Question

Pure ${\mathbf{\text{HN}}}_{\mathbf{3}}$ (atom sequence HNNN) is explosive. In aqueous solution, it is a weak acid that yields the azide ion, N. Draw resonance structures to explain why the nitrogen-nitrogen bond lengths are equal in${\mathbf{\text{N}}}_{\mathbf{3}}^{\mathbf{-}}$ but unequal in${\mathbf{\text{HN}}}_{\mathbf{3}}$ .

Short answer

Since there is no hydrogen present,all bond lengths are equal in an azide ion due to similar conjugation/resonance.

Due to the presence of hydrogen covalently bonded with nitrogen, the bond length of N-N is unequal in hydrazoic acid.

Step-by-step solution

Resonating structures of Hydrazoic acid

Three resonance structures of hydrazoic acid are drawn below. In hydrazoic acid, three nitrogen atoms and one hydrogen atom are covalently bonded.

In the first structure, three nitrogen atoms are double bonded and one hydrogen atom is bonded with one of nitrogen (formal charge 0).

In the second structure, two nitrogen atoms are bonded with a triple bond in which one has a +1 formal charge and another has zero formal charges. These are single bonded with the rest of the one nitrogen (formal charge -1) which is single bonded with hydrogen.

In the third structure, hydrogen is single-bonded with nitrogen (formal charge -1). This nitrogen is triple bonded with another nitrogen (formal charge +1) and nitrogen is attached by a single bond with this nitrogen.

The resonating structures of azide ion.

Three resonance structures of azide ion are drawn below.

In the first resonance structure, all three nitrogen atoms are double bonded in which middle nitrogen has +1 formal charge and two terminal nitrogens have -1 negative charge on each.

In the second and third structure, two nitrogen atoms are attached by a triple bond, and the left one nitrogen is attached by a single having a -2 formal charge.

The bond lengths.

Hydrazoic acid is a weak acid.In aqueous solution, the removal of hydrogen takes place in the form of ${\mathbf{H}}^{\mathbf{+}}$ and azide ion is formed.

Therefore, in azide ion there is an extra lone pair of electrons which contributes to the resonance structures of the ions. With this, the number of bonds between two nitrogen increases, the bond length is decreased because bond length is inversely proportional to the bond order.

$\text{BondLength}\propto \frac{1}{\text{BondOrder}}$