Alkane Bond Energy
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Transcript of 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
121
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