Calculate the molar mass of metal with density $1 \mathrm{gcm}^{-3}$ forming bcc structure with edge length…

Calculate the molar mass of metal with density $1 \mathrm{gcm}^{-3}$ forming bcc structure with edge length $420 \mathrm{pm}$.
  1. $32.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $22.3 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $25.5 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $43.3 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\mathrm{d}=\frac{\mathrm{Z}}{\mathrm{V}} \times \frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}}$ $1=\frac{2 \times M}{\left(4.20 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}}$ $\mathrm{M}=22.3 \mathrm{~g} / \mathrm{mol}$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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