Question

When gold crystallizes, it forms face-centered cubic cells. The unit cell edge length is 4 × 10⁻⁸ cm. Calculate the density of gold. Molar mass of gold is 197 g mol⁻¹.

Answer 1

Given: Molar mass (M) = 197 g/mol

Edge length (a) = 4 × 10⁻⁸ cm

Crystal structure = Face-centred cubic (FCC)

Atoms per unit cell (Z) = 4

Avogadro’s number (NA) = 6.022 × 10²³ mol⁻¹

The density (ρ) of a crystal is calculated using the formula:

ρ = `(Z * M)/(a^3 * N_A)`

= `(4 xx 197)/((4 xx 10^-8) * 6.022 xx 10^23)`

= `788/(6.4 xx 10^-23 * 6.022 xx 10^23)`

= `788/38.5408`

= 20.445 g/cm³