both analyzing chemical reaction data from laboratory measurements and extending our models.

  8. Usual convention: R = - A) Consider the reaction 2A  B + C Rate  time rate of change of concentration of any of the substances involved - reactants or products.

  9. Could measure the rate by measuring the composition of the reaction vessel as a function of time. Example: t = 0 NAº = moles A NBº = NCº = 0 t = t1 NA’ = moles A NB’ = NC’ = moles B, C Consider the reaction 2A  B + C

  10. Consider the reaction 2A  B + C Two moles of A gives one mole of B. Or moles of B formed must equal half the number of moles of A reacted. t = 0 NAº = moles A NBº = NCº = 0 t = t1 NA’ = moles A NB’ = NC’ = moles B, C Take deerivative of both sides with respect to t 

  11. Consider the reaction 2A  B + C The slope of such a plot is directly related to the reaction rate. NAo/V= CAo CA t

  12. In general the rate for such a reaction turns out to be a function of the concentrations of all of the substances involved f could have any form. In many cases f has the form k is a constant called the rate constant.  is the order of the reaction for the component A

  13.  = 1  1st order in A  = 3  3rd order in A Overall order of a reaction =  +  + . The order has absolutely nothing to do with the stoichiometry of the reaction, The point is that one knows nothing about , ,  from looking at the chemical equation for the reaction.

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