Question

Species having the same bond order are (a) \(\mathrm{N}_{2}\) (b) \(\mathrm{N}_{2}^{+}\) (c) \(\mathrm{N}_{2}^{-}\) (d) \(\mathrm{N}_{2}^{2-}\)

Short answer

\(\mathrm{N}_{2}^{+}\) and \(\mathrm{N}_{2}^{-}\) have the same bond order of 2.5.

Step-by-step solution

Understand Bond Order Formula

Bond order is an indication of the stability of a bond within a molecule. It can be calculated using the formula: \( \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \)

Calculate Bond Order for \(\mathrm{N}_{2}\)

For \(\mathrm{N}_{2}\), the molecular orbital configuration is \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\pi_{2p})^4 (\sigma_{2p})^2\). There are 10 bonding electrons and 4 antibonding electrons. Bond order = \(\frac{10 - 4}{2} = 3\).

Calculate Bond Order for \(\mathrm{N}_{2}^{+}\)

For \(\mathrm{N}_{2}^{+}\), remove one electron from the \(\sigma_{2p}\) bonding orbital. Then, there are 9 bonding electrons and 4 antibonding electrons. Bond order = \(\frac{9 - 4}{2} = 2.5\).

Calculate Bond Order for \(\mathrm{N}_{2}^{-}\)

For \(\mathrm{N}_{2}^{-}\), add one electron to the \(\pi^*_{2p}\) antibonding orbital. Then, there are 10 bonding electrons and 5 antibonding electrons. Bond order = \(\frac{10 - 5}{2} = 2.5\).

Calculate Bond Order for \(\mathrm{N}_{2}^{2-}\)

For \(\mathrm{N}_{2}^{2-}\), add two electrons to the \(\pi^*_{2p}\) antibonding orbitals. Then, there are 10 bonding electrons and 6 antibonding electrons. Bond order = \(\frac{10 - 6}{2} = 2\).

Compare Bond Orders

\(\mathrm{N}_{2}\) has a bond order of 3. \(\mathrm{N}_{2}^{+}\) and \(\mathrm{N}_{2}^{-}\) both have a bond order of 2.5, and \(\mathrm{N}_{2}^{2-}\) has a bond order of 2. Therefore, \(\mathrm{N}_{2}^{+}\) and \(\mathrm{N}_{2}^{-}\) have the same bond order.

Key concepts

Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms. It gives us insight into the strength and stability of a molecule. Understanding bond order is essential for analyzing the molecular structure and predicting the chemical properties of a molecule.

• The formula for calculating bond order is: \[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \]
• A higher bond order usually means stronger and shorter bonds, indicating more stability in a molecule.
• Conversely, a lower bond order suggests weaker, longer bonds and less stability.

When bond order is zero, it typically implies that the molecule is highly unstable and does not exist under normal conditions. In the case of nitrogen-based molecules such as \(\text{N}_{2}\), bond order plays a key role in understanding why \(\text{N}_{2}\) is so common and stable in nature compared to its ions.
The different bond orders for \(\text{N}_{2}\) and its ions help us see how the removal or addition of electrons affects molecular stability.

Stability of Molecules

The stability of a molecule is closely linked to its bond order, and understanding this relationship can help predict and explain why molecules behave in certain ways. Molecules with higher bond orders generally have stronger chemical bonds and are more stable.

• For example, molecular nitrogen \(\text{N}_{2}\) has a bond order of 3, which means it forms a triple bond between the two nitrogen atoms, making it a very stable molecule.
• Ions like \(\text{N}_{2}^{+}\) and \(\text{N}_{2}^{-}\), with bond orders of 2.5, are less stable than \(\text{N}_{2}\). They have undergone changes in their electron configuration, specifically through the removal or addition of electrons, weakening their overall bond strength.
• \(\text{N}_{2}^{2-}\) has an even lower bond order of 2, indicating even lesser stability due to the increase in antibonding electrons which weakens the bonds further.

The stability of these molecules or ions affects their chemical reactivity. More stable molecules react less readily under normal conditions, while less stable ones can be more reactive. This is why nitrogen gas \(\text{N}_{2}\) is extremely inert, whereas its ions are more reactive, forming different compounds.

Electron Configuration

Electron configuration is a schematic arrangement of electrons in the orbitals of atoms or molecules. It provides an understanding of the distribution of electrons which contributes to the chemical properties of a molecule.

• Each molecule, like \(\text{N}_{2}\), has a specific electron configuration that is described using molecular orbitals (MO).
• Molecular orbitals are formed by the overlapping of atomic orbitals, and they come in bonding and antibonding types.
• Bonding orbitals add stability to a molecule, while antibonding orbitals reduce stability when filled.

In \(\text{N}_{2}\), you would write the configuration as \((\sigma_{1s})^2 (\sigma^*_{1s})^2 (\sigma_{2s})^2 (\sigma^*_{2s})^2 (\pi_{2p})^4 (\sigma_{2p})^2\), indicating ten bonding and four antibonding electrons.
When you move to ions like \(\text{N}_{2}^{+}\) or \(\text{N}_{2}^{-}\), the electron configuration changes as electrons are added or removed, impacting their bond order and stability. Understanding these changes helps predict how the molecule or ion might interact in a chemical reaction.