What Went Wrong in Calculating the Density of Na Metal?

[daviddee305]

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/cm³The correct answer is 1.00 g/cm³... What went wrong in my calculations?

 

[tiny-tim]

body-centered cubic
…
[4 Na Atoms/unit cell] …

Hi daviddee305!

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)?

 

[daviddee305]

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.

 

[tiny-tim]

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.

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