Calculate the density of an element having molar mass $27 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms fcc…

Calculate the density of an element having molar mass $27 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms fcc unit cell. $\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=38.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
  1. $2.8 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $2.1 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $3.5 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $4.1 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

Density, $\rho=\frac{M \text { n }}{a^3 N_A}$ $\begin{aligned} \rho & =\frac{27 \mathrm{~g} \mathrm{~mol}^{-1} \times 4 \text { atom }}{38.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}} \\ & =2.8 \mathrm{~g} \mathrm{~cm}^{-3} \end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 2)

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