ENERGETICS 75
where A is a constant for a particular crystal type. z+ and z~ are the
charges on the ions, r^ and r~ are the ionic radii (see p. 29) and B
is a small constant of repulsion. The important quantities which
determine the magnitude of the lattice energy are, therefore, ionic
charges z. and the ionic radii r. Since z increases and r decreases
across a period it is not surprising to find that a Group II halide
has a much higher lattice energy than the corresponding Group I
halide. Calculated lattice energies for the alkali metal halides are in
good agreement with values determined from Born-Haber cycle
measurements; for example for sodium chloride, the cycle gives- 787 and the calculation - 772 kJ mol ~^1.
For other compounds, the agreement is not always so good. The
assumption that the lattice is always wholly ionic is not always true;
there may be some degree of covalent bonding or (where the ions
are very large and easily distorted) some appreciable van der Waals
forces between the ions (p. 47).
IONIC COMPOUNDS: STOICKIOMETRY
To date there is no evidence that sodium forms any chloride other
than NaCl; indeed the electronic theory of valency predicts that
Na+ and Cl~, with their noble gas configurations, are likely to be
the most stable ionic species. However, since some noble gas atoms
can lose electrons to form cations (p. 354) we cannot rely fully on
this theory. We therefore need to examine the evidence provided
by energetic data. Let us consider the formation of a number of
possible ionic compounds; and first, the formation of "sodium
dichloride", NaCl 2. The energy diagram for the formation of this
hypothetical compound follows the pattern of that for NaCl but an
additional endothermic step is added for the second ionisation
energy of sodium. The lattice energy is calculated on the assumption
that the compound is ionic and that Na^2 + is comparable in size
with Mg^2 +. The data are summarised below (standard enthalpies
in kJ):
A^ enthalpy of atomisation for sodium (unchanged) +108
Ah 2 first ionisation energy for sodium (unchanged) +496
Ah 2 ' second ionisation energy for sodium (additional) +4561
Ah 3 enthalpy of atomisation of chlorine, x 2 (since two
atoms are needed) + 242
Ah 4 electron affinity of chlorine, x 2 (two ions are formed) — 728
Ah 5 calculated lattice energy —2539