Oxidation bumblers

Oxidation numbers are one of those ancient retainers that chemistry suffers from. Convenient, but with enough bumbling exceptions to drive every student crazy. In discussing various reactions we commonly use oxidation numbers, oxidation and reduction, but not everybunny has had, or more to the point, remembers their chemistry.

The language comes from about three centuries ago, when metallurgists talked about reducing metals from their ores, e.g. getting rid of whatever else the metals were combined with by heat driven reactions. Oxidation is somewhat more recent, dating to 1777 or thereabouts when Lavoisier named oxygen (discovered by Priestly in 1774) and discussed its role in combustion and corrosion, e.g. reactions with oxygen hence oxidation.

The first use in English was a translation from Lavoisier (OED)

1789 R. Kerr tr. Lavoisier Elements Chem. iii. viii. 445 It is much to be wished that some person would undertake a series of experiments upon oxydation of metals in the several gases.

Reduction of metals comes from the earlier usage (1450)of bringing back something to an earlier state, but the first metallurgical reduction mention is

1741 tr. J. A. Cramer Elements Art Assaying Metals 186 Metals destroyed, and changed into Scoria or Ashes, are, by their Union with the same matter, again restored to their metallick Form. This Operation is called Reduction.

Mendelev constructed his periodic table by characterizing the number of atoms of each element which combined with oxygen and hydrogen

While we (and Mendelev) think of reactions as involving atoms, they really involve the transfer or sharing of the outermost electrons often called the valence electrons, the ones which are held most loosely. Oxidation numbers are a model which assigns each of these electrons completely to one of the two atoms in every bond whereas a better picture takes account of how they are shared.

An atom can, of course, have multiple bonds. The oxidation number is the difference between the number of valence electrons an isolated atom would have available for bonding and the number of electrons assigned to it in the molecule.

Isolated hydrogen atoms, H, have one electron available, carbon, C, four and oxygen, O, six. The other two electrons in carbon and oxygen are so strongly bound to the nucleus that they are never involved in the bonding and we take about the four and six being the valence electrons for C and O. In water vapor, H₂O, the electrons associated with the H atom are "transferred" to the oxygen, so the oxidation number (or effective charge) on the H atoms are +1 (electrons have negative charge, that is another story) and the oxidation number of the O atom is -2, it "has", or rather is assigned, two more electrons than the isolated O atom. In CO₂, each O atom attracts two electrons from the C atom, so the C atom "has" four less electrons than the isolated C atom would have, and an oxidation number of +4, while the O atoms have oxidation numbers of -2 each.

In reality, the electrons are shared between the atoms, it is just that on average they are closer to the oxygen atoms, e.g. the oxygen has a stronger pull on the electrons associated with the bonds. The figure below illustrates this for a series of hydrogen halides, HF through HI (F is fluorine, Cl Chorine, Br bromine, and I Iodine. Blue stands for low electron density, red for high. The assignment of the electron from the H atom to the halogen is much better justified for HF than for HI, but the oxidation number rules assign +1 to the H atom and -1 to the halogen in all cases.

Fluorine, F, is the atom which attracts electrons most strongly, it has the largest electron "affinity" and it has a very large ionization energy, the energy needed to pull an electron away from the isolated F atom. There is a convenient metric for figuring out which atom in a bond will most strongly attract the bonding electrons called electronegativity, which is a combination of the strength which an atom holds electrons, the ionization energy and the strength at which it attracts electrons, the electron affinity.

The higher the electron affinity and the ionization energy, the higher the electronegativity and visa versa. This is not how the original scale was constructed by Pauling, but it is effectively, and there is a simpler electronegativity scale due to Mullikan which states this explicitly.

χ = [½(IE + EA)] × 3.48 - 0.602

where the weird numbers are the results of matching the scale as best as possible to Pauling's original one, which for some reason known only to Pauling set the electronegativity of F as 4

F is the atom with the highest electronegativity. The larger the difference between the electronegativity of two atoms bonded together, the more polar the bond, with the electrons attracted closer to the atom with the higher electronegativity. Ionization energy and electron affinity are basic properties of atoms which determine electronegativity. From electronegativity it's pretty easy to figure out which end of a bond will be more polar, and for the purpose of assigning oxidation numbers where to push the electrons.

One arbitrarily (this will NOT be on the test) sets an electronegativity difference of 1.7 as the boundary between ionic and covalent bonds. Opinions differ.

If you are interested in the "rules" for assigning oxidation numbers, there are any number of places for finding them. The problem is that in the traditional course you learn about oxidation numbers before electronegativity and assigning oxidation numbers becomes ad hoc. Thus the attraction of teaching with what is called the atoms first approach where you start with atomic structure and properties such as ionization energy and electron affinity trends.