Q7 / 90 · JEE Main 2019 (11 Jan Shift 1) · Chemistry

A solid having density of $9 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ forms face centred cubic crystals of edge length $200 \sqrt{2} \mathrm{pm} .$ What is the molar mass of the solid? [Avogadro constant $\left.\approx 6 \times 10^{23} \mathrm{~mol}^{-1}, \pi \approx 3\right]$

  • A
    $0.0432 \mathrm{~kg} \mathrm{~mol}^{-1}$
  • B
    $0.0216 \mathrm{~kg} \mathrm{~mol}^{-1}$
  • Correct answer
    C
    $0.0305 \mathrm{~kg} \mathrm{~mol}^{-1}$
  • D
    $0.4320 \mathrm{~kg} \mathrm{~mol}^{-1}$

Solution

Density $=\frac{Z \times M}{N_{A} \times a^{3}}$ $9 \times 10^{3}=\frac{4 \times \mathrm{M}}{\left(200 \times \sqrt{2} \times 10^{-12}\right)^{3} 6 \times 10^{23}}$

Hence, the correct answer is option: 'C'.

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