Chapter 8, Problem 137A

Interpretation Introduction

(a)

Interpretation:

The Lewis structure of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ and $\text{HCOOH}$ is to be drawn.

Concept introduction:

The strategy for drawing Lewis structure is mention below.

• Calculate the number of valence electrons present in the molecule.
• Calculate the electron pairs by dividing number of valence electrons by 2.
• Determine the bond pairs.
• Determine the lone pairs.
• Check whether the central atom satisfies octet rule.

Answer to Problem 137A

The Lewis structure of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ and $\text{HCOOH}$ is shown below.

Explanation of Solution

The number of valence electron in ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ is the sum of valence electron in carbon and hydrogen atoms. The valence electron in carbon is four and the valence electron in hydrogen is one. Therefore, the valence electron in ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ is calculated as shown below.

$\begin{array}{c}\text{No}\text{.}\text{of}\text{valence}\text{electron}=2\text{C}+\text{2H}+\text{2O}\\ =2\times 4{\text{e}}^{-}+2\times 1{\text{e}}^{-}\\ =10{\text{e}}^{-}\end{array}$

The number of electron pair is calculated as shown below.

$\begin{array}{c}\text{electron}\text{pair}=\frac{10{\text{e}}^{-}}{2}\\ =5{\text{e}}^{-}\text{pairs}\end{array}$

Among five electron pairs, all five electron pairs are involved in bonding. The Lewis structure of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ is drawn below.

The number of valence electron in $\text{HCOOH}$ is the sum of valence electron in carbon, hydrogen, and oxygen atoms. The valence electron in carbon is four, the valence electron in hydrogen is one, and the valence electron in oxygen is six. Therefore, the valence electron in $\text{HCOOH}$ is calculated as shown below.

$\begin{array}{c}\text{No}\text{.}\text{of}\text{valence}\text{electron}=\text{C}+\text{2H}+\text{2O}\\ =4{\text{e}}^{-}+2\times 1{\text{e}}^{-}+\text{2}\times 6{\text{e}}^{-}\\ =18{\text{e}}^{-}\end{array}$

The number of electron pair is calculated as shown below.

$\begin{array}{c}\text{electron}\text{pair}=\frac{18{\text{e}}^{-}}{2}\\ =9{\text{e}}^{-}\text{pairs}\end{array}$

Among nine electron pairs, five electron pairs are involved in bonding and four electron pairs remain as lone pairs. The Lewis structure of $\text{HCOOH}$ is drawn below.

Interpretation Introduction

(b)

Interpretation:

The amount of energy needed to break apart ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ and $\text{HCOOH}$ molecules is to be determined.

Concept introduction:

The energy required to break a bond is termed as bond dissociation energy. The bond length depends on the bond dissociation energies. The longest bond has lowest bond energy and the shortest bond has highest bond energy.

Answer to Problem 137A

The amount of energy needed to break apart ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ molecule is $\text{1671}\text{kJ/mol}$.

The amount of energy needed to break apart $\text{HCOOH}$ molecule is $\text{1986}\text{kJ/mol}$.

Explanation of Solution

The structure of ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ is drawn below.

In ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$, there are two $\text{C}-\text{H}$ bonds and one $\text{C}\equiv \text{C}$ bond. The required energy to break all the bonds present in ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ is calculated as shown below.

$\begin{array}{c}{E}_{\text{Total}}=2E_{\text{C}-\text{H}}+E_{\text{C}\equiv \text{C}}\\ =2\times 416\text{kJ/mol}+839\text{kJ/mol}\\ =\text{1671}\text{kJ/mol}\end{array}$

Therefore, the amount of energy needed to break apart ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}$ molecule is $\text{1671}\text{kJ/mol}$.

The structure of $\text{HCOOH}$ is drawn below.

In $\text{HCOOH}$, there are one $\text{C}-\text{H}$ bond, one $\text{C}=\text{O}$ bond, one $\text{C}-\text{O}$ bond, and one $\text{O}-\text{H}$ bond. The required energy to break all the bonds present in $\text{HCOOH}$ is calculated as shown below.

$\begin{array}{c}{E}_{\text{Total}}=E_{\text{C}-\text{H}}+E_{\text{C}=\text{O}}+E_{\text{C}-\text{O}}+E_{\text{O}-\text{H}}\\ =416\text{kJ/mol}+745\text{kJ/mol}+358\text{kJ/mol}+467\text{kJ/mol}\\ =\text{1986}\text{kJ/mol}\end{array}$

Therefore, the amount of energy needed to break apart $\text{HCOOH}$ molecule is $\text{1986}\text{kJ/mol}$.