Answer to Question #135218 in General Chemistry for abby

Question

Lead, Pb, is used in solders and as radiation shield. It adopts the face centered cubic unit structure with each of the atom having a diameter of 0.35 nanometer. Find the theoretical density of lead if the molecular weight of this metal is 207.2 g/mol.

Answer 1

$$V_{atom} = {4\pi \over 3}d^3 = {4\pi \over 3}(0.35 nm)^3 = 0.18 nm^3 = 0.18*10^{-27} m^3$$

$$V_{total} = V_{atom}N_A = 0.18*10^{-27}*6.02*10^{23} = 1.0836*10^{-4} m^3$$

$$d = {m \over V_{total}} = {207.2 g \over 1.0836*10^{-4} m^3} = 191.21*10^4 g/m^3 = 1912.1 kg/m^3$$