Chemistry 125: Lecture 36 December 6, 2010 Understanding Molecular Structure & Energy through Standard Bonds Analysis of the Cambridge Structural Database shows that predicting bond distances to within 1% requires detailed categorization of bond types. Early attempts to predict heats of combustion in terms of composition proved adequate for physiology, but not for chemistry. 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. The heat of atomization of graphite was determined by Chupka and Inghram. The values of bond dissociation energies and average bond energies, 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

Are bonding models of structure realistic in geometric detail? X-Ray Diffraction

Cambridge Structural Database Total X-Ray Structures Year 36,334,442 atomic positions Jan >50,000,000 BONDS Are Bond Lengths Standard? (within ±1%)

CSD1

Number of Mean Bond Lengths Tabulated. (specialized because of influence of neighbors on precise bond distance) 175 CC 97 CN 119 CO 119 different types of CO bonds 27 different types of C sp 3 -C sp 3 bonds

CSD1 mean high 1/4 median low 1/4 # obs std dev 3 C* means a C bearing C/H only C# means any Csp 3 crowding stretches bond even moreso R 2 CH CR 3 R 2 CH CHR 2 R 3 C CR 3 RCH 2 CH 3 R 2 CH CH 3 R 3 CH CH 3 short long ~1%

C C bond lengths single 1.53 Å double 1.32 triple 1.18 aromatic 1.38 (one-and-a-half bonds) single: sp 3 -sp sp 2 -sp

N to C aromatic Bond Lengths N PlanarN Pyramidal N N + _ poor  overlap  Twist Bimodal ? N :

How Complex Must a Model be to Predict Useful Structures? To get standard deviations in bond distance of 0.015Å (~1%) the Cambridge crew defined: 682 kinds of bonds altogether 175 different kinds of CC bonds (differing in multiplicity, hybridization, attached groups, rings, etc.) 97 different types of CN bonds 119 different types of CO bonds

We want to understand all molecules Their Properties & Transformations Keys: Structure (in term of Bonds) (in terms of Bonds also?) & Energy

Are Bond Energies as Standard as Bond Distances? Obviously there must be corrections for conformation and strain, but is there an underlying energy for composition or constitution?

Adolph Oppenheim: On the Relationship of Heat of Combustion with the Constitution of Substances Ludimar Hermann: On the Regularity and Calculation of Heat of Combustion of Organic Compounds. By a frequently expressed need of physiology to be able to calculate heats of combustion, I have been led to study the current situation…

 H Combustion by C / H Content? Substance Carbons atoms/mole Hydrogens atoms/mole Theory  H combust kcal/mole Error kcal/mole Error % Graphite [1] Hydrogen c-Hexane c-Hexanol Ethene Glucose Not too bad for fuel purposes, especially if one were to include some kind of correction for partial oxidation. [-57.8]  per H 2 [-94.05]  per C = 2   57.8 H 2 C=CH 2 has extra energy to give off. One of its bonds (  ) is not very stabilizing, so it starts unusually high in energy. O1O1 O6O6 partially "pre-oxidized" Composition: Atom Additivity

How Complex Must a Model be to Predict Chemically Useful Energies? For physiology purposes you might be content with ± 5% in heat of combustion. But for predicting the equilibrium constant between c-hexane + 1/2 O 2 and c-hexanol, being off by 1% (9 kcal/mole) means being off in K eq by a factor of A useful model must go beyond composition. How about constitution? 10 7 !

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 Energies of molecular fragments are needed for predicting reaction rates.

HfHf From Streitwieser, Heathcock, & Kosower Group Additivity for  H f 4.9 average CH 2 CH 2 group CH 3

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

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

End of Lecture 36 Dec. 6, 2010 Copyright © J. M. McBride 2009, 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