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Question #44270

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The Question

The atomic orbitals of second-period elements follow the $(n+l)$ rule, but during the formation of homonuclear diatomic molecules ( $\ce{B2}$ to $\ce{N2}$ ), the small energy gap between $2s$ and $2p$ orbitals leads to $s-p$ mixing. This alters the standard Aufbau progression of molecular orbitals. Consider a hypothetical universe where $s-p$ mixing is strictly forbidden. Which of the following correctly describes the transition of properties from the actual universe to this hypothetical universe for $\ce{B2}$ and $\ce{C2}$ at $298\text{ K}$ ?

Options

A.
$\ce{B2}$ changes from paramagnetic to diamagnetic; $\ce{C2}$ changes from diamagnetic to paramagnetic. The bond orders remain $1$ and $2$ , respectively, but the nature of bonds in $\ce{C2}$ changes from two $\pi$ -bonds to one $\sigma$ -bond and two half- $\pi$ -bonds.
B.
$\ce{B2}$ changes from diamagnetic to paramagnetic; $\ce{C2}$ remains diamagnetic. The bond order of $\ce{B2}$ increases to $1.5$ , while $\ce{C2}$ retains a bond order of $2$ consisting of one $\sigma$ -bond and one $\pi$ -bond.
C.
Both $\ce{B2}$ and $\ce{C2}$ become diamagnetic. The bond order of $\ce{B2}$ remains $1$ (pure $\sigma$ -bond), while the bond order of $\ce{C2}$ increases to $3$ due to the stabilization of the $\sigma_{2p_z}$ orbital.
D.
$\ce{B2}$ remains paramagnetic; $\ce{C2}$ changes from diamagnetic to paramagnetic. The bond order of $\ce{B2}$ decreases to $0.5$ , and the HOMO of $\ce{C2}$ shifts from $\pi_{2p_{x,y}}$ to $\sigma_{2p_z}$ .

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

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Concepts Behind This Question

Energy of Subshells (n+l rule)|Molecular Orbital Mixing|Bond Energy vs Bond Length

Why This Question Is Tricky

Common Mistakes

This question tests the fundamental origin of anomalous molecular orbital diagrams in early second-period elements.

Students often memorize that B2 is paramagnetic and C2 is diamagnetic without understanding that s-p mixing is the sole cause.

By asking for the properties in a hypothetical universe without s-p mixing, the student must reconstruct the MO diagram using the standard Aufbau principle (where sigma_2pz is lower than pi_2px/y due to greater axial overlap).

This reveals the hidden variable: without s-p mixing, B2 would be diamagnetic and C2 would be paramagnetic, perfectly inverting their actual magnetic behaviors while preserving their overall bond orders.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Energy of Subshells (n+l rule)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free