Chemistry · Redox reactions and electrochemistry · Year 1

Galvanic cells and corrosion

What voltage does a battery give, and what protects an underground pipe from rust?

The situation

One winter morning the car would not start — the battery had “gone flat”; in the cold, a phone also switched off ahead of time. Both are galvanic cells: they turn the energy of a chemical reaction into electrical energy. And in the steel gas pipes under the streets of Tashkent, exactly the same kind of “cell” works all by itself and eats away the iron. Where does the voltage come from, how does it depend on concentration and temperature, and how can a pipe be protected from rust?

Topic

Galvanic cells, electrode potentials and corrosion. A look inside a car battery and a phone battery; in the laboratory, the Daniell–Jacobi cell, salt bridge, potentiometer and pH meter. The second scene — Tashkent…

Key ideas

EMF and the Nernst equation
Rechargeable batteries
Corrosion and protection

Formulas

ℰ = E_{cathode} - E_{anode}, Δ G = - n F ℰ

Electromotive force (EMF) and the Gibbs energy of the reaction; $ℰ$ > 0 — the reaction is spontaneous.

E = E^{\circ} + \frac{R T}{n F} \ln \frac{a_{ox}}{a_{red}} = E^{\circ} + \frac{0.05916}{n} \lg \frac{a_{ox}}{a_{red}}

The Nernst equation (at 25 °C $2.303 R T / F$ = 59.16 mV).

\lg K = \frac{n E^{\circ}}{0,05916}, Δ S = n F {(\frac{\partial ℰ}{\partial T})}_{p}

Equilibrium constant and reaction entropy from the EMF (Gibbs–Helmholtz).

η = a + b \lg i, b = \frac{2,303 R T}{α n F} \approx 0,12 V

The Tafel equation: when the current density increases tenfold, the overpotential increases by $b$ ; $a = - b \lg i_{0}$ .

K = \frac{Δ m}{S t}, Z = \frac{K_{0} - K}{K_{0}} \cdot 100 %, γ = \frac{K_{0}}{K}

Corrosion rate (gravimetric), inhibitor protection efficiency $Z$ and inhibition coefficient $γ$ .

Theory

Electrode potential and the galvanic cell

When a metal is dipped into a solution of its own salt, an electrical double layer forms at the boundary: active metals “release” their ions into the solution and become negatively charged, while ions from the solution settle on less active ones, which become positively charged — a potential jump appears at the boundary. It cannot be measured on its own, only relative to another electrode: the conventional zero is the standard hydrogen electrode (SHE: platinised Pt, $a (H^{+})$ = 1, $p (H_{2})$ = 101.325 kPa). The series of standard electrode potentials measured against it: Mg −2.372 · Zn −0.762 · Fe −0.447 · Ni −0.257 · Pb −0.126 · H₂ 0 · Cu +0.342 · Ag +0.800 V. If two half-cells are joined by a salt bridge (KNO₃ in agar), the result is a galvanic cell: the one with the lower potential is the anode (oxidation, “−”), the one with the higher potential is the cathode (reduction, “+”), $ℰ = E_{cathode} - E_{anode}$ . The Daniell–Jacobi cell $Zn | ZnSO_{4} | | CuSO_{4} | Cu$ : $ℰ^{\circ}$ = 0.342 − (−0.762) = 1.104 V, $Zn + Cu^{2 +} \overset{}{\to} Zn^{2 +} + Cu$ . The salt bridge almost eliminates the diffusion potential at the boundary between the two solutions (caused by the different mobilities of the ions). The EMF is measured with a high-resistance voltmeter (when no current flows); if an external resistance is connected, a current flows and the voltage falls because of polarisation and internal resistance. In practice reference electrodes are used instead of the SHE: the saturated calomel electrode (SCE, +0.241 V) and Ag/AgCl (+0.197 V). School level — “Electrolysis and corrosion”; the physical side — “Power sources, EMF, internal resistance”.

Thermodynamics and the direction of redox reactions

The maximum electrical work done by a galvanic cell equals the decrease in Gibbs energy: $Δ G = - n F ℰ$ ; for the Daniell cell $Δ G^{\circ}$ = −2·96 485·1.104 ≈ −213 kJ/mol. The equilibrium constant $\lg K = n E^{\circ} / 0.05916$ = 37.3 — the reaction goes practically to completion. From the temperature dependence of the EMF we get the entropy and enthalpy: $Δ S = n F (\partial ℰ / \partial T)$ , $Δ H = Δ G + T Δ S$ ; in the Daniell cell $\partial ℰ / \partial T$ ≈ −0.11 mV/K → $Δ S^{\circ}$ ≈ −21 J/(mol·K), $Δ H^{\circ}$ ≈ −219 kJ/mol (from tables of S°). The direction rule: if the potential of the oxidising couple is greater than that of the reducing one, the reaction proceeds ( $ℰ$ > 0). Equations are balanced by the electron balance method or the ion–electron (half-reaction) method; the medium changes the product: KMnO₄ is reduced to Mn²⁺ in acidic medium, to MnO₂ in neutral and to MnO₄²⁻ in alkaline: $MnO_{4}^{-} + 8 H^{+} + 5 e^{-} \overset{}{\to} Mn^{2 +} + 4 H_{2} O$ (+1.51 V). In analytical chemistry, oxidising agents (KMnO₄, K₂Cr₂O₇, I₂, Ce⁴⁺) and reducing agents (Na₂S₂O₃, Fe²⁺, SnCl₂) are chosen on the basis of exactly these potentials; titration curves are covered in the “Titrimetric analysis” experiment.

The Nernst equation, concentration cells and pH

Potential depends on concentration (more precisely, on activity): $E = E^{\circ} + \frac{0.05916}{n} \lg \frac{a_{ox}}{a_{red}}$ (25 °C). For a metal electrode $E = E^{\circ} + \frac{0.05916}{n} \lg c (M^{n +})$ : if the Cu²⁺ solution is diluted 100 times, the potential falls by 59 mV. Concentration cell $Cu | Cu^{2 +} (c_{1}) ‖ Cu^{2 +} (c_{2}) | Cu$ : $E^{\circ}$ cancels, $ℰ = \frac{R T}{n F} \ln \frac{c_{2}}{c_{1}}$ — electrical energy is obtained solely from the equalising of concentrations; the slope $2.303 R T / n F$ is proportional to temperature. In a real solution the activity is $a = γ c$ : in CuSO₄ (a 2:2 electrolyte) $γ$ is small, and the ideal calculation differs noticeably from the measurement. Hydrogen electrode $Pt, H_{2} | H^{+}$ : $E = - 0.05916 pH$ ; if we connect it in a cell with the SCE, $ℰ = 0.241 + 0.05916 pH$ — the pH is found from the EMF (Physical Chemistry, lecture 21); in practice a glass electrode is used instead of the hydrogen electrode (“Electrochemical analysis”). Oxidation–reduction (redox) electrode: an inert Pt picks up the potential of the couple in the solution: $E = E^{\circ} (Fe^{3 +} / Fe^{2 +}) + 0.05916 \lg \frac{[Fe^{3 +}]}{[Fe^{2 +}]}$ . The standard potential (0.771 V) applies when the activities are 1; the formal (real) potential is the value measured in a particular medium when the concentrations are equal: 0.70 V in 1 M HCl, 0.68 V in 1 M H₂SO₄ (Fe³⁺ forms complexes with chloride and sulfate).

Latimer and Frost diagrams

The standard potentials between the different oxidation states of one element are written on a Latimer diagram from left to right (from the highest state to the lowest): $Cu^{2 +} \overset{\overset{}{0.153}}{\to} Cu^{+} \overset{\overset{}{0.521}}{\to} Cu$ . The potential of a non-adjacent couple is averaged with weights $n$ : $E^{\circ} = \frac{n_{1} E_{1} + n_{2} E_{2}}{n_{1} + n_{2}}$ → $E^{\circ} (Cu^{2 +} / Cu) = (0.153 + 0.521) / 2 = 0.337$ V. The disproportionation rule: if the potential to the right of a species is greater than the one to its left, it is unstable: $2 Cu^{+} \overset{}{\to} Cu^{2 +} + Cu$ (0.521 > 0.153); likewise $2 H_{2} O_{2} \overset{}{\to} 2 H_{2} O + O_{2}$ (1.776 > 0.695); whereas Fe²⁺ is stable (−0.447 < 0.771). Frost diagram: it plots $N \cdot E^{\circ}$ (relative to the element) against the oxidation state $N$ ; the slope of the line joining two points is the $E^{\circ}$ of that couple. A species lying above the line joining its neighbours disproportionates, and the one lowest of all is the most stable. The diagram for the halogens (Cl) is in the “Patterns in s- and p-block elements” experiment.

Electrode kinetics and batteries

When a current flows, the electrode potential shifts away from its equilibrium value — this is polarisation; the shift is the overpotential $η$ . The cause is either that the electron transfer itself is slow (kinetic, or activation, polarisation) or that the substance does not reach the surface by diffusion fast enough (concentration polarisation). Even at equilibrium, electrons flow equally in both directions between the electrode and the solution — this is the exchange current $i_{0}$ . At large $η$ the Butler–Volmer equation turns into the Tafel equation: $η = a + b \lg i$ , $b = 2.303 R T / (α n F)$ ≈ 0.12 V (for hydrogen evolution on most metals; on Pt ≈ 0.03 V). The hydrogen overpotential is very small on Pt and ≈ 1 V on Hg, Pb and Zn — which is why zinc can be deposited from an aqueous solution and why a lead–acid battery works without decomposing the water: $Pb + PbO_{2} + 2 H_{2} SO_{4} \overset{}{⇌} 2 PbSO_{4} + 2 H_{2} O$ , $ℰ^{\circ}$ = 1.691 − (−0.359) = 2.050 V, 6 cells — 12.3 V (when fully charged the acid is concentrated, so ≈ 12.7 V); on discharge H₂SO₄ is consumed and the density falls from 1.28 to ≈ 1.10 g/cm³ (checked with a hydrometer). Lithium-ion battery: Li⁺ ions move in and out between the layers of graphite and LiCoO₂ (intercalation): $LiC_{6} + CoO_{2} \overset{}{⇌} C_{6} + LiCoO_{2}$ , from 4.2 V down to 3.0 V, nominal ≈ 3.7 V. Charging is electrolysis: an external source forces the reaction to run in the reverse direction (the rules for cathode and anode — “Electrolysis and corrosion”, Faraday's laws — “Electrolysis, Faraday's laws”).

Corrosion, protection, safety and the model

Electrochemical corrosion — an anodic process (Fe → Fe²⁺) and a cathodic process (reduction of H⁺ or O₂) take place at the metal surface at the same time; they balance in current at one corrosion potential $E_{corr}$ — on the Evans diagram this is the point $(E_{corr}, i_{corr})$ where the anodic and cathodic Tafel lines intersect. Gravimetric method (Physical Chemistry, lecture 25): $K = Δ m / (S t)$ , g/(m²·h); penetration rate $Π = 8.76 K / ρ$ , mm/yr. Electrochemical method: $i_{corr}$ is found by extrapolating the Tafel lines, $K = i_{corr} M / (z F)$ . An inhibitor (lecture 26) adsorbs on the surface and slows the reactions: protection efficiency $Z = (K_{0} - K) / K_{0}$ , inhibition coefficient $γ = K_{0} / K$ ; urotropin is a mixed-type inhibitor for steel in acidic medium. Sacrificial protection: a block of zinc is attached to the pipe — the zinc becomes the anode and is itself destroyed. Cathodic protection: an external source (a cathodic protection station) connects the pipe to the negative terminal; the criterion is that the pipe potential is more negative than −0.85 V relative to a Cu/CuSO₄ electrode, but is not allowed to fall below −1.1 V (hydrogen would be evolved and the coating would peel off). Safety: battery acid burns skin and eyes — wear goggles and gloves; hydrogen and oxygen are released during charging — ventilate the room and allow no sparks; do not puncture, short-circuit or heat a lithium-ion battery; work with HCl in a fume cupboard. Model: activities are taken equal to concentrations (in the concentration cell you can compare with the Davies equation); the temperature dependence of $E^{\circ}$ is taken from S° tables for Zn and Cu only; the Tafel parameters, the OCV curves of the batteries, the corrosion and soil parameters and the inhibitor isotherm are illustrative; time is sped up 300–600 times depending on the mode.

Did you know?

John Daniell created the zinc–copper cell in 1836: unlike Volta's pile, it gave a steady voltage for a long time and was widely used on nineteenth-century telegraph lines.
Gaston Planté invented the lead–acid battery in 1859 — the first rechargeable power source; for creating lithium-ion batteries John Goodenough, Stanley Whittingham and Akira Yoshino received the Nobel Prize in Chemistry in 2019.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Redox reactions — Grade 8
Electrolysis and corrosion — Grade 9