Calculate the molar mass of metal having density $22.24 \mathrm{~g} \mathrm{~cm}^{-3}$, crystallizes to form…

Calculate the molar mass of metal having density $22.24 \mathrm{~g} \mathrm{~cm}^{-3}$, crystallizes to form unit cell containing 4 particles. $\left(\mathrm{a}^3=5.6 \times 10^{-23} \mathrm{~cm}^3\right)$
  1. $280.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $140 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $210.6 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $187.4 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{V} \times \mathrm{N}_{\mathrm{A}}}=\frac{4 \times \mathrm{M}}{5.6 \times 10^{-23} \times 6.02 \times 10^{23}}$ or $22.24=\frac{4 \times M}{5.6 \times 6.02}$ $\mathrm{M}=187.43 \mathrm{~g} / \mathrm{mol}$

Asked in: MHT CET 2022 (05 Aug Shift 1)

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