Key Terms, Key Equations, Summaries, and Exercises (Chapter 16)

OpenStax

Private: Chapter Sixteen

Key Terms, Key Equations, Summaries, and Exercises (Chapter 16)


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

alkaline battery: primary battery similar to a dry cell that uses an alkaline (often potassium hydroxide) electrolyte; designed to be an improved replacement for the dry cell, but with more energy storage and less electrolyte leakage than typical dry cell

anode: electrode in an electrochemical cell at which oxidation occurs

battery: single or series of galvanic cells designed for use as a source of electrical power

cathode: electrode in an electrochemical cell at which reduction occurs

cathodic protection: approach to preventing corrosion of a metal object by connecting it to a sacrificial anode composed of a more readily oxidized metal

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

concentration cell: galvanic cell comprising half-cells of identical composition but for the concentration of one redox reactant or product

corrosion: degradation of metal via a natural electrochemical process

dry cell: primary battery, also called a zinc-carbon battery, based on the spontaneous oxidation of zinc by manganese(IV)

electrode potential (E_X): the potential of a cell in which the half-cell of interest acts as a cathode when connected to the standard hydrogen electrode

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

Faraday’s constant (F): charge on 1 mol of electrons; F = 96,485 C/mol e⁻

fuel cell: devices similar to galvanic cells that require a continuous feed of redox reactants; also called a flow battery

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

galvanization: method of protecting iron or similar metals from corrosion by coating with a thin layer of more easily oxidized zinc.

half cell: component of a cell that contains the redox conjugate pair (“couple”) of a single reactant

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

lead acid battery: rechargeable battery commonly used in automobiles; it typically comprises six galvanic cells based on Pb half-reactions in acidic solution

lithium ion battery: widely used rechargeable battery commonly used in portable electronic devices, based on lithium ion transfer between the anode and cathode

Nernst equation: relating the potential of a redox system to its composition

nickel-cadmium battery: rechargeable battery based on Ni/Cd half-cells with applications similar to those of lithium ion batteries

primary cell: nonrechargeable battery, suitable for single use only

sacrificial anode: electrode constructed from an easily oxidized metal, often magnesium or zinc, used to prevent corrosion of metal objects via cathodic protection

salt bridge: tube filled with inert electrolyte solution

secondary cell: battery designed to allow recharging

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 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

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

Key Equations

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

E_{cell}^{°} = \frac{R T}{n F} ln K

E_{cell}^{°} = \frac{0.02 57 V}{n} ln K = \frac{0.0 592 V}{n} log K (at 298.15 K)

E_{cell} = E_{cell}^{°} - \frac{R T}{n F} ln Q (Nernst equation)

E_{cell}^{°} - \frac{0.05 92 V}{n} log Q (at 298.15 K)

ΔG = −nFE_cell

Δ G^{°} = − n F E_{cell}^{°}

w_{ele} = w_{max} = − n F E_{cell}

Q = I

\times

t = n

\times

F

Summaries

16.1 Review of Redox Chemistry

Redox reactions are defined by changes in reactant oxidation numbers, and those most relevant to electrochemistry involve actual transfer of electrons. Aqueous phase redox processes often involve water or its characteristic ions, H⁺ and OH⁻, as reactants in addition to the oxidant and reductant, and equations representing these reactions can be challenging to balance. The half-reaction method is a systematic approach to balancing such equations that involves separate treatment of the oxidation and reduction half-reactions.

16.2 Galvanic Cells

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).

16.3 Electrode and Cell Potentials

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).

16.4 Potential, Free Energy, and Equilibrium

Potential is a thermodynamic quantity reflecting the intrinsic driving force of a redox process, and it is directly related to the free energy change and equilibrium constant for the process. For redox processes taking place in electrochemical cells, the maximum (electrical) work done by the system is easily computed from the cell potential and the reaction stoichiometry and is equal to the free energy change for the process. The equilibrium constant for a redox reaction is logarithmically related to the reaction’s cell potential, with larger (more positive) potentials indicating reactions with greater driving force that equilibrate when the reaction has proceeded far towards completion (large value of K). Finally, the potential of a redox process varies with the composition of the reaction mixture, being related to the reactions standard potential and the value of its reaction quotient, Q, as described by the Nernst equation.

16.5 Batteries and Fuel Cells

Galvanic cells designed specifically to function as electrical power supplies are called batteries. A variety of both single-use batteries (primary cells) and rechargeable batteries (secondary cells) are commercially available to serve a variety of applications, with important specifications including voltage, size, and lifetime. Fuel cells, sometimes called flow batteries, are devices that harness the energy of spontaneous redox reactions normally associated with combustion processes. Like batteries, fuel cells enable the reaction’s electron transfer via an external circuit, but they require continuous input of the redox reactants (fuel and oxidant) from an external reservoir. Fuel cells are typically much more efficient in converting the energy released by the reaction to useful work in comparison to internal combustion engines.

16.6 Corrosion

Spontaneous oxidation of metals by natural electrochemical processes is called corrosion, familiar examples including the rusting of iron and the tarnishing of silver. Corrosion process involve the creation of a galvanic cell in which different sites on the metal object function as anode and cathode, with the corrosion taking place at the anodic site. Approaches to preventing corrosion of metals include use of a protective coating of zinc (galvanization) and the use of sacrificial anodes connected to the metal object (cathodic protection).

16.7Electrolysis

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.

Exercises

16.1 Review of Redox Chemistry

1.

Identify each half-reaction below as either oxidation or reduction.

(a) ${Fe}^{3+} + {3e}^{−} ⟶ Fe$

(b) $Cr ⟶ {Cr}^{3+} + {3e}^{−}$

(c) ${MnO}_{4}^{2−} ⟶ {MnO}_{4}^{-} + e^{−}$

(d) ${Li}^{+} + e^{−} ⟶ Li$

2.

Identify each half-reaction below as either oxidation or reduction.

(a) ${Cl}^{−} ⟶ {Cl}_{2}$

(b) ${Mn}^{2+} ⟶ {MnO}_{2}$

(c) $H_{2} ⟶ H^{+}$

(d) ${NO}_{3}^{-} ⟶ NO$

3.

Assuming each pair of half-reactions below takes place in an acidic solution, write a balanced equation for the overall reaction.

(a) $Ca ⟶ {Ca}^{2+} + {2e}^{−},$ $F_{2} + {2e}^{−} ⟶ {2F}^{−}$

(b) $Li ⟶ {Li}^{+} + e^{−},$ ${Cl}_{2} + {2e}^{−} ⟶ {2Cl}^{−}$

(c) $Fe ⟶ {Fe}^{3+} + {3e}^{−},$ ${Br}_{2} + {2e}^{-} ⟶ {2Br}^{-}$

(d) $Ag ⟶ {Ag}^{+} + e^{−},$ ${MnO}_{4}^{-} + {4H}^{+} + {3e}^{−} ⟶ {MnO}_{2} + {2H}_{2} O$

4.

Balance the equations below assuming they occur in an acidic solution.

(a) $H_{2} O_{2} + {Sn}^{2+} ⟶ H_{2} O + {Sn}^{4+}$

(b) ${PbO}_{2} + Hg ⟶ {Hg}_{2}^{2+} + {Pb}^{2+}$

(c) $Al + {Cr}_{2} O_{7}^{2−} ⟶ {Al}^{3+} + {Cr}^{3+}$

5.

Identify the oxidant and reductant of each reaction of the previous exercise.

6.

Balance the equations below assuming they occur in a basic solution.

(a) ${SO}_{3}^{2−} (a q) + {Cu(OH)}_{2} (s) ⟶ {SO}_{4}^{2−} (a q) + Cu(OH) (s)$

(b) $O_{2} (g) + {Mn(OH)}_{2} (s) ⟶ {MnO}_{2} (s)$

(c) ${NO}_{3}^{−} (a q) + H_{2} (g) ⟶ NO (g)$

(d) $Al (s) + {CrO}_{4}^{2−} (a q) ⟶ {Al(OH)}_{3} (s) + {Cr(OH)}_{4}^{−} (a q)$

7.

Identify the oxidant and reductant of each reaction of the previous exercise.

8.

Why don’t hydroxide ions appear in equations for half-reactions occurring in acidic solution?

9.

Why don’t hydrogen ions appear in equations for half-reactions occurring in basic solution?

10.

Why must the charge balance in oxidation-reduction reactions?

16.2 Galvanic Cells

11.

Write cell schematics for the following cell reactions, using platinum as an inert electrode as needed.

(a) $Mg (s) + {Ni}^{2+} (a q) ⟶ {Mg}^{2+} (a q) + Ni (s)$

(b) $2 {Ag}^{+} (a q) + Cu (s) ⟶ {Cu}^{2+} (a q) + 2Ag (s)$

(c) $Mn (s) + {Sn(NO}_{3})_{2} (a q) ⟶ {Mn(NO}_{3})_{2} (a q) + Sn (s)$

(d) $3 {CuNO}_{3} (a q) + {Au(NO}_{3})_{3} (a q) ⟶ {3Cu(NO}_{3})_{2} (a q) + Au (s)$

12.

Assuming the schematics below represent galvanic cells as written, identify the half-cell reactions occurring in each.

(a) $Mg (s) │ {Mg}^{2+} (a q) ║ {Cu}^{2+} (a q) │ Cu (s)$

(b) $Ni (s) │ {Ni}^{2+} (a q) ║ {Ag}^{+} (a q) │ Ag (s)$

13.

Write a balanced equation for the cell reaction of each cell in the previous exercise.

14.

Balance each reaction below, and write a cell schematic representing the reaction as it would occur in a galvanic cell.

(a) $Al (s) + {Zr}^{4+} (a q) ⟶ {Al}^{3+} (a q) + Zr (s)$

(b) ${Ag}^{+} (a q) + NO (g) ⟶ Ag (s) + {NO}_{3}^{−} (a q) (acidic solution)$

(c) ${SiO}_{3}^{2−} (a q) + Mg (s) ⟶ Si (s) + Mg {(OH)}_{2} (s) (basic solution)$

(d) ${ClO}_{3}^{−} (a q) + {MnO}_{2} (s) ⟶ {Cl}^{−} (a q) + {MnO}_{4}^{−} (a q) (basic solution)$

15.

Identify the oxidant and reductant in each reaction of the previous exercise.

16.

From the information provided, use cell notation to describe the following systems:

(a) In one half-cell, a solution of Pt(NO₃)₂ forms Pt metal, while in the other half-cell, Cu metal goes into a Cu(NO₃)₂ solution with all solute concentrations 1 M.

(b) The cathode consists of a gold electrode in a 0.55 M Au(NO₃)₃ solution and the anode is a magnesium electrode in 0.75 M Mg(NO₃)₂ solution.

(c) One half-cell consists of a silver electrode in a 1 M AgNO₃ solution, and in the other half-cell, a copper electrode in 1 M Cu(NO₃)₂ is oxidized.

17.

Why is a salt bridge necessary in galvanic cells like the one in Figure 16.3?

18.

An active (metal) electrode was found to gain mass as the oxidation-reduction reaction was allowed to proceed. Was the electrode an anode or a cathode? Explain.

19.

An active (metal) electrode was found to lose mass as the oxidation-reduction reaction was allowed to proceed. Was the electrode an anode or a cathode? Explain.

20.

The masses of three electrodes (A, B, and C), each from three different galvanic cells, were measured before and after the cells were allowed to pass current for a while. The mass of electrode A increased, that of electrode B was unchanged, and that of electrode C decreased. Identify each electrode as active or inert, and note (if possible) whether it functioned as anode or cathode.

16.3 Electrode and Cell Potentials

21.

Calculate the standard cell potential for each reaction below, and note whether the reaction is spontaneous under standard state conditions.

(a) $Mg (s) + {Ni}^{2+} (a q) ⟶ {Mg}^{2+} (a q) + Ni (s)$

(b) $2 {Ag}^{+} (a q) + Cu (s) ⟶ {Cu}^{2+} (a q) + 2Ag (s)$

(c) $Mn (s) + {Sn(NO}_{3})_{2} (a q) ⟶ {Mn(NO}_{3})_{2} (a q) + Sn (s)$

(d) $3 {Fe(NO}_{3})_{2} (a q) + {Au(NO}_{3})_{3} (a q) ⟶ {3Fe(NO}_{3})_{3} (a q) + Au (s)$

22.

Calculate the standard cell potential for each reaction below, and note whether the reaction is spontaneous under standard state conditions.

(a) $Mn (s) + {Ni}^{2+} (a q) ⟶ {Mn}^{2+} (a q) + Ni (s)$

(b) $3 {Cu}^{2+} (a q) + 2Al (s) ⟶ {2Al}^{3+} (a q) + 3Cu (s)$

(c) $Na (s) + {LiNO}_{3} (a q) ⟶ {NaNO}_{3} (a q) + Li (s)$

(d) ${Ca(NO}_{3})_{2} (a q) + Ba (s) ⟶ {Ba(NO}_{3})_{2} (a q) + Ca (s)$

23.

Write the balanced cell reaction for the cell schematic below, calculate the standard cell potential, and note whether the reaction is spontaneous under standard state conditions.

$Cu (s) │ {Cu}^{2+} (a q) ║ {Au}^{3+} (a q) │ Au (s)$

24.

Determine the cell reaction and standard cell potential at 25 °C for a cell made from a cathode half-cell consisting of a silver electrode in 1 M silver nitrate solution and an anode half-cell consisting of a zinc electrode in 1 M zinc nitrate. Is the reaction spontaneous at standard conditions?

25.

Determine the cell reaction and standard cell potential at 25 °C for a cell made from an anode half-cell containing a cadmium electrode in 1 M cadmium nitrate and an anode half-cell consisting of an aluminum electrode in 1 M aluminum nitrate solution. Is the reaction spontaneous at standard conditions?

26.

Write the balanced cell reaction for the cell schematic below, calculate the standard cell potential, and note whether the reaction is spontaneous under standard state conditions.
$Pt (s) │ H_{2} (g) │ H^{+} (a q) ║ {Br}_{2} (a q), {Br}^{−} (a q) │ Pt (s)$

16.4 Potential, Free Energy, and Equilibrium

27.

For each pair of standard cell potential and electron stoichiometry values below, calculate a corresponding standard free energy change (kJ).

(a) 0.000 V, n = 2

(b) +0.434 V, n = 2

(c) −2.439 V, n = 1

28.

For each pair of standard free energy change and electron stoichiometry values below, calculate a corresponding standard cell potential.

(a) 12 kJ/mol, n = 3

(b) −45 kJ/mol, n = 1

29.

Determine the standard cell potential and the cell potential under the stated conditions for the electrochemical reactions described here. State whether each is spontaneous or nonspontaneous under each set of conditions at 298.15 K.

(a) $Hg (l) + S^{2−} (a q, 0.10 M) + 2 {Ag}^{+} (a q, 0.25 M) ⟶ 2 Ag (s) + HgS (s)$

(b) The cell made from an anode half-cell consisting of an aluminum electrode in 0.015 M aluminum nitrate solution and a cathode half-cell consisting of a nickel electrode in 0.25 M nickel(II) nitrate solution.

(c) The cell made of a half-cell in which 1.0 M aqueous bromide is oxidized to 0.11 M bromine ion and a half-cell in which aluminum ion at 0.023 M is reduced to aluminum metal.

30.

Determine ΔG and ΔG° for each of the reactions in the previous problem.

31.

Use the data in Appendix L to calculate equilibrium constants for the following reactions. Assume 298.15 K if no temperature is given.

(a) $AgCl (s) ⇌ {Ag}^{+} (a q) + {Cl}^{−} (a q)$

(b) $CdS (s) ⇌ {Cd}^{2+} (a q) + S^{2−} (a q) at 377 K$

(c) ${Hg}^{2+} (a q) + 4 {Br}^{−} (a q) ⇌ {[{HgBr}_{4}]}^{2−} (a q)$

(d) $H_{2} O (l) ⇌ H^{+} (a q) + {OH}^{−} (a q) at 25 °C$

16.5 Batteries and Fuel Cells

32.

Consider a battery made from one half-cell that consists of a copper electrode in 1 M CuSO₄ solution and another half-cell that consists of a lead electrode in 1 M Pb(NO₃)₂ solution.

(a) What is the standard cell potential for the battery?

(b) What are the reactions at the anode, cathode, and the overall reaction?

(c) Most devices designed to use dry-cell batteries can operate between 1.0 and 1.5 V. Could this cell be used to make a battery that could replace a dry-cell battery? Why or why not.

(d) Suppose sulfuric acid is added to the half-cell with the lead electrode and some PbSO₄(s) forms. Would the cell potential increase, decrease, or remain the same?

33.

Consider a battery with the overall reaction: $Cu (s) + 2 {Ag}^{+} (a q) ⟶ 2Ag (s) + {Cu}^{2+} (a q) .$

(a) What is the reaction at the anode and cathode?

(b) A battery is “dead” when its cell potential is zero. What is the value of Q when this battery is dead?

(c) If a particular dead battery was found to have [Cu²⁺] = 0.11 M, what was the concentration of silver ion?

34.

Why do batteries go dead, but fuel cells do not?

35.

Use the Nernst equation to explain the drop in voltage observed for some batteries as they discharge.

36.

Using the information thus far in this chapter, explain why battery-powered electronics perform poorly in low temperatures.

16.6 Corrosion

37.

Which member of each pair of metals is more likely to corrode (oxidize)?

(a) Mg or Ca

(b) Au or Hg

(c) Fe or Zn

(d) Ag or Pt

38.

Consider the following metals: Ag, Au, Mg, Ni, and Zn. Which of these metals could be used as a sacrificial anode in the cathodic protection of an underground steel storage tank? Steel is an alloy composed mostly of iron, so use −0.447 V as the standard reduction potential for steel.

39.

Aluminum $(E_{{Al}^{3+} /Al}^{°} = −2.07 V)$ is more easily oxidized than iron $(E_{{Fe}^{3+} /Fe}^{°} = −0.477 V),$ and yet when both are exposed to the environment, untreated aluminum has very good corrosion resistance while the corrosion resistance of untreated iron is poor. What might explain this observation?

40.

If a sample of iron and a sample of zinc come into contact, the zinc corrodes but the iron does not. If a sample of iron comes into contact with a sample of copper, the iron corrodes but the copper does not. Explain this phenomenon.

41.

Suppose you have three different metals, A, B, and C. When metals A and B come into contact, B corrodes and A does not corrode. When metals A and C come into contact, A corrodes and C does not corrode. Based on this information, which metal corrodes and which metal does not corrode when B and C come into contact?

42.

Why would a sacrificial anode made of lithium metal be a bad choice

16.7 Electrolysis

43.

If a 2.5 A current flows through a circuit for 35 minutes, how many coulombs of charge moved through the circuit?

44.

For the scenario in the previous question, how many electrons moved through the circuit?

45.

Write the half-reactions and cell reaction occurring during electrolysis of each molten salt below.

(a) CaCl₂

(b) LiH

(c) AlCl₃

(d) CrBr₃

46.

What mass of each product is produced in each of the electrolytic cells of the previous problem if a total charge of 3.33 $\times$ 10⁵ C passes through each cell?

47.

How long would it take to reduce 1 mole of each of the following ions using the current indicated?

(a) Al³⁺, 1.234 A

(b) Ca²⁺, 22.2 A

(c) Cr⁵⁺, 37.45 A

(d) Au³⁺, 3.57 A

48.

A current of 2.345 A passes through the cell shown in Figure 16.19 for 45 minutes. What is the volume of the hydrogen collected at room temperature if the pressure is exactly 1 atm? (Hint: Is hydrogen the only gas present above the water?)

49.

An irregularly shaped metal part made from a particular alloy was galvanized with zinc using a Zn(NO₃)₂ solution. When a current of 2.599 A was used, it took exactly 1 hour to deposit a 0.01123-mm layer of zinc on the part. What was the total surface area of the part? The density of zinc is 7.140 g/cm³.

License

Icon for the Creative Commons Attribution 4.0 International License

Key Equations

Summaries

16.1 Review of Redox Chemistry

16.2 Galvanic Cells

16.3 Electrode and Cell Potentials

16.4 Potential, Free Energy, and Equilibrium

16.5 Batteries and Fuel Cells

16.6 Corrosion

16.7Electrolysis

Exercises

16.1 Review of Redox Chemistry

16.2 Galvanic Cells

16.3 Electrode and Cell Potentials

16.4 Potential, Free Energy, and Equilibrium

16.5 Batteries and Fuel Cells

16.6 Corrosion

16.7 Electrolysis

License

Share This Book