While reading about cis-trans isomers I found the concept of free rotation of atoms.it says 2 atoms connected by sigma bond do not have trans sis isomer because of free rotation.while in case of pi bond free rotation is not possible. My question is : do we mean actual rotation of atoms in molecule when we say free rotation? Does the rotation happen spontaneously? What things are responsible for the rotation? Or is it just a concept to understand the concept of cis-trans isomers?

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    $\begingroup$ Are you referring to molecular rotation? hyperphysics.phy-astr.gsu.edu/hbase/molecule/rotrig.html $\endgroup$ – Gert Dec 7 '17 at 16:45
  • $\begingroup$ No I am not referring to molecular rotation $\endgroup$ – user136782 Dec 7 '17 at 17:41
  • $\begingroup$ Oh, I see what you mean now. Will answer. $\endgroup$ – Gert Dec 7 '17 at 17:50
  • $\begingroup$ related chemistry.stackexchange.com/questions/64219/… $\endgroup$ – Mithoron Dec 7 '17 at 18:47
  • $\begingroup$ With a molecule the whole thing can rotate both in the gas phase and in solution. Additionally groups of atoms within a molecule can rotate provided there is enough thermal (or light) energy to overcome any steric interaction from bulky groups or bond energy that will otherwise prevent this. Thus C-C bonds rotate relatively easily at room temperature but C=C do not as thermal energy is not enough to overcome bond energy. $\endgroup$ – porphyrin Dec 8 '17 at 15:11

You really are referring to molecular conformations:

Conformation, any one of the infinite number of possible spatial arrangements of atoms in a molecule that result from rotation of its constituent groups of atoms about single bonds.

Below are given two possible (out of many!) conformations of the ethane $\ce{C2H6}$ molecule:


Conformation 2

The single $\sigma$ bond allows free rotation around the inter-nuclear axis of the two $\ce{C}$ atoms. One consequence is that around the single bond no cis-trans isomers can exist.

But if we add a $\pi$ bond, so we have a double bond and ethene $\ce{C2H4}$, then the methylene groups can no longer freely rotate about the bond.

That's because the electron probability density added by the $\pi$ bond doesn't lie on the inter-nuclear axis, but above and below it. Double bonds, and by extension also triple bonds, are rigid, with respect to rotation of the atoms they bond. This can give rise to cis-trans isomers.

Below: highly schematised rendition of the electron density of a $\pi$ bond:

Pi bond

  • $\begingroup$ It doesn't exactly answer question, only elaborates on what OP told. Actual rotation depends on temperature. $\endgroup$ – Mithoron Dec 7 '17 at 18:21
  • $\begingroup$ Sorry to say that I still have questions.my question is that the "free rotation" is it like happening all the time? Do the c atoms keep rotating always? Is it spontaneous ? $\endgroup$ – user136782 Dec 7 '17 at 18:24
  • $\begingroup$ @user136782: Hi. Did you read the link I provided? The term 'free rotation' is a little misleading, as different parts of the molecule will still electronically repel each other. But the impossibility of cis-trans isomers about a single bond does stem from the possibility of rotation about the inter-nuclear axis. $\endgroup$ – Gert Dec 7 '17 at 18:28

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