The thermodynamic 6s inert pair effect

We confine attention here to the conversion of a metal halide MX_n into MX_{n + ‏2}:

In the simplest possible case, both halides are ionic solids and the energy changes involved are:

• absorption of the lattice energy of MXn;
• absorption of IE_(n‏+1) IE_(n‏+2) to convert Mⁿ⁺(g) into M^(n‏+2)(g);
• liberation of the enthalpy of formation of 2X^- (g) (which is nearly constant for X = F, Cl, Br and I, see Appendices 9 and 10);
• liberation of the lattice energy of MX_n+‏2. For a given M, the difference between the lattice energies of

MX_n and MX_n+‏2 is greatest for X = F, so if any saline halide MX_n+‏2 is formed, it will be the fluoride. This treatment is probably a good representation of the conversion of TlF

into TlF₃, and PbF₂ into PbF₄. If, however, the halides are covalent compounds, the energy changes in the conversion are quite different. In this case, n times the M^_X bond energy in MX_n and 2Δ_fH^o(X,g) have to be absorbed, while (n ‏+ 2) times the M^_X bond energy in MX_n‏+2 is liberated; IE_(n‏+1) and IE_(n+‏2) are not involved. The most important quantities in determining whether the conversion is possible are now the M^_X bond energies in the two halides. The limited experimental data available indicate that both sets of M^_X bond energies decrease along the series F > Cl > Br > I, and that the M^_X bond energy is always greater in MX_n than in MX_(n‏+2). The overall result is that formation of MX_n+‏2 is most likely for X = F. (The use of bond energies relative to ground-state atoms is unfortunate, but is inevitable since data are seldom available for valence state atoms; in principle, it would be better to consider the promotion energy for the change from one valence state of M to another, followed by a term representing the energy liberated when each valence state of M forms M^_X bonds. However, this is beyond our present capabilities.)

The third possibility for the MX_n to MX_n+‏2 conversion, and the one most likely in practice, is that MXn is an ionic solid and MX_n+‏2 is a covalent molecule. The problem now involves many more quantities and is too complicated for discussion here. Representative changes are the conversions of TlCl to TlCl₃, and of PbCl₂ to PbCl₄.  Finally, we must consider the effect of varying M down a group. In general, ionization energies  and lattice energies of compounds decrease as atomic and ionic radii  increase. It is where there is actually an increase in ionization energies, as is observed for the valence s electrons of Tl, Pb and Bi, that we get the clearest manifestations of the thermodynamic 6s inert pair effect.

   Where covalent bond formation is involved, a really satisfactory discussion of this inert pair effect is not yet possible, but the attempt at formulation of the problem can nevertheless be a rewarding exercise.