Calculate the molar mass of metal having density $7.8 \mathrm{~g} \mathrm{~cm}^{-3}$ and crystallized to…

Calculate the molar mass of metal having density $7.8 \mathrm{~g} \mathrm{~cm}^{-3}$ and crystallized to form bcc structure with edge length $288 \mathrm{pm}$.
  1. $120.0 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $86.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $108.1 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $56.1 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\mathrm{d}=\frac{Z}{V} \times \frac{M}{N_{\mathrm{A}}}$ $\begin{aligned} & 7.8 \times \frac{2 \times M}{\left(2.88 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\ & M=56.08 \mathrm{~g} / \mathrm{mol}\end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 2)

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