The compound CuCl has Zns structure. Its edge length is 420 pm. What is the density of the unit cell ? (Atomic mass of CuCl=99)

Explanation

To find the density of the unit cell of CuCl with a ZnS structure, we can follow these steps:

### Step 1: Understand the structure and parameters
The compound CuCl has a Zinc Blende (ZnS) structure, which is a type of face-centered cubic (FCC) lattice. In an FCC unit cell, the number of formula units (Z) per unit cell is 4.

### Step 2: Identify given values
- Edge length (a) = 420 pm = \(420 \times 10^{-12}\) m
- Atomic mass of CuCl = 99 g/mol
- Avogadro's number (N_A) = \(6.022 \times 10^{23}\) mol\(^{-1}\)

### Step 3: Convert edge length to cm
Since density is typically expressed in grams per cubic centimeter (g/cm³), we convert the edge length from picometers to centimeters:
\[ a = 420 \, \text{pm} = 420 \times 10^{-10} \, \text{cm} \]

### Step 4: Calculate the volume of the unit cell
The volume (V) of the cubic unit cell can be calculated using the formula:
\[ V = a^3 \]
Substituting the value of a:
\[ V = (420 \times 10^{-10})^3 \, \text{cm}^3 \]

### Step 5: Calculate the mass of the unit cell
The mass (m) of the unit cell can be calculated using the formula:
\[ m = Z \times \text{molar mass} / N_A \]
Substituting the values:
\[ m = 4 \times \frac{99 \, \text{g/mol}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \]

### Step 6: Calculate the density
The density (ρ) can be calculated using the formula:
\[ \rho = \frac{m}{V} \]
Substituting the values from the previous steps:
\[ \rho = \frac{4 \times \frac{99}{6.022 \times 10^{23}}}{(420 \times 10^{-10})^3} \]

### Step 7: Perform the calculations
1. Calculate the volume:
\[ V = (420 \times 10^{-10})^3 = 7.396 \times 10^{-29} \, \text{cm}^3 \]
2. Calculate the mass:
\[ m = 4 \times \frac{99}{6.022 \times 10^{23}} = 6.577 \times 10^{-22} \, \text{g} \]
3. Calculate the density:
\[ \rho = \frac{6.577 \times 10^{-22}}{7.396 \times 10^{-29}} \approx 8.874 \, \text{g/cm}^3 \]

### Final Answer
The density of the unit cell of CuCl is approximately \(8.874 \, \text{g/cm}^3\).

---