Problem 11 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

According to molecular orbital theory, which of the following will not be a viable molecule? [Main 2018] (a) \(\mathrm{He}_{2}^{2+}\) (b) \(\mathrm{He}_{2}^{+}\) (c) \(\mathrm{H}_{2}^{-}\) (d) \(\mathrm{H}_{2}^{2-}\)

Step-by-Step Solution

Answer

The nonviable molecule is \(\mathrm{H}_{2}^{2-}\) because it has a bond order of 0.

Step 1: Understanding Molecular Orbital Theory

Molecular Orbital Theory explains that electrons in molecules are not assigned to individual atoms but are found in molecular orbitals which are the result of the combination of atomic orbitals. Electrons fill these molecular orbitals in a similar way to atomic orbitals, following the Aufbau principle, the Pauli-exclusion principle, and Hund's rule.

Step 2: Calculate Bond Order

The bond order of a molecule helps determine its stability. It is calculated using the formula: \( \text{Bond Order} = \frac{(\text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals})}{2} \). A positive bond order indicates a stable molecule, while a bond order of zero or negative indicates instability and that the molecule does not exist.

Step 3: Calculate Bond Order for Each Option

1. For \(\mathrm{He}_{2}^{2+}\): Electrons = 2, Bonding = 2, Antibonding = 0, Bond Order = \(\frac{2-0}{2} = 1\).2. For \(\mathrm{He}_{2}^{+}\): Electrons = 3, Bonding = 2, Antibonding = 1, Bond Order = \(\frac{2-1}{2} = \frac{1}{2}\).3. For \(\mathrm{H}_{2}^{-}\): Electrons = 3, Bonding = 2, Antibonding = 1, Bond Order = \(\frac{2-1}{2} = \frac{1}{2}\).4. For \(\mathrm{H}_{2}^{2-}\): Electrons = 4, Bonding = 2, Antibonding = 2, Bond Order = \(\frac{2-2}{2} = 0\).

Step 4: Determine Viability of Molecules

A viable molecule must have a positive bond order. - \(\mathrm{He}_{2}^{2+}\) has a bond order of 1, which is positive, so it is viable.- \(\mathrm{He}_{2}^{+}\) and \(\mathrm{H}_{2}^{-}\) each have a bond order of \(\frac{1}{2}\), which is positive, thus they are viable.- \(\mathrm{H}_{2}^{2-}\) has a bond order of 0, indicating it is not viable as a stable molecule doesn't form.

Key Concepts

Bond Order

Bond order is a crucial concept in molecular chemistry, particularly within the framework of Molecular Orbital Theory. It helps chemists determine the stability of a molecule. The bond order is calculated using the formula: \( \text{Bond Order} = \frac{( \text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals} )}{2} \). This formula tells us the net number of bonding interactions in the molecule's structure. This is important because:

• A positive bond order indicates that a molecule is stable and can exist under normal conditions.
• A bond order of zero or less suggests that the molecule is unstable and cannot form as a stable entity.

Let's consider an example to understand this better. For the molecule \(\mathrm{H}_{2}^{2-}\), the bond order calculation gives us a value of zero. This indicates instability, meaning \(\mathrm{H}_{2}^{2-}\) cannot exist as a stable molecule. Thus, understanding bond order helps predict molecular stability and chemical reactivity.

Electron Configuration

Electron configuration in the context of molecular orbitals defines how electrons are distributed within a molecule. Electrons in a molecule fill molecular orbitals, which are formed from the overlap of atomic orbitals. This process is guided by:

• The Aufbau principle: electrons fill the lowest energy orbitals first.
• Pauli-exclusion principle: an orbital can hold a maximum of two electrons with opposite spins.
• Hund's rule: electrons occupy orbitals singly before pairing up.

In molecular systems, electron configuration influences multiple properties like stability and magnetism. If we look at \(\mathrm{He}_{2}^{+}\), it has three electrons: two fill the bonding orbital and one goes into the antibonding orbital. This uneven distribution results in a half bond order, indicating some level of stability compared to a zero bond order, but less stability than a full bond.

Molecular Stability

Molecular stability is paramount when predicting whether a given molecule can exist. This stability is closely tied to the molecule’s bond order, derived from its electron configuration within molecular orbitals. Molecules with a positive bond order, such as \(\mathrm{He}_{2}^{+}\) with a bond order of \(\frac{1}{2}\), are generally considered stable enough to form, though possibly existing as reactive intermediates or transient species.In contrast, \(\mathrm{H}_{2}^{2-}\) demonstrates a bond order of zero, leading us to conclude it lacks the sufficient stability to exist under normal conditions. This is because the electrons in bonding and antibonding orbitals cancel each other out completely, negating the forces required to maintain a stable bond. Thus, molecular stability is a direct result of these principles, informing chemists about the viability and reactive potential of molecules in various chemical processes.