By Margaret Robson Wright
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Additional info for Fundamental Chemical Kinetics: An Explanatory Introduction to the Concepts
Example text
L.. ,0 0 ::;· -=cs· sum over all quantum states i vibration for all modes of a molecule ~ v is the fundaq_i_ental vibration frequency for " i cr' = symmetry number for the internal rotation. I' is the moment of inertia for the internal rotation found from spectroscopic data N II) n{t-exp 1 ( ~d all modes =- 0 v1 are the various fundamental vibration frequencies for the vibrational modes of the molecule ;: ~ .... 0 ~ -= f') cs· j Number of vibrational modes for a linear molecule = 3N-5 Number of vibrational modes for a non-linear molecule = 3N-6 Number of vibrational modes for a non-linear molecule with x internal rotations 0 ....
C. C. C. C. Atom + linear QxQyz q,31/ 3 Aq, Bq, ~ A q, Ill 3 2 q,'fr 3 M qtf/fv3N-5 :s ~. C. 3N-3 AC · · qtJr v A s· :s ~ 0 "'I '< q,3fr3fv3N- 4 qt3qt3 fr3 fv3N-6 KkT &__2 h qt3 10-15 - 10-14 tJrJv A. C. q/_{,3fv w 1 where N = N + 1 . 3 3r3N-4 .. C. C. C. C. f/J}"'-1 where N' = N + N . C. t}N-5 -.... 0 =N+N : I" . C. C. C. -= qt3 fr3 fv3N - 7 KkT qt3 fr3 fv3N- 6 h I 0 .... C. j::. OTHER EXAMPLES BEING CALCULATED SIMILARLY Basic transition state theory 42 [Ch. 1 Reaction of two atoms, A and B, to give a linear diatomic activated complex A + B ~ AB" ~ product where 3 qt3 q1 there are no rotations or vibrations for an atom q/ J,2 a diatomic species has two rotations, and the activated complex has one vibration less than the corresponding diatomic molecule.
1 gives the standard fonns for each individual partition function. trans= "L.. exp(-/;I' (2rtmkn 312 v h Quantities involved other than universal constants and temperature m = mass of molecule sum over all quantum states i r -= fl> ;:;· rotation: linear molecule hot = L exp(- Ek';'. ) 8n 2 IkT cr CJh2 = rotational symmetry number I = moment of inertia found from spectroscopic data sum over all quantum states i -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------· rotation: non-linear molecule hot = L exp(- E;;) sum over all quantum states i 87t 2 (87t 3 I Al nlc )112 (kT)312 ah 3 cr = rotational symmetry number Dl -= ~.
