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Lesson 3 · 30 min

Galvanic cells and standard electrode potentials

Separate the two halves and make the electrons take a wire, and chemical energy becomes electrical. One table of standard potentials gives the voltage, ΔG° and equilibrium constant of any cell.

In this lesson

  • Explain the parts of a galvanic cell: anode, cathode, salt bridge and external circuit
  • Use a table of standard potentials to find which electrode is positive and to compute E°cell
  • Compute ΔG° and the equilibrium constant K from E°cell
  • Write the cell notation and the overall cell reaction

Put zinc into copper sulfate and copper plates straight onto the zinc while the solution warms slightly: the electrons jump from zinc to CuX2+\ce{Cu^2+} across a few atoms and all the energy ends up as heat. In 1836 Daniell kept the two apart — zinc in zinc sulfate, copper in copper sulfate, joined through a porous barrier — so the electrons had to travel from zinc to copper along a wire, lighting a lamp or driving a telegraph on the way. That is a galvanic cell: a spontaneous redox reaction split into halves, with the electrons sent round an external circuit.

Predict first

Build a cell from an Ag | Ag⁺ and a Cu | Cu²⁺ half-cell (1 M solutions). Which electrode is negative, and roughly what is the voltage?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Anatomy of a cell

  • The anode is where oxidation happens; the electrons it releases leave from here, so in a galvanic cell the anode is the negative electrode (zinc, say).
  • The cathode is where reduction happens; it takes in electrons from the external circuit and is the positive electrode (copper).
  • Only electrons move in the external circuit, from negative to positive; conventional current runs the other way.
  • Only ions move in the salt bridge (e.g. KNO₃ in agar): anions drift to the anode to offset the new positive charge made there, cations drift to the cathode to replace the positive charge used up. Without the bridge, charge builds up on both sides and the current stops at once.

Cell notation writes all this in one line, anode on the left: Zn(s)∣ZnX2+(aq)∥CuX2+(aq)∣Cu(s)\ce{Zn(s)} \mid \ce{Zn^2+(aq)} \parallel \ce{Cu^2+(aq)} \mid \ce{Cu(s)} — a single bar is a phase boundary, the double bar the salt bridge.

One table for every cell

The potential of one half-cell cannot be measured on its own, only the difference between two. So chemists fix a zero: the standard hydrogen electrode (SHE: 1 bar of hydrogen over platinised platinum, HX+\ce{H+} at unit activity) is defined as 0 V. Pair any half-cell with the SHE and the voltage measured is that couple’s standard electrode potential E∘E^\circ, written for reduction. The more positive E∘E^\circ, the more eagerly the oxidised form takes electrons (a stronger oxidising agent); the more negative, the more readily the reduced form gives them up (a stronger reducing agent).

Selected standard reduction potentials (25 °C, vs SHE)
Half-reactionE° / V
FX2+2 eX−→2 FX−\ce{F2} + \ce{2e-} \mathrel{\ce{->}} \ce{2F-}+2.866
MnOX4X−+8 HX++5 eX−→MnX2++4 HX2O\ce{MnO4-} + \ce{8H+} + \ce{5e-} \mathrel{\ce{->}} \ce{Mn^2+} + \ce{4H2O}+1.507
ClX2+2 eX−→2 ClX−\ce{Cl2} + \ce{2e-} \mathrel{\ce{->}} \ce{2Cl-}+1.358
OX2+4 HX++4 eX−→2 HX2O\ce{O2} + \ce{4H+} + \ce{4e-} \mathrel{\ce{->}} \ce{2H2O}+1.229
AgX++eX−→Ag\ce{Ag+} + \ce{e-} \mathrel{\ce{->}} \ce{Ag}+0.7996
FeX3++eX−→FeX2+\ce{Fe^3+} + \ce{e-} \mathrel{\ce{->}} \ce{Fe^2+}+0.771
CuX2++2 eX−→Cu\ce{Cu^2+} + \ce{2e-} \mathrel{\ce{->}} \ce{Cu}+0.3419
2 HX++2 eX−→HX2\ce{2H+} + \ce{2e-} \mathrel{\ce{->}} \ce{H2}0
FeX2++2 eX−→Fe\ce{Fe^2+} + \ce{2e-} \mathrel{\ce{->}} \ce{Fe}−0.447
ZnX2++2 eX−→Zn\ce{Zn^2+} + \ce{2e-} \mathrel{\ce{->}} \ce{Zn}−0.7618
MgX2++2 eX−→Mg\ce{Mg^2+} + \ce{2e-} \mathrel{\ce{->}} \ce{Mg}−2.372
LiX++eX−→Li\ce{Li+} + \ce{e-} \mathrel{\ce{->}} \ce{Li}−3.0401
Source: P. Vanýsek, “Electrochemical Series”, CRC Handbook of Chemistry and Physics, 91st ed. (2010).
Ecell∘=Ecathode∘−Eanode∘,ΔG∘=−nFEcell∘,lg⁡K=nEcell∘0.05916 VE^\circ_\text{cell} = E^\circ_\text{cathode} - E^\circ_\text{anode},\qquad \Delta G^\circ = -nFE^\circ_\text{cell},\qquad \lg K = \frac{nE^\circ_\text{cell}}{0.05916\ \text{V}}
Voltage, free energy and equilibrium constant are three ways of saying one thing; the last form holds at 25 °C. E° > 0 means ΔG° < 0 and K > 1: the reaction is spontaneous.
nn
electrons transferred in the overall reaction
FF
Faraday constant, 96 485 C/mol
KK
equilibrium constant of the cell reaction
0.05916 V0.05916\ \text{V}
RT·ln 10/F at 25 °C
Standard potentials · ΔG° = −nFE° · K

Galvanic cell builder

electrons →+1.104 Vsalt bridge KNO₃Zn | Zn²⁺1 Manode (−)Cu | Cu²⁺1 Mcathode (+)
-2-10+1Zn²⁺/ZnCu²⁺/Cu1.10 V
Potential ladder (E° / V vs SHE)
Voltmeter reading
+1.1037V
Standard EMF E°
1.1037 V
Electrons n
2
ΔG°
−213.0 kJ/mol
Equilibrium constant K
2.1 × 10³⁷

At the anode (oxidation) Zn→ZnX2++2 eX−\ce{Zn -> Zn^2+ + 2e-}

At the cathode (reduction) CuX2++2 eX−→Cu\ce{Cu^2+ + 2e- -> Cu}

Cell reaction CuX2++Zn→Cu+ZnX2+\ce{Cu^2+ + Zn -> Cu + Zn^2+}

Cell notation Zn(s)∣ZnX2+(aq)∥CuX2+(aq)∣Cu(s)\ce{Zn(s)} \mid \ce{Zn^2+(aq)} \parallel \ce{Cu^2+(aq)} \mid \ce{Cu(s)}

Potentials are CRC standard reduction potentials (25 °C); the reading is E(right) − E(left), with the Nernst equation (concentrations for activities) when concentrations change. The meter reads the EMF at essentially zero current; the moving electrons and ions show the direction current takes once a load is connected, and their speed is illustrative. Solution colours are computed from each ion’s absorption bands with Beer–Lambert (1 cm path).
Pick a half-cell for each side: the electron flow, the ions in the bridge, the polarity and the gap on the ladder all come from the E° values. Try Mg against Ag (the largest voltage here), Fe³⁺/Fe²⁺ against Cu (an inert platinum electrode), then swap the sides and watch the reading change sign.

Worked example

ΔG° and K of the copper–silver cell

For Cu(s)∣CuX2+∥AgX+∣Ag(s)\ce{Cu(s)} \mid \ce{Cu^2+} \parallel \ce{Ag+} \mid \ce{Ag(s)}, find E°cell, ΔG° and the equilibrium constant K at 25 °C.

Concept check

Among AgX+\ce{Ag+}, CuX2+\ce{Cu^2+}, FeX3+\ce{Fe^3+} and ZnX2+\ce{Zn^2+}, which is the strongest oxidising agent at standard conditions?

Try the calculation

What is the standard EMF of Zn(s)∣ZnX2+∥AgX+∣Ag(s)\ce{Zn(s)} \mid \ce{Zn^2+} \parallel \ce{Ag+} \mid \ce{Ag(s)}?

V

Key takeaways

  • A galvanic cell splits a spontaneous redox reaction: oxidation at the anode (negative), reduction at the cathode (positive), electrons through the wire, ions through the bridge.
  • Standard potentials are referenced to the standard hydrogen electrode and written as reductions; the more positive E°, the stronger the oxidised form.
  • E°cell = E°(cathode) − E°(anode); multiplying a half-reaction leaves E° unchanged.
  • ΔG° = −nFE° and lg K = nE°/0.05916 V at 25 °C: voltage, free energy and equilibrium constant map one to one.
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Data and references

  1. P. Vanýsek, “Electrochemical Series”, in CRC Handbook of Chemistry and Physics, 91st ed., CRC Press (2010), pp. 8-20–8-29.
  2. A. J. Bard, R. Parsons, J. Jordan (eds.), Standard Potentials in Aqueous Solution, Marcel Dekker (1985).
  3. P. Atkins, J. de Paula, J. Keeler, Atkins’ Physical Chemistry, 11th ed., Oxford University Press (2018), topic 6C–6D (electrochemical cells and electrode potentials).
  4. D. C. Harris, Quantitative Chemical Analysis, 9th ed., W. H. Freeman (2016), ch. 13 (fundamentals of electrochemistry).