Question

An element has ccp packing with a face-centered cubic unit cell. its density is 8920 kg/m3 and the unit cell volume is 4.72 x 10-26 l. calculate the molar mass (g/mol) of the element to three significant figures.

Answer 1

63.4 g/mol
   First, let's determine how many atoms per unit cell in face-centered cubic. There is 8 corners, each of which has 1 atom, and each of those atoms is shared between 8 other unit cells. So 8*1/8 = 1 atom per unit cell. Additionally, there are 6 faces, each of which has 1 atom that's shared between 2 unit cells. So 6*1/2 = 3 atoms per unit cell. So each unit cell has the mass of 1+3 = 4 atoms. Since there is 1000 liters per cubic meter, the mass per liter is 8920 kg/1000 = 8.920 kg/L. Now the mass per unit cell is 8920 g * 4.72x10^-26 = 4.21024x10^-22 g per unit cell. The mass per atom is 4.21024x10^-22 g / 4 = 1.05256x10^-22 g/atom, Finally, multiply by Avogadro's number, getting 1.05256x10^-22 g/atom * 6.0221409x10^23 atom/mol = 63.38664625704 g/mol.
   Rounding to 3 significant digits gives 63.4 g/mol.