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
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?
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 :-)