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 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

(a) \( \text{B} > \text{P} = \text{As} = \text{Bi} \).

Step 1: Identify the Molecular Shape

For a molecule of the type \( \text{ECl}_3 \), where \( \text{E} \) can be B, P, As, or Bi, the molecular geometry is determined by the number of bonding pairs and lone pairs around the central atom. Since these atoms form three bonds with Cl atoms and typically do not have any lone pairs, the geometry is trigonal planar or trigonal pyramidal, depending on the atom.

Step 2: Examine the Central Atom's Influence

The effective nuclear charge and the size of the atom \( \text{E} \) influence the bond angles. Smaller atoms like B have a higher angle due to less repulsion compared to larger atoms like P, As, and Bi. As the size of \( \text{E} \) increases, the bond angle decreases because larger atoms can accommodate more electron density.

Step 3: Analyze Bond Angle Trend

Consider electronegativity and bond repulsion factors. Usually, the order of the bond angles in terms of size is Boron (being smaller and more electronegative) having a larger bond angle than Phosphorus, Arsenic, and Bismuth which have progressively smaller angles due to their increasing atomic size and reduced electronegativity.

Step 4: Determine the Final Order

Based on the analysis, the expected trend for the bond angle \( \text{Cl-E-Cl} \) in \( \text{ECl}_3 \) compounds is \( \text{B} > \text{P} \geq \text{As} \geq \text{Bi} \). Therefore, this matches choice (a) \( \text{B} > \text{P} = \text{As} = \text{Bi} \), as they form very similar bond angles due to the trigonal pyramidal geometry shared by \( \text{P} \), \( \text{As} \), and \( \text{Bi} \).

Key Concepts

Bond Angles

The bond angle determines the shape and spatial configuration of a molecule, specifically between the atoms bonded to a central atom. Bond angles are significant because they influence the sterics of a molecule, affecting how molecules interact and react with one another.To understand why certain bond angles exist, consider two important factors:

• The number of bonds: More bonds mean electron pairs push against each other, creating wider angles.
• The size of the central atom: Smaller atoms create sharper angles because electrons are concentrated in a smaller space.

In \( \text{ECl}_3 \) compounds, the bond angle between the chlorine atoms is vital, as it establishes the base shape of the molecule and affects its polarity. When you have a smaller central atom like Boron (B), the bond angle is larger as the outer bonded electron clouds are forced to position themselves further apart, mitigating repulsion.Conversely, bigger atoms such as Phosphorus (P), Arsenic (As), and Bismuth (Bi) have smaller bond angles since they can accommodate more electron density around the nucleus without significant repulsion.

Trigonality of ECl3 Compounds

The concept of trigonality pertains to the geometric arrangement of atoms around a central atom in a molecule. In simple terms, it's how those atoms are structured in three dimensions. With \( \text{ECl}_3 \) compounds, the trigonality is either trigonal planar or trigonal pyramidal, based on the central atom and its bonding capabilities.

• **Trigonal Planar**: A shape where the central atom is in the same plane as the surrounding atoms, typically occurring with Boron in \( \text{BCl}_3 \), where there are no additional electron pairs on the central atom to cause a distortion.
• **Trigonal Pyramidal**: Here, the shape forms a pyramid base, with the central atom creating additional spatial requirements by having lone pairs or when the central atom isn't small enough to stay in one plane, which often happens with heavier elements like Phosphorus, Arsenic, and Bismuth.

The type of trigonality influences not only the visual geometry but also the molecule's chemical properties, including how it interacts with other substances. In \( \text{ECl}_3 \), Boron, due to its smaller size and electronegativity, typically forms planar structures, whereas heavier atoms form pyramidal shapes. This contrast in trigonality affects how molecules pack together in a structure and their potential reactions.

Influence of Central Atom Size

The size of the central atom plays a crucial role in molecular geometry by affecting both the bond angles and the overall shape of the molecule. When considering the \( \text{ECl}_3 \) series, from \( \text{BCl}_3 \) to \( \text{BiCl}_3 \), you see significant differences in molecular behavior as the central atom changes.

• **Electron Cloud Distribution**: Smaller atoms like Boron have electron clouds that closely verge toward the nucleus, leading to higher repulsion forces between adjacent groups, hence larger bond angles.
• **Bond Angle Reduction**: Larger central atoms such as Bismuth allow greater electron cloud dispersion, effectively minimizing repulsion between bonded pairs and lowering the bond angle.
• **Influence on Polarity and Reactivity**: The size affects how easily other atoms can interact with the molecule. For instance, larger bond angles can increase the molecule’s surface area and potential reactivity, while smaller angles may imply tighter, more rigid molecular configurations.

Moreover, the central atom size determines the overall energy stability of the molecule. Larger atoms usually result in less compact, albeit energetically favorable arrangements in compounds like \( \text{PCl}_3 \), \( \text{AsCl}_3 \), and \( \text{BiCl}_3 \), because extended structures reduce electron-electron repulsion effectively. Understanding the impact of central atom size is essential for predicting and explaining the physical and chemical properties of \( \text{ECl}_3 \) compounds.