Question

An element with density 2.8 g cm$^{-3}$ forms FCC unit cell having edge length 4 × 10$^{-8}$ cm. Calculate molar mass of the element.

• A. 33.0 g mol$^{-1}$
• B. 22.0 g mol$^{-1}$
• C. 27.0 g mol$^{-1}$
• D. 36.0 g mol$^{-1}$

Hint:

For FCC crystals, use the appropriate formula to calculate molar mass based on density and unit cell edge length.

Answer 1

The Correct Option is A

Step 1: Formula for molar mass.
Using the formula for molar mass from the unit cell density: \[ M = \frac{\rho \times N_A \times a^3}{Z} \] Where: - \( \rho \) is the density (2.8 g/cm³), - \( N_A \) is Avogadro's number, - \( a \) is the edge length (4 × 10\(^{-8}\) cm), - \( Z \) is the number of atoms per unit cell (4 for FCC).
Step 2: Calculation.
Substituting the values into the formula, we get: \[ M = \frac{(2.8 \, \text{g/cm}^3) \times (6.022 \times 10^{23} \, \text{mol}^{-1}) \times (4 \times 10^{-8} \, \text{cm})^3}{4} \] This gives the molar mass as 33.0 g/mol.
Step 3: Conclusion.
The correct answer is (A) 33.0 g mol$^{-1$.}