Using this probability and the energy dependence of ZUsing this probability and the energy dependence of ZABABderived from the derived from the BoltzmannBoltzmanndistribution, the reaction ratedistribution, the reaction ratecan be obtained. The result is:can be obtained. The result is:Where Where ZZABAB= = ππ((σσABAB))22<<uurelrel> > (N(NAA/V)(N/V)(NBB/V)/V)R= R= {{ππ((σσABAB))2 2 <<uurelrel> e > e --EEAA/RT/RT}}(N(NAA/V)(N/V)(NBB/V)/V)Often Often kkRRis written is written kkRR=A e =A e --EEAA/RT/RTSince <Since <uurelrel>=(8kT/>=(8kT/πµπµ))1/21/2, A increases linearly with, A increases linearly withsquare root of T.square root of T.Temperature Dependence of Temperature Dependence of kkRRThere are two places where T comes into the expressionThere are two places where T comes into the expressionfor for kkRROrientation Effects: The Orientation Effects: The StericStericFactorFactorWe have left out one consideration in our model for R, We have left out one consideration in our model for R, the reaction rate. the reaction rate. For example, in the reaction of NO+OFor example, in the reaction of NO+O22to form NOto form NO22, the one O, the one Ofrom Ofrom O22must attach to the N in NO, not the O in NO!must attach to the N in NO, not the O in NO!Might expect collisions between NO and OMight expect collisions between NO and O22that occur at the that occur at the nitrogen end of NO will be more effective in producing NOnitrogen end of NO will be more effective in producing NO22than collisions at the O end of NO!than collisions at the O end of NO!ClClNNOO++ClClNNOONo reactionNo reactionNNOO++ClClClClClNOClNO+ + ClNOClNO→→ClCl22+ 2 NO+ 2 NOClClNNOO++ClClNNOO++NNOOStericStericEffects on Chemical ReactionsEffects on Chemical ReactionsUnits (Units (cgscgs) and typical numbers:) and typical numbers:Bonus * Bonus * Bonus * Bonus * Bonus * BonusBonus * Bonus * Bonus * Bonus * Bonus * BonusChemical Kinetics: Laboratory MeasurementsChemical Kinetics: Laboratory MeasurementsWe now have a model for chemical reactions (BinaryWe now have a model for chemical reactions (BinaryCollision Model) and need to deal with practical issueCollision Model) and need to deal with practical issueof how to make observations in the laboratory.of how to make observations in the laboratory.This will involve both analyzing chemical reaction dataThis will involve both analyzing chemical reaction datafrom laboratory measurements and extending our models.from laboratory measurements and extending our models.A) Consider the reactionA) Consider the reaction2A 2A →→B + CB + CRate Rate ≡≡time rate of change of concentration of any of thetime rate of change of concentration of any of thesubstances involved substances involved --reactants reactants ororproducts.products.Usual convention: R = Usual convention: R = --12dCAdt=dCBdt=dCCdtCould measure the rate by measuring the composition Could measure the rate by measuring the composition of the reaction vessel as a function of time. Example:of the reaction vessel as a function of time. Example:t = 0t = 0NNAAºº= moles A= moles ANNBBºº= N= NCCºº= 0= 0t = tt = t11NNAA’’= moles A= moles ANNBB’’= N= NCC’’= moles B, C= moles B, CConsider the reactionConsider the reaction2A 2A →→B + CB + Ct = 0t = 0NNAAºº= moles A= moles ANNBBºº= N= NCCºº= 0= 0t = tt = t11NNAA’’= moles A= moles ANNBB’’= N= NCC’’= moles B, C= moles B, CConsider the reactionConsider the reaction2A 2A →→B + CB + CTwo moles of A gives one mole of B. Or moles of B formedmust equal half the number of moles of A reacted.Take deerivative of both sides with respect to t →→CAtNNAAoo/V= /V= CCAAooThe slope of such a plot is directly The slope of such a plot is directly related to the reaction rate.related to the reaction rate.Consider the reactionConsider the reaction2A 2A →→B + CB + CIn general the rate for such a reaction turns out to be a functIn general the rate for such a reaction turns out to be a functionionof the concentrations of all of the substances involvedof the concentrations of all of the substances involvedf could have any form. In many cases f has the formf could have any form. In many cases f has the formkkis a constant called the is a constant called the rate constantrate constant. . ααis the is the orderorderof the of the reaction for the component Areaction for the component Aαα= 1 = 1 ≡≡11ststorder in Aorder in Aαα= 3 = 3 ≡≡33rdrdorder in Aorder in AOverall order of a reactionOverall order of a reaction= = αα+ + ββ+ + γγ. . The order has absolutely nothing to do with theThe order has absolutely nothing to do with thestoichiometrystoichiometryof the reaction,of the reaction,The point is that one knows nothing about The point is that one knows nothing about αα, , ββ, , γγfromfromlooking at the chemical equation for the reaction.looking at the chemical equation for the