Organic Chemistry

PROBLEM 3

Name the following dienes and rank them in order of increasing stability. (Alkyl groups

stabilize dienes in the same way that they stabilize alkenes; see Section 4.11.)

We have just seen that a conjugated diene is morestable than an isolated diene.
Now we need to see why a cumulated diene is lessstable than an isolated diene. Cu-
mulated dienes are unlike other dienes in that the central carbon is sphybridized
since it has two bonds. In contrast, all the double-bonded carbons of isolated dienes
and conjugated dienes are hybridized. The sphybridization gives the cumulated
dienes unique properties. For example, the for hydrogenation of allene is sim-
ilar to the for the hydrogenation of propyne, a compound with two sphy-
bridized carbons.

Allenes have an unusual geometry. One of the porbitals of the central carbon of al-
lene overlaps a porbital of an adjacent carbon. The second porbital of the central
carbon overlaps a porbital of the other carbon (Figure 8.1a). The two porbitals of
the central carbon are perpendicular. Therefore, the plane containing one
group is perpendicular to the plane containing the other group. Thus, a
substituted allene such as 2,3-pentadiene has a nonsuperimposable mirror image
(Figure 8.1b), so it is a chiral molecule, even though it does not have any asymmetric
carbons (Section 5.4). We will not consider the reactions of cumulated dienes, because
they are rather specialized and are more appropriately covered in an advanced course
in organic chemistry.

H¬C¬H

H¬C¬H

sp^2

sp^2

allene

propyne

CH 2 CCHCH 2 + 2 H 2 3 CH 2 CH 3

Pt

∆Hº −70.5 kcal/mol (−295 kJ/mol)

CH 3 C CH + 2 H 2 CH 3 CH 2 CH 3

Pt

∆Hº

=

= −69.9 kcal/mol (−292 kJ/mol)

-¢H°

-¢H°

sp^2

p

Section 8.3 Relative Stabilities of Dienes 303

Table 8.2 Dependence of the Length of a Carbon–Carbon Single Bond on

the Hybridization of the Orbitals Used in Its Formation

Compound Hybridization Bond length (Å)

H 3 CCH 3 1.54

1.50

1.47

1.46

1.43

1.37

sp^3 −sp^3

sp^3 −sp^2

sp^2 −sp^2

sp^3 −sp

sp^2 −sp

sp−sp

H 3 CCHC 2

H

H 3 CCHC

H 2 CCHC 2

H

C

H

H 2 CCHC

H

C

HC C C CH

CH 3 CH CHCH CHCH 3 CH 2 CHCH 2 CH CH 2 CH 3 C CHCH CCH 3 CH 3 CH CH 2

CH 3

CHCH

CH 3