Standard Electrode Potential

Spec Mapping — OCR H432 Module 5.2.3 — Redox and electrode potentials, covering the standard hydrogen electrode (SHE) as the reference half-cell ($\text{Pt} \,|\, \text{H}_2(\text{g, 100 kPa}) \,|\, \text{H}^+(\text{aq, 1.00 mol dm}^{-3})$Pt∣H2​(g, 100 kPa)∣H+(aq, 1.00 mol dm−3), 298 K, $E^\circ \equiv 0.00$E∘≡0.00 V); definition of standard electrode potential as the emf measured between a half-cell under standard conditions and the SHE; experimental measurement using a high-resistance voltmeter and a salt bridge; the convention of writing all half-equations as reductions ($\text{M}^{n+} + n\text{e}^- \rightleftharpoons \text{M}$Mn++ne−⇌M); use of inert platinum electrodes for ion-only and gas half-cells; the IUPAC cell notation with single bars for phase boundaries and double bar for the salt bridge; interpretation of the electrochemical series, in which more positive $E^\circ$E∘ identifies a stronger oxidising agent (the species on the LEFT of the half-equation); and qualitative prediction of redox feasibility from a pair of $E^\circ$E∘ values, with explicit ranking of common metal-ion couples Zn$^{2+}$2+/Zn ($-0.76$−0.76), Cu$^{2+}$2+/Cu ($+0.34$+0.34), Ag$^+$+/Ag ($+0.80$+0.80), Au$^{3+}$3+/Au ($+1.50$+1.50) (refer to the official OCR H432 specification document for exact wording).

Lesson 7 closed the thermodynamics block with $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$ΔG∘=ΔH∘−TΔS∘ and noted that the electrochemical analogue of $\Delta G^\circ$ΔG∘ is the cell emf via $\Delta G^\circ = -nFE^\circ_{cell}$ΔG∘=−nFEcell∘​ — converting free-energy change into electrical work. This lesson opens the electrochemistry trilogy by building the language in which that work is described: the standard hydrogen electrode (SHE) as the universal zero, the standard electrode potential $E^\circ$E∘ of any half-cell relative to that zero, and the electrochemical series that orders every redox couple from strong reducing agents (Li at $-3.04$−3.04 V) to strong oxidising agents (F$_2$2​ at $+2.87$+2.87 V). Five worked examples walk through SHE construction, measurement of Zn$^{2+}$2+/Zn, ranking of four common metal couples, prediction of M + X$^{n+}$n+ feasibility, and the use of inert Pt for ion-only and gas couples. Lesson 9 picks up the calculation of full cell emfs and the bridge to Gibbs; Lesson 10 closes the module with redox titrations.

Key Definition: the standard electrode potential $E^\circ$E∘ of a half-cell is the emf measured between that half-cell and the standard hydrogen electrode under standard conditions (298 K, 100 kPa, all solute concentrations 1.00 mol dm$^{-3}$−3), with the SHE on the left-hand side of the cell notation. All half-equations are written as reductions, with the oxidised species on the left: $\text{M}^{n+}(\text{aq}) + n\text{e}^- \rightleftharpoons \text{M}(\text{s})$Mn+(aq)+ne−⇌M(s). A more positive $E^\circ$E∘ identifies a stronger oxidising agent on the left-hand side of the half-equation.

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Learning Objectives (OCR Spec 5.2.3)

By the end of this lesson you should be able to:

• Describe the construction of the standard hydrogen electrode (platinised platinum, H$_2$2​(g) at 100 kPa, H$^+$+(aq) at 1.00 mol dm$^{-3}$−3, 298 K) and state its conventional $E^\circ = 0.00$E∘=0.00 V
• Define standard electrode potential with full OCR precision, including the conditions and the role of the SHE
• Describe the experimental measurement of $E^\circ$E∘ for a metal half-cell using a salt bridge and a high-resistance voltmeter
• Use inert platinum electrodes for ion-only (Fe$^{3+}$3+/Fe$^{2+}$2+, MnO$_4^-$4−​/Mn$^{2+}$2+) and gas (Cl$_2$2​/Cl$^-$−, O$_2$2​/H$_2$2​O) half-cells
• Write IUPAC cell notation (anode|aq‖aq|cathode), with single bars for phase boundaries, comma for same-phase species, and double bar for the salt bridge
• Interpret values in the electrochemical series — more positive $E^\circ$E∘ = stronger oxidising agent on the LHS — and rank common metal-ion couples Zn$^{2+}$2+/Zn, Cu$^{2+}$2+/Cu, Ag$^+$+/Ag, Au$^{3+}$3+/Au
• Predict the qualitative feasibility of an M + X$^{n+}$n+ displacement reaction from the relative positions of the two half-cells in the series
• Recognise (qualitatively) that $E^\circ$E∘ values assume standard concentration, and that real cells deviate via the Nernst equation (Lesson 8 footnote — undergraduate foreshadow)

Why electrode potentials? — the conceptual setup

Every redox reaction is, fundamentally, an electron transfer from a reducing agent to an oxidising agent. If the two half-reactions take place in the same vessel (Zn dropped into CuSO$_4$4​, say), the electrons hop directly from Zn atoms to Cu$^{2+}$2+ ions and the energy is released as heat. But the same electron transfer, performed across a wire connecting two physically separated half-cells, drives a current and does electrical work — the same chemistry, but now harnessed for a useful purpose. This is the principle behind every battery from Volta's 1800 pile to a modern lithium-ion phone cell.

The driving force for this electron flow is a potential difference measured in volts. Each half-cell has its own intrinsic tendency to gain or lose electrons; the cell as a whole has a difference of these tendencies. But you cannot measure the absolute potential of a single half-cell in isolation — a voltmeter only ever reads a difference between two electrodes. So electrochemistry needs a universal reference half-cell whose potential we agree to call zero. By international agreement (IUPAC, 1953), that reference is the standard hydrogen electrode.

graph TD
  A[Redox reaction: electrons transferred] --> B{Direct contact?}
  B -->|"Yes (Zn into CuSO4)"| C[Energy released as HEAT]
  B -->|"No (separated half-cells + wire)"| D[Electrons flow through external circuit]
  D --> E[Electrical WORK done -- battery / fuel cell]
  E --> F["Measured by E_cell (volts) relative to SHE"]

The Standard Hydrogen Electrode (SHE)

The SHE is the universal zero of electrochemistry, assigned $E^\circ \equiv 0.00$E∘≡0.00 V at all temperatures (the temperature dependence is absorbed into the definition). Its construction has six elements:

1. An inert platinum electrode, providing a place where electrons can enter or leave without itself taking part in the chemistry.
2. The electrode is coated with platinum black — a finely-divided platinum sponge electrodeposited onto the underlying wire — to provide an enormous catalytic surface area on which H$_2$2​/H$^+$+ exchange equilibrates rapidly.
3. Hydrogen gas at 100 kPa (1 bar) is bubbled continuously over the electrode through a glass shroud. Standard pressure under the modern IUPAC definition is 100 kPa, not 1 atm (101.325 kPa — close, but distinguishable to better than 0.5 % in $E^\circ$E∘).
4. The electrode dips into an acidic solution containing H$^+$+(aq) at activity 1, which in practice means 1.00 mol dm$^{-3}$−3 HCl or H$_2$2​SO$_4$4​ (strictly, activity = 1 is achieved only at infinite dilution because of ion–ion interactions; the working approximation is good to about 1 % at 1.00 mol dm$^{-3}$−3).
5. The temperature is held at 298 K (25 °C) in a thermostatted bath.
6. The cell is connected to the test half-cell through a salt bridge (typically saturated KNO$_3$3​ in agar gel, or a strip of filter paper soaked in KNO$_3$3​/KCl) and to the test electrode through a high-resistance voltmeter.

The half-equation, written as a reduction with the oxidised species on the left, is:

$2\text{H}^+(\text{aq}) + 2\text{e}^- \rightleftharpoons \text{H}_2(\text{g}), \quad E^\circ = 0.00\;\text{V (by definition)}$2H+(aq)+2e−⇌H2​(g),E∘=0.00V (by definition)

The platinum itself never appears in the half-equation: it is electronically active (it conducts electrons in and out) and catalytically active (it lowers the activation barrier for the H–H bond-breaking step), but chemically inert. This is the same reason platinum is used as an inert electrode in ion-only and gas half-cells later in the lesson.

graph TD
  A["H2 gas inlet at 100 kPa (1 bar)"] --> B[Glass shroud surrounding electrode]
  B --> C["Platinised platinum electrode (Pt coated in Pt black)"]
  C --> D["1.00 mol/dm3 H+(aq) -- HCl or H2SO4 at 298 K"]
  D --> E[Salt bridge -- saturated KNO3 in agar]
  E --> F[Test half-cell]
  C --> G[High-resistance voltmeter]
  G --> F

Definition of Standard Electrode Potential

Standard electrode potential ($E^\circ$E∘) — the emf measured between a half-cell under standard conditions and the standard hydrogen electrode, with the SHE on the left-hand side of the cell notation.

Standard conditions for $E^\circ$E∘:

• Temperature 298 K (25 °C)
• Pressure 100 kPa (1 bar) for any gases
• All aqueous-solute concentrations 1.00 mol dm$^{-3}$−3 (activity = 1)
• Pure solids and liquids in their standard states

The sign convention is the IUPAC ("Stockholm") convention used by OCR: $E^\circ$E∘ carries the polarity of the right-hand electrode in the cell notation SHE‖test half-cell. So a negative $E^\circ$E∘ (e.g. Zn$^{2+}$2+/Zn at $-0.76$−0.76 V) means the test half-cell is the negative terminal of the combined SHE+test cell — and therefore the test half-cell is a stronger reducing agent than hydrogen. A positive $E^\circ$E∘ (e.g. Cu$^{2+}$2+/Cu at $+0.34$+0.34 V) means the test half-cell is the positive terminal, and therefore a weaker reducing agent (stronger oxidising agent in the reverse sense) than hydrogen.

Worked Example 1: Measuring $E^\circ$E∘ for the Zn$^{2+}$2+/Zn half-cell

1. Build the half-cell. Polish a strip of pure zinc with emery paper to remove any oxide layer; immerse it in 1.00 mol dm$^{-3}$−3 Zn$^{2+}$2+(aq) — most conveniently as ZnSO$_4$4​(aq), since the sulphate ion is electrochemically silent in this potential range.
2. Build the SHE alongside (as above).
3. Connect with a salt bridge — a glass U-tube containing saturated KNO$_3$3​ in agar gel, with the ends plugged with cotton wool to prevent stirring. The salt bridge carries ionic current (K$^+$+ migrating one way, NO$_3^-$3−​ the other) without allowing the two solutions to mix.
4. Connect the electrodes through a high-resistance voltmeter (input impedance $> 10^6 \,\Omega$>106Ω). The high impedance ensures negligible current draw, so the cell remains at equilibrium throughout the measurement.
5. Read the voltage and note the polarity. The reading is 0.76 V, with the zinc electrode at the negative terminal.

Under the IUPAC convention, with the SHE on the left, this gives:

$E^\circ(\text{Zn}^{2+}/\text{Zn}) = -0.76\;\text{V}$E∘(Zn2+/Zn)=−0.76V

Interpretation: zinc is a stronger reducing agent than hydrogen — the half-equation Zn$^{2+}$2+ + 2e$^-$− $\rightleftharpoons$⇌ Zn lies further to the left than 2H$^+$+ + 2e$^-$− $\rightleftharpoons$⇌ H$_2$2​. At equilibrium with the SHE, zinc atoms preferentially lose electrons, building up negative charge on the zinc strip, and the H$^+$+/H$_2$2​ half-cell preferentially accepts them, building up positive charge on the platinum.

Worked Example 2: Half-cells without a metal — the Fe$^{3+}$3+/Fe$^{2+}$2+ couple

Some redox systems are entirely in solution: Fe$^{3+}$3+/Fe$^{2+}$2+, MnO$_4^-$4−​/Mn$^{2+}$2+, Cr$_2$2​O$_7^{2-}$72−​/Cr$^{3+}$3+. There is no metal form of the species to dip into the solution, so a bright platinum wire is used as an inert electron-transfer surface. The platinum does not appear in the half-equation; it merely provides the electron flow.

For the iron(III)/iron(II) couple:

• Solution: 1.00 mol dm$^{-3}$−3 Fe$^{3+}$3+(aq) AND 1.00 mol dm$^{-3}$−3 Fe$^{2+}$2+(aq), in dilute H$_2$2​SO$_4$4​ to suppress hydrolysis.
• Electrode: polished platinum wire.
• Half-equation: $\text{Fe}^{3+}(\text{aq}) + \text{e}^- \rightleftharpoons \text{Fe}^{2+}(\text{aq})$Fe3+(aq)+e−⇌Fe2+(aq), $E^\circ = +0.77$E∘=+0.77 V.

For the acidified manganate(VII)/manganese(II) couple:

• Solution: 1.00 mol dm$^{-3}$−3 MnO$_4^-$4−​, 1.00 mol dm$^{-3}$−3 Mn$^{2+}$2+, 1.00 mol dm$^{-3}$−3 H$^+$+ (the H$^+$+ is required by the half-equation and so its standard concentration enters $E^\circ$E∘).
• Electrode: platinum wire.
• Half-equation: $\text{MnO}_4^-(\text{aq}) + 8\text{H}^+(\text{aq}) + 5\text{e}^- \rightleftharpoons \text{Mn}^{2+}(\text{aq}) + 4\text{H}_2\text{O(l)}$MnO4−​(aq)+8H+(aq)+5e−⇌Mn2+(aq)+4H2​O(l), $E^\circ = +1.51$E∘=+1.51 V.

The role of platinum here is exactly the same as in the SHE: a chemically inert place where electrons can enter or leave the solution.

Worked Example 3: Gas half-cells — the Cl$_2$2​/Cl$^-$− couple

Where a redox system involves a gas other than H$_2$2​ (chlorine, oxygen, nitrogen), a gas half-cell is constructed exactly like the SHE: a platinised-platinum electrode immersed in 1.00 mol dm$^{-3}$−3 of the dissolved anion, with the gas bubbled over the electrode at 100 kPa. For chlorine/chloride:

• Solution: 1.00 mol dm$^{-3}$−3 Cl$^-$−(aq), most conveniently as HCl(aq).
• Gas: Cl$_2$2​(g) at 100 kPa, bubbled over the electrode.
• Half-equation: $\text{Cl}_2(\text{g}) + 2\text{e}^- \rightleftharpoons 2\text{Cl}^-(\text{aq})$Cl2​(g)+2e−⇌2Cl−(aq), $E^\circ = +1.36$E∘=+1.36 V.

The positive $E^\circ$E∘ identifies Cl$_2$2​ as a stronger oxidising agent than H$^+$+ — consistent with chlorine's ability to oxidise H$_2$2​ to HCl in sunlight.

Cell Notation — the IUPAC Convention

The IUPAC cell notation is a compact one-line description of a complete electrochemical cell. The rules are:

• Phase boundaries are shown by a single vertical bar |.
• Salt bridge is shown by a double vertical bar ‖.
• The anode (oxidation) is written on the left; the cathode (reduction) on the right.
• Within each half-cell, the reduced species is written next to the metal electrode and the oxidised species next to the salt-bridge symbol — so the cell reads, from left to right, "oxidised$_L$L​ ‖ oxidised$_R$R​" through the salt bridge.
• Same-phase species (e.g. Fe$^{2+}$2+ and Fe$^{3+}$3+ in the same solution) are separated by a comma.
• The cell is written so that the calculated $E^\circ_{cell} = E^\circ_{right} - E^\circ_{left}$Ecell∘​=Eright∘​−Eleft∘​ is positive — i.e. the more positive electrode goes on the right.

Daniell cell (zinc + copper): $E^\circ$E∘(Cu) = $+0.34$+0.34 is more positive than $E^\circ$E∘(Zn) = $-0.76$−0.76, so copper goes on the right:

$\text{Zn(s)}\,|\,\text{Zn}^{2+}(\text{aq})\,\|\,\text{Cu}^{2+}(\text{aq})\,|\,\text{Cu(s)}$Zn(s)∣Zn2+(aq)∥Cu2+(aq)∣Cu(s)

Cell with an inert Pt electrode (Cu vs MnO$_4^-$4−​/Mn$^{2+}$2+):

$\text{Cu(s)}\,|\,\text{Cu}^{2+}(\text{aq})\,\|\,\text{MnO}_4^-(\text{aq}),\,\text{Mn}^{2+}(\text{aq}),\,\text{H}^+(\text{aq})\,|\,\text{Pt(s)}$Cu(s)∣Cu2+(aq)∥MnO4−​(aq),Mn2+(aq),H+(aq)∣Pt(s)

The platinum shows on the right because the manganate half-cell has no metal form; the comma separation indicates all three aqueous species share one solution.

The Electrochemical Series

Putting every measured $E^\circ$E∘ in order — most negative at the top, most positive at the bottom — gives the electrochemical series, which is the central reference document of all redox chemistry. By convention every half-equation is written as a reduction with the oxidised species on the left and the reduced species on the right.

Half-equation	$E^\circ$E∘ / V
Li$^+$+ + e$^-$− $\rightleftharpoons$⇌ Li	$-3.04$−3.04
K$^+$+ + e$^-$− $\rightleftharpoons$⇌ K	$-2.93$−2.93
Ca$^{2+}$2+ + 2e$^-$− $\rightleftharpoons$⇌ Ca	$-2.87$−2.87
Na$^+$+ + e$^-$− $\rightleftharpoons$⇌ Na	$-2.71$−2.71
Mg$^{2+}$2+ + 2e$^-$− $\rightleftharpoons$⇌ Mg	$-2.37$−2.37
Al$^{3+}$3+ + 3e$^-$− $\rightleftharpoons$⇌ Al	$-1.66$−1.66
Zn$^{2+}$2+ + 2e$^-$− $\rightleftharpoons$⇌ Zn	$-0.76$−0.76
Fe$^{2+}$2+ + 2e$^-$− $\rightleftharpoons$⇌ Fe	$-0.44$−0.44
2H$^+$+ + 2e$^-$− $\rightleftharpoons$⇌ H$_2$2​	$0.00$0.00
Cu$^{2+}$2+ + 2e$^-$− $\rightleftharpoons$⇌ Cu	$+0.34$+0.34
I$_2$2​ + 2e$^-$− $\rightleftharpoons$⇌ 2I$^-$−	$+0.54$+0.54
Fe$^{3+}$3+ + e$^-$− $\rightleftharpoons$⇌ Fe$^{2+}$2+	$+0.77$+0.77
Ag$^+$+ + e$^-$− $\rightleftharpoons$⇌ Ag	$+0.80$+0.80
Br$_2$2​ + 2e$^-$− $\rightleftharpoons$⇌ 2Br$^-$−	$+1.09$+1.09
Cr$_2$2​O$_7^{2-}$72−​ + 14H$^+$+ + 6e$^-$− $\rightleftharpoons$⇌ 2Cr$^{3+}$3+ + 7H$_2$2​O	$+1.33$+1.33
Cl$_2$2​ + 2e$^-$− $\rightleftharpoons$⇌ 2Cl$^-$−	$+1.36$+1.36
Au$^{3+}$3+ + 3e$^-$− $\rightleftharpoons$⇌ Au	$+1.50$+1.50
MnO$_4^-$4−​ + 8H$^+$+ + 5e$^-$− $\rightleftharpoons$⇌ Mn$^{2+}$2+ + 4H$_2$2​O	$+1.51$+1.51
F$_2$2​ + 2e$^-$− $\rightleftharpoons$⇌ 2F$^-$−	$+2.87$+2.87

Reading the table:

• The more positive $E^\circ$E∘, the stronger the oxidising agent on the left-hand side of the half-equation. F$_2$2​ ($+2.87$+2.87) is the strongest A-Level oxidising agent; MnO$_4^-$4−​ ($+1.51$+1.51) and Cr$_2$2​O$_7^{2-}$72−​ ($+1.33$+1.33) are the workhorses of redox titrations (Lesson 10).
• The more negative $E^\circ$E∘, the stronger the reducing agent on the right-hand side. Lithium ($-3.04$−3.04) is the strongest A-Level reducing agent; the alkali metals are why lithium-ion batteries deliver such high cell voltages.
• A species higher in the table (more negative $E^\circ$E∘) can in principle reduce any species lower in the table (more positive $E^\circ$E∘) when the two half-cells are combined.

Worked Example 4: Ranking four common metal couples

Rank Zn$^{2+}$2+/Zn ($-0.76$−0.76), Cu$^{2+}$2+/Cu ($+0.34$+0.34), Ag$^+$+/Ag ($+0.80$+0.80), Au$^{3+}$3+/Au ($+1.50$+1.50) by (a) reducing power of the metal, (b) oxidising power of the cation.

(a) Reducing power of the metal (M $\to$→ M$^{n+}$n+ + ne$^-$−). The metal that most readily loses electrons is the strongest reducing agent — i.e. the one whose $E^\circ$E∘ is the most negative. Order: Zn $>$> Cu $>$> Ag $>$> Au. Zinc is the powerful reducing agent here (Galvani would have recognised this — his 1791 frog-leg twitch was the Zn/Cu pair); gold metal essentially does not corrode because its $E^\circ$E∘ is far more positive than every common oxidant in nature.

(b) Oxidising power of the cation (M$^{n+}$n+ + ne$^-$− $\to$→ M). The cation that most readily gains electrons is the strongest oxidising agent — i.e. the one whose $E^\circ$E∘ is the most positive. Order: Au$^{3+}$3+ $>$> Ag$^+$+ $>$> Cu$^{2+}$2+ $>$> Zn$^{2+}$2+. Au$^{3+}$3+ in aqua regia oxidises essentially every other common metal cation reaction in this list; Zn$^{2+}$2+ in contrast is a weak oxidising agent and Zn metal is hard to reduce back from Zn$^{2+}$2+ except electrolytically.