Question

Use molecular orbital theory to explain the bonding in the azide ion \(\left(\mathrm{N}_{3}^{-}\right)\). (The arrangement of atoms is NNN.)

Short answer

Azide ion has a bond order of 3, indicating strong N-N bonds.

Step-by-step solution

Understand the Azide Ion

The azide ion, \( \mathrm{N}_3^- \), consists of three nitrogen atoms in a linear arrangement. Each nitrogen atom has five valence electrons, making a total of fifteen valence electrons for the three atoms. However, as the molecule is a negatively charged ion, there is one additional electron, making the total number of valence electrons sixteen.

Determine the Molecular Orbital Diagram

In molecular orbital (MO) theory, atomic orbitals combine to form molecular orbitals. For \( \mathrm{N}_3^- \), we consider combinations of the 2s and 2p orbitals from each nitrogen atom. The molecular orbitals formed are bonding (\( \sigma \) and \( \pi \)), non-bonding, and antibonding (\( \sigma^* \) and \( \pi^* \)). For azide, the electrons will fill the MOs from lowest to highest energy, following Hund's rule and the Pauli Exclusion Principle.

Fill the Molecular Orbitals

The electrons in the azide ion fill the molecular orbitals as follows:1. The two \( \sigma_{2s} \) bonding orbitals are filled with four electrons (two in each).2. The non-bonding orbitals \( \pi_{2px} \), \( \pi_{2py} \) are filled with four electrons (two in each).3. The \( \pi_{2px}^* \), \( \pi_{2py}^* \) orbitals are filled with four electrons (two in each).4. The \( \sigma_{2pz} \) bonding orbital contains two electrons.5. The \( \sigma_{2pz}^* \) antibonding orbital is also empty, optimizing bonding.

Calculate Bond Order

Bond order is calculated as \((\text{number of electrons in bonding MOs} - \text{number of electrons in antibonding MOs}) / 2\). For azide ion:- Bonding MOs: \( \sigma_{2s} (4) + \pi_{2px} (2) + \pi_{2py} (2) + \sigma_{2pz} (2) = 10 \) electrons- Antibonding MOs: \( \pi_{2px}^* (2) + \pi_{2py}^* (2) = 4 \) electronsBond order = \((10 - 4) / 2 = 3\).

Interpret the Results

The bond order of 3 indicates that nitrogen-nitrogen bonds in the azide ion have a triple-bond character. This high bond order suggests the azide ion is quite stable with strong N-N bonding.

Key concepts

Azide Ion

The azide ion, denoted as \(\text{N}_3^-\), is a molecule that attaches great importance in chemistry due to its intriguing structure and reactivity. It consists of three nitrogen atoms in a straight line, which contributes to its linear symmetry.
Each nitrogen atom has five valence electrons, making a total of fifteen valence electrons from the nitrogen atoms. However, because the azide ion carries a negative charge, this means one extra valence electron is added to the mix, bringing the total to sixteen. These electrons create the complex bonding situation that the azide ion displays.

Bond Order

The concept of bond order in chemistry refers to the number of bonds present between two atoms.
It gives us an insight into the strength and length of a bond – a higher bond order typically indicates a stronger, shorter bond.
To find the bond order for the azide ion using molecular orbital theory, you calculate it using this formula: \[\text{Bond order} = \frac{\text{number of electrons in bonding MOs} - \text{number of electrons in antibonding MOs}}{2}\]For azide ion \(\text{N}_3^-\), the bonding molecular orbitals contain 10 electrons while the antibonding orbitals hold 4 electrons. By applying the formula, the bond order is: \[\frac{10 - 4}{2} = 3\]This tells us that each nitrogen-nitrogen bond in the azide ion has characteristics of a triple bond, showing substantial stability.

Nitrogen-Nitrogen Bonds

In the azide ion \(\text{N}_3^-\), the nitrogen-nitrogen bonds hold a distinctive structure. With a bond order of 3, these bonds resemble the nature of triple bonds commonly found in diatomic nitrogen \(\text{N}_2\).
This suggests the bonds in \(\text{N}_3^-\) are very strong and relatively short, contributing to the overall stability of the ion.
Even though one could visualize the azide ion as having distinct triple bonds between the nitrogen atoms, the molecular orbital theory reveals a more nuanced picture.
According to this theory, the electrons are delocalized over the entire ion. This sharing of electrons happens across all three nitrogen atoms, creating a resonance stabilized structure rather than individual triple bonds. This delocalization enhances stability and is a key factor in the distinct behavior of the azide ion in various chemical reactions.