MHT CET · Chemistry · Solid State
What is the molar mass of metal having density \(8.57 \mathrm{~g} \mathrm{~cm}^{-3}\) and edge length \(3.3 Å\) ? (Packing efficiency \(=68 \%\) )
- A \(63 \mathrm{~g} \mathrm{~mol}^{-1}\)
- B \(93 \mathrm{~g} \mathrm{~mol}^{-1}\)
- C \(29 \mathrm{~g} \mathrm{~mol}^{-1}\)
- D \(39 \mathrm{~g} \mathrm{~mol}^{-1}\)
Answer & Solution
Correct Answer
(B) \(93 \mathrm{~g} \mathrm{~mol}^{-1}\)
Step-by-step Solution
Detailed explanation
Packing efficiency \(=68 \%\)
BCC unit cell
\(\mathrm{Z}=2, \mathrm{a}=3.3 Å \)
\( =3.3 \times 10^{-8} \mathrm{~cm} \)
\( \mathrm{~d}=8.57 \mathrm{~g} / \mathrm{cm}^3 \)
\( \mathrm{~d}=\frac{\mathrm{Z} \cdot \mathrm{M}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \)
\( \mathrm{M}=\frac{\mathrm{d} \times \mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3}{\mathrm{Z}}\) \(=\frac{8.57 \times 6.022 \times 10^{23} \times\left(3.3 \times 10^{-8}\right)^3}{2} \)
\( \mathrm{M}=93 \mathrm{~g} / \mathrm{mol}\)
BCC unit cell
\(\mathrm{Z}=2, \mathrm{a}=3.3 Å \)
\( =3.3 \times 10^{-8} \mathrm{~cm} \)
\( \mathrm{~d}=8.57 \mathrm{~g} / \mathrm{cm}^3 \)
\( \mathrm{~d}=\frac{\mathrm{Z} \cdot \mathrm{M}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \)
\( \mathrm{M}=\frac{\mathrm{d} \times \mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3}{\mathrm{Z}}\) \(=\frac{8.57 \times 6.022 \times 10^{23} \times\left(3.3 \times 10^{-8}\right)^3}{2} \)
\( \mathrm{M}=93 \mathrm{~g} / \mathrm{mol}\)
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