An alkali metal has density . It has cubic unit cell with edge length . Reaction of chunk of the met — Solid State Chemistry Question
Question
An alkali metal has density $4.5 \text{ g/cm}^3$. It has cubic unit cell with edge length $400 \text{ pm}$. Reaction of $7.68 \text{ cm}^3$ chunk of the metal with an excess of HCl solution gives a colourless gas which occupies $4.54 \text{ L}$ at $0^\circ\text{C}$ and 1 bar. The unit cell of metal is
Answer: B
💡 Solution & Explanation
Mass of metal = $7.68 \times 4.5 = 34.56 \text{ g}$. Moles of $H_2$ gas = $4.54 / 22.7 = 0.2 \text{ mol}$. Moles of alkali metal = $2 \times 0.2 = 0.4 \text{ mol}$. Molar mass of metal = $34.56 / 0.4 = 86.4 \text{ g/mol}$. $Z = \frac{d \times N_A \times a^3}{M} = \frac{4.5 \times 6.022 \times 10^{23} \times (4 \times 10^{-8})^3}{86.4} \approx 2$. $Z=2$ corresponds to BCC. Therefore, correct answer is B.
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