A metal 'M' (atomic mass = 31.25) crystallizes in CCP but it has some vacancy defect. If the edge le — Solid State Chemistry Question
Question
A metal 'M' (atomic mass = 31.25) crystallizes in CCP but it has some vacancy defect. If the edge length of the unit cell is 500 pm and the density of the metal is $1.6075 \text{ g/cm}^3$, then the number of moles of metal atoms missing per litre of the crystal is (1 amu = $1.67 \times 10^{-24} \text{ g}$)
Answer: 2
💡 Solution & Explanation
Theoretical density $d_{theo} = \frac{4 \times 31.25 \times 1.67 \times 10^{-24}}{(5 \times 10^{-8})^3} = \frac{125 \times 1.67 \times 10^{-24}}{125 \times 10^{-24}} = 1.670 \text{ g/cm}^3$. The density difference is $1.670 - 1.6075 = 0.0625 \text{ g/cm}^3 = 62.5 \text{ g/L}$. Moles missing per litre = $\frac{62.5 \text{ g/L}}{31.25 \text{ g/mol}} = 2.0 \text{ mol/L}$. Therefore, correct answer is 2.
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