Chapter 8, Problem 8.90QP

Interpretation Introduction

Interpretation: All the resonance forms of the sulfur-nitrogen anion, ${\text{S}}_{\text{4}}{\text{N}}^{-}$ are to be drawn and formal charges are to be assigned.

Concept introduction: Formal charges play an important role in choosing between the possible molecular structures. The preferred structure is the one in which formal charges are zero.

To determine: All the resonance forms of the sulfur-nitrogen anion, ${\text{S}}_{\text{4}}{\text{N}}^{-}$ and the formal charges.

Answer to Problem 8.90QP

Solution

All the resonance forms of the sulfur-nitrogen anion, ${\text{S}}_{\text{4}}{\text{N}}^{-}$ are shown in Figure 1 and formal charges have been assigned.

Explanation of Solution

Explanation

The given anion is ${\text{S}}_{\text{4}}{\text{N}}^{-}$. Number of valence electrons in sulfur is $6$ and number of valence electrons in nitrogen is $5$. There are four sulfur atoms and one nitrogen atom present in ${\text{S}}_{\text{4}}{\text{N}}^{-}$. There is an additional charge of $-1$ in the anion, therefore the total valence electrons are $\begin{array}{l}=\left(4\times 6\right)+\left(1\times 5\right)+1\\ =30\end{array}$

It is given that the atoms are arranged as $\text{SSNSS}$. The lone pairs of electrons on sulfur are delocalized which results in the formation of different lewis structures. The lewis structures for ${\text{S}}_{\text{4}}{\text{N}}^{-}$ are,

Figure 1

The atoms in the resonating structures are named as a,b,c,d and e.

The formal charge on each atom of resonating structure (I) of ${\text{S}}_{\text{4}}{\text{N}}^{-}$ is calculated as,

Formal charge is calculated by the formula,

$\text{Formal}\text{charge}=\text{Valence}\text{electrons}-\left(\text{Lone}\text{pair}\text{electrons}+\frac{1}{2}\text{Bond}\text{pair}\text{electrons}\right)$ (1)

Number of valence electrons in $\text{S}$ (a) is $6$.

Number of lone pair electrons in $\text{S}$ (a) is $6$.

Number of bond pair electrons in $\text{S}$ (a) is $2$.

To calculate the formal charge on $\text{S}$ (a), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (b) is $6$.

Number of lone pair electrons in $\text{S}$ (b) is $2$.

Number of bond pair electrons in $\text{S}$ (b) is $6$.

To calculate the formal charge on $\text{S}$ (b), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in nitrogen (c) is $5$.

Number of lone pair electrons in nitrogen (c) is $2$.

Number of bond pair electrons in nitrogen (c) is $6$.

To calculate the formal charge on nitrogen (c), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

$\begin{array}{c}\text{Formal}\text{charge}=5-\left(2+\frac{1}{2}\left(6\right)\right)\\ =0\end{array}$

Number of valence electrons in $\text{S}$ (d) is $6$.

Number of lone pair electrons in $\text{S}$ (d) is $4$.

Number of bond pair electrons in $\text{S}$ (d) is $4$.

To calculate the formal charge on $\text{S}$ (d), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (e) is $6$.

Number of lone pair electrons in $\text{S}$ (e) is $6$.

Number of bond pair electrons in $\text{S}$ (e) is $2$.

To calculate the formal charge on $\text{S}$ (e), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

The formal charge on each atom of resonating structure (II) of ${\text{S}}_{\text{4}}{\text{N}}^{-}$ is calculated as,

Number of valence electrons in $\text{S}$ (a) is $6$.

Number of lone pair electrons in $\text{S}$ (a) is $6$.

Number of bond pair electrons in $\text{S}$ (a) is $2$.

To calculate the formal charge on $\text{S}$ (a), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (b) is $6$.

Number of lone pair electrons in $\text{S}$ (b) is $4$.

Number of bond pair electrons in $\text{S}$ (b) is $4$.

To calculate the formal charge on $\text{S}$ (b), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in nitrogen (c) is $5$.

Number of lone pair electrons in nitrogen (c) is $2$.

Number of bond pair electrons in nitrogen (c) is $6$.

To calculate the formal charge on nitrogen (c), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

$\begin{array}{c}\text{Formal}\text{charge}=5-\left(2+\frac{1}{2}\left(6\right)\right)\\ =0\end{array}$

Number of valence electrons in $\text{S}$ (d) is $6$.

Number of lone pair electrons in $\text{S}$ (d) is $2$.

Number of bond pair electrons in $\text{S}$ (d) is $6$.

To calculate the formal charge on $\text{S}$ (d), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (e) is $6$.

Number of lone pair electrons in $\text{S}$ (e) is $6$.

Number of bond pair electrons in $\text{S}$ (e) is $2$.

To calculate the formal charge on $\text{S}$ (e), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

The formal charge on each atom of resonating structure (III) of ${\text{S}}_{\text{4}}{\text{N}}^{-}$ is calculated as,

Number of valence electrons in $\text{S}$ (a) is $6$.

Number of lone pair electrons in $\text{S}$ (a) is $4$.

Number of bond pair electrons in $\text{S}$ (a) is $4$.

To calculate the formal charge on $\text{S}$ (a), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (b) is $6$.

Number of lone pair electrons in $\text{S}$ (b) is $2$.

Number of bond pair electrons in $\text{S}$ (b) is $8$.

To calculate the formal charge on $\text{S}$ (b), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in nitrogen (c) is $5$.

Number of lone pair electrons in nitrogen (c) is $2$.

Number of bond pair electrons in nitrogen (c) is $6$.

To calculate the formal charge on nitrogen (c), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

$\begin{array}{c}\text{Formal}\text{charge}=5-\left(2+\frac{1}{2}\left(6\right)\right)\\ =0\end{array}$

Number of valence electrons in $\text{S}$ (d) is $6$.

Number of lone pair electrons in $\text{S}$ (d) is $4$.

Number of bond pair electrons in $\text{S}$ (d) is $4$.

To calculate the formal charge on $\text{S}$ (d), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (e) is $6$.

Number of lone pair electrons in $\text{S}$ (e) is $6$.

Number of bond pair electrons in $\text{S}$ (e) is $2$.

To calculate the formal charge on $\text{S}$ (e), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

The formal charge on each atom of resonating structure (IV) of ${\text{S}}_{\text{4}}{\text{N}}^{-}$ is calculated as,

Number of valence electrons in $\text{S}$ (a) is $6$.

Number of lone pair electrons in $\text{S}$ (a) is $6$.

Number of bond pair electrons in $\text{S}$ (a) is $2$.

To calculate the formal charge on $\text{S}$ (a), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (b) is $6$.

Number of lone pair electrons in $\text{S}$ (b) is $4$.

Number of bond pair electrons in $\text{S}$ (b) is $4$.

To calculate the formal charge on $\text{S}$ (b), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in nitrogen (c) is $5$.

Number of lone pair electrons in nitrogen (c) is $2$.

Number of bond pair electrons in nitrogen (c) is $6$.

To calculate the formal charge on nitrogen (c), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

$\begin{array}{c}\text{Formal}\text{charge}=5-\left(2+\frac{1}{2}\left(6\right)\right)\\ =0\end{array}$

Number of valence electrons in $\text{S}$ (d) is $6$.

Number of lone pair electrons in $\text{S}$ (d) is $2$.

Number of bond pair electrons in $\text{S}$ (d) is $8$.

To calculate the formal charge on $\text{S}$ (d), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Number of valence electrons in $\text{S}$ (e) is $6$.

Number of lone pair electrons in $\text{S}$ (e) is $4$.

Number of bond pair electrons in $\text{S}$ (e) is $4$.

To calculate the formal charge on $\text{S}$ (e), substitute the value of valence electrons, lone pair electrons and bond pair electrons in the equation (1).

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

Conclusion

All the resonance forms of the sulfur-nitrogen anion, ${\text{S}}_{\text{4}}{\text{N}}^{-}$ are shown in Figure 1 and formal charges have been assigned.