Calculate the density of Na metal.

  • #1
1. Calculate the density of Na metal. The length of the body-centered cubic unit cell is 4.24 Å.


2. Attempted solution:

[4 Na Atoms/unit cell] * [1 mol Na atoms/(6.022*10^23 atoms)] * [22.99g Na/1 mol Na] = 1.527 * 10-22 g/unit cell

(4.24 Å)3 = 7.6225 * 10-23 cm3/unit cell


[1.527 * 10-22 g/unit cell] / [7.6225 * 10-23 cm3/unit cell] = 2.00 g/cm3


The correct answer is 1.00 g/cm3... What went wrong in my calculations?
 

Answers and Replies

  • #2
tiny-tim
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body-centered cubic

[4 Na Atoms/unit cell] …

Hi daviddee305! :smile:

There are 9 atoms in a body-centered cubic cell (1 in the centre, and one at each vertex), but how many cells is each atom in (and why)? :wink:
 
  • #3
Each corner atom is shared by 8 unit cells, so only (1/8)th of each atom belongs to the body-centered cubic. Plus the one in the middle. Thank you.

That was a great follow-up question, exactly what I needed to see through these confusing diagrams in my text.
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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Each corner atom is shared by 8 unit cells, so only (1/8)th of each atom belongs to the body-centered cubic. Plus the one in the middle. Thank you.

That was a great follow-up question, exactly what I needed to see through these confusing diagrams in my text.

Yup … always go back to the definition. :biggrin:

(And now have a look at http://en.wikipedia.org/wiki/Body-centred_cubic. :wink:)
 

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