Question

A substance crystallizes in fcc structure. The unit cell edge length is 367.8 pm. Calculate the molar mass of the substance if its density is 21.5 g/cm³.

Answer 1

Given: Edge length (a) = 367.8 pm = 3.678 × 10^-8 cm, Density = 21.5 g/cm³

To find: Molar mass (M)

Formula: Density (ρ) = `"M n"/("a"^3  "N"_"A")`

Calculation: For an fcc lattice, number of atoms per unit cell is 4.

∴ n = 4

From formula,

Molar mass, M = `("a"^3  "N"_"A"  rho)/"n"`

M = `((3.678 xx 10^-8)^3 "cm"^3 xx 6.022 xx 10^23  "atom mol"^-1 xx 21.5 "g  cm"^-3)/(4  "atom")`

Calculation using log table:

`((3.678 xx 10^-8)^3 xx 6.022 xx 10^23 xx 21.5)/4`

`= ((3. 678)^3 xx 6.022 xx 2.15)/4`

= Antilog₁₀ [3 × log₁₀ 3.678 + log₁₀ 6.022 + log₁₀ 2.15 – log₁₀ 4]

= Antilog₁₀ [3 × 0.5657 + 0.7797 + 0.3324 – 0.6021]

= Antilog₁₀ [1.6971 + 0.5100]

= Antilog₁₀ [2.2071]

= 161.1

= 161.1 g mol⁻¹ 

Molar mass of the substance is 161.1 g mol⁻¹.