Answer to Question #135218 in General Chemistry for abby

Question #135218

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.


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Expert's answer
2020-09-29T06:52:05-0400
Vatom=4π3d3=4π3(0.35nm)3=0.18nm3=0.181027m3V_{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

Vtotal=VatomNA=0.1810276.021023=1.0836104m3V_{total} = V_{atom}N_A = 0.18*10^{-27}*6.02*10^{23} = 1.0836*10^{-4} m^3

d=mVtotal=207.2g1.0836104m3=191.21104g/m3=1912.1kg/m3d = {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


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