Chapter 2, Problem 26P

What is the hybridization of each carbon in ${\text{CH}}_{\text{3}}\text{CH= CHC}\equiv \text{ CH}$? What are the CCC bond angles?

Interpretation Introduction

Interpretation:

The hybridization of each carbon atom in the given molecule is to be determined along with the $\text{CCC}$ bond angles.

Concept introduction:

A carbon atom is said to be ${\text{sp}}^{\text{3}}$ hybridized if it is connected to four atoms by a single covalent bond; ${\text{sp}}^{\text{2}}$ hybridized if it is connected to three atoms by single and double covalent bonds and $\text{sp}$ hybridized if it is connected to two atoms by single and triple covalent bonds.

Multiple bonds are treated as a unit while determining the hybridization of different atoms in a molecule. For ${\text{sp}}^{\text{3}}$ hybridization, the bond angles between the atoms is $\text{109}{\text{.5}}^{\text{o}}$. For ${\text{sp}}^{\text{2}}$ hybridization, the bond angles between the atoms is ${\text{120}}^{\text{o}}$ while for $\text{sp}$ hybridization, the bond angle is ${\text{180}}^{\text{o}}$.

Answer to Problem 26P

Solution:

Carbon $(1)$ is $\text{sp}$ hybridized since it is connected to two other atoms by single and triple covalent bonds.

Carbon $(2)$ is $\text{sp}$ hybridized since it is connected to two other atoms by single and triple covalent bonds.

Carbon $(3)$ is ${\text{sp}}^{\text{2}}$ hybridized since it is directly connected to three other atoms by single and double covalent bonds.

Carbon $(4)$ is ${\text{sp}}^{\text{2}}$ hybridized since it is directly connected to three other atoms by single and double bonds.

Carbon $(5)$ is ${\text{sp}}^{\text{3}}$ hybridized since it is directly connected to four other atoms by single covalent bonds.

For carbon $(1)$, $(2)$, and $(3)$, the central carbon is $(2)$. Carbon $(2)$ is $\text{sp}$ hybridized. An $\text{sp}$ hybridized carbon has a linear geometry, and the bond angle is ${180}^{\circ }$.

For carbon $(2)$, $(3)$, and $(4)$, the central carbon is $(3)$. Carbon $(3)$ is ${\text{sp}}^{\text{2}}$ hybridized. An ${\text{sp}}^{\text{2}}$ hybridized carbon has a trigonal planar geometry and the bond angle is ${120}^{\circ }$.

For carbon $(3)$, $(4)$ and $(5)$, the central carbon is $(4)$. Carbon $(4)$ is ${\text{sp}}^{\text{2}}$ hybridized. An ${\text{sp}}^{\text{2}}$ hybridized carbon has a trigonal planar geometry and the bond angle is ${120}^{\circ }$.

Explanation of Solution

The structure for the given compound is:

We number each carbon atom in the above compound.

A carbon atom is said to be ${\text{sp}}^{\text{3}}$ hybridized when it is directly connected to four other atoms. Carbon $(5)$ is ${\text{sp}}^{\text{3}}$ hybridized as it is directly bonded to four other atoms.

A carbon atom is said to be ${\text{sp}}^{\text{2}}$ hybridized when it is directly connected to three other atoms. Both carbon $(3)$ and carbon $(4)$ are ${\text{sp}}^{\text{2}}$ hybridized as each of them are connected to three other atoms by single and double covalent bonds.

A carbon atom is said to be $\text{sp}$ hybridized when it is directly connected to two other atoms. Carbon $(1)$ and carbon $(2)$ are $\text{sp}$ hybridized each as they are directly connected to two other atoms through single and triple covalent bonds.

For carbon $(1)$, $(2)$, and $(3)$, the central carbon is $(2)$. Carbon $(2)$ is $\text{sp}$ hybridized. An $\text{sp}$ hybridized carbon has a linear geometry, and the bond angle is ${180}^{\circ }$.

For carbon $(2)$, $(3)$, and $(4)$, the central carbon is $(3)$. Carbon $(3)$ is ${\text{sp}}^{\text{2}}$ hybridized. An ${\text{sp}}^{\text{2}}$ hybridized carbon has a trigonal planar geometry, and the bond angle is ${120}^{\circ }$.

For carbon $(3)$, $(4)$, and $(5)$, the central carbon is $(4)$. Carbon $(4)$ is ${\text{sp}}^{\text{2}}$ hybridized. An ${\text{sp}}^{\text{2}}$ hybridized carbon has a trigonal planar geometry, and the bond angle is ${120}^{\circ }$.

Conclusion

The hybridization of each carbon atom in the given molecule is $\text{sp}$, $\text{sp}$, ${\text{sp}}^{\text{2}}$, ${\text{sp}}^{\text{2}}$ and ${\text{sp}}^{\text{3}}$. The CCC angles are equal to ${180}^{\circ }$, ${120}^{\circ }$ and ${120}^{\circ }$.