Chapter 6, Problem 6.97QP

In 1999 an unusual cation containing only nitrogen (N₅⁺) was prepared. Draw three resonance structures of the ion, showing formal charges. (Hint: The N atoms are joined in a linear fashion.)

Interpretation Introduction

Interpretation: The resonance structure for ${\text{N}}_{\text{5}}{}^{\text{+}}$ ion and its corresponding formal charges should be drawn.

Concept Introduction:

• Sometimes the chemical bonding of a molecule cannot be represented using a single Lewis structure. In these cases, the chemical bonding are described by delocalization of electrons and is known as resonance.
• All the possible resonance structures are imaginary whereas the resonance hybrid is real.
• These structures will differ only in the arrangement of the electrons not in the relative position of the atomic nuclei.

To find: The resonance structure for the given molecule.

Answer to Problem 6.97QP

Explanation of Solution

• Resonance structure of ${\text{N}}_{\text{5}}{}^{\text{+}}$ ion is drawn below.

In the case of ${\text{N}}_{\text{5}}{}^{\text{+}}$, the chemical bonding of a molecule cannot be represented using a single Lewis structure. The chemical bonding are described by delocalization of electrons forming 3 possible resonance structures. In all the 3 resonance structures the position, over whole charge and chemical framework remains intact.

Conclusion

The resonance structures of the ${\text{N}}_{\text{5}}{}^{\text{+}}$ ion were drawn.

Interpretation Introduction

Interpretation: The formal charges for the resonance structures has to be given.

Concept Introduction

• A formal charge (FC) is the charge assigned to an atom in a molecule, irrespective of relative electronegativity by thinking that electrons in all chemical bonds are shared equally among atoms.
• This method is used to identify the most probable Lewis structures if more than one possibility exists for a compound.
• Formal charge of an atom can be determined by the given formula.

$\text{Formal}\text{charge}\left(\text{F}\text{C}\right)\text{=}\left(\begin{array}{l}\text{no}\text{.of}\text{valence}\\ \text{electron}\text{in}\text{atom}\end{array}\right)-\frac{\text{1}}{\text{2}}\left(\begin{array}{l}\text{no}\text{.of}\text{bonding}\\ \text{electrons}\end{array}\right)-\left(\begin{array}{l}\text{no}\text{.of}\text{non-bonding}\\ \text{electrons}\end{array}\right)$

To Determine: The formal charges for the resonance structures of given molecule.

Answer to Problem 6.97QP

Explanation of Solution

Determine the formal charge for the first resonance structure of the given molecule.

The formal charge of the given compound is calculated,

• Nitrogen atom (a)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}6\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}2\end{array}$

Substituting these values to the equation,

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

• Nitrogen atom (b)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}8\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}0\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}5-\left(\frac{\text{1}}{\text{2}}\text{×8}\right)\\ \text{=}\text{+1}\end{array}$

• Nitrogen atom (c)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}6\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}2\end{array}$

Substituting these values to the equation,

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

• Nitrogen atom (d)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}8\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}0\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}5-\left(\frac{\text{1}}{\text{2}}\text{×8}\right)\\ \text{=}\text{+1}\end{array}$

• Nitrogen atom (e)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}4\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}4\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}\text{5}-\left(\frac{\text{1}}{\text{2}}\text{×4}\right)-\text{4}\\ \text{=}-\text{1}\end{array}$

Determine the formal charge for the second resonance structure of the given molecule.

The formal charge of the given compound is calculated,

• Nitrogen atom (a)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}4\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}4\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}\text{5}-\left(\frac{\text{1}}{\text{2}}\text{×4}\right)-\text{4}\\ \text{=}-\text{1}\end{array}$

• Nitrogen atom (b)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}8\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}0\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}5-\left(\frac{\text{1}}{\text{2}}\text{×8}\right)\\ \text{=}\text{+1}\end{array}$

• Nitrogen atom (c)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}6\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}2\end{array}$

Substituting these values to the equation,

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

• Nitrogen atom (d)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}8\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}0\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}5-\left(\frac{\text{1}}{\text{2}}\text{×8}\right)\\ \text{=}\text{+1}\end{array}$

• Nitrogen atom (e)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}6\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}2\end{array}$

Substituting these values to the equation,

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

Determine the formal charge for the third resonance structure of the given molecule.

The formal charge of the given resonance structure is given below.

The formal charge of the given compound is calculated,

• Nitrogen atom (a)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}6\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}2\end{array}$

Substituting these values to the equation,

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

• Nitrogen atom (b)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}8\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}0\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}5-\left(\frac{\text{1}}{\text{2}}\text{×8}\right)\\ \text{=}\text{+1}\end{array}$

• Nitrogen atom (c)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}4\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}4\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}\text{5}-\left(\frac{\text{1}}{\text{2}}\text{×4}\right)-\text{4}\\ \text{=}-\text{1}\end{array}$

• Nitrogen atom (d)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}8\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}0\end{array}$

Substituting these values to the equation,

$\begin{array}{c}\text{FC}\text{=}5-\left(\frac{\text{1}}{\text{2}}\text{×8}\right)\\ \text{=}\text{+1}\end{array}$

• Nitrogen atom (e)

$\begin{array}{c}\text{Number}\text{of}\text{valence}\text{electron=5}\\ \text{Number}\text{of}\text{bonding}\text{electron=}6\\ \text{Number}\text{of}\text{non-bonding}\text{electron}\text{=}2\end{array}$

Substituting these values to the equation,

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

Conclusion

The formal charge of the resonance structures of ${\text{N}}_{\text{5}}{}^{\text{+}}$ ion was found