Question

When a gold cristallizes , It form FCC cell the unit cell edge length is 408 pm. Calculate the density of gold molar mass of gold is 197 g/mol

Answer 1

Answer:

The density of gold is 19.26 $g/cm^{3}$

Explanation:

The Density = $\frac{M*n}{a^{3}* N_{A} }$

M = Molar mass of gold = 197 g/mol

n = Number of atoms = 4 for FCC unit cell

a = unit cell edge length = 408 pm = $408*10^{-12}$ m

$N_{A}$ =  avogadro number = $6.022 * 10^{23}$

Density = $\frac{197*4}{(408*10^{-12}) ^{3}* 6.022 * 10^{23}}$

             = 19266595.39 $g/m^{3}$

             = 19.26 $g/cm^{3}$

Therfore the density of gold = 19.26 $g/cm^{3}$