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ps4solutions - Chemistry 4511 Problem Set 4 1 For the...

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Chemistry 4511 Problem Set 4 1. For the reaction A + B Æ AB, the following data are collected: T (K) k (s -1 ) 300 5.71E-13 400 5.78E-08 500 5.82E-05 600 5.85E-03 700 0.158 800 1.862 What 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 m A = 36.4 amu and m B = 19.5 amu? First, we have the relationship k = Ae -Ea/RT so we can generate a plot of the data – ln (k) vs. 1/T: Arrhenius Plot y = -13830.42694x + 17.90986 R 2 = 1.00000 -30 -25 -20 -15 -10 -5 0 5 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 1/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: ( ) 2 1 2 8 red b AB AB Tm k Ld Z A π = = where B A B A red m m m m m + = and then solving for d AB ( ) 4 1 2 2 8 + = B A b B A AB m m TL k m m A d π which works out to (watch your units!!!) d AB = 2.098 x 10 -10 m or 2.098 angstroms @ 300 K d AB = 1.64 angstroms @ 800 K

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