1. Oxidation numbers
An oxidation number (also called oxidation state) is the apparent charge an atom would have if all its bonds were ionic. It is a bookkeeping tool for tracking electrons.
Rules for assigning oxidation numbers
- An element by itself (Na, O₂, Cu, H₂) has an oxidation number of 0.
- A monatomic ion's oxidation number equals its charge: Na⁺ is +1, Cl⁻ is −1, Mg²⁺ is +2.
- Group 1 metals in compounds: always +1.
- Group 2 metals in compounds: always +2.
- Group 17 (halogens) in binary compounds with metals: −1.
- Hydrogen: usually +1 (but −1 in metal hydrides like NaH).
- Oxygen: usually −2 (but −1 in peroxides like H₂O₂).
- Sum of oxidation numbers in a neutral compound = 0.
- Sum of oxidation numbers in a polyatomic ion = the charge of the ion.
Worked example: nitrogen in HNO₃
Let N's oxidation number = x.
H: +1, each O: −2 (three of them = −6).
Sum: (+1) + x + (−6) = 0
x = +5
Nitrogen in nitric acid has an oxidation number of +5.
2. LEO the lion says GER
The most important mnemonic in redox
LEO = Lose Electrons = Oxidation
GER = Gain Electrons = Reduction
Picture a lion that says "Leo the lion says GER!" and you'll never forget it.
When an atom loses electrons, its oxidation number increases (becomes more positive). That's oxidation. When an atom gains electrons, its oxidation number decreases (becomes more negative). That's reduction.
| Process | Electrons | Oxidation number | Example |
|---|---|---|---|
| Oxidation | Lost | Increases | Mg → Mg²⁺ + 2e⁻ (0 → +2) |
| Reduction | Gained | Decreases | Cl₂ + 2e⁻ → 2Cl⁻ (0 → −1) |
Always paired
Oxidation and reduction always happen together. You can't have one without the other. Electrons don't appear or vanish; they move from one species to another. The species that loses electrons is being oxidized; the species that gains them is being reduced.
3. Oxidizing and reducing agents
The names trip people up. The oxidizing agent is the species that causes oxidation to happen. It does this by taking electrons, so it gets reduced. The opposite is true for the reducing agent.
| Agent | What it does to the other species | What happens to itself |
|---|---|---|
| Oxidizing agent | Oxidizes it (takes its electrons) | Gets reduced |
| Reducing agent | Reduces it (gives electrons to it) | Gets oxidized |
Pattern to remember
The substance being oxidized is the reducing agent. The substance being reduced is the oxidizing agent. They are opposites. If you see "Zn → Zn²⁺ + 2e⁻," Zn is being oxidized, so Zn is the reducing agent.
4. Half-reactions
A half-reaction shows just one half of a redox process: either oxidation or reduction by itself, with electrons explicitly written.
Example: Zn + Cu²⁺ → Zn²⁺ + Cu
Oxidation half-reaction: Zn → Zn²⁺ + 2e⁻
Reduction half-reaction: Cu²⁺ + 2e⁻ → Cu
In the oxidation half-reaction, electrons appear on the right (lost). In the reduction half-reaction, electrons appear on the left (gained). When you add the two halves and cancel electrons, you get the full redox equation.
5. Balancing redox equations
Half-reaction method (simple cases)
- Write the two half-reactions: one oxidation, one reduction.
- Balance the atoms in each half-reaction (other than H and O for now).
- Balance the charge in each half-reaction by adding electrons.
- Multiply each half-reaction so that the number of electrons lost equals the number gained.
- Add the two half-reactions and cancel anything that appears on both sides (including the electrons).
Worked example: aluminum + copper(II) ions
Skeleton: Al + Cu²⁺ → Al³⁺ + Cu
Oxidation: Al → Al³⁺ + 3e⁻ (Al loses 3 electrons)
Reduction: Cu²⁺ + 2e⁻ → Cu (Cu²⁺ gains 2 electrons)
Electrons lost (3) must equal electrons gained (2). LCM = 6. Multiply the oxidation by 2 and the reduction by 3:
Oxidation × 2: 2 Al → 2 Al³⁺ + 6e⁻
Reduction × 3: 3 Cu²⁺ + 6e⁻ → 3 Cu
Add and cancel the 6e⁻:
2 Al + 3 Cu²⁺ → 2 Al³⁺ + 3 Cu
6. Electrochemical cells
An electrochemical cell uses a redox reaction to interconvert chemical energy and electrical energy. There are two types: voltaic and electrolytic. Both share four parts:
- Anode: the electrode where oxidation occurs.
- Cathode: the electrode where reduction occurs.
- External circuit: wires connecting the two electrodes; electrons flow through here.
- Internal connection: a salt bridge (voltaic) or shared electrolyte (electrolytic) that allows ions to move to maintain charge balance.
AN OX, RED CAT
ANode = OXidation. REDuction = CAThode. Always true, in any cell. Picture an angry ox and a chill red cat.
Electron flow direction
In any electrochemical cell, electrons in the external circuit flow from the anode to the cathode. The current direction (by convention, positive charge) is opposite: cathode to anode in the external wire.
7. Voltaic cells (galvanic cells, batteries)
A voltaic cell uses a spontaneous redox reaction to produce electrical energy. Every battery you've used is a voltaic cell.
Spontaneous
The chemistry wants to happen on its own. No outside energy is needed.
Chemical → electrical
The cell converts chemical PE into electrical energy that can do work (light a bulb, run a motor).
Two separate compartments
The oxidation and reduction happen in separate half-cells connected by a salt bridge. Electrons travel through the external wire to do work.
Anode is negative (−)
Oxidation releases electrons there, so the anode has excess electrons. Counterintuitive but true. In voltaic cells: anode = (−), cathode = (+).
Classic example: zinc-copper voltaic cell
Zn(s) electrode in a Zn(NO₃)₂ solution; Cu(s) electrode in a Cu(NO₃)₂ solution; salt bridge between them; wire and bulb in the external circuit.
- Zn is more active than Cu (see Table J), so Zn is oxidized at the anode: Zn → Zn²⁺ + 2e⁻
- Cu²⁺ is reduced at the cathode: Cu²⁺ + 2e⁻ → Cu
- Electrons flow through the external wire from Zn anode (−) to Cu cathode (+).
- The Zn electrode loses mass; the Cu electrode gains mass.
- The salt bridge allows ions to flow to keep both half-cells electrically neutral.
8. Electrolytic cells
An electrolytic cell uses electrical energy to drive a non-spontaneous redox reaction. Examples: electroplating, electrolysis of water, refining aluminum, recharging a battery.
| Feature | Voltaic cell | Electrolytic cell |
|---|---|---|
| Reaction | Spontaneous | Non-spontaneous (forced) |
| Energy flow | Chemical → electrical | Electrical → chemical |
| Battery needed? | No (cell IS the battery) | Yes (needs power source) |
| Anode charge | Negative (−) | Positive (+) |
| Cathode charge | Positive (+) | Negative (−) |
| Anode = oxidation | Yes | Yes (always) |
| Salt bridge? | Required | Not used; single container |
Anode charge flips, but anode = oxidation always
In voltaic cells, the anode is negative. In electrolytic cells, the anode is positive. What stays constant in both: oxidation always happens at the anode, and reduction always happens at the cathode.
Common applications of electrolytic cells
- Electroplating: coating a cheap metal with a thin layer of an expensive metal (silver-plated forks).
- Electrolysis of water: 2 H₂O → 2 H₂ + O₂. Hydrogen at the cathode, oxygen at the anode.
- Refining and producing metals: aluminum from bauxite via the Hall-Héroult process; copper purification.
- Recharging a battery: forces the spontaneous reaction backward.
9. Activity series (Reference Table J)
Table J lists metals (and a separate list of halogens) in order of activity. More active = more easily oxidized = better reducing agent.
How to use Table J for single replacement reactions
A single replacement reaction has the form: A + BC → AC + B (where A and B are metals or halogens).
- The reaction occurs if A is above B on Table J (A is more active and can displace B).
- The reaction does not occur if A is below B (A is less active).
Worked examples
- Zn + CuSO₄ → ZnSO₄ + Cu (Zn is above Cu on Table J: reaction occurs)
- Cu + ZnSO₄ → no reaction (Cu is below Zn: cannot displace it)
- Mg + 2 HCl → MgCl₂ + H₂ (Mg is above H₂: reaction occurs, gas bubbles off)
The "most active" metals
Lithium and the heavier alkali metals (K, Cs, Rb, Na) are at the top of Table J. They react violently with water. The least active metals (Au, Ag) sit at the bottom and resist corrosion: this is why gold and silver are used in jewelry and ancient artifacts are still recognizable.
Key terms
| Oxidation | Loss of electrons. Oxidation number increases. "LEO." |
| Reduction | Gain of electrons. Oxidation number decreases. "GER." |
| Oxidation number | Apparent charge of an atom if all bonds were ionic. |
| Oxidizing agent | Species that causes oxidation. Itself gets reduced. |
| Reducing agent | Species that causes reduction. Itself gets oxidized. |
| Half-reaction | Either the oxidation or the reduction part, with electrons shown. |
| Redox reaction | Reaction involving electron transfer (change in oxidation numbers). |
| Anode | Electrode where oxidation occurs. Always. "AN OX." |
| Cathode | Electrode where reduction occurs. Always. "RED CAT." |
| Voltaic cell | Uses spontaneous redox reaction to produce electricity. A battery. |
| Electrolytic cell | Uses electricity to drive a non-spontaneous reaction. Electroplating, electrolysis. |
| Salt bridge | Allows ions to flow between half-cells in a voltaic cell to maintain neutrality. |
Practice questions
Q1. In the reaction 2 Na + Cl₂ → 2 NaCl, which species is oxidized?
Answer: (1) Na, because it loses electrons. Na goes from oxidation number 0 (elemental) to +1 (in NaCl). Its oxidation number increased, so it was oxidized. Cl₂ went from 0 to −1, gaining electrons (reduced). LEO: Lose Electrons, Oxidation.
Q2. Which statement correctly describes electron flow in a voltaic cell?
Answer: (2) Electrons flow from the anode to the cathode through the external circuit. Oxidation occurs at the anode, releasing electrons. They travel through the external wire to the cathode, where they are used in reduction. The salt bridge carries ions, not electrons.
Q3. Which of these reactions will occur, according to Reference Table J?
Answer: (3) Mg + 2 HCl → MgCl₂ + H₂. A single replacement reaction occurs when the metal is more active than (above) the one it's replacing on Table J. Magnesium is above hydrogen on Table J, so it can replace H. Copper, silver, and gold are all below hydrogen, so they don't react with dilute acids like HCl.
Q4. (Part B-2) Given the half-reactions: Cu²⁺ + 2e⁻ → Cu and Zn → Zn²⁺ + 2e⁻. Identify each as oxidation or reduction. Then combine them into a balanced net redox equation, showing your reasoning.
Sample full-credit response:
Half-reaction 1: Cu²⁺ + 2e⁻ → Cu. Cu²⁺ gains 2 electrons, going from
oxidation number +2 to 0. This is reduction (GER: Gain Electrons, Reduction).
Half-reaction 2: Zn → Zn²⁺ + 2e⁻. Zn loses 2 electrons, going from
oxidation number 0 to +2. This is oxidation (LEO: Lose Electrons, Oxidation).
Combining: Each half-reaction involves 2 electrons, so they already
balance (2 lost = 2 gained). Adding them and canceling the electrons:
Zn + Cu²⁺ + 2e⁻ → Zn²⁺ + 2e⁻ + Cu
Cancel 2e⁻ on both sides:
Zn + Cu²⁺ → Zn²⁺ + Cu
Q5. (Part C) Compare voltaic cells and electrolytic cells. In your response, address (a) whether each uses a spontaneous or non-spontaneous redox reaction, (b) the direction of energy conversion in each, and (c) the charge of the anode in each type of cell. Give one real-world example of each.
Sample full-credit response:
(a) Spontaneity: A voltaic cell uses a spontaneous redox
reaction; the chemistry happens on its own and releases energy. An electrolytic cell
uses a non-spontaneous reaction; an external power source is needed to force the
reaction to happen.
(b) Energy conversion: A voltaic cell converts chemical energy into
electrical energy (it produces a current that can do work). An electrolytic cell
converts electrical energy into chemical energy (it uses input electricity to
drive a reaction that would not happen on its own).
(c) Anode charge: In a voltaic cell, the anode is negative
because oxidation releases electrons there, building up negative charge. In an electrolytic
cell, the anode is positive because the external power source pulls electrons away
from it. In both cases, oxidation still occurs at the anode (AN OX is always true).
Examples: A voltaic cell is any common battery, such as an alkaline AA
battery or a car's lead-acid battery. An electrolytic cell is used in electroplating
silverware (silver from solution is deposited onto a base metal) and in the electrolysis
of water to produce hydrogen gas.