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I was reading a book and it tells that alkene geometrical isomers are achiral. I wanted to know that is it applicable for alkene geometrical isomers? Thanks in advance.

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    $\begingroup$ You want a rule which is not there. Alkenes, like nearly all other classes of organic compounds, may or may not be chiral. Let's put it this way: having a double bond is irrelevant to chirality. $\endgroup$ – Ivan Neretin Jan 14 at 13:06
  • $\begingroup$ The statement in your book is a truism: Correct, but does not transport any additional insight into the underlying concepts. Except as an exercise question: Why do these isomers not show a stereoisomery? $\endgroup$ – Karl Jan 14 at 21:51
  • $\begingroup$ @Karl Sadly, that statement isn't true. See my answer below... $\endgroup$ – Zhe Jan 16 at 14:27
  • $\begingroup$ @Zhe I would say that calling a cumulated diene an alkene is also a truism: Correct, but not at all helpful. ;-) If it is correct. Because the central carbon atom is sp hybridised. $\endgroup$ – Karl Jan 16 at 22:15
  • $\begingroup$ Such questions always remind me of this one, no offence intended: xkcd.com/169 $\endgroup$ – Karl Jan 16 at 22:19
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While in general, you should consider chirality and alkene geometry as orthogonal concepts, the statement in your question isn't even true.

Consider the case of 2,3-pentadiene, aka, 1,3-dimethylallene. This compound is chiral. Any change in the geometry of either of the double bonds provides the other enantiomer.

2,3-pentadiene

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