Chapter 8, Problem 8.108QP

(a)

Interpretation Introduction

Interpretation: Odd-electron molecules among the given nitrogen 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 nitrogen oxide is an odd-electron molecule.

Answer to Problem 8.108QP

Solution

The molecule $\text{NO}$ is an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is $\text{NO}$. It consists of $1$ nitrogen and $1$ oxygen atoms. Nitrogen has $5$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

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

The total number of valence electrons is calculated as,

$\begin{array}{c}1\text{N}+1\text{O}=1\left(5\right)+1\left(6\right)\\ =5+6\\ =11\end{array}$

The total number of valence electrons in $\text{NO}$ is $11$. Therefore, the difference between the total number of electrons and valence electron is $16-11=5$ electrons.

One bond contains two electrons. Therefore, the number of bonds formed in $\text{NO}$ is $2\frac{1}{2}$ bonds. Hence, the bond formed is a fraction, $\text{NO}$ molecule is an odd-electron molecule.

(b)

Interpretation Introduction

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

Answer to Problem 8.108QP

Solution

The molecule ${\text{NO}}_2$ is an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{NO}}_2$. It consists of $1$ nitrogen and $2$ oxygen atoms. Nitrogen has $5$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

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

The total number of valence electrons is calculated as,

$\begin{array}{c}1\text{N}+2\text{O}=1\left(5\right)+2\left(6\right)\\ =5+12\\ =17\end{array}$

The total number of valence electrons in ${\text{NO}}_2$ is $17$. Therefore, the difference between the total number of electrons and valence electron is $24-17=7$ electrons.

One bond contains two electrons. Therefore, the number of bonds formed in ${\text{NO}}_2$ is $3\frac{1}{2}$ bonds. Hence, the bond formed is a fraction, ${\text{NO}}_2$ molecule is an odd-electron molecule.

(c)

Interpretation Introduction

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

Answer to Problem 8.108QP

Solution

The molecule ${\text{NO}}_3$ is an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{NO}}_3$. It consists of $1$ nitrogen and $3$ oxygen atoms. Nitrogen has $5$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

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

The total number of valence electrons is calculated as,

$\begin{array}{c}1\text{N}+3\text{O}=1\left(5\right)+3\left(6\right)\\ =5+18\\ =23\end{array}$

The total number of valence electrons in ${\text{NO}}_3$ is $23$. Therefore, the difference between the total number of electrons and valence electron is $32-23=9$ electrons.

One bond contains two electrons. Therefore, the number of bonds formed in ${\text{NO}}_3$ is $4\frac{1}{2}$ bonds. Hence, the bond formed is a fraction, ${\text{NO}}_3$ molecule is an odd-electron molecule.

(d)

Interpretation Introduction

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

Answer to Problem 8.108QP

Solution

The molecule ${\text{N}}_2{\text{O}}_4$ is not an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{N}}_2{\text{O}}_4$. It consists of $2$ nitrogen and $4$ oxygen atoms. Nitrogen has $5$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}\text{2N}+4\text{O}=2\left(8\right)+4\left(8\right)\\ =16+32\\ =48\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}\text{2N}+4\text{O}=2\left(5\right)+4\left(6\right)\\ =10+24\\ =34\end{array}$

The total number of valence electrons in ${\text{N}}_2{\text{O}}_4$ is $34$. Therefore, the difference between the total number of electrons and valence electron is $48-34=14$ electrons.

One bond contains two electrons. Therefore, the number of bonds formed in ${\text{N}}_2{\text{O}}_4$ is $7$ bonds. Hence, the bond formed is not a fraction, ${\text{N}}_2{\text{O}}_4$ molecule is not an odd-electron molecule.

(e)

Interpretation Introduction

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

Answer to Problem 8.108QP

Solution

The molecule ${\text{N}}_2{\text{O}}_5$ is not an odd-electron molecule.

Explanation of Solution

Explanation

The given molecule is ${\text{N}}_2{\text{O}}_5$. It consists of $2$ nitrogen and $5$ oxygen atoms. Nitrogen has $5$ valence electrons and oxygen has $6$ valence electrons. The total number of electrons required to complete an octet is calculated as,

$\begin{array}{c}\text{2N}+5\text{O}=2\left(8\right)+5\left(8\right)\\ =16+40\\ =56\end{array}$

The total number of valence electrons is calculated as,

$\begin{array}{c}\text{2N}+5\text{O}=2\left(5\right)+5\left(6\right)\\ =10+30\\ =40\end{array}$

The total number of valence electrons in ${\text{N}}_2{\text{O}}_5$ is $40$. Therefore, the difference between the total number of electrons and valence electron is $56-40=16$ electrons.

One bond contains two electrons. Therefore, the number of bonds formed in ${\text{N}}_2{\text{O}}_5$ is $8$ bonds. Hence, the bond formed is not a fraction, ${\text{N}}_2{\text{O}}_5$ molecule is not an odd-electron molecule.

Conclusion

The molecules, $\text{NO}$, ${\text{NO}}_2$ and ${\text{NO}}_3$ are odd-electron molecules.