`sp^(3)d^(2)` hybridization is not displayed by :

Options

A. `SF_(6)`
B. `BrF_(5)`
C. `PF_(5)`
D. `[CrF_(6)]^(3-)`

Answer

To determine which compound does not exhibit `sp^(3)d^(2)` hybridization, we need to calculate the steric number for each option provided. The steric number is calculated using the formula:

**Steric Number = Number of Bond Pairs + Number of Lone Pairs**

Based on the steric number, we can identify the hybridization:
- Steric Number 2: `sp`
- Steric Number 3: `sp^(2)`
- Steric Number 4: `sp^(3)`
- Steric Number 5: `sp^(3)d`
- Steric Number 6: `sp^(3)d^(2)`

Now, let's analyze each option:

### Step 1: Analyze Option A - SF6
1. **Valence Electrons**: Sulfur has 6 valence electrons.
2. **Bonding**: In SF6, sulfur forms 6 bonds with fluorine atoms.
3. **Lone Pairs**: There are no lone pairs on sulfur.
4. **Steric Number Calculation**:
- Bond Pairs = 6
- Lone Pairs = 0
- Steric Number = 6 + 0 = 6
5. **Hybridization**: `sp^(3)d^(2)`

### Step 2: Analyze Option B - BrF5
1. **Valence Electrons**: Bromine has 7 valence electrons.
2. **Bonding**: In BrF5, bromine forms 5 bonds with fluorine atoms.
3. **Lone Pairs**: There is 1 lone pair on bromine.
4. **Steric Number Calculation**:
- Bond Pairs = 5
- Lone Pairs = 1
- Steric Number = 5 + 1 = 6
5. **Hybridization**: `sp^(3)d^(2)`

### Step 3: Analyze Option C - PF5
1. **Valence Electrons**: Phosphorus has 5 valence electrons.
2. **Bonding**: In PF5, phosphorus forms 5 bonds with fluorine atoms.
3. **Lone Pairs**: There are no lone pairs on phosphorus.
4. **Steric Number Calculation**:
- Bond Pairs = 5
- Lone Pairs = 0
- Steric Number = 5 + 0 = 5
5. **Hybridization**: `sp^(3)d`

### Step 4: Analyze Option D - CrF6^3-
1. **Valence Electrons**: Chromium has 6 valence electrons, and the charge contributes additional electrons.
2. **Bonding**: In CrF6^3-, chromium forms 6 bonds with fluorine atoms.
3. **Lone Pairs**: There are no lone pairs on chromium.
4. **Steric Number Calculation**:
- Bond Pairs = 6
- Lone Pairs = 0
- Steric Number = 6 + 0 = 6
5. **Hybridization**: `sp^(3)d^(2)`

### Conclusion
- **Option A (SF6)**: `sp^(3)d^(2)`
- **Option B (BrF5)**: `sp^(3)d^(2)`
- **Option C (PF5)**: `sp^(3)d`
- **Option D (CrF6^3-)**: `sp^(3)d^(2)`

The compound that does not display `sp^(3)d^(2)` hybridization is **Option C: PF5**.