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 $ext{CaH}<em>2$, $ext{NaBH}</em>4$).
6. Oxygen (O)
   • Most compounds: $-2$.
   • Peroxides ($ext{O}<em>2^{2-}$, e.g., $ext{H}</em>2 ext{O}<em>2$, $ext{K}</em>2 ext{O}_2$): $-1$.
   • Superoxides ($ext{O}<em>2^-$, e.g., $ext{KO}</em>2$): $- frac12$ 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 $ext{KO}<em>2$: $ext{K}=+1$ (rule 3). Total $+1$ must equal $0$, so $ext{O}</em>2$ block = $-1$ ⇒ each O = $-\tfrac12$ .
• $ext{Na}<em>2 ext{O}</em>2$ shown to be a peroxide: with Na $+1$, ON(O) comes out $-1$.

Identifying Agents in a Redox Reaction (Thermite Example)

Reaction: $ext{Fe}<em>2 ext{O}</em>3 + 2 ext{Al} \rightarrow 2 ext{Fe} + \text{Al}<em>2 ext{O}</em>3$

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

Cell-Potential Example (Cr–Mn System)

1. Determine ONs (highlights only):
   • $ext{Cr}<em>2 ext{O}</em>7^{2-}$: Cr $+6$.
   • Product $ext{Cr}^{3+}$: Cr $+3$ (reduction).
   • Counter half-reaction contained $ext{MnO}<em>4^-$ (Mn $+7$) → $ext{MnO}</em>2$ (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
   
   $E<em>{\text{cell}}^{\circ} = E</em>{\text{cathode}}^{\circ} - E_{\text{anode}}^{\circ}$
   $= 1.33\,\text{V} - 1.695\,\text{V} = -0.365\,\text{V}$.
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