Problem 24 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Bond order normally gives idea of stability of a molecular species. All the molecules viz. \(\mathrm{H}_{2}, \mathrm{Li}_{2}\) and \(\mathrm{B}_{2}\) have the same bond order yet they are not equally stable. Their stability order is [Main Online April 22, 2013] (a) \(\mathrm{H}_{2}>\mathrm{B}_{2}>\mathrm{Li}_{2}\) (b) \(\mathrm{Li}_{2}>\mathrm{H}_{2}>\mathrm{B}_{2}\) (c) \(\mathrm{Li}_{2}>\mathrm{B}_{2}>\mathrm{H}_{2}\) (d) \(\mathrm{B}_{2}>\mathrm{H}_{2}>\mathrm{Li}_{2}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{H}_2 > \mathrm{B}_2 > \mathrm{Li}_2 \).

Step 1: Determine Bond Order

The bond order gives an idea of the stability of molecules. For each molecular species, the bond order is calculated using the formula: \( \text{Bond Order} = \frac{1}{2}(\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \). Calculate the bond order for \(\mathrm{H}_2\), \(\mathrm{Li}_2\), and \(\mathrm{B}_2\) by using their respective electron configurations in molecular orbitals. For \(\mathrm{H}_2\) (\(\sigma_{1s}^2\)), for \(\mathrm{Li}_2\) (\(\sigma_{1s}^2\sigma_{1s}^{*2}\sigma_{2s}^2\)), and for \(\mathrm{B}_2\) (\(\sigma_{1s}^2\sigma_{1s}^{*2}\sigma_{2s}^2\sigma_{2s}^{*2}\pi_{2p_x}^1\pi_{2p_y}^1\)). All these have a bond order of 1.

Step 2: Assess Contributing Factors to Stability

Although bond order helps determine stability, other factors like bond length, bond energy, and the presence of orbital overlaps contribute to overall molecular stability. In small diatomic molecules, bond energies are crucial. \(\mathrm{H}_2\) with a stronger hydrogen-hydrogen covalent bond is generally more stable compared to the other diatomic molecules.

Step 3: Compare Experimental Stability Data

Empirical data can provide insights into the observed stability of these molecules. While the bond orders are the same, \(\mathrm{H}_2\) is known for its high bond energy making it more stable. \(\mathrm{B}_2\) with a moderately strong bond due to \(\pi\)-bonding interactions comes second, while \(\mathrm{Li}_2\) has weak bond strength making it the least stable of the three.

Step 4: Determine Stability Order

Based on theoretical bond order analysis and empirical evidence, the stability order is \(\mathrm{H}_2 > \mathrm{B}_2 > \mathrm{Li}_2 \). This suggests that option (a) is correct.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory is a sophisticated model used to describe the electronic structure of molecules. Unlike the atomic orbital theory, which limits its focus to single atoms, molecular orbital theory provides a broader perspective by emphasizing how electrons are distributed in molecules.
This distribution is crucial in forming chemical bonds between atoms. These bonds are formed when atomic orbitals from different atoms overlap to form molecular orbitals. There are two main types: bonding and antibonding orbitals.
This overlapping creates several possibilities:

• Bonding Molecular Orbitals (BMO) are lower in energy and stabilize the molecule when occupied by electrons.
• Antibonding Molecular Orbitals (ABMO) are higher in energy and can destabilize the molecule.

To understand a molecule's stability through molecular orbital theory, one uses the concept of bond order, which is calculated based on the number of electrons in these molecular orbitals. A higher bond order generally indicates a more stable molecule. However, as seen in the example of \( ext{H}_2\), \( ext{Li}_2\), and \( ext{B}_2\), having the same bond order does not guarantee equal stability, as other factors also come into play.

Chemical Stability

Chemical stability refers to how likely a molecule is to maintain its structure without reacting or breaking apart under given conditions. While bond order provides an initial quantitative measure of molecular stability, it doesn't tell the whole story.
For instance, molecules with the same bond order might show different real-world stabilities due to additional factors:

• Bond Length: Shorter bonds are often stronger and more stable.
• Bond Energy: Amount of energy required to break a bond, with higher energy indicating greater stability.
• Interaction with Neighboring Molecules: How a molecule interacts in its environment can affect stability.

In the specific examples discussed (\( ext{H}_2\), \( ext{Li}_2\), \( ext{B}_2\)), \( ext{H}_2\) has a particularly high bond energy, which contributes significantly to its higher stability compared to the others. This energy is a direct consequence of the efficient overlap of the \( ext{1s}\) orbitals in hydrogen, forming a strong covalent bond.
This indicates that while molecular orbital theory provides a framework, real-world molecule behavior often requires consideration of various stability-related factors.

Diatomic Molecules

Diatomic molecules are the simplest form of molecules consisting of only two atoms. These species serve as fundamental building blocks in chemical studies and play significant roles in both biological and industrial processes.
Each diatomic molecule can be homonuclear, having atoms of the same element, like \( ext{H}_2\), \( ext{O}_2\), or heteronuclear, having different elements, like \( ext{CO}\) or \( ext{NO}\). Understanding these small molecules provides essential insights into larger molecular systems.
Studying diatomic molecules involves understanding:

• Bonding Characteristics: Types of bonds formed between the atoms.
• Energy Levels and Transitions: Particularly important in spectroscopy.
• Reactivity and Interactions: How these molecules participate in reactions.

In the context of the example molecules \( ext{H}_2\), \( ext{Li}_2\), and \( ext{B}_2\), diatomic molecules are crucial to dissecting factors such as bonding, electronic configuration, and ultimately, their stability. Each of these molecules reflects the diverse possibilities of bonding even among diatomic species with the same bond order, highlighting how rich and varied molecular chemistry can be.