Problem 190 - A Complete Resource Book in Chemistry for JEE Main

Question

The pair of species having identical shapes for molecules of both species is (a) \(\mathrm{CF}_{4}, \mathrm{SF}_{4}\) (b) \(\mathrm{XeF}_{2}, \mathrm{CO}_{2}\) (c) \(\mathrm{BF}_{3}, \mathrm{PCl}_{3}\) (d) \(\mathrm{PF}_{5}, \mathrm{IF}_{5}\)

Step-by-Step Solution

Answer

The answer is (b) \( \mathrm{XeF}_{2}, \mathrm{CO}_{2} \).

Step 1: Understanding Molecular Geometry

Determine the molecular shapes of the species listed in each pair. Molecular shape depends on the number of bonding pairs and lone pairs of electrons around the central atom.

Step 2: Analyzing Pair (a)

For \( \mathrm{CF}_{4} \), with 4 bonding pairs and no lone pairs, the shape is tetrahedral. For \( \mathrm{SF}_{4} \), with 4 bonding pairs and one lone pair, the shape is seesaw.

Step 3: Analyzing Pair (b)

For \( \mathrm{XeF}_{2} \), with 2 bonding pairs and 3 lone pairs, the shape is linear. For \( \mathrm{CO}_{2} \), with 2 bonding pairs and no lone pairs, the shape is also linear.

Step 4: Analyzing Pair (c)

For \( \mathrm{BF}_{3} \), with 3 bonding pairs and no lone pairs, the shape is trigonal planar. For \( \mathrm{PCl}_{3} \), with 3 bonding pairs and one lone pair, the shape is trigonal pyramidal.

Step 5: Analyzing Pair (d)

For \( \mathrm{PF}_{5} \), with 5 bonding pairs and no lone pairs, the shape is trigonal bipyramidal. For \( \mathrm{IF}_{5} \), with 5 bonding pairs and one lone pair, the shape is square pyramidal.

Step 6: Identifying the Correct Answer

Based on the analysis, both \( \mathrm{XeF}_{2} \) and \( \mathrm{CO}_{2} \) have linear shapes. Therefore, pair (b) has identical shapes for both species.

Key Concepts

VSEPR Theory

The VSEPR (Valence Shell Electron Pair Repulsion) theory is a model used to determine the geometry of molecules. According to this theory, the shape of a molecule is determined by the repulsion between electron pairs present in the valence shell of the central atom. It predicts that electron pairs—both bonding pairs (shared between two atoms) and lone pairs (non-bonding) —will arrange themselves as far apart as possible around the central atom to minimize repulsion.

• Bonding pairs : These are pairs of electrons shared between two atoms that form a chemical bond.
• Lone pairs: These are pairs of electrons that do not participate in bonding and remain on the central atom.

The fundamental idea is that different numbers of bonding and lone pairs lead to different molecular shapes. Therefore, by considering these factors, the VSEPR theory helps in predicting the 3D structure of molecules.

Linear Molecular Shape

A linear molecular shape occurs when atoms are aligned in a straight line. This often happens when the central atom has two bonding pairs and no lone pairs, as seen in the molecule CO₂. Here, the carbon atom forms double bonds with each oxygen atom, and both bonds align opposite each other at 180°.
In other cases like XeF₂, the central xenon atom has two bonding pairs and three lone pairs. Despite the presence of lone pairs, the linear shape is maintained as these pairs situate themselves around the xenon atom in a way that places the fluorine atoms opposite each other, minimizing repulsion.
This shape is characteristic of molecules where the steric number (total number of bonding pairs and lone pairs) suggests a distribution that aligns bonding pairs oppositely.

Bonding Pairs and Lone Pairs

Bonding pairs and lone pairs play a crucial role in determining molecular geometry by influencing the arrangement of atoms around the central atom.

• Bonding pairs: These are responsible for forming the bonds between atoms in a molecule. They are typically arranged to be as far from each other as possible to reduce repulsion, with linear and tetrahedral shapes being common examples.
• Lone pairs: Although they do not bond atoms to one another, lone pairs can have a significant impact. They occupy more space than bonding pairs, pushing the bonding pairs closer together which can alter the ideal geometry into a different shape, like turning a trigonal planar shape into a trigonal pyramidal one.
• Influence on shape: The number of each type of pair will determine the shape and resulting angles between bonds. For example, in SF₄, the presence of a lone pair distorts the arrangement to a 'seesaw' shape due to different repulsive forces.

Understanding these forces is key to predicting and rationalizing molecular shapes as predicted by the VSEPR theory.