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I'm studying point groups in inorganic chemistry and having a difficult time understanding some of these concepts.

In my book, Inorganic Chemistry: Fifth Edition by Miessler, Fischer, & Tarr, I am presented with a table showing that $\ce{CHFClBr}$ is in the $C_1$ point group and has no symmetry other than the identity operation.

CHFClBr

$\ce{H2C=CClBr}$ is in the $C_\mathrm s$ point group and its symmetry is listed as having only one mirror plane. H2C=CClBr

I'm having difficulty seeing this mirror plane. I would have listed this compound as being in the $C_1$ point group. Does this have something to do with the molecule being flat?

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    $\begingroup$ The molecule is planar, so the mirror plane is the mirror plane of the molecule $\endgroup$
    – orthocresol
    Commented Oct 22, 2017 at 21:39
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    $\begingroup$ I would suggest to "play" a bit with different molecules and discover their the symmetry operations and point groups: symmetry.otterbein.edu/challenge/index.html. I also noticed that students with a background in FPS games use to comprehend symmetry operations and elements better:) $\endgroup$
    – andselisk ♦
    Commented Oct 22, 2017 at 22:09
  • $\begingroup$ @andselisk Yeah, I'm way more than halfway through my homework and just now grasping it. Any reason behind the fps game thing? I play fps games and am wondering how it would help understand symmetry. $\endgroup$
    – Melanie Shebel
    Commented Oct 22, 2017 at 23:47
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    $\begingroup$ @MelanieShebel I would surmise that those people are more practiced at certain types of spatial reasoning skills. But there are other ways to develop those as well. $\endgroup$
    – Zhe
    Commented Oct 23, 2017 at 0:02
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    $\begingroup$ @MelanieShebel It's rather subjective, but I suspect that old-school non-linear labyrinth-type maps (such as good old Doom, Quake and System Shock) train spatial thinking and visual memory, and help to grasp flat screen representation of 3D entities faster because you are constantly under pressure and have to react/adapt swiftly. It also might just be my excuse for still playing those games as well, so don't take it seriously:) $\endgroup$
    – andselisk ♦
    Commented Oct 23, 2017 at 0:34

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For all symmetry operations, you should assume the atoms reduced to a point size. Then, if you have a perfectly flat molecule (like in the case of your disubstituted ethene), all atoms will be in the same mathematical plane meaning there is nothing above or below the plane.

Therefore, the plane is an element of symmetry that puts the nothing above the plane on the nothing below the plane and leaves the atoms themselves (in the plane of symmetry) untouched.

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    $\begingroup$ Is it really necessary to assume that atoms reduce to point size? I do not think so. Models as ball and sticks work well for symmetry consideration. Moreover not reducing to point size does convey the message that there are not things such as egg shaped atoms. Perhaps I am rough on this description but it should be clear what I mean. I prefere a picture in which the plane does cut the molecule in its upper and lower halves.... $\endgroup$
    – Alchimista
    Commented Oct 23, 2017 at 11:59
  • $\begingroup$ @Alchimista No, it’s not necessary but I like the picture because points will always be in the plane. I’m sorry, but there are too many negations ins your sentence about egg-shaped atoms to grasp it, can you repeat? $\endgroup$
    – Jan
    Commented Oct 24, 2017 at 7:36
  • $\begingroup$ Important that we agree. It was to say that the current molecule cannot be different on the two sides of the plane....It will take me start to atom and so on. ...I wanted to make a (needed , in my opinion) clarification :) $\endgroup$
    – Alchimista
    Commented Oct 24, 2017 at 19:28

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