Find the molar mass of an element that crystallizes forming unit cell structure having edge length $4 \times…

Find the molar mass of an element that crystallizes forming unit cell structure having edge length $4 \times 10^{-8} \mathrm{~cm}$ and containing 4 particles. ( $Q=19.7 \mathrm{~g} \mathrm{~cm}^{-3}$ )
  1. $140.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $189.8 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $160.5 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $220.0 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{V} \times \mathrm{N}_{\mathrm{A}}}$ $19.7=\frac{4 \times M}{\left(4 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}}$ $\mathrm{M}=189.75 \mathrm{~g} / \mathrm{mol}$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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