Most of the thermodynamic data available comes from experimentation. However, there are certain values that can also be obtained by theoretical means. This allows us to compare and verify the models used in the theory.
If the experimentally determined values agree with the theoretical values it provides support for the theoretical model.
Theoretical lattice enthalpy
The value of lattice enthalpy for an ionic compound can be calculated from a consideration of the electrostatic forces within the lattice. This was briefly discussed in a previous section. Fortunately the actual details of how this is done are not required for the Syllabus; suffice to know that the electrostatic forces within a lattice are dependent on the magnitude of the charges and the distances between them, the ionic radius sum.
The total electrostatic force within the ionic structure is also dependent on the type of structure. Caesium chloride, for example, has an 8-coordinated structure, whereas sodium chloride has a 6-coordinated structure. In the caesium chloride structure, each caesium and chloride ion has eight nearest neighbours to be attracted to, while in the sodium chloride structure, each sodium and chloride ion has only six nearest neighbours.
There are also ions with the same charge, rather more distant, which weaken the structure. These repulsive forces must also be taken into account when carrying out the calculation. The chemist Madelung derived the equation that is used for determining lattice energies. The constant 'M' in the equation is called the Madelung constant and is dependent on the type of crystal structure.
Where z is the ionic charge, e is the charge on an electron, and 'r' is the distance between nearest neighbour oppositely charged ions.
The point being, that the total force within each structure can be calculated from first principles and, from it, the total energy needed to separate the structure into gaseous ions, the lattice enthalpy.
Experimental lattice enthalpy
Lattice enthalpies can also be found experimentally using Born-Haber cycles. These values are obtained after many expermental studies using different systems. The thermodynamic principles of Hess' law are used to narrow the final values down to those accepted in the literature.
Pure ionic model
It is normal for the experimental values to not be exactly the same as the theoretical. This is due to the usual experimental errors and inaccuracies. However, in some cases this deviation is considerable, and when this occurs, it calls into question the actual validity of the model being used to describe the structure.
Distorted ionic model
We assume that all 'ionic' structures are equally 'ionic', which means to say that the ions are separate entities within the structure. However, it seems that in certain structures with large anions (negative ions) and small highly charged cations (positive ions), there is a tendency for the cations to draw electron density back towards themselves from the anions, creating a covalent-type interaction.
This means that the theoretical calculations are less valid, as we are not dealing with a purely ionic model. This deviation often occurs with large anions as they are unable to hold onto their outer electrons as tightly as small anions. They are more easily polarised by the strongly electron attracting positive ions. This produces a degree of covalency in the structure that is reflected in deviation from the lattice enthalpies produced theoretically, based on a purely ionic model.
Other situations that produce deviation include weakly electropositive metals, for which the ions have more of a tendency to form metal atoms. This is the case for silver salts, in which the experimentally obtained lattice enthalpies deviate considerably from the theoretical values.
Example: Theoretical and experimental values of the silver chloride and sodium chloride.
There is good agreement between theoretical and expermiental values for sodium chloride, whereas the agreement is poor as regards the values obtained for silver chloride. This indicates that the actual bonding in silver chloride deviates from that of a purely ionic model and that there is a considerable degree of covalency involved in the structure.