Standard Electrode Potentials and the SHE

Dip a strip of zinc into acid and bubbles of hydrogen stream off the metal surface immediately. Dip copper into the same acid and nothing happens. That asymmetry in reactivity is not folklore — it is a number, a standard reduction potential, and this article shows where that number comes from. Every battery, corrosion process, and biological redox reaction can be ranked by one master scale of standard electrode potentials. But a single half-reaction can never be measured alone: every electrode needs a partner to complete a circuit. Chemists solved this by inventing a universal reference electrode and defining its potential as exactly zero. This article builds that reference electrode, the standard hydrogen electrode (SHE), from first principles. You will see how half-cell potentials are defined relative to it. You will learn the sign convention for reduction potentials. You will work through two fully numeric examples, from a textbook cell to a real corrosion problem.

Key takeaways

A single electrode potential cannot be measured in isolation; only a cell voltage (a difference) is measurable.
The standard hydrogen electrode (SHE) is assigned $E^{\ominus} = 0$ V exactly, at all temperatures, by convention.
Standard electrode potentials are always tabulated as reduction potentials, measured against the SHE under standard conditions.
Standard conditions mean unit activity of ions (≈1 mol/L), 1 bar H₂ gas, and platinized platinum catalyzing the H⁺/H₂ couple.
Cell EMF is computed as $E^{\ominus}_{\text{cell}} = E^{\ominus}_{\text{cathode}} - E^{\ominus}_{\text{anode}}$ , both written as reductions.
Key idea: the SHE is an arbitrary but universally agreed zero point that converts an unmeasurable absolute potential into a self-consistent, additive scale of relative reduction potentials.

The core insight

Because absolute electrode potentials cannot be measured, chemists fix one half-reaction — the reduction of H⁺ to H₂ at unit activity and 1 bar — as the zero of an entirely relative scale, and every other standard reduction potential is simply the EMF of a cell built from that electrode paired with the SHE, with the sign convention that a positive value means the half-reaction is a stronger oxidizer (more favorable reduction) than H⁺/H₂.

The physical picture

An electrode potential is fundamentally a statement about the energy of electron transfer between a metal and a solution. When a metal like zinc contacts a solution of its own ions, an equilibrium establishes itself: $\text{Zn}^{2+} + 2e^- \rightleftharpoons \text{Zn}(s)$ . This equilibrium creates a charge separation — an electrical double layer — across the metal-solution interface, and that double layer corresponds to a potential difference. The catch is that this potential difference exists inside the same phase boundary; you cannot connect a voltmeter probe to "the solution side" without introducing another metal-solution junction, which has its own unknown potential. Every measurement is therefore inherently a difference between two half-cell potentials, never an absolute value for one alone (see Electrodes and Half-Cells, Cell EMF and Sign Conventions). The practical solution is to build one universal reference half-cell, use it in every experiment, and declare its potential to be exactly zero. The standard hydrogen electrode was chosen for this role: platinum foil, coated with finely divided platinum black to give a large catalytic surface area, immersed in an aqueous solution where the hydrogen ion activity is unity, with hydrogen gas bubbled over the electrode at exactly 1 bar pressure. The half-reaction is

2\text{H}^+(aq) + 2e^- \rightleftharpoons \text{H}_2(g)

By international convention (IUPAC), $E^{\ominus}(\text{H}^+/\text{H}_2) = 0$ V at every temperature. This is a definition, not a measurement — it fixes the origin of the scale the way the triple point of water once fixed a temperature scale. Once the SHE is fixed, any other half-cell can be measured by wiring it to a SHE through a salt bridge and a voltmeter (a high-impedance one, so no current flows and the system stays at equilibrium). The measured cell voltage, corrected to standard conditions, is the standard reduction potential of that half-cell, with the sign convention that the SHE is treated as the left-hand (reference) electrode.

Figure

The SHE wired to a zinc half-cell to measure E-standard for Zn2+/Zn

The voltmeter here would read 0.76 V, but the sign convention matters: because zinc is the cathode by convention only if the reaction actually runs that way — in fact the real spontaneous reaction is zinc dissolving and reducing H⁺, meaning Zn is the anode. Tabulated as a reduction potential, this gives $E^{\ominus}(\text{Zn}^{2+}/\text{Zn}) = -0.76$ V, the negative sign telling us hydrogen ions are reduced more readily than zinc ions at standard conditions.

Figure

Ladder of standard reduction potentials anchored at the SHE zero

The core relations

2\text{H}^+(aq,\, a=1) + 2e^- \longrightarrow \text{H}_2(g,\, p=p^{\ominus}) \qquad E^{\ominus} \equiv 0 \text{ V (all } T\text{)}

where: this is a definition, fixing the zero of the entire potential scale.

E^{\ominus}_{\text{half-cell}} = E^{\ominus}_{\text{cell}} \quad \text{when the half-cell is the cathode and SHE is the anode}

where: $E^{\ominus}_{\text{cell}}$ is the measured EMF of the cell (SHE) | (half-cell), read with the sign convention right-hand electrode minus left-hand electrode.

E^{\ominus}_{\text{cell}} = E^{\ominus}_{\text{cathode}} - E^{\ominus}_{\text{anode}}

where: both potentials are tabulated reduction potentials; the cathode is where reduction actually occurs, the anode where oxidation occurs.

\Delta_r G^{\ominus} = -nFE^{\ominus}_{\text{cell}}

where: $n$ = moles of electrons transferred, $F = 96\,485$ C mol⁻¹ (Faraday constant), linking the potential scale to standard reaction Gibbs energies.

Worked examples

Derivation AAssigning E-standard to the Zn2+/Zn couple from a measured cell voltage

Goal. Given the measured EMF of the cell Pt(s) | H₂(g, 1 bar) | H⁺(a=1) ‖ Zn²⁺(a=1) | Zn(s), assign the correct sign and value of $E^{\ominus}(\text{Zn}^{2+}/\text{Zn})$ .

Step 1. Identify the two half-reactions. The right-hand electrode (as written) is Zn²⁺/Zn; the left-hand is H⁺/H₂. Written as reductions:

\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \qquad \text{(right, reduction as tabulated)}

2\text{H}^+ + 2e^- \rightarrow \text{H}_2 \qquad \text{(left, reference, } E^{\ominus}=0\text{)}

Step 2. Apply the sign convention for cell notation. For a cell written left | right, the standard convention gives

E^{\ominus}_{\text{cell}} = E^{\ominus}_{\text{right}} - E^{\ominus}_{\text{left}} = E^{\ominus}(\text{Zn}^{2+}/\text{Zn}) - 0

Step 3. Insert the experimental measurement. Experiment shows this cell has a measured EMF of $-0.76$ V (the actual spontaneous cell reaction runs the opposite way, with Zn dissolving and H⁺ being reduced; the negative sign signals this).

Step 4. Solve for the unknown potential.

E^{\ominus}(\text{Zn}^{2+}/\text{Zn}) = E^{\ominus}_{\text{cell}} + 0 = -0.76 \text{ V}

Step 5. Sanity check with thermodynamics. With $n = 2$ and $F = 96\,485$ C mol⁻¹,

\Delta_r G^{\ominus} = -nFE^{\ominus}_{\text{cell}} = -(2)(96\,485\text{ C mol}^{-1})(-0.76\text{ V}) = +1.47\times10^{5} \text{ J mol}^{-1}

A positive $\Delta_r G^{\ominus}$ for "H₂ reduces Zn²⁺" confirms this direction is non-spontaneous — consistent with zinc metal dissolving in acid, not the reverse.

\boxed{E^{\ominus}(\text{Zn}^{2+}/\text{Zn}) = -0.76 \text{ V vs. SHE}}

Worked examples

Example 1 — Foundational: building a Daniell-type cell from tabulated SHE-referenced potentials. Given standard reduction potentials (all vs. SHE, 25 °C):

\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \qquad E^{\ominus} = +0.34 \text{ V}

\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \qquad E^{\ominus} = -0.76 \text{ V}

Find the standard EMF of the Daniell cell, Zn(s) | Zn²⁺(aq) ‖ Cu²⁺(aq) | Cu(s), and the standard Gibbs energy of reaction. Step 1. Identify cathode and anode. Cu²⁺/Cu has the higher (more positive) reduction potential, so it is reduced: it is the cathode. Zn²⁺/Zn is oxidized: it is the anode. Step 2. Apply

E^{\ominus}_{\text{cell}} = E^{\ominus}_{\text{cathode}} - E^{\ominus}_{\text{anode}} = (+0.34 \text{ V}) - (-0.76 \text{ V}) = +1.10 \text{ V}

Step 3. Compute $\Delta_r G^{\ominus}$ for the overall two-electron reaction Zn + Cu²⁺ → Zn²⁺ + Cu, with $n=2$ :

\Delta_r G^{\ominus} = -nFE^{\ominus}_{\text{cell}} = -(2)(96\,485 \text{ C mol}^{-1})(1.10 \text{ V}) = -2.12\times10^{5} \text{ J mol}^{-1} = -212 \text{ kJ mol}^{-1}

Sanity check. The value $+1.10$ V matches the textbook Daniell cell voltage exactly, and a large negative $\Delta_r G^{\ominus}$ correctly predicts a strongly spontaneous reaction — consistent with the vigorous displacement of copper by zinc observed experimentally.

Example 2 — Applied: will iron corrode in aerated acidic water? Standard reduction potentials:

\text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \qquad E^{\ominus} = -0.44 \text{ V}

\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O} \qquad E^{\ominus} = +1.23 \text{ V}

Determine whether dissolved O₂ can oxidize metallic iron under standard, acidic, aerated conditions, and compute $E^{\ominus}_{\text{cell}}$ and $\Delta_r G^{\ominus}$ per mole of Fe. Step 1. Balance electrons. Iron oxidation releases 2 electrons per Fe; oxygen reduction requires 4 electrons per O₂. The overall balanced equation is

2\text{Fe}(s) + \text{O}_2(g) + 4\text{H}^+(aq) \rightarrow 2\text{Fe}^{2+}(aq) + 2\text{H}_2\text{O}(l), \qquad n = 4

Step 2. Identify cathode/anode. O₂/H₂O has the higher potential, so it is reduced (cathode); Fe/Fe²⁺ is oxidized (anode).

E^{\ominus}_{\text{cell}} = E^{\ominus}_{\text{cathode}} - E^{\ominus}_{\text{anode}} = (+1.23 \text{ V}) - (-0.44 \text{ V}) = +1.67 \text{ V}

Step 3. Compute $\Delta_r G^{\ominus}$ for the reaction as balanced (4 electrons transferred):

\Delta_r G^{\ominus} = -nFE^{\ominus}_{\text{cell}} = -(4)(96\,485 \text{ C mol}^{-1})(1.67 \text{ V}) = -6.45\times10^{5} \text{ J mol}^{-1} = -645 \text{ kJ mol}^{-1}

Per mole of Fe, divide by 2: $\Delta_r G^{\ominus}(\text{per Fe}) \approx -322$ kJ mol⁻¹. Sanity check. The strongly positive $E^{\ominus}_{\text{cell}}$ and strongly negative $\Delta_r G^{\ominus}$ both confirm the well-known fact that iron corrodes readily in acidic, aerated water — the thermodynamic basis of rusting. (Real corrosion rates also depend on kinetics and passivation, which this standard-state calculation does not capture — see the Nernst equation for non-standard concentrations.)

Limiting cases & common traps

Situation	Correct handling
Reported potential for an oxidation half-reaction	Flip the sign; tables list reductions only, by IUPAC convention
Multiplying a half-reaction by a stoichiometric factor	Do not multiply $E^{\ominus}$ ; potential is intensive, not extensive
SHE potential at a non-standard temperature	Still defined as exactly 0 V; other tabulated values do shift with $T$
Non-unit activities or non-standard pressures	Use the Nernst equation, not the raw $E^{\ominus}$ table value
SHE in practice	Rarely used directly (H₂ gas handling, Pt poisoning); calibrated secondary electrodes like Ag/AgCl or calomel are used instead

The chemist behind it

The standard hydrogen electrode convention crystallized in the early twentieth century as electrochemists sought a reproducible, universal reference amid competing local reference electrodes (calomel, various metal/salt combinations) that made data from different laboratories hard to compare. The formalization of the modern sign convention and the SHE as the international zero point is closely associated with the recommendations that followed the 1953 IUPAC (Stockholm) convention, which resolved decades of transatlantic disagreement over whether tables should list oxidation or reduction potentials. Walther Nernst's earlier theoretical work on electrode equilibria — linking measured cell voltages to concentrations and free energies — supplied the thermodynamic scaffolding that made a universal zero point meaningful in the first place.

Origins · 1 minWalther Nernst and how this was discovered

Walther Nernst

1864–1941 · German physical chemist whose electrode-potential theory and third law of thermodynamics underpin the SHE-referenced potential scale

Ask the tutor: How does the Nernst equation adjust these standard potentials once concentrations move away from 1 mol/L?

Why is the SHE potential defined as exactly zero instead of measured

Electrode potentials are only ever accessible as differences between two half-cells, because any voltmeter connection requires a second metal-solution interface. There is no experiment that isolates one electrode's absolute potential. Chemists therefore chose one universal reference half-reaction, the H⁺/H₂ couple at unit activity and 1 bar, and assigned it exactly 0 V by international convention. Every other tabulated standard reduction potential is really the EMF of a cell built from that species paired against this fixed reference, which makes the whole scale self-consistent and reproducible across laboratories worldwide.

Why is platinized platinum used for the SHE instead of plain platinum

Platinum black — platinum electroplated as a fine, high-surface-area matte black deposit — dramatically increases the electrode's real surface area and catalytic activity for the sluggish H⁺/H₂ electron-transfer reaction. Without this roughened surface, the electrode would respond slowly to changes and would not reach true thermodynamic equilibrium quickly, making the measured potential unreliable. The large surface area also allows efficient adsorption and equilibration of hydrogen gas, which is essential since the whole reference rests on this equilibrium being genuinely established.

Is the SHE actually used in real laboratories today

Rarely, in practice. Handling flowing hydrogen gas safely, maintaining exact unit activity of H⁺, and avoiding platinum poisoning by trace sulfur or arsenic compounds make the SHE cumbersome for routine work. Most laboratories use secondary reference electrodes, such as the saturated calomel electrode or silver/silver chloride, whose potentials versus the SHE have been carefully calibrated. Reported voltages are then converted back to the SHE scale, so the SHE remains the conceptual zero even when it is not physically present on the benchtop.

Does multiplying a half-reaction change its standard potential

No. Standard electrode potential is an intensive quantity — a Gibbs energy difference per electron transferred, expressed as a voltage — and it does not scale with the amount of substance. Doubling a half-reaction's stoichiometric coefficients doubles $n$ and doubles $\Delta_r G^{\ominus}$ proportionally, but the ratio $\Delta_r G^{\ominus}/(nF)$ , which defines $E^{\ominus}$ , stays fixed. This is why you never multiply tabulated $E^{\ominus}$ values when balancing overall cell reactions; only $\Delta G$ values are additive.

How does the standard hydrogen electrode connect to the Nernst equation

The SHE fixes the reference point for standard-state conditions only: unit activities, 1 bar pressure, a specified temperature. Real systems rarely sit exactly at standard state, so the Nernst equation extends the SHE-referenced $E^{\ominus}$ values to arbitrary concentrations and pressures using the reaction quotient $Q$ . In that sense, standard electrode potentials referenced to the SHE are the fixed anchor points, and the Nernst equation is the tool that lets you calculate real, non-standard cell voltages around those anchors.

Standard Electrode Potentials and the SHE

The physical picture

The core relations

Worked examples

Worked examples

Limiting cases & common traps

The chemist behind it

Before this