I cant find the density of platinum please help?

Question

Platinum has a face-centered cubic unit cell. An early calculation of the diameter of platinum was 2.75 angstroms. Based on this what would be the density of platinum? (grams per centimeter cubed)

Atomic weight of Platinum = 195.09 g/mol

Answer 1

First, draw yourself a face centered cubic unit cell using spheres for atoms.

You will find that the atoms will touch along the face diagonal direction. That's how you will figure out the dimension of the unit cell. You will find the length of the face diagonal is 2*diameter of the atom:

d_diagonal=2*2.75e-8cm=5.5e-8 cm

To find length of the cube edge, divide the face diagonal by sqrt(2)

d_edge=3.889e-8 cm

Now you can find the volume of the unit cell:

V_cell=d_edge^3=5.882e-23 cm^3

Now you find the weight per atom:

m_atom=195.09 / 6.022e23 = 3.2396e-22 g

Count up the number of atoms in the unit cell. You will find that there are 4 atoms in one unit cell of FCC crystal structure. So the total mass of atoms in one unit cell is 4x the mass of one atom.

m_cell=4*3.2396e-22 g = 1.2958e-21 g

Now finally find density by dividing mass of one unit cell by volume of one unit cell:

density=m_cell/V_cell=1.2958e-21g / 5.882e-23 cm^3
density=22.03 g/cm^3

Answer 2

The critical missing idea you need is the atomic packing factor.

http://en.wikipedia.org/wiki/Atomic_packing_factor

From grams per mole, you can get grams per atom. With the packing factor and the diameter of the platinum atom, you can get the volume per atom.

From there, the rest is pretty easy.