Chapter 8, Problem 8.107QP

(a)

Interpretation Introduction

Interpretation: The odd-electron molecules among the given chlorine oxides are to be identified.

Concept introduction: A molecule is said to be an odd-electron when the sum of the valence electrons of all the atoms in a molecules is odd that is the total number of bonds formed in a molecule is a fraction.

To determine: If the given chlorine oxide is an odd-electron molecule.

Answer to Problem 8.107QP

Solution

The molecule ${\text{Cl}}_{\text{2}}{\text{O}}_{\text{7}}$ is not an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{Cl}}_{\text{2}}{\text{O}}_{\text{7}}$. It consists of $2$ chlorine and $7$ oxygen atoms. Chlorine has $7$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}2\text{Cl}+\text{7O}=2\left(8\right)+7\left(8\right)\\ =16+56\\ =72\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}2\text{Cl}+\text{7O}=2\left(7\right)+7\left(6\right)\\ =14+42\\ =56\end{array}$

The total number of valence electrons in ${\text{Cl}}_{\text{2}}{\text{O}}_{\text{7}}$ is $56$. Therefore, the difference between the total number of electrons and valence electron is $72-56=16$ electrons.

One bond contains two electrons. Therefore, the number of bonds formed in ${\text{Cl}}_{\text{2}}{\text{O}}_{\text{7}}$ is $8$ bonds. Hence, the bond formed is even, ${\text{Cl}}_{\text{2}}{\text{O}}_{\text{7}}$ molecule is not an odd-electron molecule.

(b)

Interpretation Introduction

To determine: If the given chlorine oxide is an odd-electron molecule.

Answer to Problem 8.107QP

Solution

The molecule ${\text{Cl}}_{\text{2}}{\text{O}}_6$ is not an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{Cl}}_{\text{2}}{\text{O}}_6$. It consists of $2$ chlorine and $6$ oxygen atoms. Chlorine has $7$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}2\text{Cl}+6\text{O}=2\left(8\right)+6\left(8\right)\\ =16+48\\ =64\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}2\text{Cl}+6\text{O}=2\left(7\right)+6\left(6\right)\\ =14+36\\ =50\end{array}$

The total number of valence electrons in ${\text{Cl}}_{\text{2}}{\text{O}}_6$ is $50$. Therefore, the difference between the total number of electrons and valence electron is $64-50=14$ electrons.

The number of bonds formed in ${\text{Cl}}_{\text{2}}{\text{O}}_6$ is $7$ bonds. Hence, ${\text{Cl}}_{\text{2}}{\text{O}}_6$ molecule is not an odd-electron molecule.

(c)

Interpretation Introduction

To determine: If the given chlorine oxide is an odd-electron molecule.

Answer to Problem 8.107QP

Solution

The molecule ${\text{ClO}}_4$ is an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{ClO}}_4$. It consists of $1$ chlorine and $4$ oxygen atoms. Chlorine has $7$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}\text{1Cl}+4\text{O}=1\left(8\right)+4\left(8\right)\\ =8+32\\ =40\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}\text{1Cl}+4\text{O}=1\left(7\right)+4\left(6\right)\\ =7+24\\ =31\end{array}$

The total number of valence electrons in ${\text{ClO}}_4$ is $31$. Therefore, the difference between the total number of electrons and valence electron is $40-31=9$ electrons.

The number of bonds formed in ${\text{ClO}}_4$ is $4\frac{1}{2}$ bonds. Hence, the bond formed is a fraction ${\text{ClO}}_4$ molecule is an odd-electron molecule.

(d)

Interpretation Introduction

To determine: If the given chlorine oxide is an odd-electron molecule.

Answer to Problem 8.107QP

Solution

The molecule ${\text{ClO}}_3$ is an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{ClO}}_3$. It consists of $1$ chlorine and $3$ oxygen atoms. Chlorine has $7$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}\text{1Cl}+3\text{O}=1\left(8\right)+3\left(8\right)\\ =8+24\\ =32\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}\text{1Cl}+3\text{O}=1\left(7\right)+3\left(6\right)\\ =7+18\\ =25\end{array}$

The total number of valence electrons in ${\text{ClO}}_3$ is $25$. Therefore, the difference between the total number of electrons and valence electron is $32-25=7$ electrons.

The number of bonds formed in ${\text{ClO}}_3$ is $3\frac{1}{2}$ bonds. Hence, the bond formed is a fraction ${\text{ClO}}_3$ molecule is an odd-electron molecule.

(e)

Interpretation Introduction

To determine: If the given chlorine oxide is an odd-electron molecule.

Answer to Problem 8.107QP

Solution

The molecule ${\text{ClO}}_2$ is an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{ClO}}_2$. It consists of $1$ chlorine and $2$ oxygen atoms. Chlorine has $7$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}\text{1Cl}+2\text{O}=1\left(8\right)+2\left(8\right)\\ =8+16\\ =24\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}\text{1Cl}+2\text{O}=1\left(7\right)+2\left(6\right)\\ =7+12\\ =19\end{array}$

The total number of valence electrons in ${\text{ClO}}_2$ is $19$. Therefore, the difference between the total number of electrons and valence electron is $24-19=5$ electrons.

The number of bonds formed in ${\text{ClO}}_2$ is $2\frac{1}{2}$ bonds. Hence, the bond formed is a fraction ${\text{ClO}}_2$ molecule is an odd-electron molecule.

Conclusion

The molecules, ${\text{ClO}}_4$, ${\text{ClO}}_3$ and ${\text{ClO}}_2$ are odd-electron molecules.