Chemistry · General chemistry II · Concept

Cell potential, Nernst equation and electrolysis

In a galvanic cell, oxidation at the anode and reduction at the cathode happen in separate compartments, so the electrons flow through a wire. The standard cell potential is E°cathode − E°anode, and a positive value means the reaction is spontaneous, since ΔG° = −nFE°. The Nernst equation corrects E for nonstandard concentrations. In electrolysis an outside source drives a nonspontaneous reaction, and the charge counts the moles of electrons.

Anode, cathode and salt bridge

Oxidation happens at the anode and reduction at the cathode. Electrons travel through the external wire from anode to cathode, and a salt bridge lets ions drift to keep each solution electrically neutral. Cell notation lists the anode first: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s).

Standard reduction potentials

Each half-reaction, written as a reduction, has a standard potential E° measured against the standard hydrogen electrode, 0 V by definition. The more positive E° is, the more readily that species is reduced. Subtract the anode’s reduction potential from the cathode’s, and never multiply a potential by a coefficient.

E_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ}

Cell potential and free energy

n is the number of moles of electrons transferred in the balanced reaction, and F = 96,485 C/mol is the Faraday constant. A positive E°cell means a negative ΔG°: spontaneous. At 298 K, E°cell also fixes the equilibrium constant.

Δ G^{\circ} = - n F E_{cell}^{\circ}

The Nernst equation

Away from standard concentrations, the cell potential shifts with the reaction quotient Q; at 298 K the constant is 0.0592 V. As a cell runs, Q grows and E falls, reaching 0 when Q = K: the battery is dead.

E = E^{\circ} - \frac{0.0592 V}{n} log Q

Electrolysis

An outside power source can drive a nonspontaneous reaction, as in electroplating or recharging a battery. The charge is current times time, q = It, in coulombs when t is in seconds; dividing by F gives moles of electrons, and the half-reaction converts them to moles of product.

n_{e^{-}} = \frac{I t}{F}

Common mistakes

Multiplying a reduction potential by the half-reaction’s coefficient: E° does not scale with the amount.
Changing the sign of the anode potential and then subtracting it as well, which counts the sign change twice.
Using minutes or hours in q = It: t must be in seconds to give coulombs.
Taking n in ΔG° = −nFE° from a half-reaction instead of the balanced overall reaction.

Key terms

Electrochemical cell: A setup in which a redox reaction moves electrons through an outside circuit. A galvanic (voltaic) cell makes electricity from a spontaneous reaction; an electrolytic cell uses electricity to drive a nonspontaneous one.
Anode: The electrode where oxidation happens. It is negative in a galvanic cell and positive in an electrolytic cell.
Cathode: The electrode where reduction happens. It is positive in a galvanic cell and negative in an electrolytic cell.
Salt bridge: A tube of ions connecting the two halves of a galvanic cell. Its ions flow to keep each half electrically neutral, so current can keep flowing.
Electrode potential: The voltage of a half-reaction measured against a reference, such as the standard hydrogen electrode. Multiplying a half-reaction by a number does not change its potential.
Standard hydrogen electrode: The reference half-cell, 2H⁺(aq) + 2e⁻ → H₂(g), whose standard reduction potential is defined as exactly 0 V.
Nernst equation: E = E° − (RT/nF) ln Q: how a cell’s voltage changes with concentrations. Here n is the number of electrons transferred and Q the reaction quotient for the reaction as written.
Faraday constant: The charge carried by one mole of electrons, about 96,485 C/mol. It converts between moles of electrons and coulombs in electrolysis and cell calculations.
Electrolysis: Using an electric current to drive a nonspontaneous redox reaction, such as splitting water. The amount of product follows from the charge passed: moles of electrons = current × time ÷ F.
Half-reaction: The oxidation half or the reduction half of a redox reaction, written with its electrons shown. To combine two half-reactions, multiply them so the electrons lost equal the electrons gained.

Work through an example

A galvanic cell pairs Zn(s) | Zn²⁺(aq) with Cu²⁺(aq) | Cu(s). With E° = +0.34 V for Cu²⁺/Cu and −0.76 V for Zn²⁺/Zn, find E°cell and ΔG°, and say which way electrons flow.

Find a standard cell potential →

Use the Nernst equation →

Find the mass plated by electrolysis →

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