Problem 69 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following has the highest bond order? (a) \(\mathrm{N}_{2}\) (b) \(\mathrm{O}_{2}\) (c) \(\mathrm{He}_{2}\) (d) \(\mathrm{H}_{2}\)

Step-by-Step Solution

Answer

\(\mathrm{N}_2\) has the highest bond order of 3.

Step 1: Recall Bond Order Formula

The bond order of a molecule can be calculated using the formula: \[ \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} \]. Bond order indicates the stability and strength of a bond; higher bond orders imply more stable and stronger bonds.

Step 2: Determine Electron Configuration of N₂

For \(\mathrm{N}_2\), the electron configuration in its molecular orbital is: \([\sigma_{1s}]^2 [\sigma^*_{1s}]^2 [\sigma_{2s}]^2 [\sigma^*_{2s}]^2 [\pi_{2p}]^4 [\sigma_{2p}]^2\). Thus, it has a total of 10 bonding electrons and 4 antibonding electrons.

Step 3: Bond Order Calculation for N₂

Using the bond order formula: \[ \text{Bond Order of } \mathrm{N}_2 = \frac{10 - 4}{2} = 3 \]. The bond order for \(\mathrm{N}_2\) is 3, indicating a very stable triple bond.

Step 4: Determine Electron Configuration of O₂

\(\mathrm{O}_2\) has the molecular orbital configuration of \([\sigma_{1s}]^2 [\sigma^*_{1s}]^2 [\sigma_{2s}]^2 [\sigma^*_{2s}]^2 [\sigma_{2p}]^2 [\pi_{2p}]^4 [\pi^*_{2p}]^2\). It includes 10 bonding electrons and 6 antibonding electrons.

Step 5: Bond Order Calculation for O₂

For \(\mathrm{O}_2\), the bond order is \[ \frac{10 - 6}{2} = 2 \]. This corresponds to a double bond.

Step 6: Determine Electron Configuration of He₂

\(\mathrm{He}_2\) would hypothetically have the electron configuration \([\sigma_{1s}]^2 [\sigma^*_{1s}]^2\) if it existed. This implies 2 bonding electrons and 2 antibonding electrons.

Step 7: Bond Order Calculation for He₂

\(\mathrm{He}_2\) has a bond order of \[ \frac{2 - 2}{2} = 0 \], indicating that it does not form a stable molecule under normal conditions.

Step 8: Determine Electron Configuration of H₂

For \(\mathrm{H}_2\), the configuration is \([\sigma_{1s}]^2\) with 2 bonding electrons and no antibonding electrons.

Step 9: Bond Order Calculation for H₂

The bond order for \(\mathrm{H}_2\) is \[ \frac{2 - 0}{2} = 1 \], indicating a single bond.

Step 10: Compare Bond Orders

The bond orders calculated are: \(\mathrm{N}_2\) has 3, \(\mathrm{O}_2\) has 2, \(\mathrm{He}_2\) has 0, and \(\mathrm{H}_2\) has 1. Therefore, \(\mathrm{N}_2\) has the highest bond order.

Key Concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory is a fundamental concept in chemistry that helps us understand how electrons are distributed within a molecule. According to this theory, instead of electrons being localized between two atoms (as seen in valence bond theory), they occupy molecular orbitals which belong to the entire molecule.

Molecular orbitals are formed by the linear combination of atomic orbitals from the bonded atoms. These molecular orbitals are categorized into bonding and antibonding orbitals depending on their energy levels.

• Bonding Orbitals: Lower energy orbitals where electrons contribute to bonding and stability of the molecule.
• Antibonding Orbitals: Higher energy orbitals that, when occupied by electrons, reduce the bond strength and stability.

MO Theory helps in predicting and explaining various molecular properties, such as bond order, magnetism, and stability. This theory is crucial for calculating the bond order, which shows the strength and stability of a bond based on the number of electrons in bonding and antibonding orbitals.

Electron Configuration

Electron configuration in atoms is the arrangement of electrons in various orbitals and subshells. Molecular Orbital Theory extends this concept to molecules by defining the electron configuration in molecular orbitals.

In MO theory, the electron configuration of molecules is written by filling electrons into molecular orbitals in order of increasing energy.

• Hund's Rule: Applies to filling degenerate orbitals such as the \([\pi_{2p}]\) orbitals, ensuring that each orbital gets one electron before pairing starts.
• Pauli Exclusion Principle: No two electrons can have identical quantum numbers; hence, molecular orbitals are filled with electrons of opposite spins.
• Aufbau Principle: Electrons fill from the lowest available energy level upward. For instance, in \( \text{O}_{2} \), electrons fill \([\sigma_{1s}]^2 [\sigma^*_{1s}]^2 [\sigma_{2s}]^2 [\sigma^*_{2s}]^2 [\sigma_{2p}]^2 [\pi_{2p}]^4 [\pi^*_{2p}]^2\).

Understanding molecular electron configuration is vital for determining bond order and predicting the magnetic properties of molecules. It provides insight into how electrons contribute to the formation and stability of chemical bonds.

Stability of Molecules

The stability of a molecule is largely determined by its bond order, which can be calculated using Molecular Orbital Theory. Bond order is a fundamental indicator of the number of bonds between a pair of atoms and thus directly relates to molecule stability.

• A higher bond order typically means more bonding electrons relative to antibonding electrons, resulting in a stronger and more stable molecule.
• Molecules with a bond order of 0 (like \( \mathrm{He}_{2} \)) are not stable under normal conditions because the number of bonding and antibonding electrons are equal, effectively canceling each other out.
• Molecule's stability is also influenced by other factors, such as molecular shape and electron repulsion, but bond order offers a primary measure.

For instance, \( \mathrm{N}_{2} \) has a bond order of 3, indicating a triple bond, which contributes to its high stability and low reactivity. Understanding bond order helps predict reaction rates and the likelihood of a molecule participating in chemical reactions.