Question

Calculate the molar mass of an element having density $19.2 \text{ g cm}^{-3}$ if it forms fcc structure $\left[ \text{a}^3 \times \text{N}_{\text{A}} = 40 \text{ cm}^3 \text{ mol}^{-1} \right]$}

• A. $192 \text{ g mol}^{-1}$
• B. $186 \text{ g mol}^{-1}$
• C. $210 \text{ g mol}^{-1}$
• D. $280 \text{ g mol}^{-1}$

Hint:

FCC fact: $Z = 4$ always

Answer 1

The Correct Option is A

Concept: For cubic crystals: \[ \rho = \frac{Z \cdot M}{a^3 \cdot N_A} \] Where:
• $Z = 4$ for fcc
• $M =$ molar mass
• $a^3 N_A = 40 \text{ cm}^3 \text{ mol}^{-1}$ (given)

Step 1: Substitute values. \[ 19.2 = \frac{4 \cdot M}{40} \]

Step 2: Solve for M. \[ M = \frac{19.2 \times 40}{4} = 19.2 \times 10 = 192 \]

Step 3: Conclusion.
Molar mass = $192 \text{ g mol}^{-1}$ Final Answer: Option (A)