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Calculate the molar mass of an element with density $2.7 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms fcc structure.
$\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=40 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
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$\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=40 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
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Verified Answer
The correct answer is:
$27 \mathrm{~g} \mathrm{~mol}^{-1}$
For fcc unit cell, $n=4$.
$\begin{aligned}
& \text { Density }(\rho)=\frac{M \text { n }}{a^3 N_A} \\
& 2.7=\frac{M \times 4}{40} \\
& M=\frac{2.7 \times 40}{4}=27 \mathrm{~g} \mathrm{~mol}^{-1}
\end{aligned}$
$\begin{aligned}
& \text { Density }(\rho)=\frac{M \text { n }}{a^3 N_A} \\
& 2.7=\frac{M \times 4}{40} \\
& M=\frac{2.7 \times 40}{4}=27 \mathrm{~g} \mathrm{~mol}^{-1}
\end{aligned}$
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