Answer and Explanation:
Every molecule has a set of <em>symmetry operations</em> that helps in determining its overall symmetry. This set of operations determines the point group of a molecule.
(a) Ethane (staggered conformation)
Ethane in the staggered conformation has:
- two
axis (the C-C line) - 3 perpendicular
rotational axis bisecting the C-C line, in the plane of the two C's and H's on the opposite sides of the two C's - no σ
plane - but has 3σ
planes containing two carbons and anti two hydrogens
<em><u>hence the point group of ethane in staggered conformation is</u></em><u> </u>
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(b) Ethane (eclipsed conformation)
Ethane in the eclipsed conformation has:
- two
axis (the C-C line) - three perpendicular
axis (in the plane of the two C's and H's on the same side of the two C's) - mirror planes include σ
and 3σ![_{d}](https://tex.z-dn.net/?f=_%7Bd%7D)
<u><em>Hence the point group of ethane in eclipsed conformation is </em></u>![D_{3h}](https://tex.z-dn.net/?f=D_%7B3h%7D)
(c) chloroethane (staggered conformation)
Chloroethane in the staggered conformation has:
- σ plane containing two carbons and chlorine and the anti hydrogen of Cl
<u><em>Hence the point group of staggered conformation in chloroethane is </em></u>
<u><em></em></u>
<u><em></em></u>
(c) 1,2-Dichloroethane (staggered anti conformation)
1,2-Dichloroethane in the staggered anti conformation has:
axis perpendicular to the C-C bond and perpendicular to the plane of Cl-C-C-Cl- contain a σ
plane through Cl-C-C-Cl, and an inversion centre
<em><u>Hence the point group in the staggered anti conformation of 1,2-Dichloroethane is </u></em>
<em><u></u></em>