AP Chemistry 9.7-9.8: Electrochemical Cells and Cell Potential

Galvanic cell

An electrochemical cell in which a spontaneous oxidation-reduction reaction produces electrical energy. It is also called a voltaic cell.

Electrolytic cell

An electrochemical cell in which an external source of electrical energy drives a nonspontaneous oxidation-reduction reaction.

How does separating the half-reactions in a galvanic cell generate an electric current?

Separating the reactants prevents direct electron transfer. Electrons instead travel through an external circuit from the oxidation half-cell to the reduction half-cell.

Half-cell

One compartment of an electrochemical cell containing a redox couple and an electrode. A complete galvanic cell contains an oxidation half-cell and a reduction half-cell.

Anode in a galvanic cell

The electrode where oxidation occurs. In a galvanic cell, the anode is the source of electrons and is the negative electrode.

Cathode in a galvanic cell

The electrode where reduction occurs. In a galvanic cell, the cathode receives electrons from the external circuit and is the positive electrode.

How can the mnemonic 'AN OX, RED CAT' be applied to electrochemical cells?

AN OX means oxidation occurs at the anode, and RED CAT means reduction occurs at the cathode. These locations do not change between galvanic and electrolytic cells, although the electrode signs do.

What are the electrode signs in an electrolytic cell?

The anode is positive and the cathode is negative. Oxidation still occurs at the anode and reduction still occurs at the cathode; only the electrode signs differ from a galvanic cell.

What occurs when a copper wire is placed in aqueous silver nitrate?

Copper is oxidized and silver ions are reduced: $\ce{Cu(s) -> Cu^{2+}(aq) + 2e^-}$ and $\ce{2Ag+(aq) + 2e^- -> 2Ag(s)}$. The solution becomes blue as $\ce{Cu^{2+}}$ forms, and gray silver deposits on the copper.

How are the half-reactions combined to obtain the net reaction for a redox cell?

Balance the half-reactions so that the electrons produced equal the electrons consumed, then add them and cancel the electrons. For copper and silver ions, the net reaction is $\ce{Cu(s) + 2Ag+(aq) -> Cu^{2+}(aq) + 2Ag(s)}$.

What is the direction of electron flow in a galvanic cell?

Electrons flow through the external circuit from the anode, where oxidation produces them, to the cathode, where reduction consumes them.

Salt bridge

A connection containing an inert electrolyte that joins the two half-cell solutions without allowing the primary reactants to mix. It permits ion migration and maintains electrical neutrality.

Why is a salt bridge necessary for sustained operation of a galvanic cell?

Oxidation creates excess positive charge in the anode compartment, while reduction removes positive ions from the cathode compartment. Ion migration through the salt bridge offsets these charge changes and completes the internal circuit.

Which ions migrate to each compartment in a copper-silver galvanic cell?

As $\ce{Cu^{2+}}$ forms at the anode, anions such as $\ce{NO3^-}$ migrate into the anode compartment. As $\ce{Ag+}$ is consumed at the cathode, cations such as $\ce{Na+}$ migrate into the cathode compartment.

Electrochemical cell

A device in which oxidation-reduction reactions are separated or controlled so that electron transfer occurs through an external circuit. Galvanic cells are electrochemical cells with spontaneous redox reactions.

Active electrode

An electrode made from a species participating in the half-reaction, such as a metal electrode that is oxidized or reduced. The copper, silver, magnesium, and chromium electrodes in the examples are active electrodes.

Why is an inert platinum electrode used in some galvanic cells?

If both members of a redox couple are dissolved species, neither can serve as a solid, conductive electrode. Platinum provides a conductive surface for electron transfer without being consumed.

How should phases and interfaces be represented in galvanic-cell notation?

A single vertical line, $\ce{|}$, represents an interface between phases within a half-cell. A double vertical line, $\ce{||}$, represents the salt bridge between half-cells; species in the same phase are separated by commas.

What is the conventional left-to-right order for writing cell notation?

Write the anode on the left and the cathode on the right, showing the components encountered from anode to cathode. For example, a copper-silver cell is written $\ce{Cu(s)|Cu^{2+}(aq)||Ag+(aq)|Ag(s)}$.

Write the cell notation for a galvanic cell with magnesium oxidized and iron(III) reduced to iron(II).

$\ce{Mg(s)|Mg^{2+}(aq)||Fe^{3+}(aq),Fe^{2+}(aq)|Pt(s)}$. Platinum is required because both iron species are aqueous.

What cell notation represents $\ce{Sn^{4+}}$ being reduced while zinc is oxidized?

$\ce{Zn(s)|Zn^{2+}(aq)||Sn^{4+}(aq),Sn^{2+}(aq)|Pt(s)}$. Zinc is the active anode, and platinum is an inert cathode electrode for the aqueous tin redox couple.

How is the cathode half-reaction identified from a galvanic-cell schematic?

The half-cell written on the right is the cathode under the standard notation convention. Its redox species undergoes reduction, while the left-hand half-cell undergoes oxidation.

Standard-state conditions for an electrochemical cell

For the conditions described here, standard state means aqueous concentrations of $1\ \mathrm{M}$, gas pressures of $1\ \mathrm{bar}$, and a temperature of $298\ \mathrm{K}$.

Cell potential, $E_{\text{cell}}$

The potential difference between two half-cells, reflecting the driving force for electron transfer. It is measured in volts, where $1\ \mathrm{V}=1\ \mathrm{J/C}$.

Why cannot the potential of a single half-cell be measured directly?

A potential reflects electron transfer between a donor and an acceptor, so a reference half-cell is required. Only the potential difference between two half-cells can be measured.

What equation calculates the cell potential from the two half-cell potentials?

$E_{\text{cell}}=E_{\text{cathode}}-E_{\text{anode}}$. When tabulated values are standard reduction potentials, use the cathode reduction potential minus the anode reduction potential.

Standard cell potential, $E^\circ_{\text{cell}}$

The cell potential when all reactants and products are in their standard states. It is calculated using $E^\circ_{\text{cell}}=E^\circ_{\text{cathode}}-E^\circ_{\text{anode}}$.

Standard hydrogen electrode (SHE)

The reference half-cell assigned a potential of exactly $0.00\ \mathrm{V}$. Under standard conditions, it consists of a platinum electrode, $1\ \mathrm{M}\ \ce{H+}$, and $\ce{H2(g)}$ at $1\ \mathrm{bar}$, based on $\ce{2H+(aq)+2e^- -> H2(g)}$.

Standard reduction potential

The potential assigned to a reduction half-reaction relative to the standard hydrogen electrode under standard conditions. Tabulated electrode potentials are conventionally written as reduction potentials.

How is the standard reduction potential of a half-cell experimentally defined?

The half-cell is connected as the cathode to a standard hydrogen electrode acting as the anode. Because $E^\circ_{\text{SHE}}=0$, the measured cell potential equals the half-cell's standard reduction potential.

What does a more positive standard reduction potential indicate about a species?

It indicates a greater tendency for the species to be reduced and therefore greater strength as an oxidizing agent. For example, $\ce{Ag+}$ is a stronger oxidant than $\ce{Pb^{2+}}$ because its reduction potential is more positive.

What does a more negative standard reduction potential indicate about a reduction reactant?

It indicates a weaker tendency to be reduced relative to the SHE and weaker oxidizing ability. The corresponding reduced form generally has a greater tendency to act as a reductant.

How can a standard reduction-potential table be used to predict which species is reduced?

The half-reaction with the more positive reduction potential is favored as the cathode reduction. The other half-reaction is reversed and operates as oxidation at the anode.

What sign of $E^\circ_{\text{cell}}$ indicates a spontaneous redox reaction under standard conditions?

A positive value, $E^\circ_{\text{cell}}>0$, indicates that the reaction as written is spontaneous under standard-state conditions. A negative value indicates that the reverse direction is spontaneous under those conditions.

Calculate $E^\circ_{\text{cell}}$ for a cell in which $\ce{Ag+}$ is reduced and copper is oxidized, given $E^\circ_{\ce{Ag+/Ag}}=+0.7996\ \mathrm{V}$ and $E^\circ_{\ce{Cu^{2+}/Cu}}=+0.340\ \mathrm{V}$.

$E^\circ_{\text{cell}}=0.7996-0.340=+0.4596\ \mathrm{V}$, or approximately $+0.46\ \mathrm{V}$. The positive value supports spontaneous operation as a galvanic cell.

What happens to the cell potential when a redox reaction is reversed?

The anode and cathode switch roles, so the sign of the cell potential reverses: $E^\circ_{\text{reverse}}=-E^\circ_{\text{forward}}$. A reaction with $E^\circ=+0.47\ \mathrm{V}$ in one direction has $E^\circ=-0.47\ \mathrm{V}$ in the reverse direction.

Does multiplying a balanced half-reaction by a coefficient multiply its standard reduction potential?

No. Electrode potential is an intensive property and does not change when a half-reaction is multiplied to balance electrons. Only the reaction stoichiometry changes.

How can the spontaneous oxidation of chromium by iron(II) ions be evaluated from reduction potentials?

Use iron(II) as the cathode reduction and reverse chromium's tabulated reduction as the anode oxidation. $E^\circ_{\text{cell}}=(-0.447)-(-0.744)=+0.297\ \mathrm{V}$, so the process is spontaneous under standard conditions.

Why is the reaction $\ce{Cu(s)+Pb^{2+}(aq)->Cu^{2+}(aq)+Pb(s)}$ nonspontaneous under standard conditions?

The calculated potential is $E^\circ_{\text{cell}}=E^\circ_{\ce{Pb^{2+}/Pb}}-E^\circ_{\ce{Cu^{2+}/Cu}}=-0.1262-0.340\approx-0.47\ \mathrm{V}$. The negative value means the reverse reaction is spontaneous.

How do oxidizing strength and reducing strength relate to a standard reduction-potential table?

Higher, more positive reduction potentials correspond to stronger oxidizing agents among the reduction reactants. The reduced forms associated with lower reduction potentials are generally stronger reducing agents.

Why does a galvanic cell require both an electronic conductor and an ionic conductor?

The external wire conducts electrons between the electrodes, while the salt bridge conducts ions within the cell. Both pathways are needed to sustain charge separation and continuous current.

In a galvanic cell, what changes occur at the anode and cathode as the cell operates?

Oxidation at the anode often increases the concentration of its cation, while reduction at the cathode consumes the cathode reactant. These concentration changes are balanced by ion movement through the salt bridge.

How are standard cell potential and standard Gibbs free-energy change related?

They are related by $\Delta G^\circ=-nFE^\circ_{\text{cell}}$, where $n$ is the number of moles of electrons transferred and $F$ is Faraday's constant, approximately $96485\ \mathrm{C/mol\ e^-}$. A positive $E^\circ_{\text{cell}}$ gives a negative $\Delta G^\circ$ and indicates a spontaneous reaction under standard conditions.

What does the number $n$ represent in $\Delta G^\circ=-nFE^\circ_{\text{cell}}$?

$n$ is the number of moles of electrons transferred in the balanced overall redox reaction. It comes from the balanced half-reactions and does not multiply the electrode potentials themselves.

How can $\Delta G^\circ$ be calculated from a standard cell potential?

Use $\Delta G^\circ=-nFE^\circ_{\text{cell}}$, with $E^\circ_{\text{cell}}$ in volts, $F=96485\ \mathrm{C\ mol^{-1}}$, and $n$ as the electron count. Since $1\ \mathrm{V}=1\ \mathrm{J/C}$, the result is in joules per mole.

What is the energetic role of a galvanic versus an electrolytic cell?

A galvanic cell converts the chemical free energy of a spontaneous reaction into electrical energy. An electrolytic cell uses electrical energy to force a nonspontaneous reaction.