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The alkyl chains of saturated fat molecules can readily rotate about their carbon-carbon single bonds, giving them flexibility and viscosity.

What is different about the carbon-carbon double bonds of unsaturated fat molecules, preventing inter-conversion of cis and trans forms?

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A double bond between 2 carbon atoms means there is a $\pi$ bond with the side orbital overlaps in 1 plane, in parallel to the axial $\sigma$ bond.

The consequence is, free rotation would need to break this $\pi$ bond, making the double bond just a single bond, what would require a strong torque and a lot of energy.

By other words, particular rotation positions around a single bond have ( almost ) the same energies. But for double bonds, the molecule energy strongly depends on on this orientation. The $\pi$ bond can exist, only if the bystander groups on both carbon atoms are about in the same plane. If they wete on about perpendicular planes, the orbitals of both atoms cannot overlap to form the bond.

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  • $\begingroup$ Poutnik we must agree that somehow is hard to see these things out of balls & sticks solid body representation.... OP please don't be confused by this comment of mine which is not adverse to the answer but it is a kind of discussion by an experienced chemist that somehow and sometimes has the same pondering of you. $\endgroup$
    – Alchimista
    Commented Jan 26, 2020 at 9:30
  • $\begingroup$ @Alchimista We need not agree on that. :-) People, for whom is less confusing quantum chemical explanation, need not such an analogy. But there are people, who can easier grasp the idea from things they can imagine. It is an analogy, so it does not say things are exactly like that. The truth is, some people have problem with analogies in general, wanting analogy not to have part of things different. $\endgroup$
    – Poutnik
    Commented Jan 26, 2020 at 9:55
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    $\begingroup$ I am down voting this for the potato part. This is so far from helpful and does convey a picture that is by far too simple for it to ever be useful. Imagine anyone actually trying to learn more about this m will always be burdened with this picture. For a triple bond is even worse, because it suggests it cannot rotate, which is wrong. $\endgroup$ Commented Jan 26, 2020 at 10:13
  • $\begingroup$ It does not suggest it cannot rotate. But OK, I will remove it. $\endgroup$
    – Poutnik
    Commented Jan 26, 2020 at 10:19
  • $\begingroup$ The removal of the potato wasn't my intent at first. Perhaps I wasn't clear that my comment wasn't aimed at rectification but pointing to the fact that a rigid anchorage of bonds and nucleus must be taken for grant as the tip of a stick cannot move inside the potato. I was fine with the analogy, contrary to Martin. $\endgroup$
    – Alchimista
    Commented Jan 26, 2020 at 11:37

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