Problem 146 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

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

Step 1: Recall Bond Order Formula

Bond order is determined using the formula: \[ \text{Bond order} = \frac{1}{2} (\text{number of bonding electrons} - \text{number of antibonding electrons}) \] Bond order gives an indication of the stability of a bond, with higher bond orders indicating stronger bonds.

Step 2: Calculate Bond Order for N2

For \(\mathrm{N}_{2}\), the molecular orbital electron configuration is \(\sigma_{1s}^{2} \sigma^{*}_{1s}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}^{2} \pi_{2p_x}^{2} = \pi_{2p_y}^{2} = \sigma_{2p_z}^{2}\).\(\mathrm{N}_{2}\) has 10 bonding and 4 antibonding electrons.\[ \text{Bond Order for } \mathrm{N}_2 = \frac{10 - 4}{2} = 3 \]

Step 3: Calculate Bond Order for N2+

\(\mathrm{N}_{2}^{+}\) means one electron is removed. The MO configuration becomes \(\sigma_{1s}^{2} \sigma^{*}_{1s}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}^{2} \pi_{2p_x}^{2} \pi_{2p_y}^{1} \sigma_{2p_z}^{2}\). It has 9 bonding and 4 antibonding electrons.\[ \text{Bond Order for } \mathrm{N}_{2}^{+} = \frac{9 - 4}{2} = 2.5 \]

Step 4: Calculate Bond Order for N2-

\(\mathrm{N}_{2}^{-}\) means one electron is added. The MO configuration becomes \(\sigma_{1s}^{2} \sigma^{*}_{1s}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}^{2} \pi_{2p_x}^{2} \pi_{2p_y}^{2} \sigma_{2p_z}^{2} \pi_{2p_x}^{1}\). It has 10 bonding and 5 antibonding electrons.\[ \text{Bond Order for } \mathrm{N}_{2}^{-} = \frac{10 - 5}{2} = 2.5 \]

Step 5: Calculate Bond Order for N22-

\(\mathrm{N}_{2}^{2-}\) means two electrons are added. The MO configuration is \(\sigma_{1s}^{2} \sigma^{*}_{1s}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}^{2} \pi_{2p_x}^{2} \pi_{2p_y}^{2} \sigma_{2p_z}^{2} \pi_{2p_x}^{2} \pi_{2p_y}^{1}\). It has 10 bonding and 6 antibonding electrons.\[ \text{Bond Order for } \mathrm{N}_{2}^{2-} = \frac{10 - 6}{2} = 2 \]

Step 6: Compare Bond Orders

The calculated bond orders are: \(\mathrm{N}_{2} = 3\), \(\mathrm{N}_{2}^{+} = 2.5\), \(\mathrm{N}_{2}^{-} = 2.5\), \(\mathrm{N}_{2}^{2-} = 2\). \(\mathrm{N}_{2}^{+}\) and \(\mathrm{N}_{2}^{-}\) have the same bond order of 2.5. They are the species with the same bond order.

Key Concepts

Molecular Orbital Theory

Molecular orbital theory is a method used to describe the electronic structure of molecules. It expands upon atomic orbitals by creating molecular orbitals that encompass all of a molecule's atoms, hence providing a more holistic view of electronic behavior. In molecular orbital theory, electrons are not associated with individual atoms but are considered to be spread across the molecule in molecular orbitals.

Key elements of this theory include:

• Molecular Orbitals (MOs): These are regions in a molecule where electrons are most likely to be found. MOs are created by the linear combination of atomic orbitals.
• Molecular Orbital Configuration: This is a symbolic form showing the arrangement of electrons in molecular orbitals, similar to electron configurations in atomic chemistry.
• Bond Order: Derived from the molecular orbital configuration, the bond order provides insight into the strength and stability of bonds within the molecule.

Understanding molecular orbital theory allows chemists to predict and explain the bonding, shape, and magnetic properties of molecules.

Bonding and Antibonding Electrons

In molecular orbital theory, electrons can fill different types of molecular orbitals, categorized mainly as bonding or antibonding. These terms help dictate the overall energy and stability of a molecule.

Bonding Electrons

• Bonding Orbitals: These result from the constructive interference of atomic orbitals and have lower energy than the original atomic orbitals.
• Effect on Stability: Electrons in bonding orbitals increase a molecule's stability because they favor atomic overlap, which reduces overall energy.

Antibonding Electrons

• Antibonding Orbitals: These are formed by destructive interference between atomic orbitals. They have higher energy than the atomic orbitals from which they derive.
• Effect on Stability: Electrons in antibonding orbitals reduce a molecule's stability as they counteract the molecule’s binding forces, leading to higher potential energy.

The interaction between bonding and antibonding electrons decides if a molecule will form or remain stable. A higher number of bonding electrons compared to antibonding ones generally results in a more stable molecule.

Stability of Chemical Bonds

Chemical bond stability is crucial for determining a molecule's reactivity and durability. The bond order, calculated using molecular orbital theory, is one such measurement of stability. It is determined by the difference between the number of bonding and antibonding electrons.

Here’s what you need to know:

• Higher Bond Order: Indicates stronger bonds and greater stability. For example, \(N_2\) has a bond order of 3, suggesting very stable bonds.
• Lower Bond Order: Implies weaker bonds with less stability. Molecules like \(N_2^{2-}\) with a bond order of 2 are less stable compared to \(N_2\).
• Zero or Negative Bond Order: Suggests that a stable bond is unlikely or nonexistent.

Thus, bond order serves as a valuable tool in chemistry for predicting the stability, strength, and length of bonds within a molecule.