Question

(a) Draw Lewis structures for ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right),\) ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) and acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) (b) What is the hybridization of the carbon atoms in each molecule? (c) Predict which molecules, if any, are planar. (d) How many \(\sigma\) and \(\pi\) bonds are there in each molecule?

Short answer

The Lewis structures for ethane (C₂H₆), ethylene (C₂H₄), and acetylene (C₂H₂) are: Ethane: H-C-C-H with 4 H atoms surrounding each C atom. Ethylene: H-C=C-H with 2 H atoms surrounding each C atom. Acetylene: H-C≡C-H with 1 H atom surrounding each C atom. Their hybridizations are sp³, sp², and sp, respectively. Ethylene and acetylene are planar, while ethane is not. Ethane has 7 sigma and 0 pi bonds, ethylene has 5 sigma and 1 pi bond, and acetylene has 3 sigma and 2 pi bonds.

Step-by-step solution

(a) Drawing Lewis Structures

To draw the Lewis structures for each hydrocarbon, we need to connect the atoms using their electrons to form molecules with complete octets. These structures represent the electron sharing between the atoms in the molecule. Ethane, C₂H₆: H - C - C - H | | H H | | H H Ethylene, C₂H₄: H - C = C - H | | H H Acetylene, C₂H₂: -C ≡ C- | | H H

(b) Hybridization of Carbon atoms

The hybridization of the carbon atoms can be determined by the number of surrounding atoms and lone pairs. Ethane: Each carbon atom is surrounded by 4 atoms, so it has sp³ hybridization. Ethylene: Each carbon atom is surrounded by 3 atoms, so it has sp² hybridization. Acetylene: Each carbon atom is surrounded by 2 atoms, so it has sp hybridization.

(c) Predicting Planar Molecules

A molecule is considered to be planar if all its atoms lie within the same plane. Ethane: The carbon atoms in ethane are sp³ hybridized and have a tetrahedral structure, so it is not planar. Ethylene: The carbon atoms in ethylene are sp² hybridized and have a trigonal planar structure, so it is planar. Acetylene: The carbon atoms in acetylene are sp hybridized and have a linear structure, so it is planar.

(d) Counting Sigma and Pi bonds

In each molecule, we need to count the number of sigma (single) and pi (double and triple) bonds. Ethane: Each carbon atom forms 3 sigma bonds with hydrogen atoms and 1 sigma bond with the other carbon atom. In total, there are 7 sigma bonds. Ethylene: Each carbon atom forms 2 sigma bonds with hydrogen atoms and 1 sigma bond with the other carbon atom. The double bond between the carbon atoms consists of 1 sigma bond and 1 pi bond. In total, there are 5 sigma bonds and 1 pi bond. Acetylene: Each carbon atom forms 1 sigma bond with a hydrogen atom. The triple bond between the carbon atoms consists of 1 sigma bond and 2 pi bonds. In total, there are 3 sigma bonds and 2 pi bonds.

Key concepts

Hybridization

Hybridization is a theory that explains the orbitals of an atom mixing to form new hybrid orbitals. These hybrid orbitals influence the bond angles and molecular geometry. In hydrocarbons like ethane, ethylene, and acetylene, the carbon atoms undergo different types of hybridization.

In **ethane** ( C_2H_6 ), each carbon is bonded to four other atoms (three hydrogens and one carbon). The hybridization for each carbon is sp³, which is typical for tetrahedral structures with 109.5-degree bond angles.
**Ethylene** ( C_2H_4 ) has a different hybridization because each carbon bonds with three atoms (two hydrogens and one carbon). This leads to sp² hybridization, common in trigonal planar structures with 120-degree angles.
**Acetylene** ( C_2H_2 ) shows yet another hybridization. Here, each carbon is bonded only to two atoms (one hydrogen and one carbon). This results in sp hybridization, giving acetylene its linear shape with a 180-degree bond angle.

Planar Molecules

Planar molecules are those where all atoms lie within the same plane. This molecular geometry is determined by the hybridization of the central atoms and the geometry allows for distinct physical properties.

In **ethane**, with its carbon atoms in sp³ hybridization, the molecule is not planar. This is due to its tetrahedral geometry, causing the atoms to be oriented in three-dimensional space.
**Ethylene** is different because its carbons are sp² hybridized, allowing the molecule to be perfectly planar. The trigonal planar structure facilitates all atoms to lie in one plane, giving it a flat shape.
**Acetylene**, with sp hybridized carbons, is linear—even stronger than just planar. Both hydrogen atoms and the carbon atoms reside along a single straight line.

Sigma Bonds

Sigma bonds (σ bonds) are fundamental to molecular structures, characterized by the head-on overlap of orbitals. They form the backbone of molecular connectivity, providing strength and stability to a molecule.

In **ethane**, all bonds are sigma bonds. Each carbon forms three sigma bonds with hydrogen atoms and one sigma bond with the adjacent carbon atom, totaling seven sigma bonds.
**Ethylene** has a familiar sigma bonding structure with two sigma bonds per carbon to hydrogen, and a sigma bond between the two carbon atoms. This results in five sigma bonds when including the double bond structure.
In **acetylene**, each carbon forms one sigma bond with hydrogen, plus one sigma bond between the carbon atoms in the triple bond. This results in three sigma bonds overall.

Pi Bonds

Pi bonds (π bonds) occur when two orbitals overlap side-by-side. They are typically found in double or triple bonded systems, adding unique electronic properties to molecules.

**Ethane** exhibits the simplest bonding—solely sigma bonds—thus having no pi bonds.
**Ethylene**, with its double bond, introduces the concept of a pi bond. The double bond between the carbon atoms consists of one sigma and one pi bond, forming because of the side-by-side overlap of p orbitals.
**Acetylene** showcases both sigma and pi bonding in its triple bond. Each pair of pi bonds adds to one sigma between the carbon atoms, making two pi bonds within the triple bond. This configuration gives acetylene its linear and robust bond arrangement.