Molecular Structure And Chemical Bonding

Spin-Only Magnetic Moment of B₂ Molecule

To find the spin-only magnetic moment of the molecule, we begin by understanding its molecular orbital (MO) electron configuration. Boron has an atomic number of 5, and therefore will have 10 electrons.

Molecular Orbital Theory tells us that the electrons will fill the molecular orbitals as follows:

• , , , , and (since both degenerate orbitals will be filled first before the ).

The orbitals are of primary interest, possessing two electrons with parallel spins due to Hund's rule.

Formula for Spin-Only Magnetic Moment:

The spin-only magnetic moment is given by:

Where is the number of unpaired electrons.

Step 1: Number of Unpaired Electrons

Here, the number of unpaired electrons (since the orbitals each contain one unpaired electron).

Step 2: Calculate the Magnetic Moment

Substitute into the formula:

Step 3: Final Answer

Upon rounding, .

Verification:

The calculated value of falls within the given range of to , confirming the correctness of our solution.

To determine which molecules follow the condition , where , , and are the principal moments of inertia, we need to understand the geometry and symmetry of each molecule.

The principal moments of inertia are representations of how mass is distributed with respect to rotation about three orthogonal axes through the center of mass of the molecule. The condition typically corresponds to a linear molecule, since for a linear molecule, rotation about the axis along the molecule (linear axis) will have a very small moment of inertia , and the two perpendicular axes will have the same moment of inertia .

1. **HCN (Hydrogen cyanide):**
   • HCN is a linear molecule with the structure H-C≡N.
   • This linear geometry makes (along the internuclear axis) negligibly small compared to and , which are equal. Hence, HCN follows .
2. **CH₃Cl (Methyl chloride):**
   • CH₃Cl has a pyramidal (approximate tetrahedral) geometry around the central carbon atom.
   • For such molecules, the principal moments of inertia do not satisfy , as the rotational symmetry is not linear.
3. **CH₃C≡CH (Propyne):**
   • CH₃C≡CH is also known as methylacetylene. It has a linear geometry along the C≡C axis.
   • Thus, it follows the condition due to its linear structure.
4. **C₆H₆ (Benzene):**
   • Benzene is a planar molecule with a hexagonal shape.
   • It is not linear and has a more complex set of moments of inertia, generally not satisfying .

Based on the analysis above, the molecules that follow the given condition are:

• HCN
• CH₃C≡CH

Therefore, the correct answers are HCN and CH₃C≡CH.

B₂ has two unpaired electrons in its molecular orbital diagram, which makes it paramagnetic.

C₂, on the other hand, has no unpaired electrons in its molecular orbital diagram, meaning it is diamagnetic.

Thus, the correct answer is (A)

Isosteric compounds are those that have the same number of atoms and a similar molecular structure, but different elements. H₃N·BH₃ and C₂H₆ are isosteric because they both contain six atoms, including the same number of hydrogen and non-hydrogen atoms.

Thus, the correct answer is (B).

The shape of the thiocyanate ion (SCN⁻) is linear. This is because the ion consists of two atoms connected by a triple bond, and there are no lone pairs of electrons on either atom. The central carbon atom in SCN⁻ is sp hybridized, resulting in a linear geometry.

Thus, the correct answer is (A) linear.