Theoretical Lattice Energy for MgF2

pollycampos

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



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.

What's wrong? Maybe the sum of ionic radius? (I added the Mg ionic radius plus 2 times F radius).

Infinitum

Hi pollycampos!!

Why add twice the fluorine radius? You need the nearest distance to the neighboring ion. What would you get, then?

pollycampos

So I added 86 + 116 = 202, and the result is:

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

Infinitum

Based on the given information, this answer looks correct. There might be errors in measuring the values that were given, and hence the discrepancy.

pollycampos

Thank you a lot, Infinitum The radius information was given by my teacher's book, so I guess it isn't wrong... I thought the results should be very close, because MgF2 is a very ionic solid, no?

Infinitum

http://en.wikipedia.org/wiki/Born%E2...ttice_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.

pollycampos

Oh yes, I think I should write that in my homework Is there another reason for the experimental value be different from the theoretical? I have to write 2 reasons.

Infinitum

Ruh-roh!! I wouldn't have explained it that way if I knew you had to write reasons

pollycampos

Ohh but I have found a pdf file talking about it https://chemicalparadigms.wikispaces...e+enthalpy.pdf, but it gave only this reason

Borek

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]

pollycampos

Thank you, I didn't know how to use the LaTeX

Borek

http://www.physicsforums.com/showthread.php?t=546968