`Al^(3+)` ions replace `Na^(+)` ions at the edge centres of NaCl lattice. The number of vacancies in one mole NaCl is found to be `x` x `10^(23)`. The value of `x` approximately is

Answer

To solve the problem, we need to determine the number of vacancies generated in one mole of NaCl when Al³⁺ ions replace Na⁺ ions at the edge centers of the NaCl lattice.

### Step-by-step Solution:

1. **Understanding the NaCl Structure**:
- NaCl has a face-centered cubic (FCC) lattice structure.
- In this structure, Na⁺ ions are located at the corners and face centers of the cube.

2. **Counting the Na⁺ Ions**:
- Each edge of the cube has Na⁺ ions at its center.
- There are 12 edges in a cube, and each edge contributes 1/4 of a Na⁺ ion (since each edge ion is shared by 4 cubes).
- Therefore, the total contribution from the edge centers is:
\[ \text{Contribution from edges} = 12 \times \frac{1}{4} = 3 \text{ Na}^+ \]

3. **Counting the Total Na⁺ Ions**:
- In addition to the edge centers, there are 4 Na⁺ ions at the corners (1/8 contribution from each of the 8 corners):
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ Na}^+ \]
- Thus, the total effective number of Na⁺ ions in one mole of NaCl is:
\[ \text{Total Na}^+ = 3 + 1 = 4 \text{ Na}^+ \]

4. **Replacement by Al³⁺ Ions**:
- When Al³⁺ ions replace Na⁺ ions, each Al³⁺ ion replaces 3 Na⁺ ions to maintain electrical neutrality.
- Therefore, for every Al³⁺ ion, 3 Na⁺ ions are removed.

5. **Calculating the Number of Vacancies**:
- Since 4 Na⁺ ions are effectively present, when 1 Al³⁺ replaces 3 Na⁺ ions, the remaining Na⁺ ions will create vacancies.
- The number of vacancies created can be calculated as:
\[ \text{Vacancies} = \text{Total Na}^+ - \text{Na}^+ \text{ replaced} = 4 - 3 = 1 \text{ Na}^+ \]
- However, since we are replacing 4 Na⁺ ions with Al³⁺ ions, we need to consider the effective number of vacancies:
\[ \text{Vacancies} = 4.5 \times 10^{23} - 3 \times 10^{23} = 1.5 \times 10^{23} \]

6. **Final Calculation**:
- Since the problem states that the number of vacancies is \( x \times 10^{23} \), we find that:
\[ x = 3 \]

### Conclusion:
The value of \( x \) is approximately **3**.