Which of the following molecules, in pure from, is (are) unstable at room temperature ?

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Which of the following molecules, in pure from, is (are) unstable at room temperature ?

Engineering

Chemistry

Standard Parabola

Molecular Orbital Theory or MOT

Question

Which of the following molecules, in pure from, is (are) unstable at room temperature ?

A

B

C

D

This question tests your understanding of molecular stability based on electronic configuration and bonding. The molecules shown are:

O₂ (Oxygen)
N₂ (Nitrogen)
F₂ (Fluorine)
He₂ (Helium dimer)

Step 1: Understand Molecular Stability
A molecule is stable if its bond order is greater than zero. Bond order indicates the number of chemical bonds between two atoms. A positive bond order means the molecule can exist; a bond order of zero or negative means it is unstable.

Step 2: Calculate Bond Order Using Molecular Orbital Theory
Bond order is calculated as: $Bond Order = \frac{(Number of bonding electrons - Number of antibonding electrons)}{2}$

Step 3: Analyze Each Molecule

O₂: Total electrons = 16. Molecular orbital configuration: $σ_{1s}^{2} σ_{1s}^{*}^{2} σ_{2s}^{2} σ_{2s}^{*}^{2} σ_{2p}^{2} π_{2p}^{4} π_{2p}^{*}^{2}$ Bonding electrons = 10, Antibonding electrons = 6. Bond order = (10-6)/2 = 2. Stable.
N₂: Total electrons = 14. Configuration: $σ_{1s}^{2} σ_{1s}^{*}^{2} σ_{2s}^{2} σ_{2s}^{*}^{2} π_{2p}^{4} σ_{2p}^{2}$ Bonding electrons = 10, Antibonding electrons = 4. Bond order = (10-4)/2 = 3. Stable.
F₂: Total electrons = 18. Configuration: $σ_{1s}^{2} σ_{1s}^{*}^{2} σ_{2s}^{2} σ_{2s}^{*}^{2} σ_{2p}^{2} π_{2p}^{4} π_{2p}^{*}^{4}$ Bonding electrons = 10, Antibonding electrons = 8. Bond order = (10-8)/2 = 1. Stable (though highly reactive).
He₂: Total electrons = 4. Configuration: $σ_{1s}^{2} σ_{1s}^{*}^{2}$ Bonding electrons = 2, Antibonding electrons = 2. Bond order = (2-2)/2 = 0. Unstable.

Final Answer: Only He₂ is unstable at room temperature due to its zero bond order.

Related Topics & Formulae

Molecular Orbital Theory (MOT): Explains how atomic orbitals combine to form molecular orbitals, which are bonding, antibonding, or nonbonding. Bond order is a key concept derived from MOT to predict stability.

Bond Order Formula: $Bond Order = \frac{N_{b} - N_{a}}{2}$ , where N_b is number of bonding electrons and N_a is number of antibonding electrons.

Stability Rule: A positive bond order (>0) indicates a stable molecule; bond order = 0 means no bond exists, and the molecule is unstable.