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Chemistry: Atoms First

16.3 Standard Reduction Potentials

Chemistry: Atoms First16.3 Standard Reduction Potentials
  1. Preface
  2. 1 Essential Ideas
    1. Introduction
    2. 1.1 Chemistry in Context
    3. 1.2 Phases and Classification of Matter
    4. 1.3 Physical and Chemical Properties
    5. 1.4 Measurements
    6. 1.5 Measurement Uncertainty, Accuracy, and Precision
    7. 1.6 Mathematical Treatment of Measurement Results
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  3. 2 Atoms, Molecules, and Ions
    1. Introduction
    2. 2.1 Early Ideas in Atomic Theory
    3. 2.2 Evolution of Atomic Theory
    4. 2.3 Atomic Structure and Symbolism
    5. 2.4 Chemical Formulas
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  4. 3 Electronic Structure and Periodic Properties of Elements
    1. Introduction
    2. 3.1 Electromagnetic Energy
    3. 3.2 The Bohr Model
    4. 3.3 Development of Quantum Theory
    5. 3.4 Electronic Structure of Atoms (Electron Configurations)
    6. 3.5 Periodic Variations in Element Properties
    7. 3.6 The Periodic Table
    8. 3.7 Molecular and Ionic Compounds
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  5. 4 Chemical Bonding and Molecular Geometry
    1. Introduction
    2. 4.1 Ionic Bonding
    3. 4.2 Covalent Bonding
    4. 4.3 Chemical Nomenclature
    5. 4.4 Lewis Symbols and Structures
    6. 4.5 Formal Charges and Resonance
    7. 4.6 Molecular Structure and Polarity
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  6. 5 Advanced Theories of Bonding
    1. Introduction
    2. 5.1 Valence Bond Theory
    3. 5.2 Hybrid Atomic Orbitals
    4. 5.3 Multiple Bonds
    5. 5.4 Molecular Orbital Theory
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  7. 6 Composition of Substances and Solutions
    1. Introduction
    2. 6.1 Formula Mass and the Mole Concept
    3. 6.2 Determining Empirical and Molecular Formulas
    4. 6.3 Molarity
    5. 6.4 Other Units for Solution Concentrations
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  8. 7 Stoichiometry of Chemical Reactions
    1. Introduction
    2. 7.1 Writing and Balancing Chemical Equations
    3. 7.2 Classifying Chemical Reactions
    4. 7.3 Reaction Stoichiometry
    5. 7.4 Reaction Yields
    6. 7.5 Quantitative Chemical Analysis
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  9. 8 Gases
    1. Introduction
    2. 8.1 Gas Pressure
    3. 8.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
    4. 8.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
    5. 8.4 Effusion and Diffusion of Gases
    6. 8.5 The Kinetic-Molecular Theory
    7. 8.6 Non-Ideal Gas Behavior
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  10. 9 Thermochemistry
    1. Introduction
    2. 9.1 Energy Basics
    3. 9.2 Calorimetry
    4. 9.3 Enthalpy
    5. 9.4 Strengths of Ionic and Covalent Bonds
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  11. 10 Liquids and Solids
    1. Introduction
    2. 10.1 Intermolecular Forces
    3. 10.2 Properties of Liquids
    4. 10.3 Phase Transitions
    5. 10.4 Phase Diagrams
    6. 10.5 The Solid State of Matter
    7. 10.6 Lattice Structures in Crystalline Solids
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  12. 11 Solutions and Colloids
    1. Introduction
    2. 11.1 The Dissolution Process
    3. 11.2 Electrolytes
    4. 11.3 Solubility
    5. 11.4 Colligative Properties
    6. 11.5 Colloids
    7. Key Terms
    8. Key Equations
    9. Summary
    10. Exercises
  13. 12 Thermodynamics
    1. Introduction
    2. 12.1 Spontaneity
    3. 12.2 Entropy
    4. 12.3 The Second and Third Laws of Thermodynamics
    5. 12.4 Free Energy
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  14. 13 Fundamental Equilibrium Concepts
    1. Introduction
    2. 13.1 Chemical Equilibria
    3. 13.2 Equilibrium Constants
    4. 13.3 Shifting Equilibria: Le Châtelier’s Principle
    5. 13.4 Equilibrium Calculations
    6. Key Terms
    7. Key Equations
    8. Summary
    9. Exercises
  15. 14 Acid-Base Equilibria
    1. Introduction
    2. 14.1 Brønsted-Lowry Acids and Bases
    3. 14.2 pH and pOH
    4. 14.3 Relative Strengths of Acids and Bases
    5. 14.4 Hydrolysis of Salt Solutions
    6. 14.5 Polyprotic Acids
    7. 14.6 Buffers
    8. 14.7 Acid-Base Titrations
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  16. 15 Equilibria of Other Reaction Classes
    1. Introduction
    2. 15.1 Precipitation and Dissolution
    3. 15.2 Lewis Acids and Bases
    4. 15.3 Multiple Equilibria
    5. Key Terms
    6. Key Equations
    7. Summary
    8. Exercises
  17. 16 Electrochemistry
    1. Introduction
    2. 16.1 Balancing Oxidation-Reduction Reactions
    3. 16.2 Galvanic Cells
    4. 16.3 Standard Reduction Potentials
    5. 16.4 The Nernst Equation
    6. 16.5 Batteries and Fuel Cells
    7. 16.6 Corrosion
    8. 16.7 Electrolysis
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  18. 17 Kinetics
    1. Introduction
    2. 17.1 Chemical Reaction Rates
    3. 17.2 Factors Affecting Reaction Rates
    4. 17.3 Rate Laws
    5. 17.4 Integrated Rate Laws
    6. 17.5 Collision Theory
    7. 17.6 Reaction Mechanisms
    8. 17.7 Catalysis
    9. Key Terms
    10. Key Equations
    11. Summary
    12. Exercises
  19. 18 Representative Metals, Metalloids, and Nonmetals
    1. Introduction
    2. 18.1 Periodicity
    3. 18.2 Occurrence and Preparation of the Representative Metals
    4. 18.3 Structure and General Properties of the Metalloids
    5. 18.4 Structure and General Properties of the Nonmetals
    6. 18.5 Occurrence, Preparation, and Compounds of Hydrogen
    7. 18.6 Occurrence, Preparation, and Properties of Carbonates
    8. 18.7 Occurrence, Preparation, and Properties of Nitrogen
    9. 18.8 Occurrence, Preparation, and Properties of Phosphorus
    10. 18.9 Occurrence, Preparation, and Compounds of Oxygen
    11. 18.10 Occurrence, Preparation, and Properties of Sulfur
    12. 18.11 Occurrence, Preparation, and Properties of Halogens
    13. 18.12 Occurrence, Preparation, and Properties of the Noble Gases
    14. Key Terms
    15. Summary
    16. Exercises
  20. 19 Transition Metals and Coordination Chemistry
    1. Introduction
    2. 19.1 Occurrence, Preparation, and Properties of Transition Metals and Their Compounds
    3. 19.2 Coordination Chemistry of Transition Metals
    4. 19.3 Spectroscopic and Magnetic Properties of Coordination Compounds
    5. Key Terms
    6. Summary
    7. Exercises
  21. 20 Nuclear Chemistry
    1. Introduction
    2. 20.1 Nuclear Structure and Stability
    3. 20.2 Nuclear Equations
    4. 20.3 Radioactive Decay
    5. 20.4 Transmutation and Nuclear Energy
    6. 20.5 Uses of Radioisotopes
    7. 20.6 Biological Effects of Radiation
    8. Key Terms
    9. Key Equations
    10. Summary
    11. Exercises
  22. 21 Organic Chemistry
    1. Introduction
    2. 21.1 Hydrocarbons
    3. 21.2 Alcohols and Ethers
    4. 21.3 Aldehydes, Ketones, Carboxylic Acids, and Esters
    5. 21.4 Amines and Amides
    6. Key Terms
    7. Summary
    8. Exercises
  23. A | The Periodic Table
  24. B | Essential Mathematics
  25. C | Units and Conversion Factors
  26. D | Fundamental Physical Constants
  27. E | Water Properties
  28. F | Composition of Commercial Acids and Bases
  29. G | Standard Thermodynamic Properties for Selected Substances
  30. H | Ionization Constants of Weak Acids
  31. I | Ionization Constants of Weak Bases
  32. J | Solubility Products
  33. K | Formation Constants for Complex Ions
  34. L | Standard Electrode (Half-Cell) Potentials
  35. M | Half-Lives for Several Radioactive Isotopes
  36. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
    14. Chapter 14
    15. Chapter 15
    16. Chapter 16
    17. Chapter 17
    18. Chapter 18
    19. Chapter 19
    20. Chapter 20
    21. Chapter 21
  37. Index

Learning Objectives

By the end of this section, you will be able to:
  • Determine standard cell potentials for oxidation-reduction reactions
  • Use standard reduction potentials to determine the better oxidizing or reducing agent from among several possible choices

The cell potential in Figure 16.4 (+0.46 V) results from the difference in the electrical potentials for each electrode. While it is impossible to determine the electrical potential of a single electrode, we can assign an electrode the value of zero and then use it as a reference. The electrode chosen as the zero is shown in Figure 16.6 and is called the standard hydrogen electrode (SHE). The SHE consists of 1 atm of hydrogen gas bubbled through a 1 M HCl solution, usually at room temperature. Platinum, which is chemically inert, is used as the electrode. The reduction half-reaction chosen as the reference is

2H+(aq, 1M)+2eH2(g,1 atm)E°=0 V2H+(aq, 1M)+2eH2(g,1 atm)E°=0 V

E° is the standard reduction potential. The superscript “°” on the E denotes standard conditions (1 bar or 1 atm for gases, 1 M for solutes). This voltage is defined as zero for all temperatures.

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 grey square, labeled “P t electrode” at the bottom of the tube. 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 grey square 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 grey arrow 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 spheres which are labeled “P t electrode atoms.” On the grey atom surface, 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.” Beneath this atomic view is the label “Half-reaction at P t surface: 2 H superscript plus ( a q, 1 M ) plus 2 e superscript negative right pointing arrow H subscript 2 ( g, 1 a t m ).”
Figure 16.6 Hydrogen gas at 1 atm is bubbled through 1 M HCl solution. Platinum, which is inert to the action of the 1 M HCl, is used as the electrode. Electrons on the surface of the electrode combine with H+ in solution to produce hydrogen gas.

A galvanic cell consisting of a SHE and Cu2+/Cu half-cell can be used to determine the standard reduction potential for Cu2+ (Figure 16.7). In cell notation, the reaction is

Pt(s)H2(g,1 atm)H+(aq,1M)Cu2+(aq,1M)Cu(s)Pt(s)H2(g,1 atm)H+(aq,1M)Cu2+(aq,1M)Cu(s)

Electrons flow from the anode to the cathode. The reactions, which are reversible, are

Anode (oxidation):H2(g)2H+(aq) + 2eCathode (reduction):Cu2+(aq)+2eCu(s)¯Overall:Cu2+(aq)+H2(g)2H+(aq)+Cu(s)Anode (oxidation):H2(g)2H+(aq) + 2eCathode (reduction):Cu2+(aq)+2eCu(s)¯Overall:Cu2+(aq)+H2(g)2H+(aq)+Cu(s)

The standard cell potential, E°cell, can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is necessary because oxidation is the reverse of reduction. The minus sign is necessary because oxidation is the reverse of reduction.

Ecell°=Ecathode°Eanode°Ecell°=Ecathode°Eanode°
+0.34 V=ECu2+/Cu°EH+/H2°=ECu2+/Cu°0=ECu2+/Cu°+0.34 V=ECu2+/Cu°EH+/H2°=ECu2+/Cu°0=ECu2+/Cu°
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 grey plug 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 grey 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 grey 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 “H subscript 2 ( g ).” The beaker on the right has an orange-brown strip that is labeled “C u strip” 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 standard hydrogen electrode in the beaker on the left into the surrounding solution. The tip of this arrow is labeled “H plus.” An arrow points downward from the label “e superscript negative” on the C u strip in the beaker on the right. A second curved arrow extends from another “e superscript negative” label into the solution below toward the label “C u superscript 2 plus” in the solution. A third “e superscript negative” label positioned at the lower left edge of the C u strip has a curved arrow extending from it to the “C u superscript 2 plus” label in the solution. A curved arrow extends from this “C u superscript 2 plus” label to a “C u” label at the lower edge of the C u strip.
Figure 16.7 A galvanic cell can be used to determine the standard reduction potential of Cu2+.

Using the SHE as a reference, other standard reduction potentials can be determined. Consider the cell shown in Figure 16.8, where

Pt(s)H2(g,1 atm)H+(aq, 1M)Ag+(aq, 1M)Ag(s)Pt(s)H2(g,1 atm)H+(aq, 1M)Ag+(aq, 1M)Ag(s)

Electrons flow from left to right, and the reactions are

anode (oxidation):H2(g)2H+(aq)+2ecathode (reduction):2Ag+(aq)+2e2Ag(s)¯overall:2Ag+(aq)+H2(g)2H+(aq)+2Ag(s)anode (oxidation):H2(g)2H+(aq)+2ecathode (reduction):2Ag+(aq)+2e2Ag(s)¯overall:2Ag+(aq)+H2(g)2H+(aq)+2Ag(s)

The standard cell potential, E°cell, can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is needed because oxidation is the reverse of reduction.

Ecell°=Ecathode°Eanode°Ecell°=Ecathode°Eanode°
+0.80 V=EAg+/Ag°EH+/H2°=EAg+/Ag°0=EAg+/Ag°+0.80 V=EAg+/Ag°EH+/H2°=EAg+/Ag°0=EAg+/Ag°

It is important to note that the potential is not doubled for the cathode reaction.

The SHE is rather dangerous and rarely used in the laboratory. Its main significance is that it established the zero for standard reduction potentials. Once determined, standard reduction potentials can be used to determine the standard cell potential, Ecell°,Ecell°, for any cell. For example, for the cell shown in Figure 16.4,

Cu(s)Cu2+(aq,1M)Ag+(aq,1M)Ag(s)Cu(s)Cu2+(aq,1M)Ag+(aq,1M)Ag(s)
anode (oxidation):Cu(s)Cu2+(aq)+2ecathode (reduction):2Ag+(aq)+2e2Ag(s)¯overall:Cu(s)+2Ag+(aq)Cu2+(aq)+2Ag(s)anode (oxidation):Cu(s)Cu2+(aq)+2ecathode (reduction):2Ag+(aq)+2e2Ag(s)¯overall:Cu(s)+2Ag+(aq)Cu2+(aq)+2Ag(s)
Ecell°=Ecathode°Eanode°=EAg+/Ag°ECu2+/Cu°=0.80 V0.34 V=0.46 VEcell°=Ecathode°Eanode°=EAg+/Ag°ECu2+/Cu°=0.80 V0.34 V=0.46 V

Again, note that when calculating Ecell°,Ecell°, standard reduction potentials always remain the same even when a half-reaction is multiplied by a factor. Standard reduction potentials for selected reduction reactions are shown in Table 16.2. A more complete list is provided in Appendix L.

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 which is labeled “H N O subscript 3 ( a q ).” The beaker on the right contains a clear, colorless solution which is labeled “A g N O subscript 3 ( a q ).” A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram and is labeled “Salt bridge.” The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The label “2 N a superscript plus” appears on the upper right portion of the tube. A curved arrow extends from this label down and to the right. The label “2 N O subscript 3 superscript negative” appears on the upper left portion of the tube. A curved arrow extends from this label down and to the left. The beaker on the left has a glass tube partially submerged in the liquid. Bubbles are rising from the grey square, labeled “SHE anode” at the bottom of the tube. A curved arrow points up to the right. The labels “2 H superscript plus” and “2 N O subscript 3 superscript negative” appear on the liquid in the beaker. A black wire extends from the grey square up the interior of the tube through a small port at the top to a rectangle with a digital readout of “positive 0.80 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 “H subscript 2 ( g ).” The beaker on the right has a silver strip that is labeled “A g cathode.” 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. The solution in the beaker on the right has the labels “N O subscript 3 superscript negative” and “A g superscript plus” on the solution. A curved arrow extends from the A g superscript plus label to the A g cathode. Below the left beaker at the bottom of the diagram is the label “Oxidation half-reaction: H subscript 2 ( g ) right pointing arrow 2 H superscript plus ( a q ) plus 2 e superscript negative.” Below the right beaker at the bottom of the diagram is the label “Reduction half-reaction: 2 A g superscript plus ( a q ) right pointing arrow 2 A g ( s ).”
Figure 16.8 A galvanic cell can be used to determine the standard reduction potential of Ag+. The SHE on the left is the anode and assigned a standard reduction potential of zero.
Selected Standard Reduction Potentials at 25 °C
Half-Reaction E° (V)
F2(g)+2e2F(aq)F2(g)+2e2F(aq) +2.866
PbO2(s)+SO42−(aq)+4H+(aq)+2ePbSO4(s)+2H2O(l)PbO2(s)+SO42−(aq)+4H+(aq)+2ePbSO4(s)+2H2O(l) +1.69
MnO4(aq)+8H+(aq)+5eMn2+(aq)+4H2O(l)MnO4(aq)+8H+(aq)+5eMn2+(aq)+4H2O(l) +1.507
Au3+(aq)+3eAu(s)Au3+(aq)+3eAu(s) +1.498
Cl2(g)+2e2Cl(aq)Cl2(g)+2e2Cl(aq) +1.35827
O2(g)+4H+(aq)+4e2H2O(l)O2(g)+4H+(aq)+4e2H2O(l) +1.229
Pt2+(aq)+2ePt(s)Pt2+(aq)+2ePt(s) +1.20
Br2(aq)+2e2Br(aq)Br2(aq)+2e2Br(aq) +1.0873
Ag+(aq)+eAg(s)Ag+(aq)+eAg(s) +0.7996
Hg22+(aq)+2e2Hg(l)Hg22+(aq)+2e2Hg(l) +0.7973
Fe3+(aq)+eFe2+(aq)Fe3+(aq)+eFe2+(aq) +0.771
MnO4(aq)+2H2O(l)+3eMnO2(s)+4OH(aq)MnO4(aq)+2H2O(l)+3eMnO2(s)+4OH(aq) +0.558
I2(s)+2e2I(aq)I2(s)+2e2I(aq) +0.5355
NiO2(s)+2H2O(l)+2eNi(OH)2(s)+2OH(aq)NiO2(s)+2H2O(l)+2eNi(OH)2(s)+2OH(aq) +0.49
Cu2+(aq)+2eCu(s)Cu2+(aq)+2eCu(s) +0.34
Hg2Cl2(s)+2e2Hg(l)+2Cl(aq)Hg2Cl2(s)+2e2Hg(l)+2Cl(aq) +0.26808
AgCl(s)+eAg(s)+Cl(aq)AgCl(s)+eAg(s)+Cl(aq) +0.22233
Sn4+(aq)+2eSn2+(aq)Sn4+(aq)+2eSn2+(aq) +0.151
2H+(aq)+2eH2(g)2H+(aq)+2eH2(g) 0.00
Pb2+(aq)+2ePb(s)Pb2+(aq)+2ePb(s) −0.1262
Sn2+(aq)+2eSn(s)Sn2+(aq)+2eSn(s) −0.1375
Ni2+(aq)+2eNi(s)Ni2+(aq)+2eNi(s) −0.257
Co2+(aq)+2eCo(s)Co2+(aq)+2eCo(s) −0.28
PbSO4(s)+2ePb(s)+SO42−(aq)PbSO4(s)+2ePb(s)+SO42−(aq) −0.3505
Cd2+(aq)+2eCd(s)Cd2+(aq)+2eCd(s) −0.4030
Fe2+(aq)+2eFe(s)Fe2+(aq)+2eFe(s) −0.447
Cr3+(aq)+3eCr(s)Cr3+(aq)+3eCr(s) −0.744
Mn2+(aq)+2eMn(s)Mn2+(aq)+2eMn(s) −1.185
Zn(OH)2(s)+2eZn(s)+2OH(aq)Zn(OH)2(s)+2eZn(s)+2OH(aq) −1.245
Zn2+(aq)+2eZn(s)Zn2+(aq)+2eZn(s) −0.7618
Al3+(aq)+3eAl(s)Al3+(aq)+3eAl(s) −1.662
Mg2(aq)+2eMg(s)Mg2(aq)+2eMg(s) −2.372
Na+(aq)+eNa(s)Na+(aq)+eNa(s) −2.71
Ca2+(aq)+2eCa(s)Ca2+(aq)+2eCa(s) −2.868
Ba2+(aq)+2eBa(s)Ba2+(aq)+2eBa(s) −2.912
K+(aq)+eK(s)K+(aq)+eK(s) −2.931
Li+(aq)+eLi(s)Li+(aq)+eLi(s) −3.04
Table 16.2

Tables like this make it possible to determine the standard cell potential for many oxidation-reduction reactions.

Example 16.4

Cell Potentials from Standard Reduction Potentials

What is the standard cell potential for a galvanic cell that consists of Au3+/Au and Ni2+/Ni half-cells? Identify the oxidizing and reducing agents.

Solution

Using Table 16.2, the reactions involved in the galvanic cell, both written as reductions, are
Au3+(aq)+3eAu(s)EAu3+/Au°=+1.498 VAu3+(aq)+3eAu(s)EAu3+/Au°=+1.498 V
Ni2+(aq)+2eNi(s)ENi2+/Ni°=−0.257 VNi2+(aq)+2eNi(s)ENi2+/Ni°=−0.257 V

Galvanic cells have positive cell potentials, and all the reduction reactions are reversible. The reaction at the anode will be the half-reaction with the smaller or more negative standard reduction potential. Reversing the reaction at the anode (to show the oxidation) but not its standard reduction potential gives:

Anode (oxidation):Ni(s)Ni2+(aq)+2eEanode°=ENi2+/Ni°=−0.257 VCathode (reduction): Au3+(aq)+3eAu(s)Ecathode°=EAu3+/Au°=+1.498 VAnode (oxidation):Ni(s)Ni2+(aq)+2eEanode°=ENi2+/Ni°=−0.257 VCathode (reduction): Au3+(aq)+3eAu(s)Ecathode°=EAu3+/Au°=+1.498 V

The least common factor is six, so the overall reaction is

3Ni(s)+2Au3+(aq)3Ni2+(aq)+2Au(s)3Ni(s)+2Au3+(aq)3Ni2+(aq)+2Au(s)

The reduction potentials are not scaled by the stoichiometric coefficients when calculating the cell potential, and the unmodified standard reduction potentials must be used.

Ecell°=Ecathode°Eanode°=1.498 V(−0.257 V)=1.755 VEcell°=Ecathode°Eanode°=1.498 V(−0.257 V)=1.755 V

From the half-reactions, Ni is oxidized, so it is the reducing agent, and Au3+ is reduced, so it is the oxidizing agent.

Check Your Learning

A galvanic cell consists of a Mg electrode in 1 M Mg(NO3)2 solution and a Ag electrode in 1 M AgNO3 solution. Calculate the standard cell potential at 25 °C.

Answer:

Mg(s)+2Ag+(aq)Mg2+(aq)+2Ag(s)Ecell°=0.7996 V(−2.372 V)=3.172 VMg(s)+2Ag+(aq)Mg2+(aq)+2Ag(s)Ecell°=0.7996 V(−2.372 V)=3.172 V

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