Electronic Structure and Oxidation States

James Richard Fromm

The stable oxidation states of the chemical elements are determined in large part by the electronic structure of their atoms. The elements in which the 3d orbitals are being filled are the first-row transition metals. The oxidation states which these metals exhibit in their compounds depend on the energy required to remove their outermost electrons. Although the 4s electrons are lower in energy when proton-electron pairs are used to build up the periodic chart, they are physically the outermost electrons of the atom and the ones most easily lost. For this reason, most of the first-row transition metals have a stable 2+ oxidation state in which both of the two 4s electrons are lost. Greater stability is generally found for electronic structures in which the subshells are either full or empty, or for electronic structures in which the d subshell is half-full. For the first-row transition metals, the stable oxidation states and their electronic configurations are:

K+, [Ar]
Ca2+, [Ar]
Sc3+, [Ar]
Ti2+, [Ar]; Ti4+, [Ar]
V2+, [Ar]3d3; V3+, [Ar]3d2; V4+, [Ar]3d1; V5+, [Ar]
Cr2+, [Ar]3d4; Cr3+, [Ar]3d3; Cr4+, [Ar]3d2; Cr6+, [Ar]
Mn2+, [Ar]3d5; Mn4+, [Ar]3d3; Mn7+, [Ar]
Fe2+, [Ar]3d6; Fe3+, [Ar]3d5
Co2+, [Ar]3d7; Co3+, [Ar]3d6
Ni2+, [Ar]3d8
Cu+, [Ar]3d10; Cu2+, [Ar]3d9
Zn2+, [Ar]3d10
Ga+, [Ar]4s23d10; Ga3+, [Ar]3d10
Ge2+, [Ar]4s23d10; Ge4+, [Ar]3d10
As3+, [Ar]4s23d10; As5+, [Ar]3d10
Se4+, [Ar]4s23d10; Se2-, [Ar]4s23d104p6
Br-, [Ar]4s23d104p6
Kr, [Ar]4s23d104p6 = [Kr]
Rb+, [Kr]

Electronic Structures and Ionization Energies

When an atom loses one electron it forms an ion and the process is known as ionization. The enthalpy difference between the gaseous atom and the gaseous ion formed from it by the loss of an electron can be measured in terms of the electrical potential required to emit electrons from the atom and for this reason is called the ionization potential. Chemists now prefer to give its values in kJ/mole rather than electron volts and refer to it as the ionization energy. Many atoms can lose more than one electron; these atoms have second, third, fourth, and even more ionization energies, in addition to the first ionization energy.

The values of the ionization energies of the elements are one of the clearest indications of the periodicity of their atomic structure. These values are simply the difference between the standard enthalpy of formation of the gaseous ions and the standard enthalpy of formation of the gaseous atoms which can be obtained using the tables of thermodynamic values. The second, third, and successive ionization energies can be obtained as the differences in enthalpies of formation of the successive gaseous cations in the same manner.

Example. Let us calculate the first ionization potential and first ionization energy of sodium from tabulated thermodynamic data. The process of ionization of sodium is

Na(g) rarrow.gif (63 bytes) Na+(g),

which is the difference between

Na(c) rarrow.gif (63 bytes) Na(g) and Na(c) rarrow.gif (63 bytes)Na+(g).

The enthalpy changes of the two processes under standard conditions are (delta>H0f(Na(g)), +107.32 kJ/mole, and (delta)H0f(Na+(g)), +609.358 kJ/mole. The difference, +502.038 kJ/mole, is the first ionization energy of sodium. The first ionization potential of sodium is then 502038/96485.309... = 5.203 eV. The ionization potential, in electron volts, refers to a single emission of an electron while the ionization energy is on a molar basis. For this reason the conversion factor between them is the product of the Avogadro number and the elementary charge, which is the Faraday constant.

Electronic Structure and Electron Affinities

Table: Electron Affinities of Gaseous Ions
Ion (delta)H0f (ion) (delta) H0f (atom) Electron Affinity
kJ/mole kJ/mole kJ/mole
H- 138.99 217.965 -78.975
F- -255.39 78.99 -334.38
Cl- -233.13 121.679 -354.809
Br- -219.07 111.884 -331.95
I- -197.0 106.838 -303.8
O- --- 249.170 -147.54
O-- --- 249.170 780.0
S- 71.0 278.805 -206.8
S-- --- 278.805 590.0

The values in this table are calculated from tables of thermodynamic properties as (delta>H0f(ion) - (delta)H0f(atom); values for oxide and sulfide in italics are calculated from auxiliary sources as (delta)H0f(dianion) - (delta)H0f(ion).

When the normal electronic structure of an atom is one or two electrons less than the number required to fill a full shell, it is found that the atoms can acquire one or two electrons to form stable anions. One of the atoms which does this is chlorine, which both in the gas phase and in most solutions readily acquires an electron to form the chloride ion. The energy involved when gaseous atoms acquire electrons and become gaseous anions is called their electron affinity. The electron affinity of those atoms which have chemically significant gaseous anions is given in the above Table.

The electron affinity of an atom at standard conditions is simply the difference between the standard molar enthalpy of formation of the gaseous atom and the standard molar enthalpy of formation of the gaseous ion:

E.A. = (delta)H0f(anion,g) - (delta)H0f(atom,g)

The electron affinity of those atoms which form stable negative ions, which usually have the electronic structure of a noble gas atom, is negative and significantly large. Although some atoms form dinegative ions, the electron affinity of an anion is large and positive because the negative charge on the electron is repelled by the negative charge on the anion. These dinegative ions are stable and significant in ionic crystals and in solutions. The electron affinity of an anion is:

E.A. = (delta)H0f(dianion,g) - (delta)H0f(anion,g)

For most atoms, the repulsion of the electronic cloud for an incoming electron is large enough that the electron affinity is positive or, if negative, is not sufficiently large to ensure a stable isolated anion. Even for those atoms listed in the table, the anions are more stable in solution or in ionic lattices than as isolated ions, as is discussed in the following section.

Sizes of Atoms and Ions

Table: Heats of Formation and Radii of Atoms and Ions
	Atom  (delta)H0f(atom)     Atomic    Ionic    (delta)H0f(ion) Ion
	                           Radius    Radius         
	      (kJ/mole)            (pm)      (pm)     (kJ/mole) 
	H     217.965              ---       ---      1536.202         H+
	Li    159.37               155        60       685.783         Li+
	Na    107.32               190        95       609.358         Na+
	K      89.24               235       133       514.26          K+
	Rb     80.88               248       148       490.101         Rb+
	Cs     76.065              ---       169       457.964         Cs+
	Be    324.3                112        31      2993.23          Be++
	Mg    147.70               160        65      2348.504         Mg++
	Ca    178.2                197        99      1925.90          Ca++
	Sr    164.4                215       113      1790.54          Sr++
	Ba    180.                 222       135      1660.38          Ba++
	B     562.7                 98        20      7468.4           B+++
	Al    326.4                143        50      5483.17          Al+++
	N     472.704               92       171         --            N---
	P     314.64               128       212         --            P---
	O     249.170               73       140         --            O--
	S     278.805              127       184         --            S--
	Se    227.07               140       198         --            Se--
	Te    196.73               160       221         --            Te--
	H     217.965               --        --      -138.99          H-
	F      78.99                71       136      -255.39          F-
	Cl    121.679               99       181      -233.13          Cl-
	Br    111.884              114       195      -219.07          Br-
	I     106.838              133       216      -197.            I-

In this table the ionic radius given is the Pauling crystal radius.

The size of an atom or ion, like its ionization potential and electron affinity, is found to be a periodic property. Unlike the ionization energy and electron affinity, however, it is not possible to simply state a size. If, however, the atom or ion is considered to be a sphere whose radius contains 90% of the electron density of the atom or ion, then a consistent table of atomic and ionic radii can be established. The atomic radii are always found to be larger than the ionic radii of the cations of the same atom because the electrons lost on ionization are the outermost electrons of the atom. In most cases these electrons are also the only electrons in that outermost orbital, and the inner orbitals are smaller. The ionic radii of anions, however, are larger than the atomic radii because the added electron must go into the outermost orbital.

Copyright 1997 James R. Fromm