Calculate the molar mass of metal having density $9.3 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms simple cubic…

Calculate the molar mass of metal having density $9.3 \mathrm{~g} \mathrm{~cm}^{-3}$ that forms simple cubic unit cell. $\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=22.6 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
  1. $210.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $105.3 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $52.6 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $70.2 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

For simple cubic unit cell, $\mathrm{n}=1$. $\text { Density }(\rho)=\frac{M n}{a^3 N_A}$ $\begin{aligned} & 9.3=\frac{\mathrm{M} \times 1}{22.6} \\ & \mathrm{M}=\frac{9.3 \times 22.6}{1}=210.2 \mathrm{~g} \mathrm{~mol}^{-1} \end{aligned}$

Asked in: MHT CET 2023 (11 May Shift 2)

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