Question

Palladium crystallizes with a face-centered cubic structure. It has a density of 12.0 g/cm³, a radius of 1.38$\AA$, and a molar mass of 106.42 g/mol. Use these data to calculate Avogadro’s number.

Answer 1

For face-centered cubic (FCC) structure,

edge length, $a = 2\sqrt{2}r$ , where, r = radius of the atom or ion

Therefore, $a$ = 2 x 1.414 x 1.38 x 10^-8 cm      [ $\because$ 1 Angstrom = 10^-8 cm]

                     = 3.90 x 10^-8 cm

Volume of the unit cell = $a$³ = (3.90 x 10^-8)³ = 5.93 x 10^-23 cm³

Mass of the unit cell = volume of the unit cell x density = 5.93 x 10^-23 x 12.0 = 7.12 x 10^-22 g

For FCC structure, the number of atoms per unit cell = 4

Thus, the mass of an atom = 7.12 x 10^-22/4 = 1.78 x 10^-22 g

Avogadro's number = molar mass / mass of an atom

Given, molar mass of palladium = 106.42 g/mol

Therefore,

Avogadro's number = 106.42/ (1.78 x 10^-22) = 5.98 x 10²³ mol^-1