Oxidation numbers Knowledge-Based Study

Study notes

1. What is an Oxidation Number?

   An oxidation number (or oxidation state) represents the hypothetical charge an atom would have if all bonds to different elements were completely ionic. It is a bookkeeping tool used in chemistry to track electron density, determine chemical nomenclature, and balance redox reactions.

   Unlike the actual physical charge on a monoatomic ion, oxidation numbers are assigned across both ionic and covalent molecular compounds using a standardized set of conventions.

   Basic Sum Rules

   • Free elements: Any atom in its pure, uncombined elemental form has an oxidation number of 0. For example, each atom in $Na$, $He$, $H_2$, $O_2$, $P_4$, and $S_8$ has an oxidation number of 0.
   • Monatomic ions: The oxidation number equals the ionic charge. For instance, the oxidation number of $Na^+$ is +1, $Ca^{2+}$ is +2, and $Cl^-$ is -1.
   • Neutral compounds: The sum of the oxidation numbers of all atoms in a neutral formula unit must equal 0.
   • Polyatomic ions: The sum of the oxidation numbers of all constituent atoms must equal the net charge of the ion.

   Hierarchical Rules for Specific Elements

   When assigning oxidation numbers in compounds, certain elements have consistent values due to their extreme electronegativities. Apply these rules in order of priority:

   1. Fluorine: Always has an oxidation number of -1 in all compounds because it is the most electronegative element.
   2. Group 1 (Alkali Metals): Always have an oxidation number of +1 in compounds (e.g., $Li^+$, $Na^+$, $K^+$).
   3. Group 2 (Alkaline Earth Metals): Always have an oxidation number of +2 in compounds (e.g., $Mg^{2+}$, $Ca^{2+}$, $Ba^{2+}$).
   4. Hydrogen: Assigned +1 when bonded to nonmetals (such as in $H_2O$, $CH_4$, $HCl$), but assigned -1 when bonded to metals in metal hydrides (such as $NaH$ and $CaH_2$).
   5. Oxygen: Usually assigned -2 in most compounds (such as $CO_2$, $H_2O$, $SO_3$). Notable exceptions include:
      • In peroxides (containing the $O_2^{2-}$ unit, such as $H_2O_2$ or $Na_2O_2$), oxygen is -1.
      • In superoxides (containing $O_2^-$, such as $KO_2$), oxygen is -1/2.
      • When bonded to the more electronegative fluorine in $OF_2$, oxygen is +2.
   6. Group 17 (Halogens): Typically -1, unless bonded to oxygen or a higher-priority halogen in interhalogen compounds (e.g., in $ClO_3^-$, chlorine has a positive oxidation state).

   The Algebraic Method

   To determine the oxidation state of an element that can exhibit variable states (such as transition metals or central nonmetal atoms), set up a simple algebraic summation equation based on the compound's overall charge.

   Example 1: Neutral Molecule ($KMnO_4$)

   Determine the oxidation number of manganese ($Mn$) in potassium permanganate:

   • Potassium is a Group 1 metal: $+1$
   • Oxygen typically exhibits: $-2$
   • Let $x$ be the oxidation number of $Mn$.

   Setting the sum to zero for a neutral compound:
   $(+1) + x + 4(-2) = 0$
   $1 + x - 8 = 0 \implies x = +7$

   Thus, manganese has an oxidation state of +7.

   Example 2: Polyatomic Ion ($Cr_2O_7^{2-}$)

   Determine the oxidation number of chromium ($Cr$) in the dichromate ion:

   • Oxygen is $-2$.
   • Let $x$ be the oxidation number of each chromium atom.
   • The sum must equal the overall charge ($-2$).

   $2x + 7(-2) = -2$
   $2x - 14 = -2$
   $2x = +12 \implies x = +6$

   Each chromium atom has an oxidation number of +6.

   The Stock System and Chemical Naming

   Many transition metals and p-block elements exhibit multiple oxidation states. To avoid ambiguity in chemical formulas and nomenclature, the Stock system uses Roman numerals in parentheses to denote the oxidation number of the cation.

   Naming Transition Metal Compounds

   • Iron oxides: In $FeO$, oxygen is $-2$, making iron $+2$; the compound is named iron(II) oxide. In $Fe_2O_3$, oxygen is $-2$, requiring iron to be $+3$; the compound is named iron(III) oxide.
   • Copper chlorides: In $CuCl$, chlorine is $-1$, so copper is $+1$ (copper(I) chloride). In $CuCl_2$, copper is $+2$ (copper(II) chloride).

   Differentiating Oxidation Number from Ionic Charge

   While often numerically identical in simple salts, formal convention distinguishes them:

   • An ionic charge represents actual electrostatic charge and is written with the numeral first followed by the sign (e.g., $2+$, $3-$).
   • An oxidation number is an assigned accounting value written with the sign preceding the numeral (e.g., $+2$, $-3$) or as Roman numerals in naming conventions.