Question

Calculate the molar mass of an element if it forms fcc unit cell structure [mass of unit cell $= 1.8 \times 10^{-22} \text{ g}$, $\text{N}_\text{A} = 6.022 \times 10^{23} \text{ mol}^{-1}$]

• A. $27.0 \text{ g mol}^{-1}$
• B. $24.4 \text{ g mol}^{-1}$
• C. $21.0 \text{ g mol}^{-1}$
• D. $30.2 \text{ g mol}^{-1}$

Hint:

Remember $Z$ values: $sc = 1, bcc = 2, fcc = 4$. If mass of unit cell is $m$, Molar mass $M = (m \times N_A) / Z$.

Answer 1

The Correct Option is A

Step 1: Concept
The mass of a unit cell is given by $(Z \times M) / N_A$, where $Z$ is the number of atoms in the unit cell.

Step 2: Meaning
For an fcc (face-centered cubic) lattice, $Z = 4$.

Step 3: Analysis
- Mass of unit cell $= (4 \times M) / 6.022 \times 10^{23} = 1.8 \times 10^{-22} \text{ g}$. - $M = (1.8 \times 10^{-22} \times 6.022 \times 10^{23}) / 4$. - $M = (18 \times 10^{-23} \times 6.022 \times 10^{23}) / 4 = (1.8 \times 60.22) / 4 \approx 108.4 / 4$.

Step 4: Conclusion
$M \approx 27.1 \text{ g/mol}$. The closest value is $27.0 \text{ g/mol}$. Final Answer: (A)