Chemistry 4511 Problem Set 4 1. For the reaction A + B ÆAB, the following data are collected: T (K)k (s-1)3005.71E-134005.78E-085005.82E-056005.85E-037000.1588001.862What is the activation energy for this reaction? If it adheres to the hard sphere collision rate, what is the sum of their radii if their masses are mA= 36.4 amu and mB= 19.5 amu? First, we have the relationship k = Ae-Ea/RTso we can generate a plot of the data – ln (k) vs. 1/T: Arrhenius Ploty = -13830.42694x + 17.90986R2= 1.00000-30-25-20-15-10-50500.00050.0010.00150.0020.00250.0030.00351/T (1/K)ln (k)From here, the slope = Ea/R which gives an Ea of 115 kJ. For the second part, assuming hard sphere collision theory accurately represents the prefactor A, we have the intercept = lnA: ()2128redbABABTmkLdZAπ==where BABAredmmmmm+=and then solving for dAB()41228⎟⎟⎠⎞⎜⎜⎝⎛+=BAbBAABmmTLkmmAdπwhich works out to (watch your units!!!) dAB= 2.098 x 10-10m or 2.098 angstroms @ 300 K dAB= 1.64 angstroms @ 800 K
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