Problem 173 - A Complete Resource Book in Chemistry for JEE Main

Question

The molecule having smallest bond angle is (a) \(\mathrm{SbCl}_{3}\) (b) \(\mathrm{AsCl}_{3}\) (c) \(\mathrm{NCl}_{3}\) (d) \(\mathrm{PCl}_{3}\)

Step-by-Step Solution

Answer

The molecule with the smallest bond angle is \( \mathrm{SbCl}_{3} \).

Step 1: Understand the Shapes of the Molecules

All given molecules are of the type \ \( \mathrm{XCl}_{3} \) where \ \( \mathrm{X} \) is a Group 15 element. Due to the presence of a lone pair on the central atom, these molecules adopt a trigonal pyramidal geometry.

Step 2: Consider the Electronegativity and Lone Pairs

The bond angle is influenced by the repulsion between the bonded pairs of electrons and lone pairs of electrons. The repulsion from lone pairs is generally greater than that from bonding pairs. As you go down Group 15 from nitrogen to antimony, the central atom's electronegativity decreases and size increases, affecting the bond angles.

Step 3: Analyze the Impact of Atomic Size

With larger central atoms like antimony, the bond pairs of the bonded elements are farther from the nucleus compared to smaller central atoms like nitrogen. The increase in size of the central atom leads to a decrease in the repulsion between bonded pairs, thereby reducing the bond angle.

Step 4: Identify the Molecule with the Smallest Bond Angle

Considering the influence of atomic size and lone pair effects, \ \( \mathrm{SbCl}_{3} \) has the central atom with the largest size among the options provided. Therefore, it will have the smallest bond angle due to minimal repulsion among the bonded pairs.

Key Concepts

Group 15 Elements

Group 15 of the periodic table includes elements like nitrogen (N), phosphorus (P), arsenic (As), and antimony (Sb). These elements are characterized by having five electrons in their outermost electron shell.
This gives them similar chemical properties. They all form a series of compounds known as \(\mathrm{XCl}_{3}\) where \(\mathrm{X}\) is a Group 15 element.
Some common properties of Group 15 elements include:

• 5 valence electrons, typically forming three covalent bonds and hosting a lone pair.
• Decrease in electronegativity as you move down the column from nitrogen to antimony.
• Increase in atomic size as you go down the group.

These trends affect their chemical behavior, like the ability of lone pairs to repel bonded pairs, impacting molecular geometry and bond angles.

Trigonal Pyramidal Geometry

The trigonal pyramidal geometry is a common molecular shape for molecules with a central atom from Group 15. This shape results when a central atom forms three sigma bonds and retains one lone pair of electrons. This arrangement arises because:

• The lone pair occupies more space than bonding pairs, due to greater electron repulsion.
• It causes the three bonded atoms to spread out in a pyramid shape to minimize repulsion.

This shape is responsible for certain physical properties, such as polarity in these compounds. A classic example is \(\mathrm{NH}_{3}\) (ammonia), where nitrogen forms a similar trigonal pyramidal structure.

Lone Pair Repulsion

Lone pair repulsion is a key factor in determining the geometry and bond angles of a molecule. In Group 15 elements with trigonal pyramidal geometry, the lone pair exerts a greater force on the bonded pairs than bonding pairs exert on each other. The reasons include:

• Lone pairs are located in orbitals closer to the central atom, enhancing repulsive interactions.
• They spread out more in space, compressing the bond angles closer than in a perfect tetrahedron.

As a result, molecules like \(\mathrm{SbCl}_{3}\) with larger central atoms have their bond angles reduced compared to smaller central atoms. The increased size causes lone pair repulsion to minimize the distance between bonding pairs, hence decreasing the bond angle.