Teaching Born Haber Cycles

I must admit, this is not my favourite topic to teach but it’s something I am working at. What I want to focus on here is not necessarily the cycle – I’m assuming you are OK with this. I’d rather focus this blog post on two other trends that can be identified using the data book:

How lattice enthalpies vary according to:

• Size of the ion
• Charge of the ion

I will also be referring to table 18 of the data book, lattice enthalpies at 298 K (experimental values)

By Benjah-bmm27 – Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=702423

Let’s start dealing with how lattice enthalpy varies with the size of the ion. The lattice enthalpies of the group 1 elements are as follows (when reacting with F^– to make alkali metal fluoride salts, eg NaF):

Li             -1049

Na          -930

K             -829

Rb           -795

Cs           -759

NB, all values are quoted in kJ mol ^-1

The trend to focus on here is that larger ions have smaller lattice enthalpies. The reason, I always find is a bit trickier but essentially as the ions are larger they cannot get as close together as in the smaller ions. This will mean less energy is released when the ionic substance is formed. The strength of the attraction in the smaller ions will be larger than the strength of attraction in the larger ions.

The above trend focuses on the metal ions but this trend is also seen in the non-metal ions, for example, as shown in the following Lithium halides:

F              -1049

Cl            -864

Br            -820

I               -764

(again, all values quoted are in kJ mol^-1)

The trend involving the charge of the ion is also clear to see. If we consider ions of approximately the same size (for example, Sodium Fluoride and Sodium Oxide) we can see that the greater the charge of the ion, the great the lattice enthalpy:

NaF        -930

MgF₂     -2540

This can also be seen with the non-metal ions by considering F- and O2- (which are both, again, approximately the same size).

CaF₂      -2651

CaO        -3401

This shows that the greater the charge on the ion, the more energy is released when the bond forms. My students sometimes muddle this and think it is the other way around. CaF₂ has more bonds than CaO, so more energy is released because more bonds are forming. This is clearly wrong.

What happens is the attraction is great as the charge of the ion increases and this releases more energy.