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 pair with identical shapes is (b) \(\mathrm{XeF}_2, \mathrm{CO}_2\).

Step 1: Understanding Molecular Geometry

Molecular geometry is determined by the arrangement of electron pairs around the central atom. This is described by the VSEPR (Valence Shell Electron Pair Repulsion) theory. For a molecule to have a specific shape, this depends on the number of bonds and lone pairs around the central atom.

Step 2: Analyze Each Pair of Species

Examine the shapes:- \(\mathrm{CF}_4\): Tetrahedral, as there are four bonding pairs and no lone pairs around carbon.\(\mathrm{SF}_4\): Seesaw shape due to four bonding pairs and one lone pair.- \(\mathrm{XeF}_2\): Linear, with two bonding pairs and three lone pairs on xenon.\(\mathrm{CO}_2\): Linear, with double bonds on carbon and no lone pairs.- \(\mathrm{BF}_3\): Trigonal planar, with three bonding pairs and no lone pairs.\(\mathrm{PCl}_3\): Trigonal pyramidal, as there are three bonding pairs and one lone pair on phosphorus.- \(\mathrm{PF}_5\): Trigonal bipyramidal, with five bonding pairs and no lone pairs.\(\mathrm{IF}_5\): Square pyramidal, with five bonding pairs and one lone pair on iodine.

Step 3: Identify Identical Shapes

Matching the shapes analyzed above, we see that both \(\mathrm{XeF}_2\) and \(\mathrm{CO}_2\) have a linear geometry. Each molecule of the pair has the same arrangement of atoms (linear), confirming they have identical shapes.

Key Concepts

VSEPR Theory

When we talk about molecular geometry, VSEPR Theory is essential. It's like the roadmap that helps us figure out the shape of a molecule. VSEPR stands for Valence Shell Electron Pair Repulsion. This theory asserts that electron pairs, whether they are in bonds or unshared (also known as lone pairs), will arrange themselves around a central atom to be as far apart as possible. This minimizes the repulsion between electron pairs.

Here's how it works:

• Electron pairs are negatively charged, which means they repel each other.
• The molecule adopts a shape that minimizes this repulsion.
• Bonds and lone pairs around a central atom determine the geometry.

The goal is to keep things balanced, not too crowded. In our solution, VSEPR helps deduce the shapes of molecules like \(\text{CF}_4\) and \(\text{SF}_4\). Even though they contain similar atoms, their shapes differ due to the differing number of lone pairs.

Linear Geometry

Linear geometry is one of the simplest shapes a molecule can have. Picture it as a straight line connecting the atoms. This linear arrangement happens when there are two bonded atoms with no lone pairs on the central atom influencing the shape. This gives a bond angle of 180 degrees.

For example:

• \(\text{XeF}_2\): Xenon forms a shape with two fluorine atoms forming a line, aided by three lone pairs that stay on the sides, maintaining the line.
• \(\text{CO}_2\): The carbon is bonded to oxygen atoms on either side, with double bonds.These arrangements create a straight path, giving the molecules their linear shape.

Molecules like these have identical linear geometries because they follow the same VSEPR logic, involving two bonds and no interfering lone pairs on the central atom.

Trigonal Planar Geometry

In the world of molecular geometry, trigonal planar is a common shape. It occurs when there are three bonds and no lone pairs on the central atom.

Imagine a triangle lying flat. This is what a trigonal planar molecule looks like:

• All three atoms around the central atom are in the same plane.
• The bond angles in a trigonal planar molecule are each 120 degrees.

A good example of this is \(\text{BF}_3\). Here, boron is the central atom, and the three fluorine atoms spread out at equal angles on a plane. This shape occurs due to the equal repulsion of the three bonding electron pairs around the central atom, leading to an arrangement that minimizes repulsion efficiently.