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Theoretical Lattice Energy for MgF2

  1. Jun 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the theoretical lattice energy for MgF2 (Born-Landé equation)

    Ionic radius Mg+2 (coordination number 6) = 86 pm
    Ionic radius F- (coordination number 3) = 116 pm
    Madelung constant = 2.408
    n = 7

    2. Relevant equations
    b0dedee27d206a607aa2c0343ad9608a.png


    3. The attempt at a solution
    I'm having problems with this equation, because its result is very different from the experimental lattice enthalpy of MgF2 (-2962 kJ/mol), and it must be similar.
    http://img411.imageshack.us/img411/4670/quiqui.jpg [Broken]
    What's wrong? Maybe the sum of ionic radius? (I added the Mg ionic radius plus 2 times F radius).
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 17, 2012 #2
    Hi pollycampos!! :smile:

    Why add twice the fluorine radius? You need the nearest distance to the neighboring ion. What would you get, then?
     
    Last edited by a moderator: May 6, 2017
  4. Jun 17, 2012 #3
    So I added 86 + 116 = 202, and the result is:
    http://img546.imageshack.us/img546/1336/quinooo.jpg [Broken]
    It's still kind of far away from the experimental result (-2962 kJ/mol), no? Or is this result right?
    Thank you in advance, Infinitum :biggrin:
     
    Last edited by a moderator: May 6, 2017
  5. Jun 17, 2012 #4
    Based on the given information, this answer looks correct. There might be errors in measuring the values that were given, and hence the discrepancy.
     
    Last edited by a moderator: May 6, 2017
  6. Jun 17, 2012 #5
    Thank you a lot, Infinitum :smile: The radius information was given by my teacher's book, so I guess it isn't wrong...:uhh: I thought the results should be very close, because MgF2 is a very ionic solid, no?
     
  7. Jun 17, 2012 #6
    http://en.wikipedia.org/wiki/Born–Landé_equation#Calculated_lattice_energies

    The equation gives approximately equal values to the actual lattice energies. Usually less. This is because the ionic crystals, however 'ionic' you might think of them, do have a degree of covalency. You can never have a perfectly ionic solid.

    Edit : In MgF2, Mg has a +2 charge, which by Fajan's rules creates a greater degree of covalency. It also is quite small, even smaller than sodium so that leads to a greater deviation from ionic behavior.
     
  8. Jun 17, 2012 #7
    Oh yes, I think I should write that in my homework :tongue: Is there another reason for the experimental value be different from the theoretical? I have to write 2 reasons.
     
  9. Jun 17, 2012 #8
    Ruh-roh!! I wouldn't have explained it that way if I knew you had to write reasons :tongue2:
     
  10. Jun 17, 2012 #9
  11. Jun 17, 2012 #10

    Borek

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    Staff: Mentor

    Please note it is much easier to use LaTeX built into forums for such equations than to input them as images.

    [tex]E=-\frac{N_A M z^+ z^- e^2}{4 \pi \epsilon_0 r_0}(1-\frac 1 n)[/tex]
     
  12. Jun 17, 2012 #11
    Thank you, I didn't know how to use the LaTeX :tongue:
     
  13. Jun 17, 2012 #12

    Borek

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    Staff: Mentor

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