Problem 80 - A Complete Resource Book in Chemistry for JEE Main

Question

In compounds of the type \(\mathrm{ECl}_{3}\), where \(\mathrm{E}=\mathrm{B}, \mathrm{P}\), As or \(\mathrm{Bi}\), the angle \(\mathrm{Cl}-\mathrm{E}-\mathrm{Cl}\) for different \(\mathrm{E}\) are in the order (a) \(\mathrm{B}>\mathrm{P}=\mathrm{As}=\mathrm{Bi}\) (b) \(\mathrm{B}>\mathrm{P}>\mathrm{As}>\mathrm{Bi}\) (c) \(\mathrm{B}<\mathrm{P}=\mathrm{As}=\mathrm{Bi}\) (d) \(\mathrm{B}<\mathrm{P}<\mathrm{As}<\mathrm{Bi}\)

Step-by-Step Solution

Answer

The correct order is (b) \( \mathrm{B} > \mathrm{P} > \mathrm{As} > \mathrm{Bi} \).

Step 1: Identifying Molecular Geometry

Begin by identifying the molecular geometry of these compounds. Compounds like \( \mathrm{ECl}_{3} \) for \( \mathrm{E} = \mathrm{B} \) are typically trigonal planar, while those for \( \mathrm{E} = \mathrm{P}, \mathrm{As}, \mathrm{Bi} \) are trigonal pyramidal due to the presence of a lone pair.

Step 2: Understanding Angle Changes in Geometry

In a trigonal planar geometry, all angles are \(120^\circ\), such as in \( \mathrm{BCl}_3 \), while in a trigonal pyramidal geometry, like \( \mathrm{PCl}_3 \), due to lone pair-lone pair repulsions, the \( \mathrm{Cl}-\mathrm{E}-\mathrm{Cl} \) bond angles are slightly less than \( 109.5^\circ \), around \( 107^\circ \).

Step 3: Comparing Electronegativity and Size Effects

As \( \mathrm{E} \) goes from \( \mathrm{B} \) to \( \mathrm{Bi} \), the size of atom \( \mathrm{E} \) increases and electronegativity decreases. This causes the lone pair-bond pair repulsion to decrease, leading to smaller bond angles for heavier elements, \( \mathrm{P} > \mathrm{As} > \mathrm{Bi} \).

Step 4: Ordering Based on Geometry and Repulsions

Thus, comparing the bond angles, \( \mathrm{BCl}_3 \) having a larger angle forms due to its planar geometry, while \( \mathrm{PCl}_3 < \mathrm{AsCl}_3 < \mathrm{BiCl}_3 \) form a descending order due to increasingly smaller angles from decreasing lone pair-bond pair repulsion.

Key Concepts

Trigonal Planar Geometry

Trigonal planar geometry is a common molecular shape that occurs in molecules where a central atom is bonded to three other atoms with no lone pairs. In such a geometry, the atoms are arranged in a plane, forming a shape that resembles a triangle. This geometry is characterized by bond angles of exactly \(120^\circ\). A classic example is \( \mathrm{BCl}_3 \) (boron trichloride), where boron (\( \mathrm{B} \)) forms three equivalent \( \mathrm{Cl}-\mathrm{B}-\mathrm{Cl} \) bonds with chlorine atoms. The absence of lone pairs on \( \mathrm{B} \) ensures that all bond angles are ideally set at \(120^\circ\) due to symmetrical electron pair distribution. Adding bond angles helps confirm this transverse symmetry: All three angles formed are equal, maintaining the planar structure. Trigonal planar molecules are usually non-polar when all peripheral atoms are identical.
When evaluating chemical behavior, stability, and interactions, this geometry is crucial as it highlights the molecule's symmetrical nature.

Trigonal Pyramidal Geometry

In trigonal pyramidal geometry, imagine a molecule where a central atom has three bonds and a lone pair of electrons. This geometry forms a pyramid-like shape with the central atom at the apex and the bonded atoms forming the base. A good example is \( \mathrm{PCl}_3 \) (phosphorus trichloride), where phosphorus atom (\( \mathrm{P} \)) creates bonds with three chlorine atoms.
Unlike trigonal planar, in trigonal pyramidal, the molecular structure is influenced by the lone pair's presence. This lone pair exerts repulsion, slightly compressing the bond angles from the ideal \( 109.5^\circ \) (the tetrahedral angle) to about \( 107^\circ \).
Lone pairs take up more space than bonding pairs, pushing the bonds closer together. It's a great showcase of how electron pair arrangement determines molecular shape. Beyond influencing physical structure, these lone pairs can affect the molecule's polarity making such molecules more reactive in certain environments.

Bond Angle Comparison

Bond angle comparison provides insights into molecular shapes and their electronic environments. Understanding these angles involves comparing structures like \( \mathrm{BCl}_3 \) (trigonal planar) and \( \mathrm{PCl}_3 \) (trigonal pyramidal). The key difference lies in electron arrangement around the central atom.

• In \( \mathrm{BCl}_3 \), all bond angles are \(120^\circ\) due to equal distribution of bonding electrons, forming a perfect planar structure.
• In \( \mathrm{PCl}_3 \), the presence of a lone pair on phosphorus reduces \( \mathrm{Cl}-\mathrm{P}-\mathrm{Cl} \) bond angles to less than \(109.5^\circ\), typically around \(107^\circ\).

Hence,
1. The bond angles in trigonal planar geometry are consistently larger due to the absence of lone pair repulsion.
2. As you progress from \( \mathrm{P} \) to heavier elements like \( \mathrm{As} \) and \( \mathrm{Bi} \), their lesser electronegativity and larger atomic sizes further decrease bond angles.This results in the following order for bond angles in \( \mathrm{ECl}_3 \): \( \mathrm{B} > \mathrm{P} > \mathrm{As} > \mathrm{Bi} \), meaning that increasing atomic size decreases bond angles gradually.