Which one of the following molecule will have all equal `X-F` bonds length? (where X=Central atom)

Options

A. `SOCl_(2)F_(2)`
B. `SeF_(4)`
C. `PBr_(2)F_(3)`
D. `IF_(7)`

Explanation

To determine which molecule has all equal X-F bond lengths, we will analyze the given options step by step.

### Step 1: Analyze SOCl2F2
- **Central Atom:** Sulfur (S)
- **Valence Electrons:** Sulfur has 6 valence electrons.
- **Single Bonded Atoms:** There are 4 single-bonded atoms (2 Cl and 2 F).
- **Hybridization Calculation:**
\[ \text{Hybridization} = \frac{1}{2} \times (\text{Valence Electrons} + \text{Single Bonded Atoms}) = \frac{1}{2} \times (6 + 4) = 5 \]
This indicates an **SP3D** hybridization.
- **Molecular Geometry:** The geometry is trigonal bipyramidal.
- **Bond Lengths:** According to Bent's rule, the more electronegative atoms (F) will occupy the axial positions, leading to two identical SF bonds and two different SCl bonds. Thus, the SF bond lengths are equal.

### Step 2: Analyze SEF4
- **Central Atom:** Selenium (Se)
- **Valence Electrons:** Selenium has 6 valence electrons.
- **Single Bonded Atoms:** There are 4 single-bonded atoms (4 F).
- **Hybridization Calculation:**
\[ \text{Hybridization} = \frac{1}{2} \times (6 + 4) = 5 \]
This indicates an **SP3D** hybridization.
- **Molecular Geometry:** The geometry is trigonal bipyramidal.
- **Bond Lengths:** There are two types of SEF bonds (2 axial and 2 equatorial), which means they are not equal.

### Step 3: Analyze PBr2F3
- **Central Atom:** Phosphorus (P)
- **Valence Electrons:** Phosphorus has 5 valence electrons.
- **Single Bonded Atoms:** There are 5 single-bonded atoms (2 Br and 3 F).
- **Hybridization Calculation:**
\[ \text{Hybridization} = \frac{1}{2} \times (5 + 5) = 5 \]
This indicates an **SP3D** hybridization.
- **Molecular Geometry:** The geometry is trigonal bipyramidal.
- **Bond Lengths:** There are different types of PF bonds (2 axial and 3 equatorial), which means they are not equal.

### Step 4: Analyze IF7
- **Central Atom:** Iodine (I)
- **Valence Electrons:** Iodine has 7 valence electrons.
- **Single Bonded Atoms:** There are 7 single-bonded atoms (7 F).
- **Hybridization Calculation:**
\[ \text{Hybridization} = \frac{1}{2} \times (7 + 7) = 7 \]
This indicates an **SP3D3** hybridization.
- **Molecular Geometry:** The geometry is pentagonal bipyramidal.
- **Bond Lengths:** There are 5 equatorial IF bonds and 2 axial IF bonds, which means they are not equal.

### Conclusion
After analyzing all the options, the only molecule that has equal bond lengths for the X-F bonds is **SOCl2F2**.

### Final Answer
The molecule with all equal X-F bond lengths is **SOCl2F2**.

---