Question

Use the localized electron model to describe the bonding in ${\mathrm{C}}_2{\mathrm{H}}_2$ (exists as $\mathrm{HCCH}$ ).

Short answer

In the HCCH molecule, both Carbon atoms are sp hybridized. The molecule has two σ C-H bonds formed by Carbon's sp hybrid orbitals and Hydrogen's atomic orbitals, one σ C-C bond formed by the sp hybrid orbitals of both Carbon atoms, and two π C-C bonds formed by the unhybridized 2p orbitals of both Carbon atoms.

Step-by-step solution

Calculate the Valence Electrons

First, we need to calculate the total number of valence electrons in the HCCH molecule. Carbon (C) has 4 valence electrons and Hydrogen (H) has 1 valence electron. So for C2H2, the total number of valence electrons is: (2 Carbon atoms × 4 valence electrons) + (2 Hydrogen atoms × 1 valence electron) = 8 + 2 = 10 valence electrons.

Determine the Central Atoms

In this molecule, the two central atoms are the Carbon atoms. They will form a bond with each other and Hydrogen atoms.

Determine the Number of Bonds

In the HCCH molecule, a Carbon atom forms a single bond with a Hydrogen atom, and the two Carbon atoms are bonded to each other. To satisfy the octet rule, the two Carbon atoms need to form a triple bond with each other. Thus, there are a total of 3 bonds in the molecule: 1. C-H (single bond) 2. C-C (triple bond)

Calculate the Hybridization of Orbitals

Next, we need to determine the type of hybridization in the Carbon atoms: When Carbon forms a triple bond with another Carbon atom, it undergoes sp hybridization. Therefore, both Carbon atoms in HCCH are sp hybridized.

Bonding Description in HCCH

Now we can describe the bonding in the HCCH molecule using the localized electron model: 1. The two Carbon atoms are sp hybridized. 2. Each Carbon atom forms a sigma (σ) bond with the Hydrogen atom using one of their two sp hybrid orbitals. 3. The two Carbon atoms form a sigma (σ) bond with each other using their remaining sp hybrid orbitals. 4. The two Carbon atoms also form two pi (π) bonds with each other, using their unhybridized 2p orbitals. So, the bonding description in the HCCH molecule can be summarized as follows: - Two σ C-H bonds formed by the sp hybrid orbitals of Carbon and atomic orbitals of Hydrogen. - One σ C-C bond, formed by the sp hybrid orbitals of both Carbon atoms. - Two π C-C bonds, formed by the unhybridized 2p orbitals of both Carbon atoms.

Key concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a crucial role in chemical bonding. For ${\mathrm{C}}_2{\mathrm{H}}_2$ (HCCH), these electrons are involved in forming bonds between the atoms. Each carbon atom contributes 4 valence electrons, while each hydrogen atom contributes 1 valence electron.

To calculate the total number of valence electrons in the ${\mathrm{C}}_2{\mathrm{H}}_2$ molecule, you sum up the contributions from all the atoms:

• Carbon: 2 atoms × 4 valence electrons = 8 electrons
• Hydrogen: 2 atoms × 1 valence electron = 2 electrons

This results in a total of 10 valence electrons. These electrons are essential for forming bonds and achieving a stable configuration for the molecule, as explained by the octet rule.

Hybridization

Hybridization is a concept used to describe the mixing of atomic orbitals to form new hybrid orbitals that can form chemical bonds in a molecule. In the ${\mathrm{C}}_2{\mathrm{H}}_2$ molecule, the carbon atoms exhibit sp hybridization.

When carbon atoms form a triple bond with each other, they each use two sp hybrid orbitals. One of these sp orbitals creates a sigma bond with a hydrogen atom, and the other sp orbital forms a sigma bond between the two carbon atoms.

• Each carbon atom uses its sp hybrid orbitals to form one $\sigma$ bond with hydrogen and one $\sigma$ bond with the other carbon.

sp hybridization results in a linear arrangement of the atoms around the carbon, which suits the structure of ${\mathrm{C}}_2{\mathrm{H}}_2$. It creates a strong and straight connection between the atoms, optimizing the overlap for sigma bonds.

Sigma and Pi Bonds

Sigma ($\sigma$) and pi ($\pi$) bonds are types of covalent bonds that form when different types of orbitals overlap. In the ${\mathrm{C}}_2{\mathrm{H}}_2$ molecule, both these bonds play a significant role in the formation of the molecule's structure.

A sigma bond is formed by the head-to-head overlap of orbitals. In ${\mathrm{C}}_2{\mathrm{H}}_2$, three sigma bonds are present:

• Two $\sigma$ C-H bonds (one each for each carbon atom)
• One $\sigma$ C-C bond

Pi bonds, on the other hand, result from the side-to-side overlap of unhybridized p orbitals. In ${\mathrm{C}}_2{\mathrm{H}}_2$, two $\pi$ C-C bonds are formed using the unhybridized 2p orbitals from each carbon atom.

These two types of bonds together account for the three bonds between the two carbon atoms: one sigma bond and two pi bonds, which complete the triple bond configuration between the carbon atoms.

Octet Rule

The octet rule is a guiding principle in chemistry, stating that atoms tend to seek a stable configuration similar to the noble gases, usually having eight electrons in their valence shell. For most atoms, this configuration is achieved by sharing, gaining, or losing electrons.

In the molecule ${\mathrm{C}}_2{\mathrm{H}}_2$, the carbon atoms adhere to the octet rule by forming a triple bond that allows each carbon to share enough electrons to complete their valence shells. Here's how this works:

• Each carbon, having 4 valence electrons, shares 3 additional electrons through one $\sigma$ bond and two $\pi$ bonds with the other carbon. This results in a total of 8 electrons in its vicinity.
• Additionally, each carbon forms a single $\sigma$ bond with a hydrogen atom, satisfying hydrogen's need to achieve the stable configuration of 2 electrons.

These interactions ensure that both hydrogen and carbon atoms have full outer shells, providing stability to the molecule.