An alkali metal has density 4.5 g/cm³. It has cubic unit cell with edge length 400 pm. Reaction of 7.68 g chunk of the metal with an excess of solution gives a colourless gas which occupies 4.54 L at

Question

An alkali metal has density 4.5 g/cm³. It has cubic unit cell with edge length 400 pm. Reaction of 7.68 g chunk of the metal with an excess of $HCl$ solution gives a colourless gas which occupies 4.54 L at 0 °C and 1 bar. The unit cell of metal is

Prashant Kotian · Accepted Answer

Correct answer: B. M + → M+ + Cl- + 0.5 . Moles of at 0 °C and 1 bar = 4.54 L / 22.7 L/mol = 0.20 mol. Moles of alkali metal reacted = 2 × 0.20 = 0.40 mol. Molar mass of metal M = 7.68 g / 0.40 mol = 19.2 g/mol. Using density: ρ = (Z × M) / (Na × a³) => 4.5 = (Z × 19.2) / (6 × 10^23 × (4 × 10^-8)³) => Z = 2. Since Z = 2, the metal forms a Body-Centred Cubic (BCC) unit cell.

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