X-ray diffraction studies show that edge length of a unit cell of NaCl is 0.56 nm. Density of NaCl was found to be `2.16g//"cc".` What type of defect is found in the solid? Calculate the percentage of `Na^(+)` and `Cl^(-)` ions that are missing.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Given Data
- Edge length of NaCl unit cell (a) = 0.56 nm = \(0.56 \times 10^{-7}\) cm
- Density of NaCl (ρ) = 2.16 g/cm³
- Molar mass of NaCl = Mass of Na (23 g/mol) + Mass of Cl (35.5 g/mol) = 58.5 g/mol
- Avogadro's number (NA) = \(6.023 \times 10^{23}\) mol⁻¹

### Step 2: Calculate the Volume of the Unit Cell
The volume (V) of the unit cell can be calculated using the edge length:
\[ V = a^3 = (0.56 \times 10^{-7} \text{ cm})^3 = 1.75 \times 10^{-21} \text{ cm}^3 \]

### Step 3: Calculate the Number of Formula Units (Z) in the Unit Cell
Using the formula for density:
\[ \rho = \frac{Z \cdot M}{V \cdot N_A} \]
Rearranging the formula to find Z:
\[ Z = \frac{\rho \cdot V \cdot N_A}{M} \]
Substituting the values:
\[ Z = \frac{2.16 \text{ g/cm}^3 \cdot 1.75 \times 10^{-21} \text{ cm}^3 \cdot 6.023 \times 10^{23} \text{ mol}^{-1}}{58.5 \text{ g/mol}} \]
Calculating this gives:
\[ Z \approx 3.905 \]

### Step 4: Determine the Type of Defect
In a perfect NaCl crystal, Z should be 4 (since NaCl has a face-centered cubic lattice). The calculated Z is 3.905, which is less than 4. This indicates that some ions are missing from the lattice. The decrease in density suggests a Schottky defect, where equal numbers of cations (Na⁺) and anions (Cl⁻) are missing.

### Step 5: Calculate the Number of Missing Ions
The number of missing formula units:
\[ \text{Missing formula units} = 4 - Z = 4 - 3.905 = 0.095 \]

### Step 6: Calculate the Percentage of Missing Ions
The percentage of missing formula units:
\[ \text{Percentage missing} = \left(\frac{\text{Missing formula units}}{4}\right) \times 100 = \left(\frac{0.095}{4}\right) \times 100 \approx 2.375\% \]

### Final Answer
- Type of defect: Schottky defect
- Percentage of missing Na⁺ and Cl⁻ ions: 2.375%