Q22 / 180 · KCET 2021 · Chemistry

A metal crystallises in bcc lattice with unit cell edge length of $300 \mathrm{pm}$ and density $6.15 \mathrm{gcm}^{-3}$. The molar mass of the metal is

  • Correct answer
    A
    $50 \mathrm{gmol}^{-1}$
  • B
    $60 \mathrm{gmol}^{-1}$
  • C
    $40 \mathrm{gmol}^{-1}$
  • D
    $70 \mathrm{gmol}^{-1}$

Solution

Given, metal crystallises in bcc lattice, therefore $Z=2$ $\begin{aligned} \text { Edge length } &=300 \mathrm{pm} \\ &=300 \times 10^{-10} \mathrm{~cm} \end{aligned}$ Density, $\begin{aligned} d &=\frac{Z M}{a^{3} N_{A}} \Rightarrow M=\frac{d a^{3} N_{A}}{Z} \\ &=\frac{6.15 \times\left(300 \times 10^{-10}\right)^{3} \times 6 \times 10^{23}}{2} \\ &-498150000 \times 10^{-7} \\ &=49.82 \mathrm{~g} \mathrm{~mol}^{-1} \\ & \cong 50 \mathrm{~g} \mathrm{~mol}^{-1} \end{aligned}$

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

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