[Single-digit Integer] Ice crystallizes in a hexagonal lattice. At the low temperatures at which the structure was determined, the lattice constants were a = 4.53 A and c = 7.41 A. How many molecules

Question

[Single-digit Integer] Ice crystallizes in a hexagonal lattice. At the low temperatures at which the structure was determined, the lattice constants were a = 4.53 A and c = 7.41 A. How many $H_2O$ molecules are contained in a unit cell? (Given that density of ice = 0.92 g/cm3)

Prashant Kotian · Accepted Answer

Correct answer: 4. For a hexagonal unit cell, the volume V is given by: V = a^2 * c * sin(60\u00b0) = (4.53 * 10^-8)^2 * 7.41 * 10^-8 * 0.866 = 1.316 * 10^-22 cm3. Mass of unit cell = Density * V = 0.92 * 1.316 * 10^-22 = 1.21 * 10^-22 g. Number of molecules per cell Z = Mass * Na / M = (1.21 * 10^-22 * 6.022 * 10^23) / 18 = 72.9 / 18 \u2248 4.

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