Ch8: Rules for Assigning Oxidation Numbers

Importance of Oxidation Numbers & Redox Reactions

  • Oxidation‐number bookkeeping is the quickest way to decide whether a chemical change is a redox process.
  • A redox reaction is one in which at least one element’s oxidation number changes between reactants and products.
  • If no element changes oxidation number, the reaction is not redox → cannot be used for electrochemical cells (e.g., batteries).
  • Later (Chem 2) you will learn special balancing rules for redox; knowing oxidation numbers now tells you when such rules are needed.

10 Fundamental Rules for Assigning Oxidation Numbers (memorize!)

  1. Free (uncombined) elements: oxidation number (ON) = 0
    • Examples: ext{Zn (s)}, ext{Na (s)}, ext{Cl}_2 (g) all have 0.
  2. Monatomic ions: ON = ionic charge (sign first when writing ON)
    • ext{Mn}^{2+} has ON +2 (charge written 2+, ON written +2).
  3. Group 1A (alkali) metals: always +1.
  4. Group 2A (alkaline-earth) metals: always +2.
  5. Hydrogen (H)
    • Usually +1.
    • -1 when bonded to metals or ext{B} (hydrides such as ext{CaH}2, ext{NaBH}4).
  6. Oxygen (O)
    • Most compounds: -2.
    • Peroxides ( ext{O}2^{2-}, e.g., ext{H}2 ext{O}2, ext{K}2 ext{O}_2): -1.
    • Superoxides ( ext{O}2^-, e.g., ext{KO}2): - frac12 per O.
    • With fluorine (e.g., ext{OF}_2): +2 because ext{F} is more electronegative.
  7. Group 7A (halogens)
    • ext{F}: always -1 (no exceptions).
    • ext{Cl, Br, I}: -1 when bonded to metals, to other non-O nonmetals, or to less-electronegative halogens; exceptions occur when bonded to O or to more-electronegative halogens.
  8. Sum in a neutral compound: \sum \text{ON} = 0.
  9. Sum in a polyatomic ion: \sum \text{ON} = \text{ion charge}.
  10. (Implied) Use algebra + rules 1–9 to deduce any unknown ON.

Oxidation Number vs. Ionic Charge (notation reminder)

  • Charge: number first, sign second (e.g.

    2+}).
  • Oxidation number: sign first, number second (e.g.

    +2).

Worked Examples of ON Calculations

  • Water: 2(+1) + (-2) = 0 → ext{H}=+1, ext{O}=-2.
  • ext{Ca(OH)}_2:

    ext{Ca}=+2 (rule 4);

    2\times\text{O}+2\times\text{H}+(+2)=0 ⇒ 2(-2)+2(+1)+2=0 ✓.
  • Nitrate ext{NO}_3^-:

    x+3(-2) = -1 ⇒ x = +5 on N.
  • Sulfate ext{SO}_4^{2-}:

    x+4(-2) = -2 ⇒ x = +6 on S.
  • Potassium superoxide ext{KO}2: ext{K}=+1 (rule 3). Total +1 must equal 0, so ext{O}2 block = -1 ⇒ each O = -\tfrac12 .
  • ext{Na}2 ext{O}2 shown to be a peroxide: with Na +1, ON(O) comes out -1.

Identifying Agents in a Redox Reaction (Thermite Example)

Reaction: ext{Fe}2 ext{O}3 + 2 ext{Al} \rightarrow 2 ext{Fe} + \text{Al}2 ext{O}3

  • Assign ONs
    • ext{Fe}2 ext{O}3: Fe +3, O -2.
    • ext{Al (s)}: 0.
    • ext{Fe (s)}: 0.
    • ext{Al}2 ext{O}3: Al +3, O -2.
  • Changes
    • Fe: +3 \rightarrow 0 (reduced).
    • Al: 0 \rightarrow +3 (oxidized).
  • Therefore
    • Oxidizing agent = substance reduced = ext{Fe}2 ext{O}3 .
    • Reducing agent = substance oxidized = ext{Al}.

Cell-Potential Example (Cr–Mn System)

  1. Determine ONs (highlights only):
    • ext{Cr}2 ext{O}7^{2-}: Cr +6.
    • Product ext{Cr}^{3+}: Cr +3 (reduction).
    • Counter half-reaction contained ext{MnO}4^- (Mn +7) → ext{MnO}2 (Mn +4) (oxidation).
  2. Identify electrodes
    • ext{Cr}^{6+} \rightarrow \text{Cr}^{3+} is the cathode (reduction).
    • ext{Mn}^{4+} \rightarrow \text{Mn}^{7+} (overall reaction reversed vs. tabulated data) functions as anode.
  3. Standard cell potential

    E{\text{cell}}^{\circ} = E{\text{cathode}}^{\circ} - E_{\text{anode}}^{\circ}
    = 1.33\,\text{V} - 1.695\,\text{V} = -0.365\,\text{V}.
  4. Negative E_{\text{cell}}^{\circ} ⇒ reaction is non-spontaneous as written.

Battery Size, Voltage & Capacity

  • Typical dry cells (AAA, AA, C, D) all supply ≈1.5\,\text{V} per cell.
  • Larger physical size ≠ higher voltage; instead, size correlates with capacity (how long the battery can deliver rated current before reactants are exhausted).
  • A large D-cell can run a device longer than an AA even though both are 1.5\,\text{V}.
  • Practicality: you would not put a heavy D-cell into an ultra-light gadget.

Primary vs. Secondary Batteries

  • Primary (non-rechargeable)
    • Redox proceeds only one direction; once reactants consumed, battery is dead.
  • Secondary (rechargeable)
    • Redox is reversible; external energy source drives reaction backward during charging.
    • Can cycle hundreds–thousands of times but not indefinitely—the electrodes slowly degrade.
    • Environmental & resource advantage: fewer single-use batteries enter waste stream; conserves limited element supplies.
Environmental / Ethical Angle
  • Discarded batteries are chemical-hazard waste (heavy metals, corrosives).
  • Promoting rechargeables minimizes waste and conserves finite mineral resources.

Pumped-Hydro Analogy: Large-Scale Energy Storage

  • Concept: Use surplus renewable energy (solar/wind) to pump water from a low reservoir to a higher one ("charging").
  • When demand rises or generation drops, release water downhill through turbines to regenerate electricity ("discharging").
  • Mirrors rechargeable-battery logic: same materials, opposite direction; exploits gravitational potential instead of chemical potential.

Study & Exam Tips

  • Re-write the 10 rules on flashcards; quiz yourself until instantaneous recall.
  • Always start with the “hard-wired” rules (groups 1A, 2A, F, O exceptions, etc.) and finish with algebra (rules 8–9).
  • Double-check sums: neutral → 0, ion → its formal charge.
  • When analyzing reactions:
    1. Assign ONs to every atom.
    2. Locate increases (oxidation) & decreases (reduction).
    3. Map to agents (reduced species = oxidizing agent; oxidized species = reducing agent).
  • For cell potentials: $$E