Chemistry 125: Lecture 36 December 7, 2009 Bond Energies Group- or bond-additivity schemes are useful for understanding heats of formation, especially when corrected for strain. Heat of atomization is the natural target for bond-energy schemes, but experimental measurement requires spectroscopic determination of the heat of atomization of elements in their standard states. After discussing the classic determination of the heat of atomization of graphite by Chupka and Inghram, the values of bond dissociation energies, and the utility of average bond energies, which, when corrected for certain “effects” (i.e. predictable errors) can lead to understanding equilibrium and rate processes through statistical mechanics. For copyright notice see final page of this file

C 6 H 12 Energy = CO 2 / H 2 O graphite / hydrogen  H combustion  H formation Energy (kcal/mole) Compared to What? easily measured How to measure? ( elements in their “standard states”) Zero is arbitrary, because the things we observe (e.g. K, k,  H) depend only on differences. Choose a convenient Zero. Energy is The Key to Understanding Equilibrium and Kinetics

HfHf APPENDIX I HEATS OF FORMATION From Streitwieser, Heathcock, & Kosower

HfHf APPENDIX I HEATS OF FORMATION From Streitwieser, Heathcock, & Kosower

HfHf APPENDIX I HEATS OF FORMATION

minimum Expt. - Theory  H f + n  4.9 Group Additivity “unstrained” 2  -4.9 = -9.8 Strainless Theory (n  -4.9) ? From Streitwieser, Heathcock, & Kosower “Transannular” Strain similar c-hexane c-octane Small-Ring Strain

Group Additivity Can one sum bond energies to get useful "Heats of Atomization"? Bond Additivity From Streitwieser, Heathcock, & Kosower

How well can “Bond Energies” predict  H atomization ? Where does  H atomization come from?

C 6 H 12 Energy atoms  H atomization CO 2 / H 2 O graphite / hydrogen  H combustion  H formation Energy (kcal/mole) Compared to What? How Can You Know  H formation for an atom? = How to measure?

Atom Energy from Spectroscopy light energy X-Y X + Y H-H kcal/mole (  H f H = 52.1) O=O kcal/mole (  H f O = 59.6) CO kcal/mole X* + Y Maybe this is the observed transition at ? 141?  H f C=O =  H f H 0 2 _ _ _  H f O 0 2 _ _ _ X*’ + Y Or maybe this is the observed transition at ? 125? spectroscopic value precise, but uncertain Which to choose? CO Hf CHf C Hf OHf O graphite O 2 C + O graphite O (  H f C = 171.3) But Nobel Laureates Worried.

Atom Energy from Equilibrium K K = e -  E/kT = 10 -(3/4)  E Room Temp = 10 -(3/4)  = ! = 10 -(3/40)  = at 10 x room temperature (~3000K) measure K to find  E < atoms in universe (est) 4

Need to Plot ln( tiny Pressure of C Atoms ) vs. (1/T) at VERY high T " Pressure of C atom  P C = b e -  H f C / RT [C atom ] [C graphite ] -  H f C / RT  e ln ( P C ) = ln ( b ) -  H f C / RT (-  H f C / R ) is the slope of ln ( P C ) vs. (1 / T)

Chupka- Inghram Oven (1955) C n gas Graphite Liner Tantalum Can (mp 3293K!) Tungsten Filament (electrons boil off to bombard and heat tantalum can) Tiny Hole (lets a little gas escape for sampling while maintaining gas-graphite equilibrium)

Chupka- Inghram Oven (1955) C n gas Tantalum Shielding keeps highest heat inside Electron Beam C n BeamC n Ion Beam + C1C1 + C2C2 + C3C3 + Magnetic Field of “Mass Spectrometer” Detected Separately Optical Pyrometer measures oven Temp by color through hole in shielding and quartz window

Heat of Atomization of Graphite (  H f of Carbon Atom) 2450 K2150 K C1C1 C3C3 C2C2

HfHf From Streitwieser, Heathcock, & Kosower William Chupka APPENDIX I HEATS OF FORMATION

Text Book? Exam Help Sessions Wednesday, Dec. 16, 8-10pm

from B. Ellison & his friends  Average Bond Energy = / 4 = 99.4 kcal mol -1 No individual bond actually equals the “average” C-H bond. (because of changes in hybridization, etc.) Bond Dissociation Energy (from spectroscopy, etc.) CH 3 -H ± 0.03 CH 2 -H110.4 ± 0.2 CH-H101.3 ± 0.3 C-H80.9 ± 0.2 Sum ± 0.6 Bond Strengths in CH 4 Heat of Atomization of CH 4 = kcal mol -1 (from heat of combustion, etc.) (good experiments!)

 ve Bond Energies Can one sum these average bond energies to get useful "Heats of Atomization” for other molecules? “2 nd C-C bond” 63 kcal/mole “3 rd bond” 54 kcal/mole From Streitwieser, Heathcock, & Kosower “2 nd C-O bond” kcal/mole! (Carbonyl group pretty stable)

 H Atomization by Additivity of Average Bond Energies? Ethene Ave. Bond Energy (kcal/mole) C-C C-H C=C C-O O-H c-Hexane c-Hexanol  -Glucose Seems Pretty Impressive! How accurate must you be to be useful? K calc = 10 -(3/4)(  H true +  H error ) K calc = 10 -(3/4)(  H calc ) K calc = K true  10 -(3/4)(  H error ) kcal error not % error determines K error factor To keep error less than  10 need <1.3 kcal/mole error!  Bond Energies 542  H atomization Error kcal/mole -4.3 Error % -0.8

 ve Bond Energies Can one sum bond energies to get accurate"Heats of Atomization"? H C O H C C H H H H H C O H C C H H H H Ketone "Enol" C O C H C O C H C=O179 C-C83 C-H99 sum361 C-O86 C=C146 O-H111 sum343 K calc = 10 -(3/4) 18 = K obs = = 10 -(3/4) 9.3 Bonds that change (the others cancel in the difference)

H C O H C C H H H H H C O H C C H H H H Ketone "Enol" H Why is Enol 9 kcal/mole "Too" Stable? O C=O179 C-C83 C-H99 sum361 C-O86 C=C146 O-H111 sum343 K calc = 10 -(3/4) 18 = K obs = = 10 -(3/4) 9.3 C(sp 2 )-H stronger than C(sp 3 )-H (don’t actually cancel) Intramolecular HOMO-LUMO Mixing H C O H C C H H H H + "Resonance Stabilization"

“Constitutional Energy” from bond additivity needs correction for effects such as: Resonance (HOMO/LUMO) Hybridization Strain C H H C H H H vs. HO C CH 2 H sp 2 sp 3 * * Polite name for error

Energy determines what can happen (equilibrium) K = e -  E/kT and how fast (kinetics) = 10 -(3/4)  E room Temp k (/sec) = e -  E /kT ‡ ‡ = (3/4)  E room Temp

What's so great about low energy? Statistics

Gibbs

Exponents & Three Flavors of Statistics 1) The Boltzmann Factor 2) The Entropy Factor 3) The Law of Mass Action

End of Lecture 36 Dec. 7, 2009 Copyright © J. M. McBride Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0