In molecules of the type `AX_(2)I_(n)` (where `I` represents lone pair and n is its number) there exists a bond between element A and X. The `angle XAX` bond angle

Options

A. Always decrease if n increases
B. Always increase if n increases
C. Will be maximum for n=3
D. Generally decrease if n decreases

Answer

To determine the bond angle \( \angle XAX \) in molecules of the type \( AX_2I_n \) (where \( I \) represents lone pairs and \( n \) is the number of lone pairs), we can analyze the situation step by step.

### Step 1: Understanding the Structure
In the molecule \( AX_2I_n \), \( A \) is the central atom, \( X \) represents the bonded atoms, and \( I_n \) indicates the lone pairs on the central atom \( A \). The arrangement of these atoms will depend on the number of lone pairs \( n \).

### Step 2: Case Analysis Based on the Value of \( n \)

#### Case 1: \( n = 1 \)
- **Structure**: There is 1 lone pair and 2 bonded pairs.
- **Hybridization**: The hybridization is \( sp^2 \) (2 sigma bonds + 1 lone pair).
- **Bond Angle**: The bond angle \( \angle XAX \) will be less than \( 120^\circ \) due to the presence of the lone pair which exerts a greater repulsive force compared to bonded pairs.

#### Case 2: \( n = 2 \)
- **Structure**: There are 2 lone pairs and 2 bonded pairs.
- **Hybridization**: The hybridization is \( sp^3 \) (2 sigma bonds + 2 lone pairs).
- **Bond Angle**: The bond angle \( \angle XAX \) will be less than \( 109.5^\circ \) because the lone pairs push the bonded pairs closer together.

#### Case 3: \( n = 3 \)
- **Structure**: There are 3 lone pairs and 2 bonded pairs.
- **Hybridization**: The hybridization is \( sp^3d \) (2 sigma bonds + 3 lone pairs).
- **Bond Angle**: The bond angle \( \angle XAX \) will be \( 180^\circ \) because the lone pairs are placed in equatorial positions to minimize lone pair-lone pair repulsion.

### Step 3: Conclusion
From the analysis, we can conclude:
- As the number of lone pairs \( n \) increases, the bond angle \( \angle XAX \) initially decreases until \( n = 3 \), where it reaches a maximum of \( 180^\circ \).
- Therefore, the bond angle will be maximum for \( n = 3 \).

### Final Answer
The bond angle \( \angle XAX \) will be maximum for \( n = 3 \).

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