Properties: hard, brittle, high mp and bp, often water soluble, electrolytes in solution or melt, usually crystalline. All of this suggests large bond energies.
Necessary conditions for an ionic compound: cation (implies neutral species has a low IP) and anion (implies neutral has a high EA)
We develop a theory of ionic bonding using simple electrostatics. Assume
that the ions behave as point charges (i.e., the ions have no volume).
Then build a lattice from condensation of gas phase ions and use Coulomb's
law to calculate the energy.
Ion Pair
q_{+}, q_{-} are the ionic charges in coulombs
r is the distance between ions in meters
_{0} is the permittivity of free space
Ion square
Since (in this example) q_{+}=-q_{-}
ion cube
Continue this over the entire lattice to give:
N_{0} = Avogadro’s number
Z^{+}, Z^{-} are the ionic charges in units of e (i.e., +1, +2, -1, -2, etc.)
r is the interionic distance
M is called the Madelung constant.
M depends solely on geometry, i.e., the kind of lattice but the internuclear
distances are factored out. Madelung constants are tabulated for all the
common lattice types.
E_{Coul} is negative (all terms are positive except Z^{-}), i.e., the bonding is favorable. In fact, too favorable: the most stable situation is when r = 0.
Why? Initial point charge assumption does not allow for nuclear-nuclear repulsion at close distances.
Correct this empirically: add a term that is repulsive at small r but negligible at larger distances. This means either an exponential term or a 1/r^{n} term with large n.
Born repulsion:
n is known as the Born exponent, B is an arbitrary constant
The lattice energy becomes
Need to find two new quantities: B and n.
Evaluate B at equilbrium because (r_{0} is the equilibrium internuclear distance measured experimentally)
So, at r = r_{0}
To find n, we must move away from the equilibrium position. This means compressing the sample, i.e. measure the compressibility, :
Sample calculation for NaCl:
= 8.854×10^{-12} SI units
e = 1.602×10^{–19} coulombs
M = 1.74756 (NaCl structure)
d = 5.628×10^{-10} m giving r_{0} = 2.814×10^{–10} m
= 4.18×10^{–11} SI
n is found by
This compares to 769.4 kJ/mole experimental (2.4% error)
lattice energies are thermodynamically negative but reported as positive values (like EA)