Chirality needs only dissymmetry, not a chiral carbon. Allenes, alkylidene cycloalkanes, spiranes and hindered biphenyls are chiral because of their shape.
In abC=C=Cab the two ends lie in perpendicular planes, so there is no plane of symmetry: penta-2,3-diene exists as a pair of enantiomers.
Penta-2,3-diene and its mirror image.A cumulene with three double bonds.
Three C=C
Flat, so cis-trans
With three cumulated double bonds the end groups lie in one plane: geometrical, not optical, isomerism. Even number of C=C: can be chiral; odd: cis-trans.
Ring versions
Alkylidenes and spiranes
Replace one C=C of an allene with a ring for an alkylidene cycloalkane, both for a spirane. They are active when each end carries two different groups.
An alkylidene cyclohexane and a spiroheptane.6,6′-Dinitrobiphenyl-2,2′-dicarboxylic acid.
Biphenyls
Blocked rotation
Bulky ortho groups (NO₂, COOH, SO₃H) stop the rings rotating. If each ring has two different ortho groups, the twisted molecule is chiral: atropisomerism.
JEE-style question
Your turn
Which is optically inactive?
(a)abC=C=C=Cab
(b)abC=C=Cab
(c)hindered aryl amine, N(d)(e), ring groups a, b
(d)None of these
Show the answer and the traps
Three cumulated double bonds keep the end groups in one plane, so (a) is flat and achiral. Option (a).
(b) is an allene with two different groups at each end: chiral. (c) has blocked rotation and no plane of symmetry: chiral too.
Watch out
Common mistakes
Assuming every cumulene is chiral.Count the double bonds: odd numbers give a flat molecule (cis-trans).
Calling a biphenyl chiral when one ring has two identical ortho groups.Each ring needs two different ortho groups.
Practice
Try these
1. Is buta-1,2-diene (CH₂=C=CHCH₃) optically active?
No: one end carries two H atoms.
2. Which is resolvable: biphenyl-2,2′-dicarboxylic acid or 6,6′-dinitrobiphenyl-2,2′-dicarboxylic acid?
The dinitro compound: each ring has two different bulky ortho groups.