Answer to Question #21662 in Physical Chemistry for susan1991

Question

The silver crystallizes in a face-centered cubic structure. The drive-side length is 409 pm. Calculate the density of silver.

Answer 1

There are therefore 4 atoms of silver in unit cell.

Mass of an atom = atomic mass / Avogadro's number
Mass of an Atom = 107.87*10^-3 / 6, 02*10 ^ 23 = 1.7912*10 ^-25 kg
Edge length of the unit cell = C = 4R / √2 = 4x 409*10 ^-12 / √2 = 1.157*10 ^-9

Volume of unit cell = C^3 = (1.157*10 ^-9) ^3 = 1, 549*10 ^-27 m^3

ρ = (number of atoms per unit cell) x (1 Atom mass) /(unit cell volume)
ρ = 1.7912*10 ^-25 kg / 1, 549*10 ^-27 m^3
ρ = 115.6 kg/m^3