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Corrosion & Batteries

Iron rusting, sacrificial anode protection, galvanic batteries — Topic #25

1 · Interactive Simulation

Mode: Iron Rusting
Mass Lost (Fe)
0.00 g
Corrosion Rate
0.00 mm/yr
E°cell
+1.23 V
[O₂] dissolved
0.26 mM
pH
7.00
ΔG°
−237 kJ/mol
Time
0.0 yr
Playback
Preset Environment
Conditions
Display
Show electrons
Show ion flux
Highlight rust
Half-rxn labels
Speed

2 · The Idea, Step by Step

Corrosion — the battery iron builds by accident

Leave a steel nail in damp air and within days it turns crumbly and orange; a gold ring stays shiny for centuries. Why the difference? Iron is "eager" to give away its electrons, and oxygen is "eager" to grab them. All that's missing is something to carry charge between them — and a thin film of water does exactly that. The moment water connects the two, iron quietly builds a tiny battery on its own surface, and that battery slowly eats the metal.

Name the parts

A battery has two electrodes, and so does a corroding surface. At an anode the metal dissolves and leaves its electrons behind: $\mathrm{Fe \to Fe^{2+} + 2e^-}$. At a cathode dissolved oxygen mops those electrons up: $\mathrm{O_2 + 2H_2O + 4e^- \to 4OH^-}$. The electrons travel through the solid metal from anode to cathode, while ions drift through the water — a complete circuit, just like a real cell. The push that drives it is the cell voltage,

$$ E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} = 0.40 - (-0.44) = +0.84\ \mathrm{V}. $$

A positive voltage means the reaction runs all by itself — iron in moist air is thermodynamically doomed. How fast metal vanishes is set by the corrosion current. A handy rule of thumb for iron is that $1\ \mu\mathrm{A/cm^2}$ of corrosion current eats about $0.012$ mm of metal per year, so a typical seawater rate near $30\ \mu\mathrm{A/cm^2}$ thins a hull by roughly $0.35$ mm every year.

From voltage to grams lost

Voltage tells you whether iron corrodes; Faraday's law tells you how much. The mass lost is $\Delta m = ItM/nF$, where $n = 2$ electrons leave each iron atom and $F = 96485$ C/mol. Two knobs change almost everything: oxygen, which feeds the cathode, and chloride, which punctures iron's thin protective oxide — which is why de-icing salt and seawater are so brutal. Warming the water speeds the chemistry exponentially through an Arrhenius factor.

Try this in the sim above

First, switch to Sacrificial Anode (Zn) and watch the iron's mass-loss curve flatten — the zinc volunteers to corrode in iron's place. Next, in Iron Rusting, drag the $[\mathrm{Cl^-}]$ slider from $0$ up toward seawater ($0.5$ M) and watch the corrosion rate climb. Finally, raise the pH into the $9\text{–}13$ range and see the rate collapse as iron passivates — then push past $13$ and watch "caustic corrosion" return.

3 · Equation Derivation

Corrosion Cell Potential & Tafel Kinetics

Corrosion is fundamentally an electrochemical process — a short-circuited galvanic cell formed on the metal surface itself. Anodic and cathodic regions are connected by the metal (electron path) and the electrolyte (ion path).

$$ \text{Anode: } \mathrm{Fe(s) \to Fe^{2+}(aq) + 2e^-} \qquad E^\circ = -0.44\ \mathrm{V} $$ $$ \text{Cathode (neutral, aerated): } \mathrm{O_2(g) + 2H_2O(l) + 4e^- \to 4OH^-(aq)} \qquad E^\circ = +0.40\ \mathrm{V} $$ $$ \text{Overall: } \mathrm{2Fe + O_2 + 2H_2O \to 2Fe(OH)_2} \qquad E^\circ_{cell} = +0.84\ \mathrm{V} $$

Symbols

SymbolMeaningSI Unit
$E^\circ_{cell}$Standard cell potentialV
$\Delta G^\circ$Standard Gibbs free energyJ/mol or kJ/mol
$n$Electrons transferred per Fe atom(2 for Fe → Fe²⁺)
$F$Faraday constant96 485 C/mol
$i_{corr}$Corrosion current densityA/m²
$\beta_a, \beta_c$Tafel slopes (anodic, cathodic)V/decade
$M$Molar mass of Fe (55.85)g/mol
$\rho$Density of Fe (7.87)g/cm³

Derivation — Mass Loss & Penetration Rate

Step 1. Thermodynamic spontaneity from the cell potential: $$ \Delta G^\circ = -nFE^\circ_{cell} = -(4)(96485)(0.84) = -324\ \mathrm{kJ/mol\ O_2} $$ The huge negative value confirms that iron wants to corrode — kinetics is the only thing that slows it down.
Step 2. By Faraday's law, the moles of Fe oxidized in time $t$ at corrosion current $I$: $$ n_{Fe} = \frac{I\,t}{nF} $$
Step 3. Mass lost from anode area $A$ at current density $i_{corr}$: $$ \Delta m = \frac{i_{corr}\,A\,t\,M}{nF} $$
Step 4. Penetration rate (engineering units, mm/year): $$ \boxed{\ CR\ \mathrm{[mm/yr]} = 3.27\times 10^{-3}\times\frac{i_{corr}\,(M/n)}{\rho}\ } $$ Here $i_{corr}$ is in $\mu$A/cm² and $M/n$ is the equivalent weight. The constant $3.27\times10^{-3}$ already absorbs Faraday's constant $F$, so do not divide by $F$ again. For iron ($M/n = 27.9$, $\rho = 7.87$) this reduces to $CR \approx 0.0116\,i_{corr}$, so for mild steel in seawater a typical $i_{corr}\approx 30\ \mu$A/cm² → $CR\approx 0.35$ mm/yr.
Step 5. Kinetics — Butler-Volmer / Tafel approximation: $$ \eta = \beta_a\log\!\frac{i_a}{i_0},\qquad i_{corr} \propto \exp\!\left(-\frac{E_a}{RT}\right) $$ Higher $T$ accelerates corrosion exponentially; this is why warm coastal climates destroy infrastructure faster.
Step 6. Effect of [Cl⁻] — chloride pits the passive Fe₂O₃ layer: $$ i_{corr}([Cl^-]) = i_0\big(1 + k\,[Cl^-]\big) $$ Empirically, $k\approx 5$ M⁻¹ for mild steel. This is why de-icing salt destroys car bodies in winter.

Sliders → Equation Mapping

SliderSymbolUsed in
[O₂]$[O_2]$cathodic limiting current
pH$[H^+]$shifts cathode reaction (acid → H₂ evolution)
[Cl⁻]chloridepitting factor in $i_{corr}$
Temperature$T$Arrhenius factor
Anode area$A$total mass loss

Worked Example

Problem. An iron pipe with 100 cm² exposed area in seawater shows $i_{corr}=30\ \mu$A/cm². How much mass is lost in 1 year?

$i_{corr}A = 30\times 10^{-6}\times 100 = 3\times 10^{-3}$ A
$\Delta m = \dfrac{It M}{nF} = \dfrac{(3\times 10^{-3})(3.156\times 10^7)(55.85)}{(2)(96485)} = \boxed{27.4\ \mathrm{g/yr}}$

Penetration rate: $\dfrac{27.4}{(7.87)(100)} = 0.0348\ \mathrm{cm/yr} \approx 0.35$ mm/yr — consistent with field data.

References:
[Atkins & de Paula — Physical Chemistry, 11th Ed., Ch. 16.7 "Corrosion"]
[Housecroft & Sharpe — Inorganic Chemistry, 5th Ed., Ch. 8.10 "Electrolysis and Corrosion"]
[Jones — Principles and Prevention of Corrosion, 2nd Ed., Ch. 3]

4 · FAQ

🧪ConceptualWhy does iron rust but gold doesn't? ▾
Whether a metal corrodes is determined by the sign of its standard reduction potential. Iron has $E^\circ(\mathrm{Fe^{2+}/Fe}) = -0.44$ V — it is more easily oxidized than water or oxygen. Gold has $E^\circ(\mathrm{Au^{3+}/Au}) = +1.50$ V — it is harder to oxidize than the cathodic half-reaction provides driving force for. So gold is thermodynamically protected, while iron is thermodynamically doomed in moist air.
Key takeaway: Corrosion is governed by the difference $E^\circ_{cathode} - E^\circ_{anode}$; if it is positive, the metal corrodes spontaneously.
🌍Real LifeWhy are zinc blocks bolted to ship hulls? ▾
These are sacrificial anodes. Zinc has $E^\circ(\mathrm{Zn^{2+}/Zn}) = -0.76$ V — even more negative than iron's −0.44 V — so it oxidizes preferentially. As long as the zinc block is electrically connected to the iron hull and submerged in seawater, electrons flow Zn → Fe, suppressing iron oxidation entirely. The zinc dissolves over months and is periodically replaced — a cheap insurance policy against expensive hull damage.
Key takeaway: A more easily oxidized "sacrificial" metal protects a less easily oxidized one by becoming the anode of a galvanic couple.
🔬SimulationWhat exactly does the simulation show? ▾
Each mode renders an iron object (pipe, plate, or hull) immersed in an electrolyte. The colored regions track where oxidation and reduction happen: anodic sites where Fe is being eaten away (red Fe²⁺ ions leaving), and cathodic sites where O₂ is being reduced (blue OH⁻ ions forming). When you turn on "Show electrons," you see the internal current flowing through the metal from anode to cathode. The mass-loss curve below integrates Faraday's law in real time using the corrosion current density implied by your slider settings.
Key takeaway: Corrosion is a galvanic cell drawn on the metal itself — the simulation makes the hidden anodes and cathodes visible.
💡Non-ObviousWhy does rust keep growing — doesn't it stop the corrosion? ▾
Rust (hydrated Fe₂O₃·xH₂O) is porous and non-adherent, unlike the protective oxide layer on aluminum (Al₂O₃) or stainless steel (Cr₂O₃). Water and oxygen pass right through rust and continue attacking the underlying metal. In contrast, Al's oxide is dense, only ~4 nm thick, and self-healing — which is why aluminum cookware lasts decades. Iron's tragedy is that its oxide flakes off, exposing fresh metal. This is also why "weathering steel" (Cor-Ten) is engineered to form a dense, stable rust layer that does self-passivate.
Key takeaway: Whether oxidation passivates or accelerates depends entirely on the morphology of the oxide layer.
🧮MathematicalHow do I convert corrosion current to mass loss? ▾
Use Faraday's law: $\Delta m = \dfrac{ItM}{nF}$. For example, if $I = 1$ mA flows through an iron sample for 1 day, then $It = 86.4$ C, and $\Delta m = \dfrac{(86.4)(55.85)}{(2)(96485)} = 0.025$ g. Engineering practice converts to penetration rate via density: $CR\ [\mathrm{mm/yr}] = i_{corr}[\mu\mathrm{A/cm^2}]\times 0.0116$ for iron. So $i_{corr} = 100$ μA/cm² gives $\sim 1.16$ mm/yr — fast enough to eat through a 5 mm pipe wall in about 4 years.
Key takeaway: Corrosion current density of 1 μA/cm² ≈ 0.0116 mm/year for iron — memorize this conversion factor.
🌌Deep / AdvancedWhat is differential aeration corrosion? ▾
When part of an iron surface has more dissolved O₂ than another part — under a paint chip, inside a crevice, or beneath a water droplet — the high-O₂ region becomes the cathode and the low-O₂ region becomes the anode. The reason is concentration: the cathode reaction $O_2 + 2H_2O + 4e^- \to 4OH^-$ requires O₂, so the part exposed to air drives the reaction. The hidden, oxygen-starved metal is forced to be the anode and dissolves rapidly. This is why rust forms under paint chips, not on them, and why crevice corrosion destroys bolts from the inside out.
Key takeaway: Corrosion concentrates where O₂ is absent, not where it is abundant — a counterintuitive fact that explains hidden damage.
🌍Real LifeHow does a lead-acid car battery work and why does it die? ▾
Discharging: $\mathrm{Pb + PbO_2 + 2H_2SO_4 \to 2PbSO_4 + 2H_2O}$, $E^\circ_{cell} = 2.05$ V per cell × 6 cells = 12.3 V. Both electrodes deposit insoluble PbSO₄ during discharge. Charging reverses this — but if the battery is left discharged, the PbSO₄ crystallizes into large, electrochemically inactive lumps ("sulfation"), and the surface area available for reaction permanently decreases. Combined with shedding of active material from vibration, this is why car batteries die after ~5 years.
Key takeaway: All batteries are reversible galvanic cells; their lifetime is set by side reactions that progressively destroy the active electrode surface.

Best resource: LibreTexts Chemistry — "Corrosion" (chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules/Electrochemistry/Corrosion); Khan Academy — Galvanic Cells & Corrosion.

5 · Common Misconceptions

❌ "Rust is just iron + oxygen — water doesn't matter."
✅ Water is essential: it provides the electrolyte for ion conduction. Pure dry oxygen at room temperature barely affects iron — that's why ancient iron pillars in arid climates (e.g. the Delhi Iron Pillar) survive 1600 years intact. The reaction is not direct O₂ attack; it is electrochemical, and electrochemistry requires an aqueous medium for the ionic half of the circuit.
📖 Atkins & de Paula — Physical Chemistry, 11th Ed., §16.7
❌ "Stainless steel doesn't rust because it has no iron in it."
✅ Stainless steel is mostly iron (typically 70–80% Fe, with 10–20% Cr). Its corrosion resistance comes from the ~3 nm thick passive Cr₂O₃ layer that forms instantly on the surface. Damage this layer (e.g. with chloride pitting in seawater) and stainless steel rusts just like ordinary steel — which is why marine-grade 316 stainless contains added Mo to stabilize the passive film against Cl⁻.
📖 Housecroft & Sharpe — Inorganic Chemistry, 5th Ed., Ch. 22 "Transition Metals"
❌ "Galvanizing protects iron because the zinc coating physically blocks oxygen."
✅ Galvanizing (zinc coating) works even when scratched. The exposed iron does not rust, because zinc — being more easily oxidized — sets up a galvanic couple in which Zn becomes the anode and the iron becomes the cathode. Iron is forced to be a cathode and is therefore protected. Pure barrier protection (paint) fails the moment it is scratched; cathodic protection from Zn does not.
📖 Jones — Principles and Prevention of Corrosion, 2nd Ed., Ch. 13 "Cathodic Protection"
❌ "Higher pH always slows corrosion."
✅ Iron is most stable around pH 9–13 (passivation by Fe(OH)₂/Fe₃O₄). But at very high pH (>14), iron actually dissolves again as ferrate FeO₄²⁻ or HFeO₂⁻ — a phenomenon called caustic corrosion in boilers. So iron has a "passivity window" in the Pourbaix diagram, not a monotonic dependence on pH.
📖 Pourbaix — Atlas of Electrochemical Equilibria (NACE, 1974), Fe diagram
❌ "A bigger battery means a higher voltage."
✅ Voltage is determined entirely by the chemistry: $E^\circ_{cell}$ depends only on which redox couples are used. A AAA cell and a D cell of the same chemistry both give 1.5 V. What differs is capacity (amp-hours) — the bigger cell holds more reactant, so it sustains current longer. Voltage and capacity are independent properties.
📖 Atkins — Physical Chemistry, §6.6 "Cells in equilibrium"
❌ "Stainless steel will protect iron just like zinc does — both are metals, after all."
✅ The opposite happens! When stainless steel (E° ≈ +0.0 V due to Cr passivation) is bolted to ordinary steel in saltwater, the ordinary steel becomes the anode and corrodes faster than it would alone. This is galvanic corrosion. Choosing the wrong fastener material can destroy a structure in months. The rule: in a connection of two metals in contact with electrolyte, the more easily oxidized one corrodes preferentially.
📖 Jones — Principles and Prevention of Corrosion, 2nd Ed., Ch. 10 "Galvanic Corrosion"

Misconceptions reference: Schmidt et al., "Students' alternative conceptions about corrosion," J. Chem. Educ. 2007, 84(10), 1620; Taber — Chemical Misconceptions: Prevention, Diagnosis and Cure (RSC, 2002), Ch. 5 "Electrochemistry."

Corrosion & Batteries
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