[Single-digit Integer] Methane crystallizes in a cubic unit cell with edge length 0.6 nm. The density of solid is only slightly greater than the density of liquid . If the density of liquid is 0.5 g/c

Question

[Single-digit Integer] Methane crystallizes in a cubic unit cell with edge length 0.6 nm. The density of solid $CH_4$ is only slightly greater than the density of liquid $CH_4$. If the density of liquid $CH_4$ is 0.5 g/cm3, the number of $CH_4$ molecules per unit cell is

Prashant Kotian · Accepted Answer

Correct answer: 4. Molar mass of = 16 g/mol. Volume of unit cell V = a^3 = (0.6 * 10^-7 cm)^3 = 2.16 * 10^-22 cm3. Mass of unit cell = Density * V = 0.5 * 2.16 * 10^-22 = 1.08 * 10^-22 g. Number of molecules per cell Z = Mass * Na / M = (1.08 * 10^-22 * 6 * 10^23) / 16 = 64.8 / 16 = 4.05 \u2248 4.

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