Which of the following compound has the smallest bond angle (X-A-X) in each series respectively ?
(A) `OSF_(2) " " OSCl_(2) " "OSBr_(2)`
`(B) SbCl_(3) " " SbBr_(3) " " SbI_(3)`
(C )` PI_(3) " " AsI_(3) " " SbI_(3)`

Options

A. `OSF_(2),SbCl_(3) and PI_(3)`
B. `OSBr_(2), SbI_(3) and PI_(3)`
C. `OSF_(2),SbI_(3) and PI_(3)`
D. `OSF_(2),SbCl_(3) and SbI_(3)`

Explanation

To determine which compound has the smallest bond angle (X-A-X) in each series, we will analyze each series based on the electronegativity of the atoms involved and the resulting crowding effects.

### Step-by-Step Solution:

**Series A: OSF₂, OSCl₂, OSBr₂**

1. **Identify the central atom:** In all three compounds, sulfur (S) is the central atom.
2. **Consider the electronegativity of the halogens:**
- Fluorine (F) is the most electronegative, followed by chlorine (Cl), and then bromine (Br).
3. **Analyze the effect of electronegativity on bond angles:**
- The more electronegative the halogen, the more it pulls the bonding electrons towards itself, reducing electron repulsion around the central atom.
- OSF₂ will have the least crowding around sulfur due to the high electronegativity of fluorine, leading to the smallest bond angle.
4. **Conclusion for Series A:** The compound with the smallest bond angle is **OSF₂**.

**Series B: SbCl₃, SbBr₃, SbI₃**

1. **Identify the central atom:** In all three compounds, antimony (Sb) is the central atom.
2. **Consider the electronegativity of the halogens:**
- Chlorine (Cl) is the most electronegative, followed by bromine (Br), and then iodine (I).
3. **Analyze the effect of electronegativity on bond angles:**
- Similar to Series A, the more electronegative the halogen, the less crowding around the central atom.
- SbCl₃ will have the least crowding due to chlorine's high electronegativity, resulting in the smallest bond angle.
4. **Conclusion for Series B:** The compound with the smallest bond angle is **SbCl₃**.

**Series C: PI₃, AsI₃, SbI₃**

1. **Identify the central atom:** The central atoms are phosphorus (P), arsenic (As), and antimony (Sb) respectively.
2. **Consider the electronegativity of the central atoms:**
- Phosphorus is the most electronegative, followed by arsenic, and then antimony.
3. **Analyze the effect of electronegativity on bond angles:**
- As we move down the group, the electronegativity decreases, leading to increased crowding around the central atom.
- PI₃ will have the most crowding due to phosphorus's high electronegativity, resulting in a larger bond angle.
- Conversely, SbI₃ will have the least crowding and thus the smallest bond angle.
4. **Conclusion for Series C:** The compound with the smallest bond angle is **SbI₃**.

### Final Answers:
- **Series A:** OSF₂
- **Series B:** SbCl₃
- **Series C:** SbI₃

### Overall Conclusion:
The compounds with the smallest bond angles in each series are:
1. OSF₂
2. SbCl₃
3. SbI₃