Library Guides: Chemistry Textbook: Galvanic and Electrolytic Cells

Galvanic and Electrolytic Cells

Galvanic Cells

By the end of this section, you will be able to:

construct a voltaic/galvanic cell from a spontaneous redox process
label the components of a galvanic cell
calculate the cell potential of a galvanic cell

You are familiar with redox reactions from the early part of the course. Redox reactions are reactions in which electrons are transferred from one substance to another. The demonstration below of spontaneous redox reaction, Figure 13.2 shows the result of immersing a coiled wire of copper into an aqueous solution of silver nitrate. A gradual but visually impressive change spontaneously occurs as the initially colorless solution becomes increasingly blue, and the initially smooth copper wire becomes covered with a porous gray solid.

This figure includes three photographs. In the first, a test tube containing a clear, colorless liquid is shown with a loosely coiled copper wire outside the test tube to its right. In the second, the wire has been submerged in the clear colorless liquid in the test tube and the surface of the wire is darkened. In the third, the liquid in the test tube is bright blue-green, the wire in the solution appears dark near the top, and a gray “fuzzy” material is present at the bottom of the test tube on the lower portion of the copper coil, giving a murky appearance to the liquid near the bottom of the test tube. — Figure 13.2 A copper wire and an aqueous solution of silver nitrate (left) are brought into contact (center) and a spontaneous transfer of electrons occurs, creating blue Cu²⁺(aq) and gray Ag(s) (right).

These observations are consistent with (i) the oxidation of elemental copper to yield copper(II) ions, Cu²⁺(aq), which impart a blue color to the solution, and (ii) the reduction of silver(I) ions to yield elemental silver, which deposits as a fluffy solid on the copper wire surface. And so, the direct transfer of electrons from the copper wire to the aqueous silver ions is spontaneous under the employed conditions. A summary of this redox system is provided by these equations:

\begin{matrix} overall reaction: & Cu (s) + 2 {Ag}^{+} (a q) ⟶ {Cu}^{2}^{+} (a q) + 2 Ag (s) \\ oxidation half-reaction: & Cu (s) ⟶ {Cu}^{2} + (a q) + 2 e^{−} \\ reduction half-reaction: & 2 {Ag}^{+} (a q) + 2 e^{−} ⟶ 2 Ag (s) \end{matrix}

Consider the construction of a device that contains all the reactants and products of a spontaneous redox system like the one here, but prevents physical contact between the reactants. Direct transfer of electrons is, therefore, prevented; transfer, instead, takes place indirectly through an external circuit that contacts the separated reactants. Therefore, a spontaneous redox reaction in which flow of electrons occurs spontaneously through an external circuit can be used as a cell (called galvanic or voltaic cell) that converts chemical energy to electrical energy. Vice verse, we can use electrical energy (from a power source) to make an otherwise non-spontaneous redox reaction to occur (such a device is called electrolytic cell). A galvanic cell uses spontaneous redox reaction to generate electrical current and an electrolytic cell uses electrical current to drive a non-spontaneous reaction. Galvanic and voltaic cells are both referred to as electrochemical cells.

A galvanic cell based on the spontaneous reaction between copper and silver(I) is depicted in Figure 13.3. The cell is comprised of two half-cells, each containing the redox conjugate pair (“couple”) of a single reactant. The half-cell shown at the left contains the Cu(0)/Cu(II) couple in the form of a solid copper foil and an aqueous solution of copper nitrate. The right half-cell contains the Ag(I)/Ag(0) couple as solid silver foil and an aqueous silver nitrate solution. An external circuit is connected to each half-cell at its solid foil, meaning the Cu and Ag foil each function as an electrode. By definition, the anode of an electrochemical cell is the electrode at which oxidation occurs (in this case, the Cu foil) and the cathode is the electrode where reduction occurs (the Ag foil). The redox reactions in a galvanic cell occur only at the interface between each half-cell’s reaction mixture and its electrode. To keep the reactants separate while maintaining charge-balance, the two half-cell solutions are connected by a tube filled with inert electrolyte solution called a salt bridge. The spontaneous reaction in this cell produces Cu²⁺ cations in the anode half-cell and consumes Ag⁺ ions in the cathode half-cell, resulting in a compensatory flow of inert ions from the salt bridge that maintains charge balance. Increasing concentrations of Cu²⁺ in the anode half-cell are balanced by an influx of NO₃⁻ from the salt bridge, while a flow of Na⁺ into the cathode half-cell compensates for the decreasing Ag⁺ concentration.

This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a blue solution and is labeled below as “1 M solution of copper (II) nitrate ( C u ( N O subscript 3 ) subscript 2 ).” The beaker on the right contains a colorless solution and is labeled below as “1 M solution of silver nitrate ( A g N O subscript 3 ).” A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small gray plug is present at each end of the tube. The plug in the left beaker is labeled “Porous plug.” At the center of the diagram, the tube is labeled “Salt bridge ( N a N O subscript 3 ). Each beaker shows a metal strip partially submerged in the liquid. The beaker on the left has an orange-brown strip that is labeled “C u anode negative” at the top. The beaker on the right has a silver strip that is labeled “A g cathode positive” at the top. A wire extends from the top of each of these strips to a rectangle indicating “external circuit” that is labeled “flow of electrons” with an arrow pointing to the right following. A curved arrow extends from the C u strip into the surrounding solution. The tip of this arrow is labeled “C u superscript 2 plus.” A curved arrow extends from the salt bridge into the beaker on the left into the blue solution. The tip of this arrow is labeled “N O subscript 3 superscript negative.” A curved arrow extends from the solution in the beaker on the right to the A g strip. The base of this arrow is labeled “A g superscript plus.” A curved arrow extends from the colorless solution to salt bridge in the beaker on the right. The base of this arrow is labeled “N O subscript 3 superscript negative.” Just right of the salt bridge in the colorless solution is the label “N a superscript plus.” Just above this region of the tube appears the label “Flow of cations.” Just left of the salt bridge in the blue solution is the label “N O subscript 3 superscript negative.” Just above this region of the tube appears the label “Flow of anions.” — Figure 13.3 A galvanic cell based on the spontaneous reaction between copper and silver(I) ions.

Cell Notation

Abbreviated symbolism is commonly used to represent a galvanic cell by providing essential information on its composition and structure. These symbolic representations are called cell notations or cell schematics, and they are written following a few guidelines:

The relevant components of each half-cell are represented by their chemical formulas or element symbols
All interfaces between component phases are represented by vertical parallel lines; if two or more components are present in the same phase, their formulas are separated by commas
By convention, the schematic begins with the anode and proceeds left-to-right identifying phases and interfaces encountered within the cell, ending with the cathode

A verbal description of the cell as viewed from anode-to-cathode is often a useful first-step in writing its schematic. For example, the galvanic cell shown in Figure 13.4 consists of a solid copper anode immersed in an aqueous solution of copper(II) nitrate that is connected via a salt bridge to an aqueous silver(I) nitrate solution, immersed in which is a solid silver cathode. Converting this statement to symbolism following the above guidelines results in the cell schematic:

Cu (s) │ 1 M {Cu (NO}_{3})_{2} (a q) ║ 1 M {AgNO}_{3} (a q) │ Ag (s)

Consider a different galvanic cell (see Figure 13.4) based on the spontaneous reaction between solid magnesium and aqueous iron(III) ions:

\begin{matrix} net cell reaction: & Mg (s) + {2Fe}^{3+} (a q) ⟶ {Mg}^{2+} (a q) + 2 {Fe}^{2+} (a q) \\ oxidation half-reaction: & Mg (s) ⟶ {Mg}^{2+} (a q) + 2 e^{−} \\ reduction half-reaction: & {2Fe}^{3+} (a q) + {2e}^{−} ⟶ 2 {Fe}^{2+} (a q) \end{matrix}

In this cell, a solid magnesium anode is immersed in an aqueous solution of magnesium chloride that is connected via a salt bridge to an aqueous solution containing a mixture of iron(III) chloride and iron(II) chloride, immersed in which is a platinum cathode. The cell schematic is then written as

Mg (s) │ 0.1 M {MgCl}_{2} (a q) ║ 0.2 M {FeCl}_{3} (a q), 0.3 M {FeCl}_{2} (a q) │ Pt (s)

Notice the cathode half-cell is different from the others considered thus far in that its electrode is comprised of a substance (Pt) that is neither a reactant nor a product of the cell reaction. This is required when neither member of the half-cell’s redox couple can reasonably function as an electrode, which must be electrically conductive and in a phase separate from the half-cell solution. In this case, both members of the redox couple are solute species, and so Pt is used as an inert electrode that can simply provide or accept electrons to redox species in solution. Electrodes constructed from a member of the redox couple, such as the Mg anode in this cell, are called active electrodes.

This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a colorless solution. The beaker on the right also contains a colorless solution. A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small gray plug is present at each end of the tube. At the center of the diagram, the tube is labeled “Salt bridge.” Each beaker shows a metal coils submerged in the liquid. The beaker on the left has a thin, gray, coiled strip that is labeled “M g anode.” The beaker on the right has a black wire that is oriented horizontally and coiled up in a spring-like appearance that is labeled “P t cathode.” Below the coil is the label “F e superscript 3 plus” with a curved right arrowing pointing from that to the label “F e superscript 2 plus.” A wire extends across the top of the diagram that connects the ends of the M g strip and P t cathode just above the opening of each beaker. At the center of the wire above the two beakers is a rectangle labeled “external circuit.” Above the rectangle is the label “flow of electrons” followed by a right pointing arrow. An arrow points down and to the right from the label “N a superscript plus” at the upper right region of the salt bride. An arrow points down and to the left from the label “C l superscript negative” at the upper left region of the salt bride. Below the graylug at the left end of the salt bridge in the surrounding solution in the left beaker is the label “C l superscript negative.” Below the coil on this side is a right arrow and the label “M g superscript 2 plus.” The label “0.1 M M g C l subscript 2” appears beneath the left beaker. The label “0.2 M F e C l subscript 3 and 0.3 M F e C l subscript 2.” appears beneath the right beaker.

Figure 13.4 A galvanic cell based on the spontaneous reaction between magnesium and iron(III) ions.

EXAMPLE 13.1

Writing Galvanic Cell Schematics A galvanic cell is fabricated by connecting two half-cells with a salt bridge, one in which a chromium wire is immersed in a 1 M CrCl₃ solution and another in which a copper wire is immersed in 1 M CuCl₂. Assuming the chromium wire functions as an anode, write the schematic for this cell along with equations for the anode half-reaction, the cathode half-reaction, and the overall cell reaction.

Solution Since the chromium wire is stipulated to be the anode, the schematic begins with it and proceeds left-to-right, symbolizing the other cell components until ending with the copper wire cathode:

Cr (s) │ 1 M {CrCl}_{3} (a q) ║ 1 M {CuCl}_{2} (a q) │ Cu (s)

The half-reactions for this cell are

\begin{matrix} anode (oxidation): & Cr (s) ⟶ {Cr}^{3+} (a q) + 3 e^{−} \\ cathode (oxidation): & {Cu}^{2+} (a q) + 2 e^{−} ⟶ Cu (s) \end{matrix}

Multiplying to make the number of electrons lost by Cr and gained by Cu²⁺ equal yields

\begin{matrix} anode (oxidation): & 2 Cr (s) ⟶ 2 {Cr}^{3+} (a q) + 6 e^{−} \\ cathode (reducation): & 3 {Cu}^{2+} (a q) + 6 e^{−} ⟶ 3 Cu (s) \end{matrix}

Adding the half-reaction equations and simplifying yields an equation for the cell reaction:

2 Cr (s) + 3 {Cu}^{2+} (a q) ⟶ 2 {Cr}^{3+} (a q) + 3 Cu (s)

Check Your Learning Omitting solute concentrations and spectator ion identities, write the schematic for a galvanic cell whose net cell reaction is shown below.

{Sn}^{4+} (a q) + Zn (s) ⟶ {Sn}^{2+} (a q) + {Zn}^{2+} (a q)

Answer:

$Zn (s) │ {Zn}^{2+} (a q) ║ {Sn}^{4+} (a q), {Sn}^{2+} (a q) │ Pt (s)$

Key Concepts and Summary

Galvanic cells are devices in which a spontaneous redox reaction occurs indirectly, with the oxidant and reductant redox couples contained in separate half-cells. Electrons are transferred from the reductant (in the anode half-cell) to the oxidant (in the cathode half-cell) through an external circuit, and inert solution phase ions are transferred between half-cells, through a salt bridge, to maintain charge neutrality. The construction and composition of a galvanic cell may be succinctly represented using chemical formulas and others symbols in the form of a cell schematic (cell notation).

Glossary

active electrode: electrode that participates as a reactant or product in the oxidation-reduction reaction of an electrochemical cell; the mass of an active electrode changes during the oxidation-reduction reaction

anode: electrode in an electrochemical cell at which oxidation occurs

cathode: electrode in an electrochemical cell at which reduction occurs

cell notation (schematic): symbolic representation of the components and reactions in an electrochemical cell

cell potential (E_cell): difference in potential of the cathode and anode half-cells

galvanic (voltaic) cell: electrochemical cell in which a spontaneous redox reaction takes place; also called a voltaic cell

inert electrode: electrode that conducts electrons to and from the reactants in a half-cell but that is not itself oxidized or reduced

Electrode and Cell Potentials

By the end of this section, you will be able to:

Describe and relate the definitions of electrode and cell potentials
Interpret electrode potentials in terms of relative oxidant and reductant strengths
Calculate cell potentials and predict redox spontaneity using standard electrode potentials

Unlike the spontaneous oxidation of copper by aqueous silver(I) ions described in section 17.2, immersing a copper wire in an aqueous solution of lead(II) ions yields no reaction. The two species, Ag⁺(aq) and Pb²⁺(aq), thus show a distinct difference in their redox activity towards copper: the silver ion spontaneously oxidized copper, but the lead ion did not. Electrochemical cells permit this relative redox activity to be quantified by an easily measured property, potential. This property is more commonly called voltage when referenced in regard to electrical applications, and it is a measure of energy accompanying the transfer of charge. Potentials are measured in the volt unit, defined as one joule of energy per one coulomb of charge, V = J/C.

When measured for purposes of electrochemistry, a potential reflects the driving force for a specific type of charge transfer process, namely, the transfer of electrons between redox reactants. Considering the nature of potential in this context, it is clear that the potential of a single half-cell or a single electrode can’t be measured; “transfer” of electrons requires both a donor and recipient, in this case a reductant and an oxidant, respectively. Instead, a half-cell potential may only be assessed relative to that of another half-cell. It is only the difference in potential between two half-cells that may be measured, and these measured potentials are called cell potentials, E_cell, defined as

E_{cell} = E_{cathode} - E_{anode}

where E_cathode and E_anode are the potentials of two different half-cells functioning as specified in the subscripts. As for other thermodynamic quantities, the standard cell potential, E°_cell, is a cell potential measured when both half-cells are under standard-state conditions (1 M concentrations, 1 bar pressures, 298 K):

E^{°}_{cell} = E^{°}_{cathode} - E^{°}_{anode}

To simplify the collection and sharing of potential data for half-reactions, the scientific community has designated one particular half-cell to serve as a universal reference for cell potential measurements, assigning it a potential of exactly 0 V. This half-cell is the standard hydrogen electrode (SHE) and it is based on half-reaction below:

2 H^{+} (a q) + 2 e^{−} ⟶ H_{2} (g)

A typical SHE contains an inert platinum electrode immersed in precisely 1 M aqueous H⁺ and a stream of bubbling H₂ gas at 1 bar pressure, all maintained at a temperature of 298 K (see Figure 13.5).

The figure shows a beaker just over half full of a blue liquid. A glass tube is partially submerged in the liquid. Bubbles, which are labeled “H subscript 2 ( g )” are rising from the dark grayquare, labeled “P t electrode” at the bottom of the tube. Below the bottom of the tube pointing to the solution in the beaker is the label “ 1 M H superscript plus ( a q).” A curved arrow points up to the right, indicating the direction of the bubbles. A black wire which is labeled “P t wire” extends from the dark grgrayare up the interior of the tube through a small port at the top. A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled “H subscript 2 ( g ) at 1 a t m.” A light greygray points to a diagram in a circle at the right that illustrates the surface of the P t electrode in a magnified view. P t atoms are illustrated as a uniform cluster of grey sgray which are labeled “P t electrode atoms.” On the grey atograyace, the label “e superscript negative” is shown 4 times in a nearly even vertical distribution to show electrons on the P t surface. A curved arrow extends from a white sphere labeled “H superscript plus” at the right of the P t atoms to the uppermost electron shown. Just below, a straight arrow extends from the P t surface to the right to a pair of linked white spheres which are labeled “H subscript 2.” A curved arrow extends from a second white sphere labeled “H superscript plus” at the right of the P t atoms to the second electron shown. A curved arrow extends from the third electron on the P t surface to the right to a white sphere labeled “H superscript plus.” Just below, an arrow points left from a pair of linked white spheres which are labeled “H subscript 2” to the P t surface. A curved arrow extends from the fourth electron on the P t surface to the right to a white sphere labeled “H superscript plus.” — A standard hydrogen electrode (SHE).

The assigned potential of the SHE permits the definition of a conveniently measured potential for a single half-cell. The electrode potential (E_X) for a half-cell X is defined as the potential measured for a cell comprised of X acting as cathode and the SHE acting as anode:

\begin{matrix} E_{cell} = E_{X} - E_{SHE} \\ E_{SHE} = 0 V (defined) \\ E_{cell} = E_{X} \end{matrix}

When the half-cell X is under standard-state conditions, its potential is the standard electrode potential, E°_X. Since the definition of cell potential requires the half-cells function as cathodes, these potentials are sometimes called standard reduction potentials.

This approach to measuring electrode potentials is illustrated in [link], which depicts a cell comprised of an SHE connected to a copper(II)/copper(0) half-cell under standard-state conditions. A voltmeter in the external circuit allows measurement of the potential difference between the two half-cells. Since the Cu half-cell is designated as the cathode in the definition of cell potential, it is connected to the red (positive) input of the voltmeter, while the designated SHE anode is connected to the black (negative) input. These connections insure that the sign of the measured potential will be consistent with the sign conventions of electrochemistry per the various definitions discussed above. A cell potential of +0.337 V is measured, and so

E^{°}_{cell} = E^{°}_{Cu} = +0.337 V

Tabulations of E° values for other half-cells measured in a similar fashion are available as reference literature to permit calculations of cell potentials and the prediction of the spontaneity of redox processes.

This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a clear, colorless solution and is labeled below as “1 M H superscript plus.” The beaker on the right contains a blue solution and is labeled below as “1 M C u superscript 2 plus.” A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small graylug is present at each end of the tube. The beaker on the left has a glass tube partially submersed in the liquid. Bubbles are rising from the gray square, labeled “Standard hydrogen electrode” at the bottom of the tube. A curved arrow points up to the right, indicating the direction of the bubbles. A black wire extends from the gray square up the interior of the tube through a small port at the top to a rectangle with a digital readout of “positive 0.337 V,” which is labeled “Voltmeter.” A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled “1 a t m H subscript 2 ( g ).” The beaker on the right has an orange-brown strip that is labeled “C u electrode” at the top. A wire extends from the top of this strip to the voltmeter. An arrow points toward the voltmeter from the left which is labeled “e superscript negative flow.” Similarly, an arrow points away from the voltmeter to the right. A curved arrow extends from the surrounding solution to the standard hydrogen electrode in the beaker. The end of the arrow is labeled “H subscript 2” and tip of this arrow is labeled “2 H superscript plus.” A curved arrow extends from the “C u superscript 2 plus” label in the solution to a “C u” label at the lower edge of the C u electrode. Between the two beakers is the label “T equals 298 K.” — A cell permitting experimental measurement of the standard electrode potential for the half-reaction ${Cu}^{2+} (a q) + 2 e^{−} ⟶ Cu (s)$

[link] provides a listing of standard electrode potentials for a selection of half-reactions in numerical order, and a more extensive alphabetical listing is given in Appendix L.

Selected Standard Reduction Potentials at 25 °C
Half-Reaction	E° (V)
$F_{2} (g) + {2e}^{−} ⟶ {2F}^{−} (a q)$	+2.866
${PbO}_{2} (s) + {SO}_{4}^{2−} (a q) + {4H}^{+} (a q) + {2e}^{−} ⟶ {PbSO}_{4} (s) + {2H}_{2} O (l)$	+1.69
${MnO}_{4}^{−} (a q) + {8H}^{+} (a q) + {5e}^{−} ⟶ {Mn}^{2+} (a q) + {4H}_{2} O (l)$	+1.507
${Au}^{3+} (a q) + {3e}^{−} ⟶ Au (s)$	+1.498
${Cl}_{2} (g) + {2e}^{−} ⟶ {2Cl}^{−} (a q)$	+1.35827
$O_{2} (g) + {4H}^{+} (a q) + {4e}^{−} ⟶ {2H}_{2} O (l)$	+1.229
${Pt}^{2+} (a q) + {2e}^{−} ⟶ Pt (s)$	+1.20
${Br}_{2} (a q) + {2e}^{−} ⟶ {2Br}^{−} (a q)$	+1.0873
${Ag}^{+} (a q) + e^{−} ⟶ Ag (s)$	+0.7996
${Hg}_{2}^{2+} (a q) + {2e}^{−} ⟶ 2Hg (l)$	+0.7973
${Fe}^{3+} (a q) + e^{−} ⟶ {Fe}^{2+} (a q)$	+0.771
${MnO}_{4}^{−} (a q) + {2H}_{2} O (l) + {3e}^{−} ⟶ {MnO}_{2} (s) + {4OH}^{−} (a q)$	+0.558
$I_{2} (s) + {2e}^{−} ⟶ {2I}^{−} (a q)$	+0.5355
${NiO}_{2} (s) + {2H}_{2} O (l) + {2e}^{−} ⟶ {Ni(OH)}_{2} (s) + {2OH}^{−} (a q)$	+0.49
${Cu}^{2+} (a q) + {2e}^{−} ⟶ Cu (s)$	+0.34
${Hg}_{2} {Cl}_{2} (s) + {2e}^{−} ⟶ 2Hg (l) + {2Cl}^{−} (a q)$	+0.26808
$AgCl (s) + e^{−} ⟶ Ag (s) + {Cl}^{−} (a q)$	+0.22233
${Sn}^{4+} (a q) + {2e}^{−} ⟶ {Sn}^{2+} (a q)$	+0.151
${2H}^{+} (a q) + {2e}^{−} ⟶ H_{2} (g)$	0.00
${Pb}^{2+} (a q) + {2e}^{−} ⟶ Pb (s)$	−0.1262
${Sn}^{2+} (a q) + {2e}^{−} ⟶ Sn (s)$	−0.1375
${Ni}^{2+} (a q) + {2e}^{−} ⟶ Ni (s)$	−0.257
${Co}^{2+} (a q) + {2e}^{−} ⟶ Co (s)$	−0.28
${PbSO}_{4} (s) + {2e}^{−} ⟶ Pb (s) + {SO}_{4}^{2−} (a q)$	−0.3505
${Cd}^{2+} (a q) + {2e}^{−} ⟶ Cd (s)$	−0.4030
${Fe}^{2+} (a q) + {2e}^{−} ⟶ Fe (s)$	−0.447
${Cr}^{3+} (a q) + {3e}^{−} ⟶ Cr (s)$	−0.744
${Mn}^{2+} (a q) + {2e}^{−} ⟶ Mn (s)$	−1.185
${Zn(OH)}_{2} (s) + {2e}^{−} ⟶ Zn (s) + {2OH}^{−} (a q)$	−1.245
${Zn}^{2+} (a q) + {2e}^{−} ⟶ Zn (s)$	−0.7618
${Al}^{3+} (a q) + {3e}^{−} ⟶ Al (s)$	−1.662
${Mg}^{2} (a q) + {2e}^{−} ⟶ Mg (s)$	−2.372
${Na}^{+} (a q) + e^{−} ⟶ Na (s)$	−2.71
${Ca}^{2+} (a q) + {2e}^{−} ⟶ Ca (s)$	−2.868
${Ba}^{2+} (a q) + {2e}^{−} ⟶ Ba (s)$	−2.912
$K^{+} (a q) + e^{−} ⟶ K (s)$	−2.931
${Li}^{+} (a q) + e^{−} ⟶ Li (s)$	−3.04

Calculating Standard Cell Potentials What is the standard potential of the galvanic cell shown in [link]?

Solution The cell in [link] is galvanic, the spontaneous cell reaction involving oxidation of its copper anode and reduction of silver(I) ions at its silver cathode:

\begin{matrix} cell reaction: & Cu (s) + 2 {Ag}^{+} (a q) ⟶ {Cu}^{2+} (a q) + 2 Ag (s) \\ anode half-reaction: & Cu (s) ⟶ {Cu}^{2+} (a q) + 2 e^{−} \\ cathode half-reaction: & 2 {Ag}^{+} (a q) + 2 e^{−} ⟶ 2 Ag (s) \end{matrix}

The standard cell potential computed as

\begin{matrix} E^{°}_{cell} & = & E^{°}_{cathode} - E^{°}_{anode} \\ = & E^{°}_{Ag} - E^{°}_{Cu} \\ = & 0.7996 V - 0.34 V \\ = & +0.46 V \end{matrix}

Check Your Learning What is the standard cell potential expected if the silver cathode half-cell in [link] is replaced with a lead half-cell: ${Pb}^{2+} (a q) + 2 e^{−} ⟶ Pb (s)$ ?

Answer:

−0. 47 V

Intrepreting Electrode and Cell Potentials

Thinking carefully about the definitions of cell and electrode potentials and the observations of spontaneous redox change presented thus far, a significant relation is noted. The previous section described the spontaneous oxidation of copper by aqueous silver(I) ions, but no observed reaction with aqueous lead(II) ions. Results of the calculations in [link] have just shown the spontaneous process is described by a positive cell potential while the nonspontaneous process exhibits a negative cell potential. And so, with regard to the relative effectiveness (“strength”) with which aqueous Ag⁺ and Pb²⁺ ions oxidize Cu under standard conditions, the stronger oxidant is the one exhibiting the greater standard electrode potential, E°. Since by convention electrode potentials are for reduction processes, an increased value of E° corresponds to an increased driving force behind the reduction of the species (hence increased effectiveness of its action as an oxidizing agent on some other species). Negative values for electrode potentials are simply a consequence of assigning a value of 0 V to the SHE, indicating the reactant of the half-reaction is a weaker oxidant than aqueous hydrogen ions.

Applying this logic to the numerically ordered listing of standard electrode potentials in [link] shows this listing to be likewise in order of the oxidizing strength of the half-reaction’s reactant species, decreasing from strongest oxidant (most positive E°) to weakest oxidant (most negative E°). Predictions regarding the spontaneity of redox reactions under standard state conditions can then be easily made by simply comparing the relative positions of their table entries. By definition, E°_cell is positive when E°_cathode > E°_anode, and so any redox reaction in which the oxidant’s entry is above the reductant’s entry is predicted to be spontaneous.

Reconsideration of the two redox reactions in [link] provides support for this fact. The entry for the silver(I)/silver(0) half-reaction is above that for the copper(II)/copper(0) half-reaction, and so the oxidation of Cu by Ag⁺ is predicted to be spontaneous (E°_cathode > E°_anode and so E°_cell > 0). Conversely, the entry for the lead(II)/lead(0) half-cell is beneath that for copper(II)/copper(0), and the oxidation of Cu by Pb²⁺ is nonspontaneous (E°_cathode < E°_anode and so E°_cell < 0).

Recalling the chapter on thermodynamics, the spontaneities of the forward and reverse reactions of a reversible process show a reciprocal relationship: if a process is spontaneous in one direction, it is non-spontaneous in the opposite direction. As an indicator of spontaneity for redox reactions, the potential of a cell reaction shows a consequential relationship in its arithmetic sign. The spontaneous oxidation of copper by lead(II) ions is not observed,

Cu (s) + {Pb}^{2+} (a q) ⟶ {Cu}^{2+} (a q) + Pb (s) E^{°}_{f o r w a r d} = −0.47 V (negative, non-spontaneous)

and so the reverse reaction, the oxidation of lead by copper(II) ions, is predicted to occur spontaneously:

Pb (s) + {Cu}^{2+} (a q) ⟶ {Pb}^{2+} (a q) + Cu (s) E^{°}_{f o r w a r d} = +0.47 V (positive, spontaneous)

Note that reversing the direction of a redox reaction effectively interchanges the identities of the cathode and anode half-reactions, and so the cell potential is calculated from electrode potentials in the reverse subtraction order than that for the forward reaction. In practice, a voltmeter would report a potential of −0.47 V with its red and black inputs connected to the Pb and Cu electrodes, respectively. If the inputs were swapped, the reported voltage would be +0.47 V.

Predicting Redox Spontaneity Are aqueous iron(II) ions predicted to spontaneously oxidize elemental chromium under standard state conditions? Assume the half-reactions to be those available in [link].

Solution Referring to the tabulated half-reactions, the redox reaction in question can be represented by the equations below:

Cr (s) + {Fe}^{2+} (a q) ⟶ {Cr}^{3+} (a q) + Fe (s)

The entry for the putative oxidant, Fe²⁺, appears above the entry for the reductant, Cr, and so a spontaneous reaction is predicted per the quick approach described above. Supporting this predication by calculating the standard cell potential for this reaction gives

\begin{matrix} E^{°}_{cell} & = & E^{°}_{cathode} - E^{°}_{anode} \\ = & E^{°}_{Fe(II)} - E^{°}_{Cr} \\ = & −0.447 V - −0.774 V = +0.297 V \end{matrix}

The positive value for the standard cell potential indicates the process is spontaneous under standard state conditions.

Check Your Learning Use the data in [link] to predict the spontaneity of the oxidation of bromide ion by molecular iodine under standard state conditions, supporting the prediction by calculating the standard cell potential for the reaction. Repeat for the oxidation of iodide ion by molecular bromine.

Answer:

$\begin{matrix} I_{2} (s) + 2 {Br}^{−} (a q) ⟶ 2 I^{−} (a q) + {Br}_{2} (l) & E^{°}_{cell} = +0.5518 V (spontaneous) \\ {Br}_{2} (s) + 2 I^{−} (a q) ⟶ 2 {Br}^{−} (a q) + I_{2} (l) & E^{°}_{cell} = −0.5518 V (nonspontaneous) \end{matrix}$

Key Concepts and Summary

The property of potential, E, is the energy associated with the separation/transfer of charge. In electrochemistry, the potentials of cells and half-cells are thermodynamic quantities that reflect the driving force or the spontaneity of their redox processes. The cell potential of an electrochemical cell is the difference in between its cathode and anode. To permit easy sharing of half-cell potential data, the standard hydrogen electrode (SHE) is assigned a potential of exactly 0 V and used to define a single electrode potential for any given half-cell. The electrode potential of a half-cell, E_X, is the cell potential of said half-cell acting as a cathode when connected to a SHE acting as an anode. When the half-cell is operating under standard state conditions, its potential is the standard electrode potential, E°_X. Standard electrode potentials reflect the relative oxidizing strength of the half-reaction’s reactant, with stronger oxidants exhibiting larger (more positive) E°_X values. Tabulations of standard electrode potentials may be used to compute standard cell potentials, E°_cell, for many redox reactions. The arithmetic sign of a cell potential indicates the spontaneity of the cell reaction, with positive values for spontaneous reactions and negative values for nonspontaneous reactions (spontaneous in the reverse direction).

Key Equations

$E_{cell}^{°} = E_{cathode}^{°} - E_{anode}^{°}$

Glossary

standard cell potential $(E_{cell}^{°})$: the cell potential when all reactants and products are in their standard states (1 bar or 1 atm or gases; 1 M for solutes), usually at 298.15 K

standard hydrogen electrode (SHE): half-cell based on hydrogen ion production, assigned a potential of exactly 0 V under standard state conditions, used as the universal reference for measuring electrode potential

standard electrode potential ( $(E_{X}^{°})$ ): electrode potential measured under standard conditions (1 bar or 1 atm for gases; 1 M for solutes) usually at 298.15 K

Electrolysis

By the end of this section you will be able to:

Describe the process of electrolysis
Compare the operation of electrolytic cells with that of galvanic cells
Perform stoichiometric calculations for electrolytic processes

Electrochemical cells in which spontaneous redox reactions take place (galvanic cells) have been the topic of discussion so far in this chapter. In these cells, electrical work is done by a redox system on its surroundings as electrons produced by the redox reaction are transferred through an external circuit. This final section of the chapter will address an alternative scenario in which an external circuit does work on a redox system by imposing a voltage sufficient to drive an otherwise nonspontaneous reaction, a process known as electrolysis. A familiar example of electrolysis is recharging a battery, which involves use of an external power source to drive the spontaneous (discharge) cell reaction in the reverse direction, restoring to some extent the composition of the half-cells and the voltage of the battery. Perhaps less familiar is the use of electrolysis in the refinement of metallic ores, the manufacture of commodity chemicals, and the electroplating of metallic coatings on various products (e.g., jewelry, utensils, auto parts). To illustrate the essential concepts of electrolysis, a few specific processes will be considered.

The Electrolysis of Molten Sodium Chloride

Metallic sodium, Na, and chlorine gas, Cl₂, are used in numerous applications, and their industrial production relies on the large-scale electrolysis of molten sodium chloride, NaCl(l). The industrial process typically uses a Downs cell similar to the simplified illustration shown in [link]. The reactions associated with this process are:

\begin{array}{l} \underline{\begin{array}{l} anode: 2 {Cl}^{−} (l) ⟶ {Cl}_{2} (g) + {2e}^{−} \\ cathode: {Na}^{+} (l) + e^{−} ⟶ Na (l) \end{array}} \\ cell: 2 {Na}^{+} (l) + {2Cl}^{−} (l) ⟶ 2Na (l) + {Cl}_{2} (g) \end{array}

The cell potential for the above process is negative, indicating the reaction as written (decomposition of liquid NaCl) is not spontaneous. To force this reaction, a positive potential of magnitude greater than the negative cell potential must be applied to the cell.

This diagram shows a tank containing a light blue liquid, labeled “Molten N a C l.” A vertical dark grey divider with small, evenly distributed dark dots, labeled “Porous screen” is located at the center of the tank dividing it into two halves. Dark grey bars are positioned at the center of each of the halves of the tank. The bar on the left, which is labeled “Anode” has green bubbles originating from it. The bar on the right which is labeled “Cathode” has light grey bubbles originating from it. An arrow points left from the center of the tank toward the anode, which is labeled “C l superscript negative.” An arrow points right from the center of the tank toward the cathode, which is labeled “N a superscript plus.” A line extends from the tops of the anode and cathode to a rectangle centrally placed above the tank which is labeled “Voltage source.” An arrow extends upward above the anode to the left of the line which is labeled “e superscript negative.” A plus symbol is located to the left of the voltage source and a negative sign it located to its right. An arrow points downward along the line segment leading to the cathode. This arrow is labeled “e superscript negative.” The left side of below the diagram is the label “2 C l superscript negative right pointing arrow C l subscript 2 ( g ) plus 2 e superscript negative.” At the right, below the diagram is the label “2 N a superscript plus plus 2 e superscript negative right pointing arrow 2 N a ( l ).” — Cells of this sort (a cell for the electrolysis of molten sodium chloride) are used in the *Downs process* for production of sodium and chlorine, and they typically use iron cathodes and carbon anodes.

The Electrolysis of Water

Water may be electrolytically decomposed in a cell similar to the one illustrated in [link]. To improve electrical conductivity without introducing a different redox species, the hydrogen ion concentration of the water is typically increased by addition of a strong acid. The redox processes associated with this cell are

\begin{matrix} \underline{\begin{array}{l} anode: 2 H_{2} O (l) ⟶ O_{2} (g) + {4H}^{+} (a q) + {4e}^{−} & E_{anode}^{°} & = & +1.229 V \\ cathode: 2 H^{+} (a q) + {2e}^{−} ⟶ H_{2} (g) & E_{cathode}^{°} & = & 0 V \end{array}} \\ \begin{matrix} cell: 2 H_{2} O (l) ⟶ {2H}_{2} (g) + O_{2} (g) & E_{cell}^{°} & = & −1.229 V \end{matrix} \end{matrix}

Again, the cell potential as written is negative, indicating a nonspontaneous cell reaction that must be driven by imposing a cell voltage greater than +1.229 V. Keep in mind that standard electrode potentials are used to inform thermodynamic predictions here, though the cell is not operating under standard state conditions. Therefore, at best, calculated cell potentials should be considered ballpark estimates.

This figure shows an apparatus used for electrolysis. A central chamber with an open top has a vertical column extending below that is nearly full of a clear, colorless liquid, which is labeled “H subscript 2 O plus H subscript 2 S O subscript 4.” A horizontal tube in the apparatus connects the central region to vertical columns to the left and right, each of which has a valve or stopcock at the top and a stoppered bottom. On the left, the stopper at the bottom has a small brown square connected just above it in the liquid. The square is labeled “Anode plus.” A black wire extends from the stopper at the left to a rectangle which is labeled “Voltage source” on to the stopper at the right. The left side of the rectangle is labeled with a plus symbol and the right side is labeled with a negative sign. The stopper on the right also has a brown square connected to it which is in the liquid in the apparatus. This square is labeled “Cathode negative.” The level of the solution on the left arm or tube of the apparatus is significantly higher than the level of the right arm. Bubbles are present near the surface of the liquid on each side of the apparatus, with the bubbles labeled as “O subscript 2 ( g )” on the left and “H subscript 2 ( g )” on the right. — The electrolysis of water produces stoichiometric amounts of oxygen gas at the anode and hydrogen at the anode.

The Electrolysis of Aqueous Sodium Chloride

When aqueous solutions of ionic compounds are electrolyzed, the anode and cathode half-reactions may involve the electrolysis of either water species (H₂O, H⁺, OH^-) or solute species (the cations and anions of the compound). As an example, the electrolysis of aqueous sodium chloride could involve either of these two anode reactions:

\begin{matrix} (i) 2 {Cl}^{−} (a q) ⟶ {Cl}_{2} (g) + 2 e^{−} & E_{anode}^{°} & = & +1.35827 V \\ (ii) 2 H_{2} O (l) ⟶ O_{2} (g) + 4 H^{+} (a q) + 4 e^{−} & E_{anode}^{°} & = & +1.229 V \end{matrix}

The standard electrode (reduction) potentials of these two half-reactions indicate water may be oxidized at a less negative/more positive potential (–1.229 V) than chloride ion (–1.358 V). Thermodynamics thus predicts that water would be more readily oxidized, though in practice it is observed that both water and chloride ion are oxidized under typical conditions, producing a mixture of oxygen and chlorine gas.

Turning attention to the cathode, the possibilities for reduction are:

\begin{matrix} (iii) {2H}^{+} (a q) + 2 e^{−} ⟶ H_{2} (g) & E_{cathode}^{°} & = & 0 V \\ (iv) {2H}_{2} O (l) + 2 e^{−} ⟶ H_{2} (g) + 2 {OH}^{−} (a q) & E_{cathode}^{°} & = & −0.8277 V \\ (v) {Na}^{+} (a q) + e^{−} ⟶ Na (s) & E_{cathode}^{°} & = & −2.71 V \end{matrix}

Comparison of these standard half-reaction potentials suggests the reduction of hydrogen ion is thermodynamically favored. However, in a neutral aqueous sodium chloride solution, the concentration of hydrogen ion is far below the standard state value of 1 M (approximately 10^-7 M), and so the observed cathode reaction is actually reduction of water. The net cell reaction in this case is then

cell: 2 H_{2} O (l) + 2 {Cl}^{−} (a q) ⟶ H_{2} (g) + {Cl}_{2} (g) + 2 {OH}^{−} (a q) E_{cell}^{°} = −2.186 V

This electrolysis reaction is part of the chlor-alkali process used by industry to produce chlorine and sodium hydroxide (lye).

CHEMISTRY IN EVERYDAY LIFE

Electroplating

An important use for electrolytic cells is in electroplating. Electroplating results in a thin coating of one metal on top of a conducting surface. Reasons for electroplating include making the object more corrosion resistant, strengthening the surface, producing a more attractive finish, or for purifying metal. The metals commonly used in electroplating include cadmium, chromium, copper, gold, nickel, silver, and tin. Common consumer products include silver-plated or gold-plated tableware, chrome-plated automobile parts, and jewelry. The silver plating of eating utensils is used here to illustrate the process. ([link]).

This figure contains a diagram of an electrochemical cell. One beakers is shown that is just over half full. The beaker contains a clear, colorless solution that is labeled “A g N O subscript 3 ( a q ).” A silver strip is mostly submerged in the liquid on the left. This strip is labeled “Silver (anode).” The top of the strip is labeled with a red plus symbol. An arrow points right from the surface of the metal strip into the solution to the label “A g superscript plus” to the right. A spoon is similarly suspended in the solution and is labeled “Spoon (cathode).” It is labeled with a black negative sign on the tip of the spoon’s handle above the surface of the liquid. An arrow extends from the label “A g superscript plus” to the spoon on the right. A wire extends from the top of the spoon and the strip to a rectangle labeled “Voltage source.” An arrow points upward from silver strip which is labeled “e superscript negative.” Similarly, an arrow points down at the right to the surface of the spoon which is also labeled “e superscript negative.” A plus sign is shown just outside the voltage source to the left and a negative is shown to its right. — This schematic shows an electrolytic cell for silver plating eating utensils.

In the figure, the anode consists of a silver electrode, shown on the left. The cathode is located on the right and is the spoon, which is made from inexpensive metal. Both electrodes are immersed in a solution of silver nitrate. Applying a sufficient potential results in the oxidation of the silver anode

anode: Ag (s) ⟶ {Ag}^{+} (a q) + e^{−}

and reduction of silver ion at the (spoon) cathode:

{cathode: Ag}^{+} (a q) + e^{−} ⟶ Ag (s)

The net result is the transfer of silver metal from the anode to the cathode. Several experimental factors must be carefully controlled to obtain high-quality silver coatings, including the exact composition of the electrolyte solution, the cell voltage applied, and the rate of the electrolysis reaction (electrical current).

Quantitative Aspects of Electrolysis

Electrical current is defined as the rate of flow for any charged species. Most relevant to this discussion is the flow of electrons. Current is measured in a composite unit called an ampere, defined as one coulomb per second (A = 1 C/s). The charge transferred, Q, by passage of a constant current, I, over a specified time interval, t, is then given by the simple mathematical product

Q = I t

When electrons are transferred during a redox process, the stoichiometry of the reaction may be used to derive the total amount of (electronic) charge involved. For example, the generic reduction process

M^{n +} (a q) + {ne}^{−} ⟶ M (s)

involves the transfer of n mole of electrons. The charge transferred is, therefore,

Q = n F

where F is Faraday’s constant, the charge in coulombs for one mole of electrons. If the reaction takes place in an electrochemical cell, the current flow is conveniently measured, and it may be used to assist in stoichiometric calculations related to the cell reaction.

EXAMPLE X.X

Converting Current to Moles of Electrons In one process used for electroplating silver, a current of 10.23 A was passed through an electrolytic cell for exactly 1 hour. How many moles of electrons passed through the cell? What mass of silver was deposited at the cathode from the silver nitrate solution?

Solution Faraday’s constant can be used to convert the charge (Q) into moles of electrons (n). The charge is the current (I) multiplied by the time

n = \frac{Q}{F} = \frac{\frac{10.23 C}{s} \times 1 hr \times \frac{60 min}{hr} \times \frac{60 s}{min}}{9 {6,485 C/mol e}^{−}} = \frac{36,830 C}{96,485 C/mol e^{−}} = 0.381 {7 mol e}^{−}

From the problem, the solution contains AgNO₃, so the reaction at the cathode involves 1 mole of electrons for each mole of silver

{cathode: Ag}^{+} (a q) + e^{−} ⟶ Ag (s)

The atomic mass of silver is 107.9 g/mol, so

mass Ag = {0.3817 mol e}^{−} \times \frac{1 mol Ag}{{1 mol e}^{−}} \times \frac{107.9 g Ag}{1 mol Ag} = 4 1.19 g Ag

Check Your Learning Aluminum metal can be made from aluminum(III) ions by electrolysis. What is the half-reaction at the cathode? What mass of aluminum metal would be recovered if a current of 25.0 A passed through the solution for 15.0 minutes?

Answer:

${Al}^{3+} (a q) + 3 e^{−} ⟶ Al (s);$ 0.0777 mol Al = 2.10 g Al.

EXAMPLE X.X

Time Required for Deposition In one application, a 0.010-mm layer of chromium must be deposited on a part with a total surface area of 3.3 m² from a solution of containing chromium(III) ions. How long would it take to deposit the layer of chromium if the current was 33.46 A? The density of chromium (metal) is 7.19 g/cm³.

Solution First, compute the volume of chromium that must be produced (equal to the product of surface area and thickness):

volume = (0.010 mm \times \frac{1 cm}{10 mm}) \times (3.3 m^{2} \times (\frac{10,000 {cm}^{2}}{1 m^{2}})) = {33 cm}^{3}

Use the computed volume and the provided density to calculate the molar amount of chromium required:

mass = volume \times density = 33 {cm}^{3} \times \frac{7.19 g}{{cm}^{3}} = 237 g Cr

mol Cr = 237 g Cr \times \frac{1 mol Cr}{52.00 g Cr} = 4.56 mol Cr

The stoichiometry of the chromium(III) reduction process requires three moles of electrons for each mole of chromium(0) produced, and so the total charge required is:

Q = 4.56 mol Cr \times \frac{3 {mol e}^{−}}{1 mol Cr} \times \frac{96485 C}{{mol e}^{−}} = 1.32 \times 10^{6} C

Finally, if this charge is passed at a rate of 33.46 C/s, the required time is:

t = \frac{Q}{I} = \frac{1.32 \times 10^{6} C}{33.46 C/s} = 3.95 \times 10^{4} s = 11.0 hr

Check Your Learning What mass of zinc is required to galvanize the top of a 3.00 m $\times$ 5.50 m sheet of iron to a thickness of 0.100 mm of zinc? If the zinc comes from a solution of Zn(NO₃)₂ and the current is 25.5 A, how long will it take to galvanize the top of the iron? The density of zinc is 7.140 g/cm³.

Answer:

11.8 kg Zn requires 382 hours.

Key Concepts and Summary

Nonspontaneous redox processes may be forced to occur in electrochemical cells by the application of an appropriate potential using an external power source—a process known as electrolysis. Electrolysis is the basis for certain ore refining processes, the industrial production of many chemical commodities, and the electroplating of metal coatings on various products. Measurement of the current flow during electrolysis permits stoichiometric calculations.

Key Equations

Q = I $\times$ t = n $\times$ F

Glossary

electrolysis: process using electrical energy to cause a nonspontaneous process to occur

electrolytic cell: electrochemical cell in which an external source of electrical power is used to drive an otherwise nonspontaneous process