Chemistry 125: Lecture 36December 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 DatabaseT

otal

X-R

ay S

truc

ture

s

Year

36,334,442atomic

positionsJan 2010

http://www.ccdc.cam.ac.uk

>50,000,000BONDS

Are Bond Lengths

Standard?(within ±1%)

CSD1

CSD1

Number ofMean BondLengths Tabulated.(specialized because ofinfluence of neighborson precise bond distance)

175CC

97CN

119CO

119 different types of CO bonds27 different typesof Csp3-Csp3 bonds

CSD1

mean high1/4

median low1/4

#obs

stddev

3

C* meansa C bearingC/H only

C# meansany Csp3

crowdingstretches bond

evenmoreso

R2CH CR3

R2CH CHR2

R3C CR3

RCH2 CH3

R2CH CH3

R3CH CH3

shortlong

~1%

C C bond lengths

single 1.53 Ådouble 1.32triple 1.18

aromatic 1.38(one-and-a-half bonds)

single: sp3-sp2 1.50 sp2-sp2 1.46

N to

Caromatic

BondLengths

N Planar N Pyramidal

N

N+

_

poor overlap

Twist

Bimodal?

N

:

••

How Complex Must a Model beto 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.

1868

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…

HCombustion by C / H Content?

SubstanceCarbons

atoms/moleHydrogensatoms/mole

Theory Hcombust

kcal/moleError

kcal/moleError

%

Graphite [1] 0 -94.05 - -

Hydrogen 0 2 -57.8 - -

c-Hexane 6 12 -911.1 -881.6 -29.5 -3

c-Hexanol 6 12 -911.1 -842.7 -68.4 -8

Ethene 2 4 -303.7

Glucose 6 12 -911.1 -670.4 -240.7 -36

Not too bad for fuel purposes, especially if one were to include some kind of correction for partial oxidation.

[-57.8] per H2

[-94.05] per C

= 2 94.05 + 2 57.8

H2C=CH2 has extra energy to give off. One of its bonds () is not very stabilizing,

so it starts unusually high in energy.

O1

O6

partially"pre-oxidized"

-316.2 +12.5 +4

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 O2 and c-hexanol, being off by 1% (9 kcal/mole) means being

off in Keq by a factor ofA useful model must go beyond composition.

How about constitution?

107!

C6H12

Energy

-911.1

= -29.5

CO2 / H2O

graphite / hydrogen

-881.6Hcombustion

Hformation

Ene

rgy

(kca

l/m

ole)

Comparedto What?

easilymeasured

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

APPENDIX I

HEATS OF FORMATION

From Streitwieser, Heathcock, & Kosower

Hf

APPENDIX I

HEATS OF FORMATION

From Streitwieser, Heathcock, & Kosower

Hf

From Streitwieser, Heathcock, & Kosower

APPENDIX I

HEATS OF FORMATION

Energies of molecular fragments are needed for predicting reaction rates.

Hf

From Streitwieser, Heathcock, & Kosower

4.6

5.6

4.7

4.8

Group Additivity for Hf

4.9average CH2

CH2 group

CH3

CH3

minimum

Expt. - Theory

Hf + n 4.9

Group Additivity

“unstrained” same as

chain

2 -4.9 = -9.8

StrainlessTheory

(n -4.9)

?

From Streitwieser, Heathcock, & Kosower

“Transannular” Strain

similar

c-hexane

c-octane

Small-Ring Strain

crunch

0 5-5

Group Additivity

Can one sum bond energies to getuseful "Heats of Atomization"?

Bond Additivity

From Streitwieser, Heathcock, & Kosower

How well can “Bond Energies”

predict Hatomization?

Where does Hatomization come from?

C6H12

Energy1680.1

atoms

Hatomization 1650.6

-911.1 -29.5

CO2 / H2O

graphite / hydrogen

-881.6Hcombustion

Hformation

Ene

rgy

(kca

l/m

ole)

Comparedto What?

How CanYou KnowHformation

for an atom?

= - 881.6

+ 911.1

+ 1650.6

How to measure?

Atom Energy from Spectroscopy

lightenergy

X-Y

X + Y

H-H 104.2 kcal/mole (Hf H = 52.1)

O=O 119.2 kcal/mole (Hf O = 59.6)

CO 257.3 kcal/mole

X* + YMaybe this is the observed transition at 257.3?

141? 257.3

Hf C=O = -26.4

Hf H 02___

Hf O 02___

X*’+ YOr maybe this is the observed transition at 257.3?

125? 257.3

spectroscopic value precise, but uncertain

Which to choose?

CO

Hf C

Hf O

graphite O2

C + O

graphite O

(Hf C = 171.3)

But Nobel Laureates Worried.

Atom Energy from Equilibrium K

K = e-E/kT = 10-(3/4)E kcal/mole@ Room Temp

= 10-(3/4)= 10-127 !

= 10-(3/40)= 10-13

at 10 x room temperature (~3000K)

measure K to find E

< 1080 atoms in universe (est)

4

Need to Plot ln(tiny Pressure of C Atoms) vs. (1/T)at VERY high T

" "

Pressure of Catom PC = b e-Hf C / RT

[Catom]

[Cgraphite]-Hf C / RT e

ln( PC ) = ln( b ) - Hf C / RT

(-Hf C / R ) is the slope of ln( PC ) vs. (1 / T)

Chupka-Inghram

Oven(1955)

Cn

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)

Cn

gas

Tantalum Shielding

keeps highest heat

inside

Electron Beam

Cn Beam

Cn Ion Beam+

C1+

C2+C3

+

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

(Hf of Carbon Atom)

2450 K 2150 K

€

PC = be−ΔH fC / RT

€

ln PC( ) = ln b( ) −ΔH fC

RTC1

C3

C2

Hf

From Streitwieser, Heathcock, & Kosower

William Chupka 1923-2007

APPENDIX I

HEATS OF FORMATION

End of Lecture 36Dec. 6, 2010

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