Question

Iron forms a face centered cubic structure. The covalent radius of silver is 126. pm. The molar mass of silver is 55.845 g/mol. Find the density of silver in g/cm3 from this information. Compare this to the literature value of 7.874 g/cm3.

Answer 1

Ans.

Covalent radius,r = 126 pm = 126 x 10^-12m = 126 x 10^-12 x 10² cm = 126 x 10^-10cm

Molar mass = 55.845g/mol

Density formula is given by

(since volume of the cube = a³)

where m = molar mass

a = edge length of the cube

But, the number of atoms per unit cell has to be accounted. In FCC structure, there are 4 atoms per unit cell.

where Z = no. of atoms per unit cell.

This density formula is for 1 mol of atoms. So, the formula for 1 atom will be

where N_a = Avogadro's number = 6.022 x 10²³ mol^-1

For FCC structure, the relation between the edge length of the cube and radius of atom is

Substitute all the values in the density expression

The density calculated is 8.195 g/cm³ which is lower than the literature value, which could be due to defects in the structure.