Full set of Notes with Fill-Ins - San Jose State University

This came out a bit tedious again.Chem 155 Unit 10 Page 180 of 316We need a coherent section with the layer-bylayerapproach.The whole derivation needs to be scrapped.Extinction Cross Section Exercise:Relate the cross-section “a” to the molar extinctioncoefficient, ε, in Beer’s law. Use this to answer thequestion: can the absorption cross section of amolecule be bigger than the molecule itself?Beer’s law: A = εbC = -Log(P/Po)Basic theory: P = Po⋅exp(-aNx)Recall: Ln(x) = 2.303Log(x)Molar : C = N(cm -3 )(1000cm 3 /L)/(6.023⋅10 23 /mol) =C = 1000 N / N A1. Let x = b (the full path length), solve for aNb,convert to Log from Ln.P = Po exp(-aNb)ln(P/Po) = -aNbaNb = -ln(P/Po) = -2.303Log(P/Po)2. Substitute εbC for –Log(P/Po)aNb = 2.303εbC3. Substitute 1000 N / N A for C, cancel terms, solvefor ε.aNb = 2.303εb (1000 N / N A )aNb = 2.303εb (1000 N / N A )a = 2303 ε / N APage 180 of 316