How Do You Calculate the Density of LiCl in a Face-Centered Cubic Structure?

[roeb]

Homework Statement

The distance between the Li+ and Cl- ions in a LiCl is .257 nm. Use this and the molecular mass of LiCl 42.4 g/mol to compute the density of LiCl.

Homework Equations

The Attempt at a Solution

I am surprisingly having a lot of difficultly with this problem.
The LiCl crystal is face centered (as far as I can tell) so there is an entire LiCl and either a Li or Cl in the center (I think Cl, but I'm not sure).

If I follow the example in the book I can simply find the answer, but it doesn't make sense.

$$\rho$$ = m/V = 42.4 / (2 * 6.02 x 10^23 * r0^3)

This works but I don't understand it. Here is how I attempted to do it...

$$\rho$$ = m/V = (42.4 + 1/2 42.4) / (6.02 x 10^23 * r0^3)

I am assuming that since the problem doesn't give the information I can't look up whether or not Cl is in the middle or even the mass of Li and Cl separately. So I took 1/2 the mass of LiCl hoping that would average out. Unfortunately that gives an incorrect answer.

Does anyone have a way to explain why 1/2 is the correct factor in this case? It seems strange to me.

 

[roeb]

sorry, i seem to have confused fcc with bcc...