Born Haber Cycles

Lattice enthalpy is the ionic equivalent of covalent bond energy. In covalently bonded molecules it's fairly easy to define a single bond - but this isn't possible in an ionic lattice where every positive ion is being attracted to every negative ion from all directions (and vice versa). So we can't isolate a single bond between one anion and one cation - so we just worry about the attractive energy of a given amount.

Born Haber cycles give a theoretical value for lattice enthalpies, using experimentally derived values. The reason why there are often discrepancies between the theoretical and experimental values, is because the model assumes a purely ionic system .

I'm afraid you're not making much sense to me.

If you are calculating a value from a theoretical model like the Born-Haber cycle, this gives you a theoretical value. The experimental value (one that is measured experimentally) may agree or disagree with that theoretical value. If it does, you have a good model, if it doesn't the model doesn't work well for that substance.

That can't be right because according to all my textbooks, my teacher and various website, the Born Haber cycles gives an experimental value for the lattice energy. I know that it is experimental, I just don't understand how because ionisation energy and electron affinity values are theoretical values.

I guess I'm taking the two terms a bit too literally.

The values calculated from the Born-Haber cycle could be considered to be ''indirect'' experimental values if all of the other values are experimental. Ionisation energies are fairly straight forward to measure. You can also measure electron affinities, it's just a real pain to do so.

ionisation, electron affinity and atomisation energies are theoretical

No idea what you are trying to say here - all these are determined experimentally.

What makes them "theoretical"?

You start with the ions and combine them to create the lattice. This process produces energy. If ions were just point charges, that would be the only process present, and the energy produced would be exactly the lattice energy. However, when ions combine they create a compound, which is in part covalent, Thus the energy produced can be split into two parts (or two stages of the ion combination) - one is responsible for the creation of the covalent bond, the other is responsible for the creation of lattice from the product of the first stage. We are not able to measure these things separately, so the lattice energy calculated from the BH cycle is overestimated by the first part.

What you're saying is that the BH cycle gives a value that assumes the compound is purely ionic, but the value the BH cycle gives DOES take into account the degree of covalency in the bond?

just to clarify, do ionisation energy and electron affinity values assume that the atoms that form pure ions, or do they take into account the degree of covalency the bond might have?

Sorry, you've lost me. A gives B but A gives C?



Ionisation and affinity are properties of an ion. They don't depend on the identity of the counterion - so they can't take covalent character of the salt into account.

So just to clarify the value of enthalpy of formation is what results in the the theoretical lattice energy being less exothermic than the experimental lattice?

No. Think of it in this context: you do an experiment to find out the lattice enthalpy of a molecule, e.g. Al2Cl3 using a born haber cycle. You use a combination of the enthalpy of formation, atomisation, ionisation and electron affinity to calculate the lattice enthalpy. The value you get from doing this experiment is your experimental value.

There is also a theoretical value. This theoretical value is based on a model, the "perfect ionic model" which predicts a theoretical value based on the following assumptions:
- Is purely ionic, with no covalent character in bonding
- Charge density of ionic radii is evenly distributed in perfect spheres

Depending on how different your experimental value is to this theoretical value based on the perfect ionic model tells you whether your experimental value fits the perfect ionic model or doesn't.

If your experimental value is very different for lattice enthalpy, such as in the case of Aluminium chloride, this tells us that Al2Cl3 doesn't fit the perfectly ionic model. This would suggest aluminium chloride has some covalent character in bonding which distorts the charge density of electrons so is't perfectly ionic. It's this that makes the lattice enthalpy of your compound from experimental value different from the theoretical value.

On the other hand the experimental value and theoretical value could be very similar suggesting the ionic bonding in compound formed has no/very little covalent character and so is perfectly ionic with evenly spread charge density, e.g. NaCl.

Hope that explains it.

This is good



But you have not chosen a very good example. At room temperature aluminium chloride is covalent (it is Al₂Cl₆ and at higher temperatures it becomes AlCl₃)

The classic example is silver chloride, whose experimental and theoretical lattice enthalpies are very different...

but why? which specific part of the BH cycle process for calculating lattice enthalpy makes it different to the theoretical one?

Lattice enthalpy = electron affinity + ionisation enthalpy + atomisation enthalpy - enthalpy of formation

It's mostly the atomisation and formation enthalpies which make the experimental different from theoretical for the reasons I said earlier.

Silver chloride for instance has some covalent character in its bonding. This reduces the amount of energy needed to form one mole of gaseous element from its compound as covalent bonding is weaker than electrostatic attraction in ionic bonding so less energy needed to break its bonds, so is less exothermic than theoretical. The same thing applies in the enthalpy of formation to make the experimental value different from the theoretical.

The key point is the covalent character in bonding is what makes the experimental different from theoretical.