(compiled from various data sources, which vary!)

for groups 1 & 2 cations versus group 6/17 & group 7/17 anions

(individual ionic formula not quoted, I expect you to be able to work them out!)

M = group 1 or group 2 metal  and X = group 6/16 non–metal or group 7/17 halogen

The formulae are either MX, M₂X, MX₂ or MX e.g. NaCl, Na₂O, MgCl₂, MgO etc.

expt. means calculated from the Born–Haber cycle using experimental data bar the ΔH^θ_LE

theo. means calculated assuming a perfect theoretical pure ionic structure a 'model' ionic lattice.

Here the lattice enthalpies (kJ/mol) of Group 1 and 2 metal halides and oxides are compared, together with the radii of the constituent ions.

Coulombs inverse square law

Most lattice enthalpy trends can be explained with reference to Coulomb's proportionality inverse–square law relating the attractive force F between two electrically charged particles c₊ and c_–, a distance d apart in terms of the particle centres e.g. the nuclei of a simple monatomic ions.

F c₊ x c_– / d²

Note that d = r₊ + r_–

(d = total of the two ionic radii, assuming a simple lattice structure)

 

Typical trends in lattice enthalpies of group 1/2 metal halides, oxides and sulfides

As you would expect certain patterns are clear and consistent e.g.

The smaller the ionic radii and the greater the charge on the ions, the stronger the ionic bond and the greater the lattice enthalpy e.g.

Decrease in lattice enthalpy from LiF to CsF as the cation radius increases decreasing the electrostatic force between the ions.

Increase lattice enthalpy from KI to KF as the anion radius decreases.

This argument assumes the compounds are highly ionic, with little covalent character in the bonding.

 

Comparing ionic compounds which have two isoelectronic ions

Comparing the lattice enthalpy of compounds whose ions are isoelectronic e.g.

Compare NaF and MgO, where all ions are isoelectronic for [1s²2s²2p⁶] = [Ne]

[Ne] = [Na⁺], [F^–], [Mg²⁺] = [O^2–]

and they both have a 'sodium chloride' crystal lattice structure.

The lattice enthalpy of magnesium oxide is approximately 4x greater than that of sodium fluoride.

On a simple electrostatic argument, this fits in with Coulomb's inverse square law

i.e. ignoring radii differences, you have a force ratio of 1 : 4

NaF (c⁺ x c^– = 1+ x 1– = 1) versus MgO (c⁺ x c^– = 2+ x 2– = 4),

 

Trends in melting points of group 1 and group 2 metal halides

This also shows up in terms of melting points: NaCl 1074 K and MgO 3125 K

See 2.2m for more on melting points.

 

Lattice enthalpy anomalies due to covalent character

When you have a more highly charged cation and/or a larger polarizable anion, you tend to get some covalent character.

The greater the difference in experimental lattice enthalpies versus theoretically calculated lattice enthalpies, the greater the degree of covalent character of the 'ionic ' bond.

Comparing the experimental and theoretical lattice enthalpies of:

barium fluoride 2352 and 2341 kJmol^-1 (large cation, small anion)

Large radius Ba²⁺ ion of low polarising power

and small F^- ion, difficult to polarise.

The two lattice enthalpies are quite similar

lithium iodide 761 and 740 kJmol^-1 (small cation, large anion)

Small highly polarising Li⁺ cation

and large more polarizable I^- anion.

The two lattice enthalpies are significantly different.

so, a greater % difference in the lithium iodide compared to barium fluoride.

Comparison of experimental and theoretical lattice enthalpies