alkane bond energy

7/28/2019 Alkane Bond Energy

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Section 8--Sigma Bonds and Bond Rotation


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Sigma Bonds and Bond Rotation

Rotation is possible around single bonds (sigma bonds). Theorientations of atoms and groups that result from rotation are calledconformations.

Different conformations may have different energies. An analysis ofthe energy changes with rotation around a bond is calledconformational analysis.

Conformational Analysis of Ethane: H3C-CH3

An energy barrier of close to 12.6 kJ/molis observed during rotation around the

C-C bond in ethane. This energy barrieris attributed to torsional strain. C

H

HH

H

H

H


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.

An analysis of the rotation around the C-C bond in ethane showsthere are two extreme conformations. These two conformationscalled eclipsed and staggered are shown below. These twoconformations interconvert by simple rotation around the C-C bond

The Conformations of Ethane

C C

H

HH

H

H

H

eclipsed

rotation

staggered

C C

H

HH

H

HH

rotation

H

H

H

HH

HHH

HH HH

The intersection of the three bonds represents the orientation of

the three H around the front carbon, and the lines to the circlerepresent the orientation of the three H around the back carbon.

The relative orientations of the hydrogens around the two carbons

are easier to see in a Newman projection formula, wherein thestructure is viewed along the carbon-carbon bond.


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Relative Energies of the Staggered and Eclipsed Conformations

The rotational barrier of11.72 kJ/mol is associated with theeclipsed conformation where the H on the two carbons arealigned. This energy barrier is called the torsional barrier, and

the source of the increased energy, relative to the staggeredconformation, is called torsional strain. The cause of the torsionalstrain in the eclipsed conformation of ethane is not simplynonbonding repulsive interactions between the H (steric strain).


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RelativePotentialEn

ergy

Rotation0 60 120 180 degrees

H

H

H

HH

HHH

HHH

H

H

H

H

HH

H HH

HH HH

2.8

staggered

eclipsed

staggered

eclipsed

etc.

Conformational Energy Diagram for Ethane

The diagram below shows the change in potential energy in ethane withrotation around the C-C bond. In one complete rotation of 360o, three equalbarriers of 11.72 kJ/mol are encountered.

At room temperature, there is

sufficient thermal energy forrotation to be very fast (~1011

rotations per second).


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The Conformations in Propane: CH3-CH2-CH3

There are two equivalent C-C bonds in propane:

HC

CC

H

H

H

H H

H

HThe conformationalfeatures are the same

for the two C-C bonds.

It is easier to see these conformational features by examining propaneas a substituted ethane where a methyl group has replaced an H.

eclipsed

rotation

staggered

rotationH

HH HH

CH3

HH

CH3

H

H

H

H

C C

CH3

H

HH

HC C

H

HH

H

HH

The barrier to rotation inpropane is ~13.8 kJ/mol,slightly higher than thetorsional barrier in ethane.Again there are three equal

barriers in one completerotation, each occurring at aneclipsed conformation. Inpropane, the eclipsing of aCH3 group with an H does notsignificantly increase thebarrier.


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Summary of the Conformational Propertiesof Ethane and Propane

ethane

three equivalent barriersof 11.72 kJ/mol

propane

two equivalent C-C bonds,each with three equivalentbarriers of 13.8 kJ/mol

H

C C

CH3

H

HH

H

H

C C

H

H

HH

H

Conformational Features of the Butanes

There are two constitutional isomers of C4H10, butane and isobutane,

with different conformational features.

butane isobutane

CH3CH2CH2CH3 CH3CHCH3CH3


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Butane

.

There are two different C-C bonds in butane, two "terminal" bonds

(1) and one "internal" bond (2)

C C

H3C

CH3H

H

H

H

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Conformational Features of the Terminal Bonds in Butane

The two equivalent terminal bonds in butane have the conformationalfeatures observed in propane, except that the energy barrier to rotationis slightly higher (15.1 kJ/mol compared with 13.8 kJ/mol).

propaneH

C C

CH3

H

HH

H

butane (terminal bond)H

C C

CH2CH3

H

HH

H

two equivalent C-C bonds,

each with three equivalentbarriers of 13.8 kJ/mol

two equivalent terminalC-C bonds, each with threeequivalent barriers of 15.1 kJ/mol


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The Conformational Features of Isobutane

All three C-C bondsin isobutane areequivalent.

isobutane

CH3-CH

CH3

CH3

.The conformational features may be more easily seen whenisobutane is analyzed as a disubstituted ethane

staggered eclipsed

rotationC C

H

HH

HCH3

CH3

C CH

HH

HCH3

CH3

During a complete rotation around the C-C bond, there are three equivalentstaggered and three equivalent eclipsed conformations. In the eclipsedconformation, there are two alignments of CH3~H resulting in an energybarrier close to 16.7 kJ/mol.


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Overview of the Conformational Features of CH3-CX3 Systems

.

In a complete rotation around the C-C bond, there are three equivalentenergy barriers. In simple ethane, the barrier is assigned to torsionalstrain. As CH3 or other alkyl groups replace H, the barrier increases aselements of steric strain (nonbonded repulsive interactions) areintroduced

energybarrier(kJ/mol) 11.72 13.8 15.1 16.7

increasing steric strain

ethane propane butane isobutane

H

C C

H

H

HH

HH

C C

CH3

H

HH

HH

C C

CH2CH3

H

HH

HH

C C

CH3

CH3

HH

H


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Section 10--The Relative Stability of Cycloalkanes:Ring Strain


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Stability of Isomers

.The relative stability ofisomeric hydrocarbons may be determined bymeasuring their heats of combustion under identical conditions

An Example: The Isomeric Butanes

:The heats of combustion of the isomeric butanes are

CH3CH2CH2CH3(g) + 6.5 O2(g) 4CO2(g) + 5H2O(l)Hcomb = -2876.5 kJ/molCH3CHCH3(g) + 6.5 O2(g) 4CO2(g) + 5H2O(l)

Hcomb = -2868.1 kJ/molCH3


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Heats of Combustion of the Cycloalkanes:A Measure of their Relative Stabilities

The cycloalkanes form a homologous series (CH2)n withn>3.

The general reaction for the combustion of a cycloalkane is:

(CH2)n + 1.5n O2 nCO2 + nH2O + heat

As n increases, more heat is evolved. In order to use the heats of

combustion to determine the relative stabilities of the cycloalkanestructures, the amount of heat evolved must be adjusted for thenumber of CH2 groups. The table that follows provides thisinformation.


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Heats of Combustion of Cycloalkanes

cycloalkane (CH2)n n Hcomb(kJ/mol)

heat evolvedper CH2 group

(kJ/mol)

cyclopropane 3 2091 697

cyclobutane 4 2744 686

cyclopentane 5 3320 664

cyclohexane 6 3952 659

cycloheptane 7 4637 662cyclooctane 8 5310 664

cyclononane 9 5981 664

cyclodecane 10 6636 664

unbranched alkanes (659)

.

Note: The total amount of heat evolved increases with the size of thecycloalkane, as expected. However, the amount of heat evolved perCH2 group is highest for the smallest cycloalkanes, and is lowest forcyclohexane, where the amount is consistent with that evolved in thecombustion of unbranched alkanes


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Ring Strain in Cycloalkanes

"

Because the amount of heat evolved in the combustion of cyclohexane isconsistent with the value expected from the combustion of unbranched(and unstrained) alkanes, it is assumed that cyclohexane is free of any

"strain energy.

The greater amounts of heat evolved per CH2 group in the othercycloalkanes are assumed to be due to elements of "ring strain" that leadto higher energies. The total amount of ring strain is calculated by

multiplying 659 kJ/mol x n, where n is the number of CH2 groups, andsubtracting this value from the measured heat of combustion.


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Calculated Ring Strain in the Cycloalkanes

cycloalkane n Hcomb(kJ/mol)

cyclopropane 3 1976 2091 115cyclobutane 4 2634 2744 110

cyclopentane 5 3293 3320 27

cyclohexane 6 3952 3952 0.0

cycloheptane 7 4610 4637 27cyclooctane 8 5268 5310 42

cyclononane 9 5927 5981 54cyclodecane 10 6586 6636 50

measured

Hcomb(kJ/mol)

calculated

ringstrain

(kJ/mol)

.

According to the above calculations, the greatest amount of strainenergy is found in the very small cycloalkanes, cyclopropane andcyclobutane. Cyclohexane is "strain-free," and the largercycloalkanes through cyclodecane have very small amounts of strain


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Section 11--The Origin of Ring Strain in Cyclopropane andCyclobutane: Angle Strain and Torsional Strain


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The Origin of Ring Strain in the Smaller Cycloalkanes:Angle Strain and Torsional Strain

The smaller cycloalkanes, cyclopropane and cyclobutane, evolveconsiderably more heat in combustion than expected for a hydrocarbonof their size. This difference, due to a higher energy content in thesehydrocarbons, is called "ring strain."

Angle Strain

One source of ring strain in the small cycloalkanes is "angle strain,"which is due to bonding factors.

The sp3 hybridizedcarbon in an alkaneprojects the hybridorbitals with atetrahedral bond angle

of 109.5o.

109.5o Cyclopropane has thegeometry of a regulartriangle with internalangles of 60o. Theinternal angle deviates

from the idealized angleby 49.5o.

60o

The compression of the

internal internuclear anglein cyclopropane is calledangle strain.


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The Conformation of Cyclobutane

.

Cyclobutane has a bent geometry. This conformation is formedby a slight rotation around the C-C bonds. This rotationreduces the severe torsional strain in the planar geometry

Clockwise andcounterclockwiserotations around theC-C bond give thebent geometry.

H

H

H

H

H

HH

H

There is reducedtorsional strain in thebent geometry.

HH

H

H

H

H

H

H 88o

There is a slightclosing of the internalangle increasing anglestrain in the bentstructure.

C

C

CC

H

H

H

H

H

HH

H


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The Chair Conformation of Cyclohexane

.

The most stable conformation of cyclohexane is the chair in whichthere is neither angle nor torsional strain. The chair has the usual wigwag geometry of an alkane induced by linking a series of tetrahedralcarbons

chair

109.5o

HH

H

H

H

HH

HH

H

HH

Newmanprojection

view

A Newman projection shows thatthe hydrogens are in a staggeredconformation free of torsional strain.

H

H

H

H

CH2

CH2


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The Boat Conformation

Another conformation ofcyclohexane that is freeof angle strain is the boat. H

H

H

H

H

H

HH

H H

H

H

The "pure" boat

conformation (above) hastorsional strain fromeclipsed H as revealed bythe Newman projections

along the C1-C2 and C5-C4bonds.

1

2

5

4

"pure" boat

H

H

H

HH

H

H

H

1 2

45

1.83

.

In addition, there is steric strain from nonbonded repulsiveinteraction between the two "flagpole" H that are closer than the 2.5 minimum distance apart for two H


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Some Key Observations

chair 1 chair 2boat

(1) The energy barrier of 45.2 kJ/mol leads to a rate of

~105 chair-chair interconversions per second at roomtemperature.

.

(2) The difference in energy of 23 kJ/mol between the chairand twist-boat conformations means that, at room temperature,

more than 99% of the cyclohexane molecules are in the morestable chair conformations. However, because of the rapidequilibrium, some cyclohexane molecules are always passingthrough the less stable twist-boat conformation


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Quiz Chapter 4 Section 12

Name the following conformations of cyclohexane. Rank them in orderfrom most to least stable. Indicate the type of strain energy present ineach conformation.

I II III IV

Stability order (most to least): > > >

Types of

strain energy:

Name: planar half-chair chair boat

III IV II I

severe angle

and torsional

strain

angle and

torsional

strain

torsional

and steric

strain

no torsional

angle strain or

steric strain

alkane bond energy

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