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Density of an Ionic Crystal

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data
    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 teh density of LiCl.

    2. Relevant equations

    3. 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.

    [tex]\rho[/tex] = 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...

    [tex]\rho[/tex] = 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.
  2. jcsd
  3. Nov 29, 2008 #2
    sorry, i seem to have confused fcc with bcc...
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