Electrochemistry
Standard Electrode Potential
E° measured vs SHE (H+/H2 at 1 M, 1 atm) — Cu2+/Cu = +0.34 V, Zn2+/Zn = −0.76 V, F2/F− = +2.87 V
The standard electrode potential E° of a redox couple is the voltage of its half-cell, measured under standard conditions (1 M solute concentration, 1 atm gas pressure, 25°C, pure solid electrodes), versus the Standard Hydrogen Electrode (SHE) defined to be exactly 0.00 V. SHE consists of a platinized platinum electrode in contact with H+ at unit activity and H2 at 1 atm. By IUPAC convention, all E° values are reported as reduction potentials (the half-reaction written as oxidized + n e− → reduced). Cu2+/Cu = +0.34 V, Zn2+/Zn = −0.76 V, F2/F− = +2.87 V (most oxidizing), Li/Li+ = −3.04 V (most reducing). Walther Nernst introduced the concept in 1889; the IUPAC convention was fixed in 1953.
- ReferenceSHE = 0.000 V (definition)
- Strongest oxidizerF2/F− +2.87 V
- Strongest reducerLi/Li+ −3.04 V
- Daniell cell+1.10 V (Cu/Zn)
- Conditions1 M, 1 atm, 25°C
- IntroducedNernst 1889 (Nobel 1920)
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Why standard electrode potential matters
- Predicts spontaneous redox direction. If E°cell = E°cathode − E°anode > 0, the reaction proceeds spontaneously as written. The Daniell cell (Zn anode, Cu cathode) gives +0.34 − (−0.76) = +1.10 V, so Zn metal does displace Cu2+ from solution.
- Connects to Gibbs free energy. ΔG° = −nFE°cell, so a 1 V cell voltage with n = 2 corresponds to ΔG° = −193 kJ/mol of cell reaction. The same factor F = 96485 C/mol connects energy, voltage, and electron count throughout electrochemistry.
- Connects to equilibrium constant. ΔG° = −RT ln K, so E°cell = (RT/nF) ln K. At 25°C, log K = nE°cell/0.0592. A 1 V cell voltage with n = 2 corresponds to K ≈ 1034 — equilibrium lies essentially completely on the product side.
- Activity series of metals follows directly. Sorted from most negative E° to least: Li, K, Ca, Na, Mg, Al, Zn, Fe, Ni, Sn, Pb, H, Cu, Ag, Au. Each metal in the list displaces every metal below it from aqueous solution. This is why Zn nails dissolved in CuSO4 get coated with copper, but the reverse (Cu nail in ZnSO4) does nothing.
- Battery voltage is a sum of half-cell E° values. A Li-ion cell with E°(Li+/Li) = −3.04 V (anode) and E°(Co4+/Co3+) ~ +0.9 V (cathode, in oxide host) gives ~3.9 V; the actual cell voltage 3.7 V matches once SEI overpotential is subtracted. The high voltage of Li-ion comes directly from Li/Li+'s extreme reducing potential.
- Corrosion and passivation are predictable. Iron's E°(Fe2+/Fe) = −0.44 V is below O2/H2O's +1.23 V, so iron oxidizes in aerated water; aluminum's E°(Al3+/Al) = −1.66 V is even more negative but Al is protected by a tenacious Al2O3 film (passivation). Pourbaix diagrams overlay E° with pH dependence to map all stable phases.
- Used in analytical chemistry. A pH meter is a glass electrode whose voltage versus a Ag/AgCl reference follows the Nernst equation: E = E° − 0.0592 · pH. Calibrating against pH 4.00 and 7.00 buffers fixes E° and the slope, allowing 0.01 pH precision in routine work.
Common misconceptions
- E° depends on stoichiometry. No — E° is intensive, like temperature or pressure. Doubling the half-reaction (2 Cu2+ + 4 e− → 2 Cu) does not double E°. Multiplying changes ΔG° (extensive) but not E°. This is why E° tables list each couple once regardless of "balancing" multipliers.
- You should reverse the sign for the anode. Old textbook convention. The IUPAC standard (1953) keeps both half-cells as reduction potentials and computes E°cell = E°cathode − E°anode. Reversing signs of "oxidation potentials" gives the same number but invites errors and is now retired.
- SHE is easy to set up in lab. SHE is fragile (Pt blackening, H2 bubbling, gas-tight seal), so virtually no one uses it in practice. Daily lab work uses Ag/AgCl (E° = +0.197 V vs SHE) or saturated calomel (E° = +0.241 V vs SHE) and converts at the end.
- Larger E° means faster reaction. E° is a thermodynamic quantity; kinetics depend on activation energy and overpotential. The H2O/H2 reduction has E° = 0 V but is extremely sluggish on most surfaces — overpotentials of 0.5-1.0 V are typical, which is exactly why hydrogen evolution requires Pt or Ni catalysts.
- E° values are exactly reproducible everywhere. Reported tables agree to ~10-30 mV across IUPAC, NIST, and CRC for most couples, but values for transition metals with multiple oxidation states (Mn, Cr, V) differ by 50-100 mV between sources because of activity vs concentration distinctions and definition of "standard". Always cite the source you used.
- Negative E° means the half-reaction does not occur. No — negative E° just means it doesn't proceed spontaneously when paired with SHE. Coupled to a more negative half-cell, even Li/Li+ "reduction" becomes spontaneous (e.g., Li metal stripped at the anode of a Li-ion cell on charge).
How E° values are measured and used
Build a galvanic cell with two half-cells: the unknown couple on one side and SHE on the other, connected by a salt bridge. Measure the open-circuit voltage with a high-impedance voltmeter; the reading equals E°unknown − 0 = E°unknown, with sign determined by which electrode is positive. For a Cu electrode in 1 M Cu2+ paired with SHE, the Cu electrode reads +0.34 V positive, so E°(Cu2+/Cu) = +0.34 V (Cu acts as cathode versus SHE: it gets reduced). For a Zn electrode in 1 M Zn2+ paired with SHE, the Zn electrode reads −0.76 V (Zn acts as anode: it gets oxidized), so E°(Zn2+/Zn) = −0.76 V.
The Nernst equation extends E° to non-standard conditions: E = E° − (RT/nF) ln Q, where Q is the reaction quotient. At 25°C, RT/F = 0.0257 V, and the prefactor (0.0592/n) V per decade of Q is the working form chemists memorize. For Ag/AgCl in saturated KCl (~3.5 M Cl−), Q for AgCl + e− → Ag + Cl− is [Cl−] = 3.5, giving E = 0.222 − 0.0592 log(3.5) = 0.190 V at 25°C — close to the tabulated +0.197 V.
Connection to thermodynamics: ΔG° = −nFE°. A spontaneous cell (E° > 0) corresponds to negative ΔG°, and the equilibrium constant K relates by ΔG° = −RT ln K, so log K = nE°/0.0592 at 25°C. The Daniell cell at +1.10 V with n = 2 has log K = 37, K ≈ 1037 — Zn essentially quantitatively reduces Cu2+. This linkage between voltage, free energy, and equilibrium is one of the most useful Rosetta stones in physical chemistry.
Comparison: reference electrodes and offsets
| Reference electrode | Composition | E° vs SHE (V) | Notes |
|---|---|---|---|
| SHE (primary) | Pt | H2 (1 atm) | H+ (1 M) | 0.000 (definition) | Fragile; rarely used in routine lab |
| Ag/AgCl (saturated KCl) | Ag | AgCl | KCl (sat'd, 3.5 M) | +0.197 | Modern lab workhorse, pH meters |
| Ag/AgCl (3 M KCl) | Ag | AgCl | KCl (3 M) | +0.210 | Slightly higher activity |
| SCE (saturated calomel) | Hg | Hg2Cl2 | KCl (sat'd) | +0.241 | Older literature; Hg makes it disfavored |
| NCE (normal calomel) | Hg | Hg2Cl2 | KCl (1 M) | +0.280 | Less common variant |
| Cu/CuSO4 | Cu | CuSO4 (saturated) | +0.318 | Field corrosion measurements |
| RHE (reversible H electrode) | Pt | H2 | local pH | 0.000 − 0.0592·pH | Pinned to local pH; useful in fuel-cell electrochem |
Reduction potential table — selected couples
| Half-reaction | E° (V) vs SHE | Comment |
|---|---|---|
| F2 + 2 e− → 2 F− | +2.87 | Strongest oxidizer; corrodes Pt |
| O3 + 2 H+ + 2 e− → O2 + H2O | +2.07 | Why ozone is a powerful disinfectant |
| MnO4− + 8 H+ + 5 e− → Mn2+ + 4 H2O | +1.51 | Permanganate titration |
| Au3+ + 3 e− → Au | +1.50 | Why gold is "noble" |
| Cl2 + 2 e− → 2 Cl− | +1.36 | Chlorine bleach, water treatment |
| O2 + 4 H+ + 4 e− → 2 H2O | +1.23 | Fuel cell cathode reaction |
| Ag+ + e− → Ag | +0.80 | Silver tarnishing, electrochem mirrors |
| Cu2+ + 2 e− → Cu | +0.34 | Daniell cell cathode |
| 2 H+ + 2 e− → H2 | 0.000 | Definition (SHE) |
| Pb2+ + 2 e− → Pb | −0.13 | Lead-acid battery anode (oxidized) |
| Fe2+ + 2 e− → Fe | −0.44 | Iron rusting starts here |
| Zn2+ + 2 e− → Zn | −0.76 | Daniell cell anode |
| Al3+ + 3 e− → Al | −1.66 | Passivated by Al2O3 film |
| Mg2+ + 2 e− → Mg | −2.37 | Sacrificial anode (boats, pipes) |
| Na+ + e− → Na | −2.71 | Reactive with water |
| Li+ + e− → Li | −3.04 | Strongest reducer; Li-ion battery anode |
Applications and examples
- Daniell cell. Zn anode in 1 M ZnSO4, Cu cathode in 1 M CuSO4, salt bridge (KCl agar). E°cell = 0.34 − (−0.76) = +1.10 V. The textbook teaching cell, demonstrated by John Frederic Daniell in 1836; ran on the first commercial telegraph lines.
- Lead-acid battery. Pb (anode, oxidized to PbSO4) and PbO2 (cathode, reduced to PbSO4) in 4-6 M H2SO4. E° values of −0.36 V and +1.69 V give cell voltage 2.05 V, six in series for the 12 V SLI car battery — the same chemistry from 1859 (Planté) still ubiquitous today.
- Cathodic protection. Steel hulls and underground pipelines are wired to a sacrificial Mg or Zn anode (E° = −2.37 or −0.76 V), making the steel the cathode in a galvanic couple so it cannot oxidize. The anode dissolves preferentially and is replaced periodically.
- Electrolytic refining. Crude copper (with Au, Ag, Ni, Fe impurities) is the anode in CuSO4; pure copper deposits at the cathode. The applied voltage is set just above E°(Cu2+/Cu) = +0.34 V so Cu dissolves and redeposits but Au, Ag (E° > 0.34) drop as anode mud (recovered for >$10/kg) and Fe, Ni stay in solution.
- pH measurement. A glass electrode reads E vs Ag/AgCl with sensitivity 59.16 mV/pH unit at 25°C (the Nernst slope). Two-point calibration with pH 4.00 and 7.00 buffers determines E° and slope; resolution of 0.01 pH = 0.6 mV is routine.
Frequently asked questions
Why is the Standard Hydrogen Electrode set to exactly 0 V?
Absolute electrode potentials cannot be measured because no voltmeter can read just one half-cell — the second probe always introduces its own metal-solution junction. The community needed a reference, and in 1953 IUPAC chose the Standard Hydrogen Electrode (SHE): a platinized platinum surface in contact with H+ at unit activity (approximated by 1 mol/L strong acid) and H2 at 1 atm, with the half-reaction 2 H+ + 2 e- → H2 defined as E° = 0.000 V at all temperatures. SHE was selected because (1) hydrogen is universally available, (2) the platinum-hydrogen interface is reversible and reproducible to ~1 mV, and (3) the 0 V choice puts most metallic E° values within +/-3 V, a convenient range. Modern routine work uses Ag/AgCl or saturated calomel as secondary references with known offsets.
How do you calculate cell voltage from electrode potentials?
Use E°cell = E°cathode − E°anode, where both half-cells are looked up as reduction potentials. The cathode is the half-cell that actually undergoes reduction (more positive E°), the anode is oxidation (more negative E°). For the Daniell cell with Zn anode and Cu cathode: E°cathode = E°(Cu2+/Cu) = +0.34 V, E°anode = E°(Zn2+/Zn) = −0.76 V; E°cell = 0.34 − (−0.76) = +1.10 V. A positive cell potential indicates spontaneous discharge. Equivalent statement: take the difference of the two reduction potentials, with the more positive one as cathode. Never reverse signs to make oxidation potentials — the IUPAC convention since 1953 keeps everything as reduction.
What does Nernst's equation add to E°?
E° applies only at standard conditions. Walther Nernst's 1889 equation gives the voltage at any concentration: E = E° − (RT/nF) ln Q, where R is the gas constant, T is temperature in Kelvin, n is electrons transferred, F is Faraday's constant (96485 C/mol), and Q is the reaction quotient (products/reactants with activities). At 25°C, RT/F = 0.0257 V and the logarithmic prefactor reduces to 0.0592/n V per decade. For a 10x dilution of the cathode species, voltage drops by 0.0592/n V; for a 10x dilution of the anode species, voltage rises by the same. Nernst won the 1920 Nobel Prize in Chemistry for this and related thermodynamic work.
Why is fluorine the strongest oxidizing agent and lithium the strongest reducer?
F2/F− has E° = +2.87 V, the highest in standard tables. Fluorine has the highest electronegativity (4.0 Pauling), small atomic radius and tightly held electrons, and the F-F bond dissociation energy is anomalously low (158 kJ/mol versus 243 for Cl-Cl), all of which make accepting electrons very favorable. Li/Li+ has E° = −3.04 V, the lowest. Li has a low ionization energy (520 kJ/mol) and exceptionally large enthalpy of hydration (−520 kJ/mol) due to the small Li+ ionic radius (76 pm), which together make releasing the 2s electron and forming aqueous Li+ very favorable. Cesium has even lower IE but smaller hydration energy, putting Cs/Cs+ at −3.03 V, just barely above Li.
What is the difference between SHE, Ag/AgCl, and SCE reference electrodes?
All three are reference half-cells with reproducible potentials. SHE (Standard Hydrogen Electrode, E° = 0.000 V by definition) is the primary standard but inconvenient because it requires bubbling hydrogen and a fragile platinized Pt surface. Saturated calomel electrode (SCE, Hg/Hg2Cl2/saturated KCl) reads E° = +0.241 V vs SHE; it is more rugged but contains mercury and is being phased out. Silver/silver chloride (Ag/AgCl in saturated KCl) reads E° = +0.197 V vs SHE; it is the modern workhorse for pH meters, biosensors, and electroanalytical cells. To convert any measurement: E(SHE) = E(SCE) + 0.241 V or E(SHE) = E(Ag/AgCl) + 0.197 V; many older papers report potentials versus SCE so the conversion matters when reading literature.
How does pH affect electrode potentials?
Half-reactions involving H+ or OH− shift with pH following the Nernst equation. For a couple like O2/H2O (E° = +1.23 V at pH 0), the formal potential at pH 7 drops to +0.81 V because the half-reaction O2 + 4 H+ + 4 e− → 2 H2O contains four protons; each pH unit shifts the potential by −0.0592 V per electron-equivalent. Pourbaix diagrams (E vs pH plots, named for Marcel Pourbaix who introduced them in 1945) summarize this for every metal-water system: regions of immunity (metal stable), corrosion (metal dissolves), and passivity (oxide protects metal). Iron's Pourbaix diagram explains why iron rusts in neutral aerated water but is passivated in concentrated NaOH or HNO3.