According to hybridisation theory, the % s-character in `sp, sp^(2) and sp^(3)` hybrid orbitals is 50, 33.3 and 25 respectively, but this is not true for all the species. When `theta` is the bond angle between equivalent hybrid orbitals then % s and p-character in hybrid orbitals (when only s and p-orbitals are involved in hybridisation) can be calculated by the following formula :
`costheta=(S)/(S-1)=(P-1)/(P)`
Q. Smallest `Ohat(S)O` bond angle is found in :

Options

A. `SO_(2)F_(2)`
B. `SO_(2)Cl_(2)`
C. `SO_(2)(CF_(3))_(2)`
D. `SO_(2)(CH_(3))_(2)`

Answer

To determine the smallest O-S-O bond angle among the given compounds (SO2F2, SO2Cl2, SO2CF3 whole twice, and SO2CH3 whole twice), we will use the concept of hybridization and the effect of electronegativity on bond angles.

### Step-by-Step Solution:

1. **Identify the Hybridization of Sulfur:**
- The hybridization of sulfur in all these compounds can be determined by calculating the steric number.
- The steric number (SN) is calculated using the formula:
\[ \text{SN} = \text{Number of valence electrons of central atom} + \text{Number of monovalent atoms} \]
- For sulfur (S), it has 6 valence electrons. Each of the compounds has 2 double-bonded oxygen atoms and 2 monovalent atoms (F, Cl, CF3, CH3).
- Thus, for each compound:
\[ \text{SN} = 6 + 2 = 8 \]
- Since the steric number is 4 (considering 2 double bonds as 1 each), the hybridization of sulfur is \( sp^3 \).

2. **Analyze the Effect of Electronegativity:**
- The bond angles in hybridized orbitals can be affected by the electronegativity of the substituents.
- The order of electronegativity is:
\[ \text{F} > \text{Cl} > \text{C} > \text{H} \]
- More electronegative atoms (like F) will pull electron density towards themselves, resulting in a decrease in bond angles due to increased repulsion between lone pairs and bonding pairs.

3. **Compare the Compounds:**
- **SO2F2:** Contains highly electronegative fluorine atoms, which will decrease the O-S-O bond angle.
- **SO2Cl2:** Chlorine is less electronegative than fluorine, so the bond angle will be larger than in SO2F2.
- **SO2CF3:** The presence of CF3 (which is less electronegative than F) will also lead to a larger bond angle than in SO2F2.
- **SO2CH3:** The methyl group (CH3) is the least electronegative, which will lead to the largest O-S-O bond angle.

4. **Conclusion:**
- Since the electronegativity of the substituents affects the bond angle, the compound with the least electronegative substituents will have the smallest O-S-O bond angle.
- Therefore, the smallest O-S-O bond angle is found in **SO2CH3 whole twice**.

### Final Answer:
The smallest O-S-O bond angle is found in **SO2CH3 whole twice**.