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Electrochemistry (A Level)

Physical Chemistry Weightage: A2 · Paper 4 Topic 24
“Welcome! At AS you used oxidation numbers to spot redox reactions. At A Level you put numbers on the electron pull of every species. Electrode potentials let you build a cell, say which way the electrons flow, predict whether a reaction will go, and work out how a change in concentration shifts the voltage. Electrolysis runs the same ideas in reverse and lets you count electrons by measuring a current. Learn the definitions word for word, then practise the signs, the half-equations and the calculations.”
— SCORECHEM ACADEMIC TEAM

0. What Examiners Want

This guide covers Topic 24 of Cambridge International AS & A Level Chemistry 9701 (2025–27) and follows the learning outcomes below, word for word. The right-hand column shows where each one is taught.

24.1 Electrolysis. Candidates should be able to: Section
1 predict the identities of substances liberated during electrolysis from the state of electrolyte (molten or aqueous), position in the redox series (electrode potential) and concentration 1
2 state and apply the relationship F = Le between the Faraday constant, F, the Avogadro constant, L, and the charge on the electron, e 2, 3
3 calculate: (a) the quantity of charge passed during electrolysis, using Q = It; (b) the mass and/or volume of substance liberated during electrolysis 2
4 describe the determination of a value of the Avogadro constant by an electrolytic method 3
24.2 Standard electrode potentials E°, standard cell potentials E°cell and the Nernst equation. Candidates should be able to: Section
1 define the terms: (a) standard electrode (reduction) potential (b) standard cell potential 4
2 describe the standard hydrogen electrode 4
3 describe methods used to measure the standard electrode potentials of: (a) metals or non-metals in contact with their ions in aqueous solution (b) ions of the same element in different oxidation states 5
4 calculate a standard cell potential by combining two standard electrode potentials 6
5 use standard cell potentials to: (a) deduce the polarity of each electrode and hence explain/deduce the direction of electron flow in the external circuit of a simple cell (b) predict the feasibility of a reaction 6, 7
6 deduce from E° values the relative reactivity of elements, compounds and ions as oxidising agents or as reducing agents 7
7 construct redox equations using the relevant half-equations 7
8 predict qualitatively how the value of an electrode potential, E, varies with the concentrations of the aqueous ions 8
9 use the Nernst equation, e.g. E = E° + (0.059/z) log [oxidised species]/[reduced species], to predict quantitatively how the value of an electrode potential varies with the concentrations of the aqueous ions; examples include Cu2+(aq) + 2e− ⇌ Cu(s), Fe3+(aq) + e− ⇌ Fe2+(aq) 8
10 understand and use the equation ΔG° = –nE°cellF 9
How marks are earned in Electrochemistry (A Level)
  • Definitions and descriptions: the standard electrode potential and standard cell potential in full, and the standard hydrogen electrode with its platinum, hydrogen at 101 kPa and 1.00 mol dm−3 H+. Labelling a diagram of a measuring cell is a regular task.
  • Cells: E°cell from two data values, the polarity of each electrode, the direction of electron flow, and the overall equation.
  • Predictions: will this reaction go? Which is the stronger oxidising agent? Always give the two E° values and the calculated E°cell.
  • Calculations: Q = It, moles of electrons, mass or volume, the Faraday and Avogadro constants, the Nernst equation and ΔG° = −nE°cellF. Use the Data Booklet: F = 9.65 × 104 C mol−1, e = 1.60 × 10−19 C, L = 6.02 × 1023 mol−1.
  • Graphs and data: read or draw how E changes with log of a concentration, and take the E° values you need from the Data Booklet (Table 5), which is given in the exam.
⚠️ Examiner Trap: Always use the Data Booklet. Paper 4 gives you the table of standard electrode potentials, so do not quote values from memory or from another textbook. Some textbooks use +1.51 V for MnO4−/Mn2+ where the Data Booklet gives +1.52 V. The question will expect the Data Booklet value, and the mark scheme is built on it.

1. Electrolysis and What Is Discharged

Electrolysis is the decomposition of an ionic compound, molten or in aqueous solution, by passing an electric current through it. Electrical energy is used to make a reaction happen that does not go by itself. The current comes from a d.c. supply, and the ions move through the liquid: positive ions towards the negative electrode, negative ions towards the positive one.

Electrolysis of molten zinc chloride showing the cathode, anode and ion movement
An electrolytic cell. Zn2+ ions gain electrons at the negative cathode (reduction); Cl− ions lose electrons at the positive anode (oxidation). Electrons are pushed round the external circuit by the supply.

Molten electrolytes. Only two kinds of ion are present, so the products are fixed. The metal forms at the cathode and the non-metal at the anode.

Molten compound Cathode (−) Anode (+)
NaCl Na+ + e− → Na 2Cl− → Cl2 + 2e−
PbBr2 Pb2+ + 2e− → Pb 2Br− → Br2 + 2e−
Al2O3 (in molten cryolite) Al3+ + 3e− → Al 2O2− → O2 + 4e−

Aqueous electrolytes. Water adds two more ions, H+ and OH−, so at each electrode there are two competing species. Three things decide which one is discharged:

  1. The position in the redox series. At the cathode the ion with the more positive E° is reduced more easily. At the anode the species with the less positive E° is oxidised more easily.
  2. The concentration. E° values apply at 1.00 mol dm−3. A very different concentration can swap the order of two close values.
  3. The electrode material. A reactive (active) electrode such as copper can itself be oxidised.

At the cathode. H+ is reduced to H2 (E° = 0.00 V at 1.00 mol dm−3; in neutral water, where [H+] = 10−7 mol dm−3, the electrode potential is about −0.41 V). Compare this with the metal ion.

Metal ion E° / V (Data Booklet) Compared with H+ Cathode product
Ag+ +0.80 far more positive Ag
Cu2+ +0.34 more positive Cu
Zn2+ −0.76 more negative H2
Mg2+ −2.38 far more negative H2
Na+ −2.71 far more negative H2

Reactive metals (Group 1, Group 2 and aluminium) are never obtained from aqueous solution: hydrogen is discharged instead. The rule at A Level: an ion with an E° more negative than H+ is not discharged from aqueous solution; hydrogen is formed instead.

At the anode. The competition is between OH− (water) and the anion present.

Table of products at each electrode for five electrolytes
Products for five common electrolytes. In every row ask: which ions are present, which has the more positive E° (cathode) or less positive E° (anode), and how concentrated is the solution?

Worked example: electrolysis of aqueous sodium chloride. Ions present: Na+, H+, Cl−, OH−.

Copper electrodes. When aqueous copper(II) sulfate is electrolysed with inert electrodes (graphite or platinum), copper is deposited at the cathode and oxygen forms at the anode; the blue colour fades and the solution becomes acidic because H+ accumulates. With copper electrodes, the anode itself dissolves, since Cu → Cu2+ + 2e− (E° = +0.34 V) is easier than oxidising water (+1.23 V). The anode loses the same mass that the cathode gains and the colour of the solution does not change. This is how copper is purified.

⚠️ Examiner Trap: ‘Which is discharged?’ needs a reason. Writing ‘hydrogen at the cathode’ earns the product mark only. To earn the reasoning mark quote the two E° values and compare them (‘H+ is more easily reduced than Na+, E° 0.00 V against −2.71 V’), and for a halide at the anode mention the concentration.

2. Quantitative Electrolysis

The amount of substance liberated is proportional to the charge that flows. The steps are always the same.

Chain of four steps from current and time to mass or volume with a worked example
From current and time to mass or volume in four steps, with lead from molten lead(II) bromide as the example.

Charge. Q = I × t, where Q is in coulombs (C), I in amperes (A) and t in seconds. Convert minutes and hours to seconds first.

The Faraday constant. The charge on one mole of electrons is F. Since one electron carries e = 1.60 × 10−19 C and a mole contains L = 6.02 × 1023 electrons,

F = L × e    = 6.02 × 1023 × 1.60 × 10−19 ≈ 9.65 × 104 C mol−1

The Data Booklet gives F = 9.65 × 104 C mol−1. Moles of electrons passed = Q / F.

Electrons per mole of product come from the half-equation.

Half-equation Electrons per mole of product Charge per mole of product / C
Ag+ + e− → Ag 1 9.65 × 104
Cu2+ + 2e− → Cu 2 1.93 × 105
Al3+ + 3e− → Al 3 2.90 × 105
2H+ + 2e− → H2 2 1.93 × 105
2Cl− → Cl2 + 2e− 2 1.93 × 105
4OH− → O2 + 2H2O + 4e− 4 3.86 × 105

Worked example 1 (mass). Molten lead(II) bromide is electrolysed for 20.0 minutes with a current of 1.50 A. Find the mass of lead formed. [Ar: Pb = 207]

  1. Q = It = 1.50 × (20.0 × 60) = 1800 C
  2. moles of electrons = 1800 / 9.65 × 104 = 0.01865 mol
  3. Pb2+ + 2e− → Pb, so moles of Pb = 0.01865 / 2 = 0.00933 mol
  4. mass = 0.00933 × 207 = 1.93 g

Worked example 2 (volume). A current of 0.50 A is passed through dilute sulfuric acid for 30.0 minutes. Calculate the volume of oxygen formed at room temperature and pressure.

  1. Q = 0.50 × 1800 = 900 C; moles of electrons = 900 / 9.65 × 104 = 9.33 × 10−3 mol
  2. 4OH− → O2 + 2H2O + 4e−, so moles of O2 = 9.33 × 10−3 / 4 = 2.33 × 10−3 mol
  3. volume = 2.33 × 10−3 × 24.0 = 0.0560 dm3 = 56.0 cm3

Worked example 3 (time needed). How long does a current of 0.500 A take to deposit 2.00 g of silver? [Ar: Ag = 107.9]

  1. moles of Ag = 2.00 / 107.9 = 0.01854 mol; Ag+ + e− → Ag, so moles of electrons = 0.01854 mol
  2. Q = 0.01854 × 9.65 × 104 = 1789 C
  3. t = Q / I = 1789 / 0.500 = 3577 s = 59.6 min

Worked example 4 (hydrogen at s.t.p.). A current of 1.04 A is passed for 6.00 min through dilute sulfuric acid. Q = 1.04 × 360 = 374 C, so moles of electrons = 3.88 × 10−3 mol and moles of H2 = 1.94 × 10−3 mol. Volume = 1.94 × 10−3 × 22.4 = 0.0435 dm3 = 43.5 cm3 at s.t.p. (at r.t.p. it is 46.6 cm3). Check which gas volume the question gives.

⚠️ Examiner Trap: Minutes, and the number of electrons. The two commonest slips are using minutes instead of seconds in Q = It, and using the wrong number of electrons per mole. Write the half-equation next to your working. For oxygen the figure is four electrons, so the volume of oxygen is only half the volume of hydrogen from the same charge.

Comparing two electrolytes in series. If the same current flows through two cells for the same time, the same charge passes through both, so the moles of electrons are equal. Use that to link the two products: for example 1 mol of silver and ½ mol of copper are formed by the same charge.

3. Finding the Avogadro Constant

Electrolysis lets you count atoms indirectly, because the charge needed to deposit a known amount of metal tells you the charge on one mole of electrons, F. Since F = Le and the charge on one electron e is known, L = F / e.

Apparatus for the electrolysis of copper sulfate with copper electrodes, ammeter and variable resistor
Apparatus for finding the charge on a mole of electrons by weighing a copper cathode before and after electrolysis.

Method.

  1. Clean the two copper electrodes with fine sandpaper, rinse with distilled water, then with propanone, dry and weigh the cathode accurately.
  2. Set up the circuit in series: d.c. supply, ammeter, variable resistor and the two electrodes in aqueous copper(II) sulfate. The cathode is connected to the negative terminal.
  3. Switch on and start a stopwatch. Adjust the variable resistor to keep the current constant (for example 0.20 A) and record it.
  4. After a measured time (for example 34 minutes) switch off, remove the cathode, rinse with distilled water and propanone, dry gently and reweigh.
  5. Calculate the mass of copper deposited and then the charge per mole of electrons.

Calculation (typical data). Current 0.20 A for 34 min; mass gained by the cathode 0.13 g. [Ar: Cu = 63.5]

  1. Q = 0.20 × (34 × 60) = 408 C
  2. moles of Cu = 0.13 / 63.5 = 2.05 × 10−3 mol; Cu2+ + 2e− → Cu, so moles of electrons = 4.09 × 10−3 mol
  3. charge on one mole of electrons, F = 408 / 4.09 × 10−3 = 9.96 × 104 C mol−1
  4. L = F / e = 9.96 × 104 / 1.60 × 10−19 = 6.23 × 1023 mol−1

Sources of error and improvements.

⚠️ Examiner Trap: Which electrode do you weigh, and what do you divide by? The cathode gains mass as copper is deposited. The charge on one mole of electrons needs the electrons, so remember the factor of 2 for Cu2+. Dividing Q by moles of copper gives the charge per mole of copper (193 000 C), not F.

4. Electrode Potentials and the SHE

A metal in contact with its ions sets up an equilibrium, for example Zn2+(aq) + 2e− ⇌ Zn(s). The position of this equilibrium decides how strongly the electrode tends to push electrons into the circuit or to pull them in. We cannot measure the potential of a single electrode, only the difference between two. So all values are measured against one agreed reference electrode, the standard hydrogen electrode, whose potential is defined as exactly 0.00 V.

Standard electrode (reduction) potential, E°. The e.m.f. of a half-cell, measured relative to the standard hydrogen electrode, under standard conditions. Standard conditions are a temperature of 298 K, a concentration of 1.00 mol dm−3 for all aqueous ions, and a pressure of 101 kPa for any gas.

Standard cell potential, E°cell. The e.m.f. of a cell, measured under standard conditions, when the two half-cells are both standard half-cells. (The e.m.f. is the potential difference when no current flows.)

Electrode potentials are written as reduction potentials: the half-equation has the electrons on the left, oxidised form + ne− ⇌ reduced form.

The standard hydrogen electrode (SHE).

Standard hydrogen electrode with hydrogen gas bubbling over a platinum foil in hydrochloric acid
The standard hydrogen electrode. By definition E° = 0.00 V for 2H+(aq) + 2e− ⇌ H2(g).
⚠️ Examiner Trap: The platinum is not a reactant. Platinum is the electrode surface and catalyst, not a species in the equation. When you describe the SHE, give all three conditions (101 kPa, 1.00 mol dm−3 H+, 298 K) and say that the hydrogen is bubbled over the platinum. Quote the pressure in kPa (101 kPa, or the value the question gives).

5. Measuring Standard Electrode Potentials

To measure an E° value you build a cell from the half-cell under test and a SHE, join them with a salt bridge and connect a high-resistance voltmeter. The reading is the E° of the half-cell (with a sign given by the polarity, section 6). The high resistance means almost no current flows, so the voltmeter reads the e.m.f. and the concentrations do not change.

Three types of half-cell: metal and metal ion, non-metal and non-metal ion, and two ions of the same element
Every half-cell you meet is one of these three types. Types 2 and 3 need an inert platinum electrode to carry the electrons.

Type 1: a metal in contact with its ions (24.2.3a). For Cu2+/Cu, a copper rod dips into 1.00 mol dm−3 Cu2+(aq) (for example copper(II) sulfate).

Type 2: a non-metal in contact with its ions (24.2.3a). For Cl2/Cl−, chlorine gas at 101 kPa is bubbled over platinum foil in 1.00 mol dm−3 Cl−(aq). Platinum is needed because chlorine does not conduct.

Type 3: two ions of the same element in different oxidation states (24.2.3b). For Fe3+/Fe2+, a platinum foil dips into a solution containing both Fe3+ and Fe2+, each at 1.00 mol dm−3. The platinum just carries electrons to or from the solution. The same design applies to MnO4−/Mn2+ (with 1.00 mol dm−3 H+ as well) and Cr2O72−/Cr3+.

Cell used for the measurement. The figure below shows a zinc half-cell measured against the SHE. Know every labelled part.

Cell for measuring the standard electrode potential of zinc against the standard hydrogen electrode
A: high-resistance voltmeter. B: salt bridge. C: hydrogen gas at 101 kPa. D: platinum foil (platinum black). E: zinc rod. F: 1.00 mol dm−3 Zn2+(aq). Everything at 298 K.

Why these details matter.

⚠️ Examiner Trap: Do not use a metal wire as a salt bridge, and never use chloride in a silver cell. The salt bridge must contain ions that do not react with either half-cell. Potassium nitrate is the standard choice. A wire or a chloride bridge would give a wrong reading (chloride precipitates silver chloride). Always say ‘high-resistance voltmeter’, not just ‘voltmeter’.

6. Cell Potentials, Polarity and Electron Flow

When two half-cells are joined, one acts as the source of electrons and the other as the sink. A standard cell potential is found by combining two standard electrode potentials.

E°cell = E°(more positive electrode) − E°(less positive electrode)
A zinc-copper cell with polarity, electron flow, salt bridge and overall equation
The Zn/Cu cell. Zinc (E° = −0.76 V) is the negative pole and is oxidised; copper (E° = +0.34 V) is the positive pole and is reduced. Electrons flow through the wire from zinc to copper.

Worked example. Zn2+ + 2e− ⇌ Zn E° = −0.76 V; Cu2+ + 2e− ⇌ Cu E° = +0.34 V.

Silver and copper. Ag+ + e− ⇌ Ag has E° = +0.80 V, so silver is the positive pole. E°cell = 0.80 − 0.34 = +0.46 V. Overall: 2Ag+ + Cu → 2Ag + Cu2+. Notice that the E° of silver is not doubled even though the equation needs 2Ag+.

Compare the two kinds of cell. An electrochemical (voltaic) cell generates a voltage from a spontaneous reaction. An electrolytic cell uses a supply to force a reaction that is not spontaneous.

Comparison table of electrolytic and electrochemical cells
The only things that never change are the chemistry: oxidation is at the anode and reduction is at the cathode in both kinds of cell. The signs (+/−) of the electrodes are what swap.
⚠️ Examiner Trap: Anode and cathode signs. In an electrolytic cell the anode is positive; in a voltaic cell the anode is negative. Do not memorise the sign, memorise ‘anode = oxidation’. For a voltaic cell, electrons leave the negative pole, which is where oxidation occurs.

7. Feasibility, Oxidising Power and Redox Equations

Predicting feasibility. A reaction is feasible under standard conditions if the E°cell for the overall reaction is positive. Method:

  1. Write the two half-equations as reductions with their E° values.
  2. The reaction goes forward for the half-cell with the more positive E° (it is reduced) and backwards for the other (it is oxidised).
  3. Combine them so the electrons cancel, and calculate E°cell = E°(reduction) − E°(oxidation). Positive means feasible.
Anticlockwise rule worked for Fe3+ and iodide
The anticlockwise rule: with the more positive half-equation on top, the reactants are the top-left and bottom-right species. Here Fe3+ oxidises I− to I2.

Worked example. Will Fe3+ oxidise I− to I2? Fe3+ + e− ⇌ Fe2+ E° = +0.77 V; I2 + 2e− ⇌ 2I− E° = +0.54 V. Fe3+ is reduced, I− oxidised. E°cell = 0.77 − 0.54 = +0.23 V, so the reaction is feasible: 2Fe3+ + 2I− → 2Fe2+ + I2.

Oxidising and reducing agents from E°. The more positive the E°, the stronger the oxidising agent (the left-hand species); the more negative the E°, the stronger the reducing agent (the right-hand species).

Ladder of standard electrode potentials from sodium to permanganate showing oxidising and reducing power
The E° ladder (Data Booklet values). A species on the left of a half-equation will oxidise any species on the right of a half-equation lower down the ladder.
If E° is… The left-hand species (oxidised form) is… The right-hand species (reduced form) is…
very positive (e.g. MnO4−/Mn2+ +1.52 V; F2/F− +2.87 V) a strong oxidising agent a very weak reducing agent
near zero (e.g. Cu2+/Cu +0.34 V) a moderate oxidising agent a moderate reducing agent
very negative (e.g. Mg2+/Mg −2.38 V; Na+/Na −2.71 V) a very weak oxidising agent a strong reducing agent

The halogens. E°(Cl2/Cl−) = +1.36 V, E°(Br2/Br−) = +1.07 V, E°(I2/I−) = +0.54 V. So the oxidising power falls Cl2 > Br2 > I2 and the reducing power of the halide ions rises Cl− < Br− < I−. Chlorine oxidises bromide (E°cell = 1.36 − 1.07 = +0.29 V) and iodide, but bromine does not oxidise chloride (E°cell = 1.07 − 1.36 = −0.29 V).

Constructing redox equations (24.2.7). Use the half-equations from the Data Booklet.

  1. Reverse the half-equation of the species being oxidised.
  2. Multiply by whole numbers so the electrons are equal.
  3. Add the equations and cancel the electrons (and any species that appears on both sides).

Example 1: manganate(VII) and iron(II) in acid. MnO4− + 8H+ + 5e− → Mn2+ + 4H2O (+1.52 V); Fe2+ → Fe3+ + e− (+0.77 V). Multiply the iron half-equation by 5: MnO4− + 8H+ + 5Fe2+ → Mn2+ + 5Fe3+ + 4H2O; E°cell = 1.52 − 0.77 = +0.75 V.

Example 2: dichromate(VI) and iron(II). Cr2O72− + 14H+ + 6e− → 2Cr3+ + 7H2O (+1.33 V) with 6Fe2+ → 6Fe3+ + 6e− gives Cr2O72− + 14H+ + 6Fe2+ → 2Cr3+ + 6Fe3+ + 7H2O; E°cell = 1.33 − 0.77 = +0.56 V.

Example 3: manganate(VII) and iodide. 2MnO4− + 16H+ + 10e− → 2Mn2+ + 8H2O and 10I− → 5I2 + 10e− give 2MnO4− + 16H+ + 10I− → 2Mn2+ + 5I2 + 8H2O; E°cell = 1.52 − 0.54 = +0.98 V.

What a positive E°cell does not tell you.

⚠️ Examiner Trap: ‘Feasible’ is not ‘fast’. If a question asks why a reaction predicted to be feasible is not seen, the answer is the rate is very slow (high activation energy) or the conditions are not standard. It is never that E° is wrong. Show the calculation: write both E° values and the subtraction, and state the sign of E°cell.

8. Concentration and the Nernst Equation

Electrode potentials in the Data Booklet are for 1.00 mol dm−3. At other concentrations the potential E changes, because the position of the electrode equilibrium changes.

Qualitative prediction (Le Chatelier). Take Cu2+(aq) + 2e− ⇌ Cu(s).

The same applies to any half-equation: raising the concentration of the oxidised species (left side) makes E more positive; raising the concentration of the reduced species (right side) makes E less positive. For MnO4− + 8H+ + 5e− ⇌ Mn2+ + 4H2O, H+ is on the left, so a higher [H+] makes E more positive: manganate(VII) is a stronger oxidising agent in more acidic solution. For a whole cell, the effect of a change on Ecell is the sum of the effects on the two electrodes.

Quantitative: the Nernst equation. At 298 K,

E = E° + (0.059 / z) log10 ( [oxidised species] / [reduced species] )
z = number of electrons in the half-equation. Solids and pure liquids are left out of the ratio.
Graphs of electrode potential against log of concentration for Ag+/Ag, Cu2+/Cu and Fe3+/Fe2+
E against log concentration is a straight line. Its intercept at log = 0 is E° and its gradient is 0.059/z V (0.059 for Ag+, 0.030 for Cu2+). Reading values from a graph like this is a typical Paper 4 task.

Worked example 1: Cu2+/Cu. Calculate E for Cu2+(aq) + 2e− ⇌ Cu(s) when [Cu2+] = 0.001 mol dm−3. E° = +0.34 V, z = 2, and copper metal is a solid.

Worked example 2: Fe3+/Fe2+. Fe3+(aq) + e− ⇌ Fe2+(aq), E° = +0.77 V, z = 1, [Fe3+] = 0.50 mol dm−3, [Fe2+] = 1.0 mol dm−3.

Worked example 3: a whole cell. A cell is made from Cu(s) | Cu2+(aq, 0.001 mol dm−3) and Ag+(aq, 1.00 mol dm−3) | Ag(s). E(Cu2+/Cu) = +0.25 V (example 1) and E(Ag+/Ag) = +0.80 V (log 1.00 = 0). So Ecell = 0.80 − 0.25 = +0.55 V, larger than the standard value of +0.46 V because the lower [Cu2+] pushes the copper half-cell more negative.

Worked example 4: concentration of silver ions from a measured voltage. In the cell Cu(s) | Cu2+(aq, 1.00 mol dm−3) || Ag+(aq, x) | Ag(s), E°cell = +0.46 V and Ecell = 0.46 + 0.059 log[Ag+]. When [Ag+] = 0.010 mol dm−3, Ecell = 0.46 + 0.059 × (−2) = +0.34 V. Reversing, a reading of +0.40 V means log[Ag+] = (0.40 − 0.46) / 0.059 = −1.02, so [Ag+] = 0.096 mol dm−3.

⚠️ Examiner Trap: Which way up does the ratio go, and what is z? The oxidised species is on top (the left of the reduction half-equation), the reduced species is underneath. z is the electrons in the half-equation as you write it: 1 for Fe3+/Fe2+ and Ag+/Ag, 2 for Cu2+/Cu. Remember that a tenfold dilution of Cu2+ changes E by only 0.030 V, not 0.059 V. For a concentration below 1.00 mol dm−3 the log is negative, so check that E has moved in the direction Le Chatelier predicts.

9. E and Gibbs Free Energy

Electrical energy is the link between cell voltage and the feasibility you met in Topic 23. For a cell reaction in which n moles of electrons are transferred per mole of reaction,

ΔG° = −n E°cell F
ΔG° in J mol−1 (divide by 1000 for kJ mol−1), E°cell in V, F = 9.65 × 104 C mol−1
Link between sign of cell potential and sign of Gibbs free energy with a worked example
A positive E°cell always goes with a negative ΔG°. Both say the reaction is feasible under standard conditions.

Worked example 1. Zn + Cu2+ → Zn2+ + Cu, E°cell = +1.10 V, n = 2. ΔG° = −2 × 9.65 × 104 × 1.10 = −2.12 × 105 J mol−1 = −212 kJ mol−1 (negative, so feasible).

Worked example 2. 2Fe3+ + 2I− → 2Fe2+ + I2, E°cell = +0.23 V, n = 2. ΔG° = −2 × 9.65 × 104 × 0.23 = −44.4 kJ mol−1.

Worked example 3 (finding E°cell). A reaction in which 2 mol of electrons are transferred has ΔG° = −317 kJ mol−1. E°cell = −ΔG° / (nF) = 317 000 / (2 × 9.65 × 104) = +1.64 V.

⚠️ Examiner Trap: Units and the minus sign. ΔG° = −nE°cellF comes out in J mol−1. Divide by 1000 before quoting kJ mol−1. Keep the minus sign: a positive E°cell gives a negative ΔG°. If your answers disagree in sign, one of them is wrong.

10. Quick Sheet and Checklist

Quantity Statement to learn
E° e.m.f. of a half-cell relative to the standard hydrogen electrode, at 298 K, 1.00 mol dm−3, 101 kPa
E°cell e.m.f. of a cell under standard conditions; E°(more positive) − E°(less positive)
SHE H2(g) 101 kPa over Pt black in 1.00 mol dm−3 H+, 298 K; E° = 0.00 V
Charge Q = It, with t in seconds
Faraday F = Le = 9.65 × 104 C mol−1
Moles of electrons Q / F; then use the half-equation for the product
Nernst (298 K) E = E° + (0.059/z) log([ox]/[red])
Gibbs ΔG° = −nE°cellF

Equations to learn. Pb2+ + 2e− → Pb; Al3+ + 3e− → Al; 2H+ + 2e− → H2; 4OH− → O2 + 2H2O + 4e−; MnO4− + 8H+ + 5e− → Mn2+ + 4H2O; Cr2O72− + 14H+ + 6e− → 2Cr3+ + 7H2O.

Checklist. Before the exam you should be able to:

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