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Inorganic and Applied Chemistry

Example 2- P:

Density of tungsten (W)

The transition metal tungsten (W) assumes bcc-structure. The atomic radius of tungsten atoms is 1.37 Å (r

= 1.37×10-8cm) and the molar mass of tungsten is Mw = 183.84 g/mole. What is the density of tungsten

metal?

We know that when we are dealing with bcc-structures each unit cell contains 2 atoms (see Table 2- 3 on

page 84). The density of tungsten metal can thus be determined as follows:

Volumeof unitcell

Densityof tungsten Mass of^2 W^ atoms

The mass of 2 tungsten atoms can be calculated from the molar mass and Avogadro’s number.

g

mole

mole

g

N

M

Massof W atom

A

w 22

6. 022 1023 1 2 6.^10610

183. 84

2 2

The volume of the unit cell is determined from the atomic radius since we know the connection between

the side length of the unit cell b and the atomic radius raccording to Table 2- 3 on page 84.

23 3

3

8

½

3

½

(^31). 3710 3. 16710
3
4
3
4
Volumeof unitcell b r^ cm cm



!
"^

$
%
&
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!
"^

$
%
&
'
The density of tungsten metal can now be calculated.
3
23 3
22
19. 28 /
3. 16710
6. 10610
g cm
cm
g
Densityof tungsten
(^)
The calculations can also go the other way. If the density of a metal and packing structure is known, the
atomic radius can be calculated. We are going to try this in the following example.
Chemical compounds