Thermodynamic aspects: the Irving–Williams series

   In aqueous solution, water is replaced by other ligands (equation 1.1) and the position of equilibrium will be related to the difference between two LFSEs, since Δ_oct is ligand-dependent.

      (1.1)

Table 1.1 lists overall stability constants for [M(en(₃]²⁺‏ and [M(EDTA)]^2- high-spin complexes for d⁵ to d¹⁰ first row M²⁺‏ ions. For a given ligand and cation charge, ΔS^o should be nearly constant along the series and the variation in log β_n should approximately parallel the trend in values of ^_ΔH^o. Table 1.1 shows that the trend from d⁵ to d¹⁰ follows a ‘single hump’, with the ordering of log β_n for the high-spin ions being: Mn²⁺‏ < Fe^2‏+ < Co^2‏+ < Ni^2‏+ < Cu²⁺‏ > Zn^2+‏

Table 1.1 Overall stability constants for selected high-spin d-block metal complexes.

   This is called the Irving–Williams series and is observed for a wide range of ligands. The trend is a ‘hump’ that peaks at Cu²⁺‏ (d⁹) and not at Ni²⁺‏ (d⁸) as might be expected from a consideration of LFSEs  while the variation in LFSE values is a contributing factor, it is not the sole arbiter. Trends in stability constants should bear a relationship to trends in ionic radii (see Appendix 6); the pattern in values of rion for 6- coordinate high-spin ions is: Mn²⁺‏ > Fe^2+‏ > Co²⁺‏ > Ni^2‏+ < Cu^2+‏ < Zn^2‏+  We might expect rion to decrease from Mn²⁺‏ to Zn²⁺‏ as Z_eff increases, but once again we see a dependence on the d n configuration with Ni²⁺‏ being smallest. In turn, this predicts the highest value of log β_n for Ni^2‏+. Why, then, are copper(II) complexes so much more stable than might be expected? The answer lies in the Jahn–Teller distortion that a d⁹ complex suffers; the six metal–ligand bonds are not of equal length and thus the concept of a ‘fixed’ ionic radius for Cu^2+‏ is not valid. In an elongated complex such as [Cu(H₂O)₆]^2‏+, there are four short and two long Cu^_O bonds. Plots of stepwise stability constants for the displacement of H₂O by NH₃ ligands in [Cu(H₂O)₆]²⁺‏ and [Ni(H₂O)₆]^2‏+ are shown in Figure 1.1; for the first four substitution steps, complex stability is greater for Cu^2‏+ than Ni²⁺‏, reflecting the formation of four short (strong) Cu^_N bonds. The value of logK₅ for Cu^2+‏ is consistent with the formation of a weak (axial) Cu^_N bond; logK₆ cannot be measured in aqueous solution.

Fig. 1.1 Stepwise stability constants (logKn) for the displacement of H₂O by NH₃ from [Ni(H₂O)₆]²⁺‏ (d⁸) and [Cu)H₂O)] ^2+‏ (d⁹).

The magnitude of the overall stability constant for complexation of Cu²⁺‏ is dominated by values of K_n for the first four steps and the thermodynamic favourability of these displacement steps is responsible for the position of Cu²⁺‏ in the Irving–Williams series.

Fig. 1.2 The variation in values of E^o(M²⁺‏/M) as a function of d n configuration for the first row metals; the point for d⁰ corresponds to M = Ca.