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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.
Solution
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.
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