How many of the following molecules have trigonal hipyramidal electronic geometry for their central atom?

Options

A. `XeO_3F_2`
B. `XeF_2`
C. `XeF_4`
D. `XeOF_2`

Answer

To determine how many of the given molecules have a trigonal bipyramidal electronic geometry for their central atom, we will analyze each molecule one by one based on their molecular formula and the number of bonds and lone pairs around the central atom.

### Step-by-Step Solution

1. **Identify the Molecules**: The given molecules are:
- \( \text{XCO}_3\text{F}_2 \)
- \( \text{XCOF}_2 \)
- \( \text{XCO}_4 \)
- \( \text{XCOF}_2 \) (Note: This seems to be a repetition; we will treat it as the same as the second one.)

2. **Determine the Hybridization and Geometry**:
- **For \( \text{XCO}_3\text{F}_2 \)**:
- The central atom (X) is bonded to 5 atoms (3 O and 2 F).
- Number of sigma bonds = 5, Number of lone pairs = 0.
- Hybridization = Number of sigma bonds + Lone pairs = 5 + 0 = 5.
- Hybridization type = \( \text{sp}^3\text{d} \) → Geometry = Trigonal bipyramidal.

- **For \( \text{XCOF}_2 \)**:
- The central atom (X) is bonded to 2 F atoms and has 3 lone pairs.
- Number of sigma bonds = 2, Number of lone pairs = 3.
- Hybridization = 2 + 3 = 5.
- Hybridization type = \( \text{sp}^3\text{d} \) → Geometry = Trigonal bipyramidal.

- **For \( \text{XCO}_4 \)**:
- The central atom (X) is bonded to 4 O atoms and has 2 lone pairs.
- Number of sigma bonds = 4, Number of lone pairs = 2.
- Hybridization = 4 + 2 = 6.
- Hybridization type = \( \text{sp}^3\text{d}^2 \) → Geometry = Octahedral (not trigonal bipyramidal).

- **For \( \text{XCOF}_2 \)** (the repeated molecule):
- This is the same as the second molecule analyzed above.
- It has the same hybridization and geometry as before: \( \text{sp}^3\text{d} \) → Geometry = Trigonal bipyramidal.

3. **Count the Molecules with Trigonal Bipyramidal Geometry**:
- From the analysis:
- \( \text{XCO}_3\text{F}_2 \) → Trigonal bipyramidal
- \( \text{XCOF}_2 \) → Trigonal bipyramidal
- \( \text{XCO}_4 \) → Not trigonal bipyramidal
- \( \text{XCOF}_2 \) → Trigonal bipyramidal (repeat)

- Therefore, the total number of molecules with trigonal bipyramidal geometry is **3**.

### Final Answer
**3 molecules have trigonal bipyramidal electronic geometry for their central atom.**