Question

How many of the following molecules are linear with no lone pairs of electrons on the central atom?
\[ \text{BeCl}_2,\ \text{O}_3,\ \text{SCl}_2,\ \text{XeF}_2,\ \text{SnCl}_2,\ \text{PbCl}_2,\ \text{HgCl}_2 \]

• A. \(2\)
• B. \(3\)
• C. \(4\)
• D. \(1\)

Hint:

Linear molecules are not always free from lone pairs. For example: \[ \text{XeF}_2 \] is linear but contains three lone pairs on xenon.

Answer 1

The Correct Option is A

Concept: The shape of molecules is determined using VSEPR theory. A molecule will be:

• Linear if bond pairs are arranged at \(180^\circ\)

• Free from lone pairs on central atom if all valence electrons participate in bonding
We examine each molecule carefully.

Step 1: Analyse \(\text{BeCl}_2\). Central atom: Be Be forms two bonds and has no lone pair. Geometry: Linear Hence: \[ \text{BeCl}_2 \text{ satisfies the condition} \]

Step 2: Analyse \(\text{O}_3\). Central oxygen contains one lone pair. Shape: Bent Hence it does not satisfy the condition.

Step 3: Analyse \(\text{SCl}_2\). Sulfur has two lone pairs. Shape: Bent Hence it does not satisfy the condition.

Step 4: Analyse \(\text{XeF}_2\). Xe has three lone pairs. Although shape is linear, lone pairs are present. Hence it does not satisfy the condition.

Step 5: Analyse \(\text{SnCl}_2\) and \(\text{PbCl}_2\). Both contain one lone pair on central atom. Shape: Bent Thus they do not satisfy the condition.

Step 6: Analyse \(\text{HgCl}_2\). Central atom Hg forms two bonds and has no lone pair. Shape: Linear Hence: \[ \text{HgCl}_2 \text{ satisfies the condition} \]

Step 7: Count the valid molecules. The valid molecules are: \[ \text{BeCl}_2,\ \text{HgCl}_2 \] Total number: \[ \boxed{2} \] Hence, the correct option is: \[ \boxed{(A)} \]