Question

Calculate theoretical density of: A) MgO B) Ni

Use r_Ni = 0.06 nm , r_Mg = 0.07 nm, r_O = 0.14 nm for calculations.

Please show all the work!

Answer 1

Theoretical density of MgO

Its type if NaCl and therefore it has 4 atoms of both Mg and O each.

Calculate radius of unit cell

Radius of unit cell = 2 x ( radius of Mg atom and radius of O atom)

2*(0.07+0.14)=0.42 nm

Convert nm to cm

0.42*10^-7cm / 1 pm

4.2 x10^-8 cm

Volume = (radius )^3

(4.2E-8)^3=7.41E-23 cm^3

Calculate mass of 4 atoms of Mg and O

4 ( Molar mass of Mg + molar mass of O ) / NA     …( Na is Avogadro number)

4(24.305+15.998/6.02E23)

2.68E-22 g

Lets plug in the values.

Density of MgO = mass / volume = 2.68E-22 g / 7.41E-23 cm^3

Density of MgO is 3.61 g/cm^3

part B

Ni

Ni has simple cubic structure so that there is 1 atom of Ni in a cell.

Calculate edge of unit cell.

Radius = sqrt (3) a / 4

Lets rearrange above equation in terms of a

a = radius x 4 / sqrt ( 3)

0.14*4/(sqrt(3))=0.3233 nm

Convert radius into cm

0.3232 nm x 1E-7 cm/1 nm

3.232 E-8 cm

Volume = a^3

Volume = ( 3.232E-8)^3

= 3.38 E-23 cm^3

Mass of Ni atoms = 1 x 58.693 / 6.02E23

9.75E-23 g

Lets find density

Density = mass/volume

9.75E-23/3.38E-23

9.75/3.38=2.89 g/cm^3