Chapter 10, Problem 10.17P

(a)

Interpretation Introduction

Interpretation:

Lewis structure for a resonance form of each ion of ${\text{BrO}}_3^{-}$ with the lowest possible formal charges is to be drawn. Also, the oxidation number of the atom is to be determined.

Concept introduction:

The steps to draw the Lewis structure of the molecule are as follows:

Step 1: Find the central atom and place the other atoms around it. The atom in a compound which has the lowest group number or lowest electronegativity considered as the central atom.

Step 2: Calculate the total number of valence electrons.

Step 3: Connect the other atoms around the central atoms to the central atom with a single bond and lower the value of valence electrons by 2 of every single bond.

Step 4: Allocate the remaining electrons in pairs so that each atom can get 8 electrons.

Formula to calculate the formal charge of the atom is as follows:

  $\text{Formal}\text{charge}=\left(\begin{array}{l}\text{number}\text{of}\\ \text{valence}\\ \text{electrons}\end{array}\right)-\left(\left(\begin{array}{l}\text{number}\text{of}\\ \text{non-bonding}\\ \text{electrons}\end{array}\right)+\left(\frac{1}{2}\right)\left(\begin{array}{l}\text{number}\text{of}\\ \text{bonding}\\ \text{electrons}\end{array}\right)\right)$        (1)

The formula to calculate the oxidation number of an atom is as follows:

  $\text{Oxidation}\text{number}=\left(\begin{array}{l}\text{number}\text{of}\\ \text{valence}\\ \text{electrons}\end{array}\right)-\left(\left(\begin{array}{l}\text{number}\text{of}\\ \text{non-bonding}\\ \text{electrons}\end{array}\right)+\left(\begin{array}{l}\text{number}\text{of}\\ \text{bonding}\\ \text{electrons}\end{array}\right)\right)$        (2)

Answer to Problem 10.17P

The possible Lewis structures for a resonance form of each ion of ${\text{BrO}}_3^{-}$ with the lowest possible formal charges are,

The oxidation numbers of $\text{Br}$ is $+5$ and the oxidation number of oxygen is $–2$.

Explanation of Solution

Lewis structures for a resonance form of ${\text{BrO}}_3^{-}$ is,

For structure I:

Substitute 7 for valence electrons, 2 for the number of nonbonded electrons and 6 for the number of bonding electrons in equation (1) to calculate the formal charge on $\text{Br}$ atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(7\right)-\left(\left(2\right)+\left(\frac{1}{2}\right)\left(6\right)\right)\\ =+2\end{array}$

Substitute 6 for valence electrons, 6 for nonbonded electrons and 2 for the number of bonding electrons in equation (1) to calculate the formal charge on each oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(6\right)+\left(\frac{1}{2}\right)\left(2\right)\right)\\ =-1\end{array}$

For structure II:

Substitute 7 for valence electrons, 2 for the number of nonbonded electrons and 8 for the number of bonding electrons in equation (1) to calculate the formal charge on $\text{Br}$ atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(7\right)-\left(\left(2\right)+\left(\frac{1}{2}\right)\left(8\right)\right)\\ =+1\end{array}$

Substitute 6 for valence electrons, 6 for nonbonded electrons and 2 for the number of bonding electrons in equation (1) to calculate the formal charge on each single bonded oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(6\right)+\left(\frac{1}{2}\right)\left(2\right)\right)\\ =-1\end{array}$

Substitute 6 for the value of valence electrons, 4 for the number of nonbonded electrons and 4 for the number of bonding electrons in equation (1) to calculate the formal charge on the double bonded oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(4\right)+\left(\frac{1}{2}\right)\left(4\right)\right)\\ =0\end{array}$

For structure III:

Substitute 7 for valence electrons, 2 for the number of nonbonded electrons and 10 for the number of bonding electrons in equation (1) to calculate the formal charge on $\text{Br}$ atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(7\right)-\left(\left(2\right)+\left(\frac{1}{2}\right)\left(10\right)\right)\\ =0\end{array}$

Substitute 6 for valence electrons, 6 for nonbonded electrons and 2 for number of bonding electrons in equation (1) to calculate the formal charge on the single bonded oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(6\right)+\left(\frac{1}{2}\right)\left(2\right)\right)\\ =-1\end{array}$

Substitute 6 for the value of valence electrons, 4 for the number of nonbonded electrons and 4 for the number of bonding electrons in equation (1) to calculate the formal charge on each double bonded oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(4\right)+\left(\frac{1}{2}\right)\left(4\right)\right)\\ =0.\end{array}$

Therefore, structure II has the more acceptable and reasonable distribution of formal charges.

The oxidation numbers of $\text{Br}$ is $+5$ and the oxidation number of oxygen is $–2$.

Conclusion

${\text{BrO}}_3^{-}$ has three possible resonating structures. Structure II is more acceptable and has a more distributed formal charge.

(b)

Interpretation Introduction

Interpretation:

Lewis structure for a resonance form of each ion of ${\text{SO}}_3^{2-}$ with the lowest possible formal charges is to be drawn. Also, the oxidation number of the atom is to be determined.

Concept introduction:

The steps to draw the Lewis structure of the molecule are as follows:

Step 1: Find the central atom and place the other atoms around it. The atom in a compound which has the lowest group number or lowest electronegativity considered as the central atom.

Step 2: Calculate the total number of valence electrons.

Step 3: Connect the other atoms around the central atoms to the central atom with a single bond and lower the value of valence electrons by 2 of every single bond.

Step 4: Allocate the remaining electrons in pairs so that each atom can get 8 electrons.

Formula to calculate the formal charge of the atom is as follows:

  $\text{Formal}\text{charge}=\left(\begin{array}{l}\text{number}\text{of}\\ \text{valence}\\ \text{electrons}\end{array}\right)-\left(\left(\begin{array}{l}\text{number}\text{of}\\ \text{non-bonding}\\ \text{electrons}\end{array}\right)+\left(\frac{1}{2}\right)\left(\begin{array}{l}\text{number}\text{of}\\ \text{bonding}\\ \text{electrons}\end{array}\right)\right)$        (1)

The formula to calculate the oxidation number of an atom is as follows:

  $\text{Oxidation}\text{number}=\left(\begin{array}{l}\text{number}\text{of}\\ \text{valence}\\ \text{electrons}\end{array}\right)-\left(\left(\begin{array}{l}\text{number}\text{of}\\ \text{non-bonding}\\ \text{electrons}\end{array}\right)+\left(\begin{array}{l}\text{number}\text{of}\\ \text{bonding}\\ \text{electrons}\end{array}\right)\right)$        (2)

Answer to Problem 10.17P

The possible Lewis structures for a resonance form of each ion of ${\text{SO}}_3^{2-}$ with the lowest possible formal charges are,

The oxidation numbers of. $\text{S}$ is $+4$ and the oxidation number of oxygen is $–2$.

Explanation of Solution

Lewis structure for a resonance form of ${\text{SO}}_3^{2-}$ is,

For structure I:

Substitute 6 for valence electrons, 2 for the number of nonbonded electrons and 6 for the number of bonding electrons in equation (1) to calculate the formal charge on $\text{S}$ atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(2\right)+\left(\frac{1}{2}\right)\left(6\right)\right)\\ =+1\end{array}$

Substitute 6 for valence electrons, 6 for nonbonded electrons and 2 for the number of bonding electrons in equation (1) to calculate the formal charge on each oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(6\right)+\left(\frac{1}{2}\right)\left(2\right)\right)\\ =-1\end{array}$

For structure II:

Substitute 6 for valence electrons, 2 for the number of nonbonded electrons and 8 for the number of bonding electrons in equation (1) to calculate the formal charge on $\text{S}$ atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(2\right)+\left(\frac{1}{2}\right)\left(8\right)\right)\\ =0\end{array}$

Substitute 6 for valence electrons, 6 for nonbonded electrons and 2 for the number of bonding electrons in equation (1) to calculate the formal charge on each single bonded oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(6\right)+\left(\frac{1}{2}\right)\left(2\right)\right)\\ =-1\end{array}$

Substitute 6 for the value of valence electrons, 4 for the number of nonbonded electrons and 4 for the number of bonding electrons in equation (1) to calculate the formal charge on the double bonded oxygen atom.

  $\begin{array}{c}\text{Formal}\text{charge}=\left(6\right)-\left(\left(4\right)+\left(\frac{1}{2}\right)\left(4\right)\right)\\ =0.\end{array}$

Therefore, structure II has the more acceptable and reasonable distribution of formal charges.

The oxidation numbers of. $\text{S}$ is $+4$ and the oxidation number of oxygen is $–2$.

Conclusion

${\text{SO}}_3^{2-}$ has two possible resonating structures.