Question

Why must all six atoms in \(\mathrm{C}_{2} \mathrm{H}_{4}\) lie in the same plane?

Short answer

In ethene (C2H4), carbon undergoes sp2 hybridization, leading to a trigonal planar geometry with bond angles of 120°. All six atoms must lie in the same plane due to this molecular geometry and the combination of σ and π bonding. The spatial arrangement of electron domains and bond angles ensures an even distribution of the carbon and hydrogen atoms within the plane.

Step-by-step solution

Identify the central atom and hybridization

In ethene, the central atom is carbon. We have two carbon atoms connected by a double bond, and each carbon atom is also connected to two hydrogen atoms. To determine the hybridization of carbon, we look at the number of electron domains (regions of high electron density) around each carbon atom: one double bond (counted as a single electron domain) and two single bonds. This adds up to three electron domains, which means carbon undergoes sp2 hybridization in ethene.

Determine the geometrical shape and bond angles based on hybridization

The geometry of sp2 hybridization is trigonal planar with bond angles of 120°. This means that the three electron domains around each carbon will arrange themselves in a planar shape, equidistant from one another. In ethene, two of the domains are occupied by bonds to hydrogen atoms, while the third contains the double bond to the other carbon atom.

Understand the bonding in ethene as a combination of σ and π bonds

In ethene, each carbon atom forms three σ (sigma) bonds, two with hydrogen atoms and one with the other carbon atom (a single bond). The remaining carbon p-orbitals overlap laterally to form a π (pi) bond between the carbon atoms. π bonds aren't as symmetrical as σ bonds, so their electron density is concentrated above and below the plane formed by the other atoms in the molecule.

Confirm the planar nature of ethene

Due to the trigonal planar geometry that arises from sp2 hybridization, the atoms in C2H4 must exist in one plane. The spatial arrangement of the electron domains around each carbon atom and the combined σ and π bonding push the atoms into a flat arrangement. Furthermore, the bond angles (120°) ensure that the carbon and hydrogen atoms position evenly within the plane. In conclusion, the planar nature of ethene (C2H4) arises from the sp2 hybridization of carbon and the associated molecular geometry, which requires that all six atoms lie in the same plane.