## Thermite Born-Haber Cycle and Al2O3 Lattice Energy

Hi all,

On my inorganic exam last week, I wrote a question asking the students to construct a Born-Haber cycle to calculate the heat of reaction for the thermite reaction (nicely timed as our lab staff had just done the demo outside of our classroom for the Gen Chem students). The data that I provided were the first three ionization energies for Fe and Al, the heats of formation for Fe and Al in the gas phase, and the lattice energies for Al_{2}O_{3} and Fe_{2}O_{3}.

Now, here is where things got interesting and surprising to me. I found a thermochemical lattice energy for Fe_{2}O_{3} online (WebElements) and in the CRC Handbook. But I could not find a thermochemical lattice energy for Al_{2}O_{3} anywhere. The best I could do was a calculated value. I turned that into a "learning experience" and asked the students as a follow-up how their answer might have changed if I had found a thermochemical lattice energy for Al_{2}O_{3}. But here is my question: Does anyone know why it is difficult to find a thermochemical lattice energy for Al_{2}O_{3}? It seems like it should not be that much harder to do than Fe_{2}O_{3}.

I began reading your post thinking, "Oh, we did this on our final, I know the answer to this!" only to discover that, no, you had a completely different question.

What's a thermochemical lattice energy?

The thermochemical lattice energy is the closest thing you can get to an "experimental lattice energy." This is the lattice energy derived from a Born-Haber cycle in which all of the other enthalpies have been measured or estimated.

In comparison, a theoretical lattice energy is one calculated based on a model of electrostatic attractions and repulsions in the lattice, i.e. using the Born-Landé equation or the Born-Mayer equation or the Kapustinksii equation. These theoretical lattice energies are typically underestimates of the thermochemical lattice energies, particularly for lattices that deviate from the hard-sphere ionic model.

Given that our illustrious leader was unable to find said *large* number in a CRC or other handy desk references, would you be so kind as to illuminate us living in the darkeness as to the source of your fair wisdom?

Adam

DelH Sub for Al = 10.7 + 294.0 kJ/mol = 304.7

(Wikipedia)

IEs for Al: 578, 1820, 2750 kJ/mol (Tro, 1st ed.)

O2 BDE = 498 kJ/mol (Tro 1st Ed)

EAs for O (in Del H sign conv.) -141, +844 kJ/mol (Tro)

DelHform Al2O3 = -1675.7 kJ/mol (Tro)

I then committed math.

Here's another number (15916 kJ/mol, with no minus sign, see bottom of page of following link) with no reference, so perhaps the author just "did the math" too. This is a lovely web resource, by the way.

http://ibchem.com/IB/ibnotes/full/ene_htm/15.2.htm

And this site gives a reason for why it is not often quoted in books, but it also doesn't give a reference. Haven't heard this one before.

http://www.chemistry-react.org/go/Faq/Faq_11426.html

I suspect you may have put your finger on it, Maggie. Alumina is just so far from "(Al

^{3+})_{2}(O^{2-})_{3}" that to call it an ionic lattice might be considered silly by those "in the know". Certainly, it's pretty darned covalent, and nobody would try to derive the lattice energy for diamond".As for the minus sign, like Electron Affinity, I've seen Lattice Energy (by genchem texts) defined as either the energy

releasedwhen the lattice forms (thus positive) and theenthalpyof lattice formation (and thus negative). Like all sign conventions:1. You're 40% likely to screw it up on a given day.

2. If you really understand it, you can figure it out.

3. It will give the students fits.

4. We're stuck with the ambiguity, because it's all convention. If you withdraw $20 from your bank account, what was the sign of that transaction?

for those of you more conversant in this topic, is it possible to do a quick BH cycle lattice energy calc for Al(+3) AlO3(-3) (assuming some geometry) and my second question is, given that the structure of Al2O3 is the same no matter what you call it, shouldn't the number be the same? I mean, isn't Al(AlO3) just another way of describing Al2O3 (presumably both have bridging oxygens...)

confused, and sorry if this question is confusing.

So, as much as I enjoyed this entry on calculating the lattice energy of alumina, it didn't come *close* to my enjoyment of the disclaimer:

Before attempting any practical work based on the advice and suggestions on this website, you must do the following. Identify any hazards, assess the risks from these hazards, and then decide appropriate control measures to reduce the risks. You must have these approved by those in authority in your school or college laboratory. Do not rely on what is said on this website.

Nice. Way to keep it concise, targeted, and appropriate.

Three years later and I'm sure the conversation is still ongoing. I decided to not let the absence of a thermochemical lattice energy for Al2O3 bother me, and I asked my students a very similar question on our third mdterm. (ie, here's the thermite reaction - can you use all the provided data to calculate an enthalpy change value for the thermite reaction.)

I then added on a small part b in which I said, "Whoa, those lattice enthalpy values for Fe2O3 and Al2O3 are very different from the values we've seen in lecture and on homework. How are they different and why?" The correct answer, of course, is that the 3+ charge on the metal ions leads to a huge value. (A huge negative value.) Some students also pointed out that Al3+ and Fe3+ are fairly small ions, so the small interionic radius would lead to large (again, large negative) lattice enthalpies.

Hi All,

When I saw this I thought "hey, we had that problem when looking for data to make problems for tests too!". I took a look around and stumbled across this problem set for that same problem with a different number: http://www.chem.purdue.edu/chemsafety/Equip/Al2O3LatticeEnergy.htm

I don't really like that they drop signs entirely, but it is worth seeing if the numerical values match what you have been using.

If a source doesn't specify how they are reporting the energy (E lattice or U) they wil probably mess up the sign.

I also saw the 15916 number in the literature (http://pubs.acs.org/doi/abs/10.1021/ic025902a).

Fun.

-Kyle

Hello,

13 years later, and just realizing this post is almost as old as me, I decided that I should contribute.

Going about writing a paper on some chemistry regarding thermites, I felt that a lot of databases neglected many of the chemical combinations that could be used for thermites. I am glad that I have found atleast one forum that guided me a little closer to my goal.

Thanks guys for being cool science people.