Question

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

Short answer

In ethylene (C2H4), each carbon atom is sp2 hybridized, forming a trigonal planar arrangement of three sp2 hybrid orbitals that form σ bonds with two hydrogen atoms and another carbon atom. The double bond between the two carbon atoms consists of a σ bond in the plane formed by these sp2 hybrid orbitals, and a π bond formed by the side-by-side overlap of 2p orbitals from each carbon atom above and below this plane. Consequently, all six atoms in ethylene lie in the same plane, which is essential for the formation of the π bond, as it allows the unhybridized 2p orbitals from each carbon atom to overlap appropriately.

Step-by-step solution

Recalling the molecular structure of ethylene (C2H4)

Ethylene (C2H4) consists of two carbon atoms and four hydrogen atoms. A carbon atom has four valence electrons, and each hydrogen atom has one valence electron. In ethylene, The two carbon atoms form a double bond with each other, and each carbon is singly bonded to two hydrogen atoms.

Hybridization of the carbon atoms in C2H4

In ethylene, each carbon atom is sp2 hybridized. It means that one 2s and two 2p orbitals of each carbon atom mix together to form three sp2 hybrid orbitals. The hybridization leaves one unhybridized 2p orbital in each carbon atom. The three sp2 hybrid orbitals form a trigonal planar arrangement, and the unhybridized 2p orbital remains perpendicular to the plane formed by the sp2 hybrid orbitals.

Formation of σ (sigma) and π (pi) bonds in ethylene

The carbon-carbon double bond in ethylene consists of a σ (sigma) bond and a π (pi) bond. The σ bond is formed by the head-on overlap of two sp2 hybrid orbitals from each carbon atom. The π bond is formed by the side-by-side overlap of the unhybridized 2p orbitals of the two carbon atoms. Each carbon atom forms two more σ bonds with hydrogen atoms through the remaining sp2 hybrid orbitals.

Explaining the planar structure of ethylene

In ethylene, each carbon atom has a trigonal planar arrangement of three sp2 hybrid orbitals, forming σ bonds with two hydrogen atoms and another carbon atom. The double bond between the two carbon atoms also has a σ bond in the plane formed by these sp2 hybrid orbitals, and a π bond formed by the side-by-side overlap of 2p orbitals from each carbon atom above and below this plane. As a result, all six atoms in ethylene (C2H4) lie in the same plane. The planar structure of ethylene is essential for the formation of the π bond, as it allows the unhybridized 2p orbitals from each carbon atom to overlap appropriately.

Key concepts

sp2 Hybridization

Understanding the concept of sp2 hybridization is key to grasping the molecular structure of ethylene. Here's what happens: a single 2s orbital of a carbon atom blends with two of its three 2p orbitals. This reshuffling results in the creation of three new equivalent orbitals known as sp2 hybrid orbitals. Why does this matter? Well, these orbitals are instrumental in forming strong sigma bonds with other atoms.

Interestingly, the remaining unhybridized 2p orbital stands perpendicularly to the plane that contains the sp2 hybrid orbitals. What does it do there? It ends up participating in the formation of pi bonds, which, as we'll see shortly, is a crucial player in the game of chemical bonding.

Sigma and Pi Bonds

Let's delve into the world of sigma and pi bonds. In the case of ethylene, we witness the marvelous teamwork between these two types of bonds that hold the molecular structure together. A sigma bond, the first kind of bond formed during a chemical bond between atoms, arises from the head-on overlap of sp2 hybrid orbitals. They're the glue holding the carbon atoms to hydrogen and to each other firmly.

Role of Pi Bonds in Ethylene

Contrasting sigma bonds, pi bonds form from the side-to-side overlap of unhybridized 2p orbitals. They're like the stitching running along the edge of fabric, offering additional strength. They're sideways, allowing for a peculiar kind of overlap that's restricted to the space above and below the plane of the atoms in sigma bonds. Together, these sigma and pi bonds explain the stability and the unique reactivity of compounds like ethylene.

Planar Molecular Geometry

Now, we tackle the planar molecular geometry of ethylene. The name 'planar' says it all—it means flat, as in all the crucial parts of the molecule lie in a single plane. This arrangement isn't by chance; the sp2 hybridization mandates it. The three sp2 hybrid orbitals spread out to maximize their distance from one another, settling in a flat, triangular shape that's technically called trigonal planar geometry.

Each of the carbon atoms is at the center of its own trigonal plane, bonded to other atoms at the corners. Consequently, this flattish orchestration is perfect for the pi bond to shine; it necessitates the p orbitals to be parallel and close enough to engage in the pivotal side-to-side overlap. Humanity has a lot to thank this geometry for—without it, materials like plastics wouldn't exist as we know them today.