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I am currently teaching a course on groups, and want to give my students "real life" examples of symmetry groups to think about. The ethane molecule would be one such. But, the on-line sources don't all agree on the exact shape. I'm fairly sure ethane looks like either this

enter image description here

or this.

enter image description here

I oriented the molecules in such a way that the carbon atoms are on top of each other. The difference between the two choices is how the groups of three hydrogen atoms relate to each other. In the latter alternative the molecule is its own mirror image with respect to the plane bisecting the line segment joining the carbon atoms. Meaning that the hydrogen atoms also pair up in a way that they are on top of each other. However, in the former version this is not the case, and you would need to rotate one triple of hydrogen atoms by 60 degrees to move them on top of each other.

To turn this into a homework problem I would like to know which is correct?

Wikipedia suggests that the one on the top is correct. However, the picture below also appears in some places. Like here.

My theory: Whatever little I know about physics/chemistry suggests to me that the top one is more likely. The reason being that the similarly charged hydrogen atoms repel each other (possibly this is only a dipole or a higher order effect?). Therefore it stands to reason that one triple of hydrogen atoms is aligned in a way that they use the "in-between" angles.

Nitpick: The "correct" answer probably is that neither of these two images is quite right. You see, I generated them using the tetrahedron (=methane) angle of 109.5 degrees everywhere (simpler for me to do it that way). But Wikipedia says that the angle between the carbon-carbon bond and a carbon-hydrogen bond is slightly larger, 111.17 degrees. So the hydrogen atoms at the top should be pushed a teensy bit further up and similarly the ones at the bottom a little further down. A bigger similar effect is that in the actual molecule the distance between the carbon atoms is larger than the carbon-hydrogen distance. Neither of these has an effect on the collection of symmetries the molecule has, but the answer to my main question does have an impact. That's why I am asking.

If somebody is inclined to elaborate on the reason(s) why we don't have that methane angle everywhere, I will be educated further :-)

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  • $\begingroup$ Sorry about not knowing which tags would be most appropriate. Or whether this question is a good fit for Chemistry.SE at all :-( $\endgroup$
    – Jyrki Lahtonen
    Commented Jan 23, 2021 at 8:33
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    $\begingroup$ This question about the confirmations of butane might be of interest to you: chemistry.stackexchange.com/q/11015/4945 $\endgroup$
    – Martin - マーチン ♦
    Commented Jan 23, 2021 at 8:46
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    $\begingroup$ @Martin-マーチン Conformations :-) $\endgroup$
    – Poutnik
    Commented Jan 23, 2021 at 9:07
  • $\begingroup$ I'm sorry about the low level of this question. When I was in high school (40 years ago) I read a book (in Finnish) that could be called Organic chemistry 101+102. It did explain the existence of different conformations in more complex molecules such as cyclohexane. I was blissfully unaware of this phenomenon also appearing in such a simple molecule as ethane. $\endgroup$
    – Jyrki Lahtonen
    Commented Jan 23, 2021 at 18:42
  • $\begingroup$ And I'm aware of the fact that the actual groups of rotational symmetries of the two conformations are isomorphic. In a sense the same group acting on different sets of points of the 3D space. $\endgroup$
    – Jyrki Lahtonen
    Commented Jan 24, 2021 at 17:56

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You need to know the terms "staggered" and "eclipsed", because that's what we call these two conformations. Now to the point: the real ethane molecule rotates and changes shape all the time, so both geometries are possible, albeit the top one is more likely, because it is the energy minimum. To make the molecule stop in the staggered conformation, you have to freeze it to nearly absolute zero, or maybe put some bulky groups in place of hydrogens.

This, BTW, is the reason why I dislike to use ethane molecule as an example when I teach space groups to kids. Better use something rigid.

So it goes.

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  • $\begingroup$ Thank you. Particularly for the last comment of ethane not being rigid! $\endgroup$
    – Jyrki Lahtonen
    Commented Jan 23, 2021 at 8:40
  • $\begingroup$ Plus 1 especially for the final advice. $\endgroup$
    – Alchimista
    Commented Jan 23, 2021 at 10:41

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