Question

When platinum crystallizes, it forms face-centered cubic cells. The unit cell edge length is 392.3 pm. Calculate the density of platinum in g/cm3.?

Answer 1

1 cm = (10 × 10^10)pm 
Therefore;
 the unit length of the cell is equivalent to 3.923 × 10^-8 cm
The volume  of the cubic cell is given by (length)³
 = (3.923×10^-8)³
 = 6.0375 × 10^-23 cm³
Density is calculated by dividing mass with the volume
The atomic mass of platinum 195.064 g/mol ,
Therefore,
The average mass of one atom is; (Avogadro's constant = 6.0×10^23 particles)
        195.064 ÷ 6.022 × 10^23 atoms/mol
           = 3.239 × 10^-22 g/atom
The mass of the 4 platinum atoms in the face centered cubic unit cell:
  (3.239 × 10^-22) × 4 = 129.56× 10^-23 g/unit cell
Therefore;
 Density = (129.56× 10^-23)÷(6.0375 ×10^-23)
                                   = 21.459 g/cm³