Respuesta :
Answer and Explanation:
Every molecule has a set of symmetry operations 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 [tex]C_{3}[/tex] axis (the C-C line)
- 3 perpendicular [tex]C_{2}[/tex] 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[tex]_{h}[/tex] plane
- but has 3σ[tex]_{d}[/tex] planes containing two carbons and anti two hydrogens
hence the point group of ethane in staggered conformation is [tex]D_{3d}[/tex]
(b) Ethane (eclipsed conformation)
Ethane in the eclipsed conformation has:
- two [tex]C_{3}[/tex] axis (the C-C line)
- three perpendicular [tex]C_{2}[/tex] 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[tex]_{h}[/tex] and 3σ[tex]_{d}[/tex]
Hence the point group of ethane in eclipsed conformation is [tex]D_{3h}[/tex]
(c) chloroethane (staggered conformation)
Chloroethane in the staggered conformation has:
- no rotational axis
- σ plane containing two carbons and chlorine and the anti hydrogen of Cl
Hence the point group of staggered conformation in chloroethane is [tex]C_{s}[/tex]
(c) 1,2-Dichloroethane (staggered anti conformation)
1,2-Dichloroethane in the staggered anti conformation has:
- [tex]C_{2}[/tex] axis perpendicular to the C-C bond and perpendicular to the plane of Cl-C-C-Cl
- contain a σ[tex]_{h}[/tex] plane through Cl-C-C-Cl, and an inversion centre
Hence the point group in the staggered anti conformation of 1,2-Dichloroethane is [tex]C_{2h}[/tex]
