Q49 / 150 · MHT CET 2023 (10 May Shift 1) · Chemistry
Calculate the molar mass of an element with density $2.7 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms fcc structure.
$\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=40 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
- A$112 \mathrm{~g} \mathrm{~mol}^{-1}$
- B$54 \mathrm{~g} \mathrm{~mol}^{-1}$
- Correct answerC$27 \mathrm{~g} \mathrm{~mol}^{-1}$
- D$78 \mathrm{~g} \mathrm{~mol}^{-1}$
Solution
For fcc unit cell, $n=4$.
$\begin{aligned}
& \text { Density }(\rho)=\frac{M \text { n }}{a^3 N_A} \\
& 2.7=\frac{M \times 4}{40} \\
& M=\frac{2.7 \times 40}{4}=27 \mathrm{~g} \mathrm{~mol}^{-1}
\end{aligned}$
Hence, the correct answer is option: 'C'.