Problem 195 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

(b) XeF₂ and CO₂ have identical linear shapes.

Step 1: Identify the Shape of Each Molecule

First, determine the molecular geometry of each given molecule using VSEPR (Valence Shell Electron Pair Repulsion) theory. This will allow us to check which molecules have the same shape: - **PF₅**: Has trigonal bipyramidal geometry. - **IF**: This is incorrect as a solitary IF molecule (iodine monofluoride) doesn't have a shape that matches the others in pairs. - **XeF₂**: Has linear geometry. - **CO₂**: Also has linear geometry. - **CF₄**: Has tetrahedral geometry. - **SF**: Missing subscripts make it hard to determine shape; assuming sulfur tetrafluoride (SF₄), it has seesaw geometry. - **BF₃**: Has trigonal planar geometry. - **PCl₃**: Likely the intended molecule, which has a trigonal pyramidal geometry.

Step 2: Match Similar Shapes

Compare the shapes identified in Step 1 to find the pair with identical shapes: - **PF₅** (trigonal bipyramidal) vs **IF** does not match. - **XeF₂** (linear) vs **CO₂** (linear) matches. - **CF₄** (tetrahedral) vs **SF₄** (assumed) does not match. - **BF₃** (trigonal planar) vs **PCl₃** (trigonal pyramidal) does not match.

Step 3: Select the Correct Pair

Based on the geometry comparison: - The pair **XeF₂** and **CO₂** both have a linear shape. Therefore, they are the pair of species having identical shapes for their molecules. This corresponds to option (b).

Key Concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a key concept for predicting the geometry of molecules. This theory is based on the idea that electron pairs surrounding an atom will repel each other. This repulsion causes them to arrange themselves as far apart as possible in three-dimensional space. As a result, VSEPR theory helps predict the shape of molecules by considering both bonded atoms and lone pairs of electrons.

• Electron pairs can be bonding pairs or lone pairs.
• Bonding pairs are shared between atoms, forming chemical bonds.
• Lone pairs are non-bonding and remain with a single atom.

In VSEPR theory, the repulsion between lone pairs is stronger than that between bonded pairs. This understanding allows chemists to predict not just the bond angles but also the overall shape of the molecule.

Trigonal Bipyramidal

Trigonal bipyramidal geometry is one of the common shapes predicted by VSEPR theory. It arises when a central atom is surrounded by five electron pairs. These can be either bonding pairs or a combination of bonding and lone pairs. A molecule like phosphorus pentafluoride (1PF_{5}1) is a classic example. It possesses five bonding pairs around the phosphorus, creating this distinct geometry. You can think of it as a combination of a planar triangular base with a pair of atoms above and below the center.

• Three atoms form the plane, termed equatorial, with bond angles of 120 degrees.
• Two additional atoms are positioned axially, forming angles of 90 degrees with the plane.

This shape is particularly efficient for accommodating five pairs, balancing the repulsive interactions between them.

Linear Geometry

Linear geometry is the simplest form of molecular shape, characterized by three atoms in a straight line. VSEPR theory predicts this shape for molecules where the central atom is surrounded by two regions of electron density. Examples like xenon difluoride (1XeF_{2}1) and carbon dioxide (1CO_{2}1) illustrate linear geometry. Here, both molecules have only bonding pairs arranged 180 degrees apart.

• There are no lone pairs affecting the geometry.
• The bond angle is simply 180 degrees.

Linear geometry is particularly common in diatomic molecules or those with multiple central atoms having similar arrangements.

Trigonal Planar

Trigonal planar geometry is found in molecules where a central atom is surrounded by three atoms or groups in the same plane. An example is boron trifluoride (1BF_{3}1), where the boron atom is connected to three fluorine atoms forming a planar triangular shape. The lack of lone pairs on the central atom enables the three bonded pairs to spread out at equal angles.

• The bond angles in a trigonal planar geometry are 120 degrees.
• Presence of equal angles shows that it is perfectly planar and symmetrical.

This geometry often appears in main group chemistry, especially with atoms possessing three bonding pairs without lone pairs.