An oxidation state represents the hypothetical charge an atom would possess if all its bonds were considered completely ionic. This value, also called the oxidation number, is a bookkeeping tool chemists use to track electron movement in chemical reactions. Transition metals present a unique challenge because they can exhibit multiple stable oxidation states. Therefore, the oxidation state must be mathematically derived from the compound’s chemical formula using the known fixed states of the other elements.
Establishing the Fixed Rules for Oxidation States
To determine the variable oxidation state of a transition metal, one must rely on the fixed oxidation states of other elements in the compound. Any element in its uncombined, elemental form, such as solid iron (\(\text{Fe(s)}\)) or oxygen gas (\(\text{O}_2\)), always has an oxidation state of zero. In compounds, Group 1 metals are consistently assigned \(+1\), and Group 2 metals always have \(+2\).
Fluorine is always assigned an oxidation state of \(-1\) in all of its compounds. Oxygen is typically assigned \(-2\) in most compounds, though exceptions exist, such as \(-1\) in peroxides. Hydrogen generally carries \(+1\) when bonded to nonmetals, but it assumes \(-1\) when it forms a binary compound with a metal (a metal hydride).
The final two rules govern the total sum of all oxidation states within a chemical species. For any neutral compound, the sum of all individual oxidation states must equal zero. If the chemical species is a polyatomic ion, the sum of all oxidation states must equal the net charge of that ion.
Calculating Oxidation States in Neutral Compounds
Finding a transition metal’s oxidation state in a neutral compound involves setting up an algebraic equation where the sum of all known and unknown states equals zero. The unknown transition metal state is treated as a variable, typically denoted as \(X\).
Consider the compound iron(III) oxide, \(\text{Fe}_2\text{O}_3\), which is neutral. We assign the unknown state \(X\) to iron (\(\text{Fe}\)) and use the fixed rule of \(-2\) for oxygen (\(\text{O}\)). Since the formula contains two iron atoms and three oxygen atoms, the equation is set up as: \((2 \times X) + (3 \times -2) = 0\).
Solving the equation gives \(2X + (-6) = 0\), which simplifies to \(2X = 6\). Dividing both sides by \(2\) reveals that the oxidation state of iron is \(\boldsymbol{+3}\).
A second example is copper(II) chloride, \(\text{CuCl}_2\), where copper (\(\text{Cu}\)) is the unknown \(X\). Chlorine (\(\text{Cl}\)) is typically assigned a fixed state of \(-1\). The resulting equation is \((1 \times X) + (2 \times -1) = 0\), which simplifies to \(X – 2 = 0\). Therefore, the oxidation state of copper is \(\boldsymbol{+2}\). Once the oxidation state is determined, the compound is named using the Stock system, indicating the state with a Roman numeral, such as Iron(\(\text{III}\)) oxide.
Determining Oxidation States in Ionic Compounds
When a transition metal is part of a polyatomic ion, the calculation must equal the ion’s net charge, not zero. This net charge is indicated by a superscript on the ion’s formula, such as the \(-1\) charge on the permanganate ion (\(\text{MnO}_4^-\)). The known fixed rules for the non-metal elements remain the same.
To determine the oxidation state of manganese (\(\text{Mn}\)) in \(\text{MnO}_4^-\), we let \(X\) be the unknown state and assign oxygen its fixed state of \(-2\). The equation is set up so the sum equals the ion’s charge of \(-1\): \((1 \times X) + (4 \times -2) = -1\). This simplifies to \(X – 8 = -1\). Adding \(8\) to both sides of the equation yields \(X = \boldsymbol{+7}\).
For the dichromate ion (\(\text{Cr}_2\text{O}_7^{2-}\)), chromium (\(\text{Cr}\)) is the unknown, and the net charge is \(-2\). There are two chromium atoms and seven oxygen atoms, resulting in the equation: \((2 \times X) + (7 \times -2) = -2\). This calculation becomes \(2X – 14 = -2\). Adding \(14\) to both sides gives \(2X = 12\), and dividing by \(2\) reveals the oxidation state of each chromium atom is \(\boldsymbol{+6}\).