# Theoretical Lattice Energy for MgF2

1. Jun 16, 2012

### 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
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.
http://img411.imageshack.us/img411/4670/quiqui.jpg [Broken]

Last edited by a moderator: May 6, 2017
2. Jun 17, 2012

### Infinitum

Hi pollycampos!!

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
3. Jun 17, 2012

### pollycampos

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?

Last edited by a moderator: May 6, 2017
4. Jun 17, 2012

### 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.

Last edited by a moderator: May 6, 2017
5. Jun 17, 2012

### pollycampos

Thank you a lot, Infinitum 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?

6. Jun 17, 2012

### Infinitum

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.

7. Jun 17, 2012

### pollycampos

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.

8. Jun 17, 2012

### Infinitum

Ruh-roh!! I wouldn't have explained it that way if I knew you had to write reasons :tongue2:

9. Jun 17, 2012

### pollycampos

10. Jun 17, 2012

### Staff: Mentor

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

$$E=-\frac{N_A M z^+ z^- e^2}{4 \pi \epsilon_0 r_0}(1-\frac 1 n)$$

11. Jun 17, 2012

### pollycampos

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

12. Jun 17, 2012