How many molecules are there in the unit cell of sodium chioride?

Explanation

To determine how many molecules are there in the unit cell of sodium chloride (NaCl), we need to analyze the structure of NaCl and calculate the contributions of sodium ions (Na⁺) and chloride ions (Cl⁻) within the unit cell.

### Step-by-Step Solution:

1. **Identify the Structure of NaCl**:
- Sodium chloride crystallizes in a face-centered cubic (FCC) lattice, also known as the rock salt structure.

2. **Determine the Position of Ions**:
- In the NaCl structure:
- Chloride ions (Cl⁻) are located at the corners of the cube and at the face centers.
- Sodium ions (Na⁺) are located at the edge centers and at the body center of the cube.

3. **Calculate the Contribution of Na⁺ Ions**:
- **Na⁺ at Edge Centers**: There are 12 edges in a cube, and each edge center contributes 1/4 of an ion to the unit cell.
- Contribution from Na⁺ at edge centers = 12 edges × (1/4) = 3 Na⁺ ions.
- **Na⁺ at Body Center**: There is 1 body center, which contributes fully (1 ion).
- Contribution from Na⁺ at body center = 1.
- **Total Contribution of Na⁺**:
- Total Na⁺ = 3 (from edges) + 1 (from body center) = 4 Na⁺ ions.

4. **Calculate the Contribution of Cl⁻ Ions**:
- **Cl⁻ at Corners**: There are 8 corners in a cube, and each corner contributes 1/8 of an ion to the unit cell.
- Contribution from Cl⁻ at corners = 8 corners × (1/8) = 1 Cl⁻ ion.
- **Cl⁻ at Face Centers**: There are 6 faces, and each face center contributes 1/2 of an ion to the unit cell.
- Contribution from Cl⁻ at face centers = 6 faces × (1/2) = 3 Cl⁻ ions.
- **Total Contribution of Cl⁻**:
- Total Cl⁻ = 1 (from corners) + 3 (from face centers) = 4 Cl⁻ ions.

5. **Total Number of NaCl Units in the Unit Cell**:
- Since there are 4 Na⁺ ions and 4 Cl⁻ ions in the unit cell, the total number of NaCl formula units (or molecules) in the unit cell is:
- Total NaCl units = 4.

### Final Answer:
There are **4 molecules of sodium chloride (NaCl)** in the unit cell.