Select the correct statement.

Options

A. `BF_(3) and NH_(3)` have same dipole moment
B. Dipole moment of `NH_(3)` is smaller than that of `BF_(3)`
C. `BF_(3)` molecule has a planar structure, while the `NH_(3)` molecule is tetrahedral
D. The nitrogen atom has unshared pair of electrons, while the boron atom has a free (vacant) valence orbital.

Explanation

To solve the question, we need to analyze the statements regarding the molecules BF3 and NH3 and determine which one is correct. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the Hybridization and Geometry of BF3
1. **Identify the central atom**: In BF3, boron (B) is the central atom.
2. **Calculate the steric number (S)**:
- Valence electrons of boron = 3
- Monovalent atoms attached (3 fluorine atoms) = 3
- Cationic charge = 0
- Anionic charge = 0
- Formula: S = 1/2 (valence electrons + monovalent atoms - cationic charge + anionic charge)
- Calculation: S = 1/2 (3 + 3 - 0 + 0) = 3
3. **Determine hybridization**: A steric number of 3 corresponds to sp² hybridization.
4. **Determine geometry**: The geometry for sp² hybridization is trigonal planar.

### Step 2: Determine the Hybridization and Geometry of NH3
1. **Identify the central atom**: In NH3, nitrogen (N) is the central atom.
2. **Calculate the steric number (S)**:
- Valence electrons of nitrogen = 5
- Monovalent atoms attached (3 hydrogen atoms) = 3
- Cationic charge = 0
- Anionic charge = 0
- Calculation: S = 1/2 (5 + 3 - 0 + 0) = 4
3. **Determine hybridization**: A steric number of 4 corresponds to sp³ hybridization.
4. **Determine geometry**: The geometry for sp³ hybridization is tetrahedral, but due to the presence of one lone pair, the shape is trigonal pyramidal.

### Step 3: Analyze Dipole Moments
1. **BF3**:
- The molecule is planar with symmetrical distribution of dipole moments from the fluorine atoms, resulting in a net dipole moment of zero.
2. **NH3**:
- The molecule has a trigonal pyramidal shape with an asymmetrical distribution of dipole moments due to the lone pair on nitrogen, resulting in a net dipole moment that is not zero.

### Step 4: Evaluate the Statements
1. **Statement 1**: BF3 and NH3 have the same dipole moment. (Incorrect)
2. **Statement 2**: Dipole moment of NH3 is smaller than that of BF3. (Incorrect)
3. **Statement 3**: BF3 molecule has a planar structure while NH3 is tetrahedral. (Incorrect; NH3 is trigonal pyramidal)
4. **Statement 4**: The nitrogen atom has an unshared pair of electrons while the boron atom has a free vacant valence orbital. (Correct)

### Conclusion
The correct statement is **Statement 4**: The nitrogen atom has an unshared pair of electrons while the boron atom has a free vacant valence orbital.

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