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Question: Answered & Verified by Expert
Calculate the molar mass of metal with density $1 \mathrm{gcm}^{-3}$ forming bcc structure with edge length $420 \mathrm{pm}$.
ChemistrySolid StateMHT CETMHT CET 2022 (10 Aug Shift 1)
Options:
  • A $32.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  • B $22.3 \mathrm{~g} \mathrm{~mol}^{-1}$
  • C $25.5 \mathrm{~g} \mathrm{~mol}^{-1}$
  • D $43.3 \mathrm{~g} \mathrm{~mol}^{-1}$
Solution:
2409 Upvotes Verified Answer
The correct answer is: $22.3 \mathrm{~g} \mathrm{~mol}^{-1}$
$\mathrm{d}=\frac{\mathrm{Z}}{\mathrm{V}} \times \frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}}$
$1=\frac{2 \times M}{\left(4.20 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}}$
$\mathrm{M}=22.3 \mathrm{~g} / \mathrm{mol}$

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