Chemistry · Lesson

Batteries, fuel cells and corrosion

Connect electrochemical principles to stored-cell inventories, externally supplied fuel and corrosion. Distinguish delivered charge, electrical energy and the conditions needed for continued operation.

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By the end, you can

Distinguish primary/secondary cells from continuously supplied fuel cells.
Convert charge and charge-weighted mean voltage into energy.
Explain local corrosion coupling and limits of protection.

A battery’s usable inventory and operating mode matter

A primary cell is designed for single use; a secondary cell can be recharged through an appropriately designed driven process. Stored reacting material, electrode structure and operating conditions constrain what it can deliver. Rechargeability is a device/chemistry property, not permission to reverse every primary cell experimentally.

During charging, strict anode/cathode reaction roles can reverse relative to discharge. Fixed hardware is often described as the positive and negative electrodes to avoid ambiguity. State the operating mode when assigning oxidation, reduction and polarity.

Ampere-hours and watt-hours describe different quantities

Delivered ampere-hours measure charge: 1 A h = 3600 C. Electrical energy is ∫V dq_el. If the supplied mean voltage is correctly weighted by delivered charge, energy is V_meanq_el; multiplying an arbitrary endpoint voltage by all charge need not be valid.

An original hypothetical cell delivers 2.00 A h with charge-weighted mean loaded voltage 3.70 V. It delivers 7.20 × 10³ C and electrical energy 26.6 kJ, or 7.40 W h. These are supplied example outputs, not a real battery specification or a claim about its chemical efficiency.

A supplied fuel has its own reaction and carrier paths

A fuel cell uses externally supplied reactants rather than only a stored reacting inventory. In a specified hydrogen proton-exchange-membrane model, hydrogen oxidation is H₂ → 2 H⁺ + 2e⁻ and oxygen reduction is (1/2)O₂ + 2 H⁺ + 2e⁻ → H₂O. Protons cross the membrane; electrons use the external circuit. Other electrolyte technologies can carry other ions.

An ideal electrochemically consumed 0.0100 mol H₂ transfers 0.0200 mol electrons, consumes 0.00500 mol O₂ and forms 0.0100 mol water, with charge about 1.93 × 10³ C. Supplied feed can exceed consumed fuel if utilization is incomplete. Water at the operating outlet does not establish zero lifecycle emissions; hydrogen production and the system boundary matter.

Track the specified hydrogen fuel cell’s stoichiometric inventory

Quantity or path	Model amount	Stoichiometric reason	Scope
H₂ consumed	0.0100 mol	One H₂ supplies 2 e⁻	Electrochemical consumption
Electrons transferred	0.0200 mol	n(e⁻) = 2n(H₂)	External conducting circuit
O₂ consumed	0.00500 mol	One O₂ per 2 H₂	Specified hydrogen/oxygen net reaction
Water formed	0.0100 mol	One water per H₂	Product phase depends on operation
Electrical charge	1.93 × 10³ C	q_el = n(e⁻)F	Ideal desired-reaction bookkeeping
Proton path	Membrane transport	H⁺ cancels from the net reaction	Specific PEM electrolyte model

Ideal supplied PEM hydrogen-cell model, desired reaction fraction1, no crossover or parasitic reactions. Quantities refer to 0.0100 mol H₂ consumed electrochemically, not total fuel fed. Protons and electrons follow different paths; water phase and operating voltage are not specified here.

Local reactions can couple on one metal surface

Corrosion can join metal oxidation at one surface region to a cathodic reaction elsewhere through electronic and ionic paths. For a specified neutral oxygenated-water iron model, oxidation is Fe → Fe²⁺ + 2e⁻ and a cathodic oxygen reaction is O₂ + 2 H₂O + 4e⁻ → 4 OH⁻. Doubling iron oxidation cancels four electrons; further precipitation and oxidation can form variable hydrated rust products.

A thermodynamic tendency alone does not give the corrosion rate. Environment, transport and passive-film behavior matter. Cathodic protection can use a connected sacrificial metal, while effectiveness depends on the environment, continuing electrical connection and available protective material. Rust is not universally one exact pure Fe₂O₃ phase or an automatically protective film.

Worked examples

Convert delivered charge into energy

The original hypothetical cell delivers 2.00 A h at supplied charge-weighted mean loaded voltage 3.70 V. Find charge and electrical energy.

Convert charge: 2.00 × 3600 = 7200 C.
Use the specified mean: energy = 3.70 × 7200 = 26640 J.
Report 26.6 kJ at three significant figures.
Equivalently, 3.70 V × 2.00 A h = 7.40 W h.

Delivered charge: 7.20 × 10³ C. Electrical energy: 26.6 kJ or 7.40 W h. Charge and energy are different quantities.

Try it yourself

Does an ampere-hour measure electrical energy directly?
Show the answer and reasoning
No.
It measures charge; the voltage history is also needed for energy.
What kind of mean voltage supports energy = V_meanq_el when voltage varies?
Show the answer and reasoning
A charge-weighted mean.
It represents the voltage in the energy integral over delivered charge.
Do the specified PEM model’s electrons cross the membrane along with its protons?
Show the answer and reasoning
No.
Protons use the membrane while electrons use the external conducting path.
Does a potential table alone determine a real metal’s corrosion rate?
Show the answer and reasoning
No.
Kinetics, environment, transport and film behavior also matter.

What to carry forward

Keep stored inventory, recharge operation and external fuel supply distinct.
Charge is not energy; retain the loaded voltage history.
Name a fuel-cell electrolyte before describing its ionic carrier.
Corrosion tendency, rate and protection effectiveness need different evidence.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.