Question

What is the molar mass of an element that crystallizes in a body-centered cubic unit cell with a density equal to 0.971 g/cm³ and radius of 1.853 A?

Answer 1

edge length of the unit cell

Calculate the value for 4r (refer to the above diagram):

radius for barium = 1.853 A or 185.3 pm

4r = 741.2 pm

2) Apply the Pythagorean Theorem:

d² + (d√2)² = (741.2)²

3d² = 549377

d² = 183125.813333. . .

d = 427.9 pm

Convert pm to cm:

427.9 pm x 1 cm/10¹⁰ pm = 330.6 x 10¯¹⁰ cm = 4.279 x 10¯⁸ cm

Calculate the volume of the unit cell:

(4.279 x 10¯⁸ cm)³ = 7.8365 x 10¯²³ cm³

Calculate mass of the 2 atoms in the body-centered cubic unit cell:

0.971 g/cm³ times 7.8365 x 10¯²³ cm³ = 7.6075 x 10¯²³ g

The mass of one atom :

7.6075 x 10¯²³ g / 2 = 3.8037 x 10¯²³ g

5) The atomic weight in g/mol:

3.8037 x 10¯²³ g times 6.022 x 10²³ mol¯¹ = 22.91 g/mol