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Valence and oxidation states

The valence of an element can be defined either as the number of hydrogen atoms that can combine with it to form a simple binary hydride, or as twice the number of oxygen atoms that can combine with it to form a simple binary oxide (that is, not a peroxide or a superoxide). The valences of the main-group elements are directly related to the group number: the hydrides in the main groups 1–2 and 13–17 follow the formulae MH, MH, MH, MH, MH, MH, and finally MH. The highest oxides instead increase in valence, following the formulae M O, MO, M O, MO, M O, MO, M O. Today the notion of valence has been extended by that of the oxidation state, which is the formal charge left on an element when all other elements in a compound have been removed as their ions.

The electron configuration suggests a ready explanation from the number of electrons available for bonding; indeed, the number of valence electrons starts at 1 in group 1, and then increases towards the right side of the periodic table, only resetting at 3 whenever each new block starts. Thus in period 6, Cs–Ba have 1–2 valence electrons; La–Yb have 3–16; Lu–Hg have 3–12; and Tl–Rn have 3–8. However, towards the right side of the d- and f-blocks, the theoretical maximum corresponding to using all valence electrons is not achievable at all; the same situation affects oxygen, fluorine, and the light noble gases up to krypton.

A full explanation requires considering the energy that would be released in forming compounds with different valences rather than simply considering electron configurations alone. For example, magnesium forms Mg rather than Mg cations when dissolved in water, because the latter would spontaneously disproportionate into Mg and Mg cations. This is because the enthalpy of hydration (surrounding the cation with water molecules) increases in magnitude with the charge and radius of the ion. In Mg, the outermost orbital (which determines ionic radius) is still 3s, so the hydration enthalpy is small and insufficient to compensate the energy required to remove the electron; but ionising again to Mg uncovers the core 2p subshell, making the hydration enthalpy large enough to allow magnesium(II) compounds to form. For similar reasons, the common oxidation states of the heavier p-block elements (where the ns electrons become lower in energy than the np) tend to vary by steps of 2, because that is necessary to uncover an inner subshell and decrease the ionic radius (e.g. Tl uncovers 6s, and Tl uncovers 5d, so once thallium loses two electrons it tends to lose the third one as well). Analogous arguments based on orbital hybridisation can be used for the less electronegative p-block elements.

For transition metals, common oxidation states are nearly always at least +2 for similar reasons (uncovering the next subshell); this holds even for the metals with anomalous d s or d s configurations (except for silver), because repulsion between d-electrons means that the movement of the second electron from the s- to the d-subshell does not appreciably change its ionisation energy. Because ionising the transition metals further does not uncover any new inner subshells, their oxidation states tend to vary by steps of 1 instead. The lanthanides and late actinides generally show a stable +3 oxidation state, removing the outer s-electrons and then (usually) one electron from the (n−2)f-orbitals, that are similar in energy to ns. The common and maximum oxidation states of the d- and f-block elements tend to depend on the ionisation energies. As the energy difference between the (n−1)d and ns orbitals rises along each transition series, it becomes less energetically favourable to ionise further electrons. Thus, the early transition metal groups tend to prefer higher oxidation states, but the +2 oxidation state becomes more stable for the late transition metal groups. The highest formal oxidation state thus increases from +3 at the beginning of each d-block row, to +7 or +8 in the middle (e.g. OsO), and then decrease to +2 at the end. The lanthanides and late actinides usually have high fourth ionisation energies and hence rarely surpass the +3 oxidation state, whereas early actinides have low fourth ionisation energies and so for example neptunium and plutonium can reach +7. The very last actinides go further than the lanthanides towards low oxidation states: mendelevium is more easily reduced to the +2 state than thulium or even europium (the lanthanide with the most stable +2 state, on account of its half-filled f-shell), and nobelium outright favours +2 over +3, in contrast to ytterbium.

As elements in the same group share the same valence configurations, they usually exhibit similar chemical behaviour. For example, the alkali metals in the first group all have one valence electron, and form a very homogeneous class of elements: they are all soft and reactive metals. However, there are many factors involved, and groups can often be rather heterogeneous. For instance, hydrogen also has one valence electron and is in the same group as the alkali metals, but its chemical behaviour is quite different. The stable elements of group 14 comprise a nonmetal (carbon), two semiconductors (silicon and germanium), and two metals (tin and lead); they are nonetheless united by having four valence electrons. This often leads to similarities in maximum and minimum oxidation states (e.g. sulfur and selenium in group 16 both have maximum oxidation state +6, as in SO and SeO, and minimum oxidation state −2, as in sulfides and selenides); but not always (e.g. oxygen is not known to form oxidation state +6, despite being in the same group as sulfur and selenium).