Ethane mirror planes

Problem 4-1. (a) Locate the four mirror plattes of cyclopropatte. (b) How many of the mirror planes of benzene can you find (c) How many mirror planes does ethane have in the staggered, eclipsed, and gauche conformations ... 

Problem 4-2. Classify all the mirror planes of cyclopropane, benzene, and the staggered, eclipsed, and gauche conformations of ethane as vertical, horizontal or diagonal mirrors. 

D2d A molecule is D2d if it has a C2 axis and two perpendicular C2 axes (as for D2 above), plus two dihedral mirror planes these are mirror planes that bisect two C2 axes (in general, that bisect the C2 axes perpendicular to the principal axis). Example allene (propadiene). Staggered ethane is D3d (it has D3 symmetry elements plus three dihedral mirror planes. Dnd symmetry can be hard to spot. 

The symmetry elements of the point groups (a) >3, (b) D2d and (c) Dgh- (a) A twisted form of ethane, neither perfectly staggered nor eclipsed, viewed along the C3 axis, (b) Allene, where the planes xz and yz are planes and the C 2 axes lie at 45° to the x and y axes in the xy plane, (c) Benzene. Note that the Cg axis includes C3, C2, Sg and S3 axes. Also shown are the three axes (one of which lies along x) and the three C axes (one of which lies along y). The xy plane is CTh and there are vertical mirror planes including each C 2 and C axis the center of the molecule is an inversion center, i. 

We limit the list of operations by identifying equivalences so that there is no redundancy each arrangement of the labelled atoms in the molecule is generated only once. The hydrogen atoms of ethane are particularly useful for this. If we chose the carbon atoms, then there are only ever two arrangements the carbon atoms sit on the C3 axis and in the three mirror planes and so are unchanged by C3 or 3 rotations or any simple reflection. They are also swapped over by Si and Si any C2 rotation or i. The carbon atoms do not show the full effect of these operations because they are at special symmetry positions. For the same reason, in planar molecules like BF3, no atom sets show the full effects of symmetry operations in particular, the mirror plane containing all the atoms will always... 

Figure 2.10 Labelling used for the sets of equivalent Cj axes and dihedral mirror planes for the purposes of constructing the multiplication table for ethane. Note that the aa planes have been labeled so that / initially contains H, B initially contains H2 and C initially contains H3, the C2 axes have also been labeled for the plane to which they are perpendicular.

Note, however, that in a molecule with an asymmetric center, rapid internal rotation does not guarantee magnetic equivalence even when nuclei are rendered chemically equivalent by the rotation. For example, in a 1,2-disubstituted ethane, the two protons attached to a given carbon atom are enantiotopic, hence chemically equivalent in an ordinary achiral solvent, as we saw in Section 4.9. Of the three conformations III—V, III and IV are mirror images, the average of which must have vA = vh and vx = vY, while V contains a plane of symmetry, so that the same equalities hold here. On the other hand, HA and HB are not magnetically equivalent, because the vicinal coupling constants are not necessarily... 

Chelate ring conformations in chelated diaminoethane (ethane-1,2-diamine, en), designated as 8 and X. Views looking into the N—M—N plane (centre H atoms bound to C atoms disposed roughly in the plane, Heq, and perpendicular to the plane, Hax, also included) and along the C—C bond (sides H atoms removed for clarity) are shown. Ready interconversion between the two conformations (which are mirror images) is possible, as only a small energy barrier exists between them. 

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