X. Electrochemistry

Key focus of this chapter: reduction potential

This chapter reviews standard reduction potentials, electrochemical cells, standard free-energy changes, and quantitative electrolysis.

A. Standard reduction potential, Eo (V)

: a measure of the tendency of a half-reaction to gain electrons, referenced to the standard hydrogen electrode

(2H+(aq) + 2e–  →  H2(g)    Eo = 0 V)

A more positive standard reduction potential indicates a greater thermodynamic tendency for reduction. Standard conditions use unit activities (approximately 1 M for ideal dilute solutes), gases at 1 bar, and the specified temperature; tables are commonly quoted at 25 °C. Reversing a half-reaction reverses the potential’s sign. Multiplying stoichiometric coefficients does not multiply the potential.

 1. Standard electrode potential

Meaning

The reduced form is more readily oxidized than H₂ under standard conditions → oxidation.

The oxidized form is more readily reduced than H⁺ under standard conditions → reduction.

Reduction half-reaction

Oxidation tendency

(anode)


Reduction tendency

(cathode)


Standard reduction half-reactions for Na+, Zn2+, H+, Cu2+, Ag+, and Cl2. Na+(aq) + e− → Na(s).

Question: Which listed half-reaction has the greatest tendency to undergo reduction under standard conditions?

Standard reduction choices with balanced Na+ + e− → Na; Ag+ has the greatest listed reduction potential, +0.80 V.

Answer: C. Ag+ has the most positive standard reduction potential among the choices (+0.80 V), so it has the greatest tendency to accept electrons under standard conditions.

2. Anode and cathode

Meaning

Galvanic cells

Electrolytic cells

Anode

Loss of electrons (oxidation)

Negative (-)

Positive (+)

Cathode

Gain of electrons (reduction)

Positive (+)

Negative (-)

B. Cell potentials

1. Electromotive force (EMF)

The electromotive force is the open-circuit potential difference between the cathode and anode, measured in volts (1 V = 1 J/C).

E°cell = E°red,cathode − E°red,anode = E°reduction + E°oxidation. Under standard conditions, E°cell > 0 corresponds to ΔG° < 0 for the reaction as written. Under other conditions, use the actual E and ΔG.

Under standard conditions, positive E°cell corresponds to negative ΔG° and a spontaneous reaction as written.

Question: Determine whether the reaction as written is spontaneous under standard conditions.

2. Shorthand notation

  • Example: Write the cell notation for the spontaneous reaction between Cu(s) and Ag+(aq).

Cu(s) is oxidized at the anode, and Ag+(aq) is reduced at the cathode. The listed Cu2+/Cu reduction potential is +0.34 V; reversing that half-reaction gives an oxidation potential of −0.34 V. Thus E°cell = +0.80 V − 0.34 V = +0.46 V.

Step


Reactions

Reduction half-reactions


Oxidation and reduction

Multiply coefficients to balance electrons


Galvanic cell notation


Shorthand notation

Galvanic cell diagram


C. Electrochemical cells

: devices in which redox reactions and electrical energy are coupled: galvanic cells generate electrical energy, whereas electrolytic cells consume it to drive a nonspontaneous reaction.

Oxidation always occurs at the anode and reduction at the cathode. Electrode polarity changes with cell type. Electrons travel through the external circuit; ions carry current through the electrolyte and salt bridge. The E° sign summaries refer to standard-state reaction thermodynamics.

Cell type

Features

Voltaic cell

Daniell cell

Molten NaCl electrolysis: oxidation at the positive anode and reduction at the negative cathode, driven by an external DC source.

D. Standard free-energy change

ΔG° = −nFE°cell, whereas ΔG = −nFE for the actual cell conditions. Here n is the number of electrons transferred per balanced reaction and F is the Faraday constant. With F in C/mol and E in V, molar reaction free energy is in J/mol.

The Nernst equation is E = E° − (RT/nF)ln Q. At 25 °C, E = E° − (0.05916 V/n)log10Q. Q uses activities; pure solids and liquids are omitted. At equilibrium, E = 0 and Q = K, giving ln K = nFE°/(RT).

Standard molar reaction Gibbs energy: ΔG° = −nFE°cell, with F = 96,500 C/mol and energy in J/mol of reaction.

Question: Calculate the standard molar free-energy change, ΔG°, for the reaction as written.

Fe/Ni cell: Fe becomes Fe2+, two electrons transfer, E°cell = +0.19 V and ΔG° = −36,670 J/mol before rounding.

E. Quantitative electrolysis

1. Electric charge Q (coulombs, C)

Q = It: current I is measured in amperes (A), time t in seconds (s), and charge Q in coulombs (C). One ampere equals one coulomb per second.

2. Faraday constant, F

F ≈ 96,485 C/mol is the charge per mole of electrons; the worked examples use the rounded value 96,500 C/mol. One faraday of charge is the charge carried by one mole of electrons. The amount of electrons transferred is n(e−) = Q/F.

Question: What charge, in coulombs and faradays, is transferred when a direct current of 5.0 A is passed through an aqueous solution of AgNO3 for 32 minutes and 10 seconds?

Use Q = It and 1 faraday ≈ 96,500 C. Distinguish the Faraday constant F from the amount of charge expressed in faradays.

Charge Q = It = 9650 C before rounding; 0.10 mol electrons and 0.10 faraday; Q rounds to 9.7 × 10³ C.

Question: How many grams of Pb are produced from a lead storage battery when this battery is charged for 42 minutes and 50 seconds with a constant current of 2 A?

PbSO4(s) + H+(aq) + 2e–  →   Pb(s) + HSO4–(aq)

Assume 100% current efficiency and use M(Pb) = 207 g/mol and F = 96,500 C/mol. Treat the specified current as exact for this idealized exercise.

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