A crystalline solid AB adopts sodium chloride type structure with edge length of the unit cell as 745 pm and formula mass of 74.5 g The density of the crystalline compound is

Options

A. `2.16 g cm^(-3)`
B. `0.99 g cm^(-3)`
C. `1.88 g cm^(-3)`
D. `1.197 g cm^(-3)`

Answer

To calculate the density of the crystalline solid AB that adopts a sodium chloride type structure, we can follow these steps:

### Step 1: Identify the parameters
- **Edge length (a)** of the unit cell = 745 pm = 745 x 10^-10 cm
- **Formula mass (M)** = 74.5 g/mol
- **Number of atoms per unit cell (Z)** for NaCl structure = 4

### Step 2: Convert edge length to centimeters
We need to convert the edge length from picometers to centimeters:
\[ a = 745 \, \text{pm} = 745 \times 10^{-12} \, \text{m} = 745 \times 10^{-10} \, \text{cm} \]

### Step 3: 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 \( a \):
\[ V = (745 \times 10^{-10} \, \text{cm})^3 \]
\[ V = 4.14 \times 10^{-28} \, \text{cm}^3 \]

### Step 4: Calculate the mass of the unit cell
The mass of the unit cell can be calculated using the formula:
\[ \text{Mass of unit cell} = \frac{M}{N_A} \times Z \]
Where \( N_A \) (Avogadro's number) = \( 6.022 \times 10^{23} \) mol^-1.
Substituting the values:
\[ \text{Mass of unit cell} = \frac{74.5 \, \text{g/mol}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \times 4 \]
\[ \text{Mass of unit cell} = \frac{74.5}{6.022 \times 10^{23}} \times 4 \]
\[ \text{Mass of unit cell} \approx 4.94 \times 10^{-22} \, \text{g} \]

### Step 5: Calculate the density
Density \( d \) can be calculated using the formula:
\[ d = \frac{\text{Mass of unit cell}}{\text{Volume of unit cell}} \]
Substituting the values:
\[ d = \frac{4.94 \times 10^{-22} \, \text{g}}{4.14 \times 10^{-28} \, \text{cm}^3} \]
\[ d \approx 1190.10 \, \text{g/cm}^3 \]
\[ d \approx 1.19 \, \text{g/cm}^3 \]

### Final Answer
The density of the crystalline compound AB is approximately **1.19 g/cm³**.

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