What is the molar mass of metal having density $8.57 \mathrm{~g} \mathrm{~cm}^{-3}$ and edge length $3.3 Å$…
What is the molar mass of metal having density $8.57 \mathrm{~g} \mathrm{~cm}^{-3}$ and edge length $3.3 Å$ ? (Packing efficiency $=68 \%$ )
- $63 \mathrm{~g} \mathrm{~mol}^{-1}$
- $93 \mathrm{~g} \mathrm{~mol}^{-1}$
- $29 \mathrm{~g} \mathrm{~mol}^{-1}$
- $39 \mathrm{~g} \mathrm{~mol}^{-1}$
Solution
Packing efficiency $=68 \%$
BCC unit cell
$\begin{aligned}
& \mathrm{Z}=2, \mathrm{a}=3.3 Å \\
& =3.3 \times 10^{-8} \mathrm{~cm} \\
& \mathrm{~d}=8.57 \mathrm{~g} / \mathrm{cm}^3 \\
& \mathrm{~d}=\frac{\mathrm{Z} \cdot \mathrm{M}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \\
& \mathrm{M}=\frac{\mathrm{d} \times \mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3}{\mathrm{Z}}=\frac{8.57 \times 6.022 \times 10^{23} \times\left(3.3 \times 10^{-8}\right)^3}{2} \\
& \mathrm{M}=93 \mathrm{~g} / \mathrm{mol}
\end{aligned}$
Asked in: MHT CET 2021 (22 Sep Shift 1)
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