Question

# What is the molar mass of an element that crystallizes in a body-centered cubic unit cell...

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?

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

#### Earn Coins

Coins can be redeemed for fabulous gifts.