Question

Gold can be alloyed with zinc to form AuZn (unit cell edge 319 pm) in a body-centered cubic lattice. What is the density of the alloy?

Answer 1

edge length = a = 319 pm = 319 pm = 319 x 10^-12 m = 319 x 10^-10 cm

volume = a^3 = ( 319 x 10^-10 )^3 = 3.25 x 10^-23 cm^3

number of Au atoms in BCC = 1

mass of Au atom = 1 x 197 / (6.023 x 10^23) = 3.27 x 10^-22 g

number of Zn atoms in BCC = 1

mass of Zn atom = 1 x 65.38 / (6.023 x 10^23) = 1.086 x 10^-22 g

AuZn mass = 3.27 x 10^-22 g + 1.086 x 10^-22 g = 4.36 x 10^-22 g

density = mass / volume

             = 4.36 x 10^-22 g / 3.25 x 10^-23 cm^3

              = 13.4 g / cm^3