Calculate the molar mass of an element having density $21 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms fcc unit…

Calculate the molar mass of an element having density $21 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms fcc unit cell $\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=36 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
  1. $\quad 292.00 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $189.00 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $140.00 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $108.00 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \operatorname{Density}(\rho)=\frac{M \text { n }}{a^3 N_A} \\ & \therefore \quad 21 \mathrm{~g} \mathrm{~cm}^{-3}=\frac{\mathrm{M} \times 4}{36 \mathrm{~cm}^3 \mathrm{~mol}^{-1}} \\ & \therefore \quad \mathrm{M}=\frac{21 \mathrm{~g} \mathrm{~cm}^{-3} \times 36 \mathrm{~cm}^3 \mathrm{~mol}^{-1}}{4} \\ & =189.00 \mathrm{~g} \mathrm{~mol}^{-1} \\ & \end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 2)

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