oxidation states in aqueous solution

   In the preceding sections, we have, with some degree of success, attempted to rationalize irregular trends in some thermodynamic properties of the first row d-block metals. Now we consider the variation in E^o values for equilibrium 1.1 the more negative the value of E^o, the less easily M²⁺‏ is reduced.

            (1.1)

   This turns out to be a difficult problem. Water is relatively easily oxidized or reduced, and the range of oxidation states on which measurements can be made under aqueous conditions is therefore restricted, e.g. Sc(II) and Ti(II) would liberate H₂. Values of E^o(M^2+‏/M) are related to energy changes accompanying the processes:

   In crossing the first row of the d-block, the general trend is for  Δ_hydH^o to become more negative. There is also a successive increase in the sum of the first two ionization energies albeit with discontinuities at Cr and Cu (Figure 1.1).

Fig. 1.1 The variation in the sum of the first and second ionization energies as a function of d n configuration for the first row metals; the point for d⁰ corresponds to M = Ca.

   Values of Δ_aH^o vary erratically and over a wide range with a particularly low value for zinc (Table 5.2). The net effect of all these factors is an irregular variation in values of E^o)M²⁺‏/M) across the row, and it is clearly not worthwhile discussing the relatively small variations in LFSEs.  Consider now the variations in E^o(M³⁺‏/M²⁺‏) across the row. The enthalpy of atomization is no longer relevant and we are concerned only with trends in the third ionization energy (Table 1.1) and the hydration energies of M^2+‏ and M³⁺‏. Experimental values for E^o(M³⁺‏/M²⁺‏) (Table 1.1) are restricted to the middle of the series; Sc(II) and Ti(II) would reduce water while Ni(III), Cu(III) and Zn(III) would oxidize it. In general, larger values of IE₃ correspond to more positive E^o values; this suggests that a steady increase in the difference between the hydration energies of M³⁺‏ and M^2+‏ (which would become larger as the ions become smaller) is outweighed by the variation in IE₃. The only pair of metals for which the change in E^o appears out of step is vanadium and chromium.

Table 1.1 Standard reduction potentials for the equilibrium M^3‏ً+(aq)+ ‏ e^- ⇋ M²⁺‏ً(aq) and values of the third ionization energies.

   The value of IE₃ for Cr is 165 kJ mol^-1 greater than for V and so it is harder to oxidize gaseous Cr^2+‏ than V^2‏+. In aqueous solution however, Cr^2‏+ is a more powerful reducing agent than V²⁺‏.  These oxidations correspond to changes in electronic configuration of d³ → d² for V and d⁴ → d³ for Cr. The V²⁺‏, V^3‏+, Cr²⁺‏ and Cr^3‏+ hexaaqua ions are high-spin; oxidation of V^2+‏ is accompanied by a loss of LFSE while there is a gain in LFSE (i.e. more negative) upon oxidation of Cr²⁺‏ (minor consequences of the Jahn–Teller effect are ignored). Using values of Δ_oct from Table 20.2, these changes in LFSE are expressed as follows:

Change in LFSE on oxidation of V^2‏+ is

Change in LFSE on oxidation of Cr^2‏+ is

    The gain in LFSE upon formation of Cr³⁺‏ corresponds to ≈150 kJ mol^-1 and largely cancels out the effect of the third ionization energy. Thus, the apparent anomaly of E^o(Cr³⁺/Cr²⁺‏) can be mostly accounted for in terms of LFSE effects – a considerable achievement in view of the simplicity of the theory.