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An element with molar mass 27 g/mol forms a cubic unit cell with edge length of 405 pm. If the density of the element is 2.7 g/cm3, what is the nature of the cubic unit cell? - Chemistry

Sum

An element with molar mass 27 g/mol forms a cubic unit cell with edge length of 405 pm. If the density of the element is 2.7 g/cm3, what is the nature of the cubic unit cell?

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Solution

Given: Edge length (a) = 405 pm = 4.05 × 10-8 cm
Molar mass = 27 g mol-1, Density (ρ) = 2.7 g/cm3 

To find: Nature of cubic unit cell

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

Calculation: From the formula,

Density, ρ = `"M n"/("a"^3 "N"_"A")`

∴ `2.7 "g cm"^-3 = (27 "g" "mol"^-1 xx "n")/((4.05 xx 10^-8)^3 "cm"^3  xx  6.022  xx  10^23 "atom mol"^-1)`

∴ n = `(2.7 "g cm"^-3 xx (4.05 xx 10^-8)^3 "cm"^3 xx 6.022 xx 10^23 "atom mol"^-1)/(27 "g mol"^-1)`

= 4.00

∴ Number of atoms in unit cell = 4

Since unit cell contains 4 atoms, it has face-centred cubic (fcc) or ccp structure.

The nature of the given cubic unit cell is face-centred cubic (fcc) or ccp unit cell.

Concept: Cubic System
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Balbharati Chemistry 12th Standard HSC Maharashtra State Board
Chapter 1 Solid State
Exercise | Q 9 | Page 27
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