Oxidation numbers Knowledge-Based Study

Study notes

1. What Is an Oxidation Number?

   An oxidation number (or oxidation state) is an indicator of the degree of oxidation of an atom in a chemical substance. It represents the hypothetical charge that an atom would have if all bonds to different atoms were completely ionic, with bonding electrons assigned entirely to the more electronegative element.

   Key aspects of oxidation numbers include:

   • They serve as an essential bookkeeping tool to track the redistribution of valence electrons during chemical processes.
   • Unlike formal charges or real ionic charges, an oxidation number does not necessarily reflect an actual physical charge on an atom in a covalent molecule.
   • They allow chemists to systematically determine which species gain or lose electrons during oxidation–reduction (redox) reactions.

   Standard Assignment Rules

   To assign oxidation numbers correctly, apply the following established rules in hierarchical order:

   1. Free Elements: The oxidation number of any uncombined element in its elemental form is zero. Examples: $O_2$, $N_2$, $P_4$, and $Fe$ all have an oxidation state of 0.
   2. Monatomic Ions: The oxidation state of a monatomic ion equals its charge. For example, in $Na^+$ it is +1, and in $S^{2-}$ it is -2.
   3. Fluorine: As the most electronegative element, fluorine always has an oxidation number of -1 in all its compounds.
   4. Group 1 and Group 2 Metals: Alkali metals (Group 1) always exhibit an oxidation state of +1, and alkaline earth metals (Group 2) always exhibit an oxidation state of +2 in their compounds.
   5. Hydrogen: Hydrogen typically has an oxidation number of +1 when bonded to nonmetals (such as in $HCl$ or $H_2O$). It has an oxidation state of -1 when bonded to reactive metals as a hydride (such as in $NaH$ or $CaH_2$).
   6. Oxygen: Oxygen usually has an oxidation number of -2. Notable exceptions include peroxides (such as $H_2O_2$), where it is -1; superoxides (such as $KO_2$), where it is -$\frac{1}{2}$; and compounds with fluorine (such as $OF_2$), where it is +2.

   Summation Rules and Step-by-Step Calculation

   The total sum of oxidation states in any species depends on its overall charge:

   • In a neutral compound, the algebraic sum of the oxidation numbers of all constituent atoms must equal zero.
   • In a polyatomic ion, the algebraic sum of the oxidation numbers must equal the net charge of the ion.

   Worked Example 1: Potassium Permanganate ($KMnO_4$)

   To determine the oxidation state of manganese ($Mn$):

   • Potassium ($K$) is an alkali metal: $+1$
   • Oxygen ($O$) is assigned its standard state: $-2$
   • Let the oxidation state of $Mn$ be $x$.
   • Set up the equation: $(+1) + x + 4(-2) = 0 \implies 1 + x - 8 = 0 \implies x = +7$

   Therefore, the oxidation number of manganese in $KMnO_4$ is +7.

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

   To determine the oxidation state of chromium ($Cr$):

   • Each oxygen has an oxidation number of $-2$.
   • Let the oxidation state of each chromium atom be $y$.
   • Set up the ionic sum equation: $2y + 7(-2) = -2 \implies 2y - 14 = -2 \implies 2y = +12 \implies y = +6$

   Each chromium atom in $Cr_2O_7^{2-}$ has an oxidation number of +6.

   Tracking Redox Reactions

   By monitoring changes in oxidation numbers from reactants to products, we can identify and analyze redox processes:

   • Oxidation: An algebraic increase in oxidation number, which corresponds to the loss of electrons.
   • Reduction: An algebraic decrease in oxidation number, which corresponds to the gain of electrons.
   • Oxidizing Agent (Oxidant): The species that causes oxidation in another substance by accepting electrons; its constituent atom undergoes a decrease in oxidation number.
   • Reducing Agent (Reductant): The species that causes reduction in another substance by donating electrons; its constituent atom undergoes an increase in oxidation number.

   Example Analysis

   Consider the reaction: $$Zn(s) + Cu^{2+}(aq) ightarrow Zn^{2+}(aq) + Cu(s)$$

   • $Zn$ changes from 0 to +2 (increase in oxidation number: $Zn$ is oxidized and acts as the reducing agent).
   • $Cu$ changes from +2 to 0 (decrease in oxidation number: $Cu^{2+}$ is reduced and acts as the oxidizing agent).