Calculate the density of a metal having molar mass $197 \mathrm{~g} \mathrm{~mol}^{-1}$ if it forms fcc…

Calculate the density of a metal having molar mass $197 \mathrm{~g} \mathrm{~mol}^{-1}$ if it forms fcc structure. $\left[\mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}=40 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
  1. $23.5 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $21.2 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $17.5 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $19.7 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

$\begin{aligned} \rho=\frac{\mathrm{n} \times \mathrm{M}}{\mathrm{a}^3 \mathrm{~N}_{\mathrm{A}}} & =\frac{4 \times 197 \mathrm{~g} \mathrm{~mol}^{-1}}{40 \mathrm{~cm}^3 \mathrm{~mol}^{-1}} \\ & =19.7 \mathrm{~g} \mathrm{~cm}^{-3}\end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 2)

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