20.E: Exercises

20.1: Electrode Potentials and their Measurement

Conceptual Problems

1. Is \(2NaOH_{(aq)} + H_2SO_{4(aq)} \rightarrow Na_2SO_{4(aq)} + 2H_2O_{(l)}\) an oxidation–reduction reaction? Why or why not?
2. If two half-reactions are physically separated, how is it possible for a redox reaction to occur? What is the name of the apparatus in which two half-reactions are carried out simultaneously?
3. What is the difference between a galvanic cell and an electrolytic cell? Which would you use to generate electricity?
4. What is the purpose of a salt bridge in a galvanic cell? Is it always necessary to use a salt bridge in a galvanic cell?
5. One criterion for a good salt bridge is that it contains ions that have similar rates of diffusion in aqueous solution, as K⁺ and Cl⁻ ions do. What would happen if the diffusion rates of the anions and cations differed significantly?
6. It is often more accurate to measure the potential of a redox reaction by immersing two electrodes in a single beaker rather than in two beakers. Why?

Conceptual Answer

5. A large difference in cation/anion diffusion rates would increase resistance in the salt bridge and limit electron flow through the circuit.

1. Numerical Problems

1. Copper(I) sulfate forms a bright blue solution in water. If a piece of zinc metal is placed in a beaker of aqueous CuSO₄ solution, the blue color fades with time, the zinc strip begins to erode, and a black solid forms around the zinc strip. What is happening? Write half-reactions to show the chemical changes that are occurring. What will happen if a piece of copper metal is placed in a colorless aqueous solution of \(ZnCl_2\)?
2. Consider the following spontaneous redox reaction: NO₃⁻(aq) + H⁺(aq) + SO₃²⁻(aq) → SO₄²⁻(aq) + HNO₂(aq).

1. Write the two half-reactions for this overall reaction.
2. If the reaction is carried out in a galvanic cell using an inert electrode in each compartment, which electrode corresponds to which half-reaction?
3. Which electrode is negatively charged, and which is positively charged?

3. The reaction Pb(s) + 2VO²⁺(aq) + 4H⁺(aq) → Pb²⁺(aq) + 2V³⁺(aq) + 2H₂O(l) occurs spontaneously.

1. Write the two half-reactions for this redox reaction.
2. If the reaction is carried out in a galvanic cell using an inert electrode in each compartment, which reaction occurs at the cathode and which occurs at the anode?
3. Which electrode is positively charged, and which is negatively charged?

4. Phenolphthalein is an indicator that turns pink under basic conditions. When an iron nail is placed in a gel that contains [Fe(CN)₆]³⁻, the gel around the nail begins to turn pink. What is occurring? Write the half-reactions and then write the overall redox reaction.

5. Sulfate is reduced to HS⁻ in the presence of glucose, which is oxidized to bicarbonate. Write the two half-reactions corresponding to this process. What is the equation for the overall reaction?

6. Write the spontaneous half-reactions and the overall reaction for each proposed cell diagram. State which half-reaction occurs at the anode and which occurs at the cathode.

1. Pb(s)∣PbSO₄(s)∣SO₄²⁻(aq)∥Cu²⁺(aq)∣Cu(s)
2. Hg(l)∣Hg₂Cl₂(s)∣Cl⁻(aq) ∥ Cd²⁺(aq)∣Cd(s)

7. For each galvanic cell represented by these cell diagrams, determine the spontaneous half-reactions and the overall reaction. Indicate which reaction occurs at the anode and which occurs at the cathode.

1. Zn(s)∣Zn²⁺(aq) ∥ H⁺(aq)∣H₂(g), Pt(s)
2. Ag(s)∣AgCl(s)∣Cl⁻(aq) ∥ H⁺(aq)∣H₂(g)∣Pt(s)
3. Pt(s)∣H₂(g)∣H⁺(aq) ∥ Fe²⁺(aq), Fe³⁺(aq)∣Pt(s)

8. For each redox reaction, write the half-reactions and draw the cell diagram for a galvanic cell in which the overall reaction occurs spontaneously. Identify each electrode as either positive or negative.

1. Ag(s) + Fe³⁺(aq) → Ag⁺(aq) + Fe²⁺(aq)
2. Fe³⁺(aq) + 1/2H₂(g) → Fe²⁺(aq) + H⁺(aq)

9. Write the half-reactions for each overall reaction, decide whether the reaction will occur spontaneously, and construct a cell diagram for a galvanic cell in which a spontaneous reaction will occur.

1. 2Cl⁻(aq) + Br₂(l) → Cl₂(g) + 2Br⁻(aq)
2. 2NO₂(g) + 2OH⁻(aq) → NO₂⁻(aq) + NO₃⁻(aq) + H₂O(l)
3. 2H₂O(l) + 2Cl⁻(aq) → H₂(g) + Cl₂(g) + 2OH⁻(aq)
4. C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g)

10. Write the half-reactions for each overall reaction, decide whether the reaction will occur spontaneously, and construct a cell diagram for a galvanic cell in which a spontaneous reaction will occur.

1. Co(s) + Fe²⁺(aq) → Co²⁺(aq) + Fe(s)
2. O₂(g) + 4H⁺(aq) + 4Fe²⁺(aq) → 2H₂O(l) + 4Fe³⁺(aq)
3. 6Hg²⁺(aq) + 2NO₃⁻(aq) + 8H⁺ → 3Hg₂²⁺(aq) + 2NO(g) + 4H₂O(l)
4. CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

Numerical Answers

reduction: SO₄²⁻(aq) + 9H⁺(aq) + 8e⁻ → HS⁻(aq) + 4H₂O(l)

oxidation: C₆H₁₂O₆(aq) + 12H₂O(l) → 6HCO₃⁻(g) + 30H⁺(aq) + 24e⁻

overall: C₆H₁₂O₆(aq) + 3SO₄²⁻(aq) → 6HCO₃⁻(g) + 3H⁺(aq) + 3HS⁻(aq)

1. reduction: 2H⁺(aq) + 2e⁻ → H₂(aq); cathode;

oxidation: Zn(s) → Zn²⁺(aq) + 2e⁻; anode;

overall: Zn(s) + 2H⁺(aq) → Zn²⁺(aq) + H₂(aq)

2. reduction: AgCl(s) + e⁻ → Ag(s) + Cl⁻(aq); cathode;

oxidation: H₂(g) → 2H⁺(aq) + 2e⁻; anode;

overall: AgCl(s) + H₂(g) → 2H⁺(aq) + Ag(s) + Cl⁻(aq)

3. reduction: Fe³⁺(aq) + e⁻ → Fe²⁺(aq); cathode;

oxidation: H₂(g) → 2H⁺(aq) + 2e⁻; anode;

overall: 2Fe³⁺(aq) + H₂(g) → 2H⁺(aq) + 2Fe²⁺(aq)

20.2: Standard Electrode Potentials

Conceptual Problems

1. Is a hydrogen electrode chemically inert? What is the major disadvantage to using a hydrogen electrode?
2. List two factors that affect the measured potential of an electrochemical cell and explain their impact on the measurements.
3. What is the relationship between electron flow and the potential energy of valence electrons? If the valence electrons of substance A have a higher potential energy than those of substance B, what is the direction of electron flow between them in a galvanic cell?
4. If the components of a galvanic cell include aluminum and bromine, what is the predicted direction of electron flow? Why?
5. Write a cell diagram representing a cell that contains the Ni/Ni²⁺ couple in one compartment and the SHE in the other compartment. What are the values of E°_cathode, E°_anode, and E°_cell?
6. Explain why E° values are independent of the stoichiometric coefficients in the corresponding half-reaction.
7. Identify the oxidants and the reductants in each redox reaction.

1. Cr(s) + Ni²⁺(aq) → Cr²⁺(aq) + Ni(s)
2. Cl₂(g) + Sn²⁺(aq) → 2Cl⁻(aq) + Sn⁴⁺(aq)
3. H₃AsO₄(aq) + 8H⁺(aq) + 4Zn(s) → AsH₃(g) + 4H₂O(l) + 4Zn²⁺(aq)
4. 2NO₂(g) + 2OH⁻(aq) → NO₂⁻(aq) + NO₃⁻(aq) + H₂O(l)

8. Identify the oxidants and the reductants in each redox reaction.

1. Br₂(l) + 2I⁻(aq) → 2Br⁻(aq) + I₂(s)
2. Cu²⁺(aq) + 2Ag(s) → Cu(s) + 2Ag⁺(aq)
3. H⁺(aq) + 2MnO₄⁻(aq) + 5H₂SO₃(aq) → 2Mn²⁺(aq) + 3H₂O(l) + 5HSO₄⁻(aq)
4. IO₃⁻(aq) + 5I⁻(aq) + 6H⁺(aq) → 3I₂(s) + 3H₂O(l)

9. All reference electrodes must conform to certain requirements. List the requirements and explain their significance.

10. For each application, describe the reference electrode you would use and explain why. In each case, how would the measured potential compare with the corresponding E°?

1. measuring the potential of a Cl⁻/Cl₂ couple
2. measuring the pH of a solution
3. measuring the potential of a MnO₄⁻/Mn²⁺ couple

Conceptual Answers

5. Ni(s)∣Ni²⁺(aq)∥H⁺(aq, 1 M)∣H₂(g, 1 atm)∣Pt(s)

\(E^\circ_{\textrm{anode}} \\ E^\circ_{\textrm{cathode}} \\ E^\circ_{\textrm{cell}}\)

\( \mathrm{Ni^{2+}(aq)}+\mathrm{2e^-}\rightarrow\mathrm{Ni(s)};\;-\textrm{0.257 V} \\ \mathrm{2H^+(aq)}+\mathrm{2e^-}\rightarrow\mathrm{H_2(g)};\textrm{ 0.000 V} \\ \mathrm{2H^+(aq)}+\mathrm{Ni(s)}\rightarrow\mathrm{H_2(g)}+\mathrm{Ni^{2+}(aq)};\textrm{ 0.257 V} \)

1. oxidant: Ni²⁺(aq); reductant: Cr(s)
2. oxidant: Cl₂(g); reductant: Sn²⁺(aq)
3. oxidant: H₃AsO₄(aq); reductant: Zn(s)
4. oxidant: NO₂(g); reductant: NO₂(g)

Numerical Problems

1. Draw the cell diagram for a galvanic cell with an SHE and a copper electrode that carries out this overall reaction: H₂(g) + Cu²⁺(aq) → 2H⁺(aq) + Cu(s).
2. Draw the cell diagram for a galvanic cell with an SHE and a zinc electrode that carries out this overall reaction: Zn(s) + 2H⁺(aq) → Zn²⁺(aq) + H₂(g).
3. Balance each reaction and calculate the standard electrode potential for each. Be sure to include the physical state of each product and reactant.

1. Cl₂(g) + H₂(g) → 2Cl⁻(aq) + 2H⁺(aq)
2. Br₂(aq) + Fe²⁺(aq) → 2Br⁻(aq) + Fe³⁺(aq)
3. Fe³⁺(aq) + Cd(s) → Fe²⁺(aq) + Cd²⁺(aq)

4. Balance each reaction and calculate the standard reduction potential for each. Be sure to include the physical state of each product and reactant.

1. Cu⁺(aq) + Ag⁺(aq) → Cu²⁺(aq) + Ag(s)
2. Sn(s) + Fe³⁺(aq) → Sn²⁺(aq) + Fe²⁺(aq)
3. Mg(s) + Br₂(l) → 2Br⁻(aq) + Mg²⁺(aq)

5. Write a balanced chemical equation for each redox reaction.

1. H₂PO₂⁻(aq) + SbO₂⁻(aq) → HPO₃²⁻(aq) + Sb(s) in basic solution
2. HNO₂(aq) + I⁻(aq) → NO(g) + I₂(s) in acidic solution
3. N₂O(g) + ClO⁻(aq) → Cl⁻(aq) + NO₂⁻(aq) in basic solution
4. Br₂(l) → Br⁻(aq) + BrO₃⁻(aq) in basic solution
5. Cl(CH₂)₂OH(aq) + K₂Cr₂O₇(aq) → ClCH₂CO₂H(aq) + Cr³⁺(aq) in acidic solution

6. Write a balanced chemical equation for each redox reaction.

1. I⁻(aq) + HClO₂(aq) → IO₃⁻(aq) + Cl₂(g) in acidic solution
2. Cr²⁺(aq) + O₂(g) → Cr³⁺(aq) + H₂O(l) in acidic solution
3. CrO₂⁻(aq) + ClO⁻(aq) → CrO₄²⁻(aq) + Cl⁻(aq) in basic solution
4. S(s) + HNO₂(aq) → H₂SO₃(aq) + N₂O(g) in acidic solution
5. F(CH₂)₂OH(aq) + K₂Cr₂O₇(aq) → FCH₂CO₂H(aq) + Cr³⁺(aq) in acidic solution

7. The standard cell potential for the oxidation of Pb to Pb²⁺ with the concomitant reduction of Cu⁺ to Cu is 0.39 V. You know that E° for the Pb²⁺/Pb couple is −0.13 V. What is E° for the Cu⁺/Cu couple?

8. You have built a galvanic cell similar to the one in Figure 19.7 using an iron nail, a solution of FeCl₂, and an SHE. When the cell is connected, you notice that the iron nail begins to corrode. What else do you observe? Under standard conditions, what is E_cell?

9. Carbon is used to reduce iron ore to metallic iron. The overall reaction is as follows:

2Fe₂O₃•xH₂O(s) + 3C(s) → 4Fe(l) + 3CO₂(g) + 2xH₂O(g)

Write the two half-reactions for this overall reaction.

10. Will each reaction occur spontaneously under standard conditions?

1. Cu(s) + 2H⁺(aq) → Cu²⁺(aq) + H₂(g)
2. Zn²⁺(aq) + Pb(s) → Zn(s) + Pb²⁺(aq)

11. Each reaction takes place in acidic solution. Balance each reaction and then determine whether it occurs spontaneously as written under standard conditions.

1. Se(s) + Br₂(l) → H₂SeO₃(aq) + Br⁻(aq)
2. NO₃⁻(aq) + S(s) → HNO₂(aq) + H₂SO₃(aq)
3. Fe³⁺(aq) + Cr³⁺(aq) → Fe²⁺(aq) + Cr₂O₇²⁻(aq)

12. Calculate E°_cell and ΔG° for the redox reaction represented by the cell diagram Pt(s)∣Cl₂(g, 1 atm)∥ZnCl₂(aq, 1 M)∣Zn(s). Will this reaction occur spontaneously?

13. If you place Zn-coated (galvanized) tacks in a glass and add an aqueous solution of iodine, the brown color of the iodine solution fades to a pale yellow. What has happened? Write the two half-reactions and the overall balanced chemical equation for this reaction. What is E°_cell?

14. Your lab partner wants to recover solid silver from silver chloride by using a 1.0 M solution of HCl and 1 atm H₂ under standard conditions. Will this plan work?

Numerical Answers

1. Pt(s)∣H₂(g, 1 atm) | H⁺(aq, 1M)∥Cu²⁺(aq)∣Cu(s)

1. Cl₂(g) + H₂(g) → 2Cl⁻(aq) + 2H⁺(aq); E° = 1.358 V
2. Br₂(l) + 2Fe²⁺(aq) → 2Br⁻(aq) + 2Fe³⁺(aq); E° = 0.316 V
3. 2Fe³⁺(aq) + Cd(s) → 2Fe²⁺(aq) + Cd²⁺(aq); E° = 1.174 V

Conceptual Problems

1. The order of electrode potentials cannot always be predicted by ionization potentials and electron affinities. Why? Do you expect sodium metal to have a higher or a lower electrode potential than predicted from its ionization potential? What is its approximate electrode potential?
2. Without referring to tabulated data, of Br₂/Br⁻, Ca²⁺/Ca, O₂/OH⁻, and Al³⁺/Al, which would you expect to have the least negative electrode potential and which the most negative? Why?
3. Because of the sulfur-containing amino acids present in egg whites, eating eggs with a silver fork will tarnish the fork. As a chemist, you have all kinds of interesting cleaning products in your cabinet, including a 1 M solution of oxalic acid (H₂C₂O₄). Would you choose this solution to clean the fork that you have tarnished from eating scrambled eggs?
4. The electrode potential for the reaction Cu²⁺(aq) + 2e⁻ → Cu(s) is 0.34 V under standard conditions. Is the potential for the oxidation of 0.5 mol of Cu equal to −0.34/2 V? Explain your answer.
5. Refer to Table 19.2 to predict
   1. Which species—Sn⁴⁺(aq), Cl⁻(aq), Ag⁺(aq), Cr³⁺(aq), and/or H₂O₂(aq)—can oxidize MnO₂(s) to MNO₄⁻ under standard conditions.
   2. Which species—Sn⁴⁺(aq), Cl⁻(aq), Ag⁺(aq), Cr³⁺(aq), and/or H₂O₂(aq)—is the strongest oxidizing agent in aqueous solution.

Conceptual Answer

3. No; E° = −0.691 V for Ag₂S(s) + 2e⁻ → Ag(s) + S²⁻(aq), which is too negative for Ag₂S to be spontaneously reduced by oxalic acid [E° = 0.49 V for 2CO₂(g) + 2H⁺(aq) + 2e⁻ → H₂C₂O₄(aq)]

5.

1. Ag⁺(aq); H₂O₂(aq)
2. H₂O₂(aq)

20.3: Ecell, ΔG, and K

Conceptual Problems

1. State whether you agree or disagree with this reasoning and explain your answer: Standard electrode potentials arise from the number of electrons transferred. The greater the number of electrons transferred, the greater the measured potential difference. If 1 mol of a substance produces 0.76 V when 2 mol of electrons are transferred—as in Zn(s) → Zn²⁺(aq) + 2e⁻—then 0.5 mol of the substance will produce 0.76/2 V because only 1 mol of electrons is transferred.
2. What is the relationship between the measured cell potential and the total charge that passes through a cell? Which of these is dependent on concentration? Which is dependent on the identity of the oxidant or the reductant? Which is dependent on the number of electrons transferred?
3. In the equation w_max = −nFE°_cell, which quantities are extensive properties and which are intensive properties?
4. For any spontaneous redox reaction, E is positive. Use thermodynamic arguments to explain why this is true.
5. State whether you agree or disagree with this statement and explain your answer: Electrochemical methods are especially useful in determining the reversibility or irreversibility of reactions that take place in a cell.
6. Although the sum of two half-reactions gives another half-reaction, the sum of the potentials of the two half-reactions cannot be used to obtain the potential of the net half-reaction. Why? When does the sum of two half-reactions correspond to the overall reaction? Why?
7. Occasionally, you will find high-quality electronic equipment that has its electronic components plated in gold. What is the advantage of this?
8. Blood analyzers, which measure pH, \(P_\mathrm{CO_2}\), and \(P_\mathrm{O_2}\), are frequently used in clinical emergencies. For example, blood \(P_\mathrm{CO_2}\) is measured with a pH electrode covered with a plastic membrane that is permeable to CO₂. Based on your knowledge of how electrodes function, explain how such an electrode might work. Hint: CO₂(g) + H₂O(l) → HCO₃⁻(aq) + H⁺(aq).
9. Concentration cells contain the same species in solution in two different compartments. Explain what produces a voltage in a concentration cell. When does V = 0 in such a cell?
10. Describe how an electrochemical cell can be used to measure the solubility of a sparingly soluble salt.

Conceptual Answers

3. extensive: w_max and n; intensive: E°_cell

7. Gold is highly resistant to corrosion because of its very positive reduction potential.

Numerical Problems

1. The chemical equation for the combustion of butane is as follows:

\(\mathrm{C_4H_{10}(g)+\frac{13}{2}O_2(g)\rightarrow4CO_2(g)+5H_2O(g)}\)

This reaction has ΔH° = −2877 kJ/mol. Calculate E°_cell and then determine ΔG°. Is this a spontaneous process? What is the change in entropy that accompanies this process at 298 K?

2. How many electrons are transferred during the reaction Pb(s) + Hg₂Cl₂(s) → PbCl₂(aq) + 2Hg(l)? What is the standard cell potential? Is the oxidation of Pb by Hg₂Cl₂ spontaneous? Calculate ΔG° for this reaction.

3. For the cell represented as Al(s)∣Al³⁺(aq)∥Sn²⁺(aq), Sn⁴⁺(aq)∣Pt(s), how many electrons are transferred in the redox reaction? What is the standard cell potential? Is this a spontaneous process? What is ΔG°?

4. Explain why the sum of the potentials for the half-reactions Sn²⁺(aq) + 2e⁻ → Sn(s) and Sn⁴⁺(aq) + 2e⁻ → Sn²⁺(aq) does not equal the potential for the reaction Sn⁴⁺(aq) + 4e⁻ → Sn(s). What is the net cell potential? Compare the values of ΔG° for the sum of the potentials and the actual net cell potential.

5. Based on Table 19.2 and Chapter 29, do you agree with the proposed potentials for the following half-reactions? Why or why not?

1. Cu²⁺(aq) + 2e⁻ → Cu(s), E° = 0.68 V
2. Ce⁴⁺(aq) + 4e⁻ → Ce(s), E° = −0.62 V

6. For each reaction, calculate E°_cell and then determine ΔG°. Indicate whether each reaction is spontaneous.

1. 2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g)
2. K₂S₂O₆(aq) + I₂(s) → 2KI(aq) + 2K₂SO₄(aq)
3. Sn(s) + CuSO₄(aq) → Cu(s) + SnSO₄(aq)

7. What is the standard change in free energy for the reaction between Ca²⁺ and Na(s) to give Ca(s) and Na⁺? Do the sign and magnitude of ΔG° agree with what you would expect based on the positions of these elements in the periodic table? Why or why not?

8. In acidic solution, permanganate (MnO₄⁻) oxidizes Cl⁻ to chlorine gas, and MnO₄⁻ is reduced to Mn²⁺(aq).

1. Write the balanced chemical equation for this reaction.
2. Determine E°_cell.
3. Calculate the equilibrium constant.

9. Potentiometric titrations are an efficient method for determining the endpoint of a redox titration. In such a titration, the potential of the solution is monitored as measured volumes of an oxidant or a reductant are added. Data for a typical titration, the potentiometric titration of Fe(II) with a 0.1 M solution of Ce(IV), are given in the following table. The starting potential has been arbitrarily set equal to zero because it is the change in potential with the addition of the oxidant that is important.

Titrant (mL)	E (mV)
2.00	50
6.00	100
9.00	255
10.00	960
11.00	1325
12.00	1625
14.00	1875

1. Write the balanced chemical equation for the oxidation of Fe²⁺ by Ce⁴⁺.
2. Plot the data and then locate the endpoint.
3. How many millimoles of Fe²⁺ did the solution being titrated originally contain?

10. The standard electrode potential (E°) for the half-reaction Ni²⁺(aq) + 2e⁻ → Ni(s) is −0.257 V. What pH is needed for this reaction to take place in the presence of 1.00 atm H₂(g) as the reductant if [Ni²⁺] is 1.00 M?

11. The reduction of Mn(VII) to Mn(s) by H₂(g) proceeds in five steps that can be readily followed by changes in the color of the solution. Here is the redox chemistry:

1. MnO₄−(aq) + e⁻ → MnO₄²⁻(aq); E° = +0.56 V (purple → dark green)
2. MnO₄²⁻(aq) + 2e⁻ + 4H⁺(aq) → MnO₂(s); E° = +2.26 V (dark green → dark brown solid)
3. MnO₂(s) + e⁻ + 4H⁺(aq) → Mn³⁺(aq); E° = +0.95 V (dark brown solid → red-violet)
4. Mn³⁺(aq) + e⁻ → Mn²⁺(aq); E° = +1.51 V (red-violet → pale pink)
5. Mn²⁺(aq) + 2e⁻ → Mn(s); E° = −1.18 V (pale pink → colorless)

1. Is the reduction of MnO₄⁻ to Mn³⁺(aq) by H₂(g) spontaneous under standard conditions? What is E°cell?
2. Is the reduction of Mn³⁺(aq) to Mn(s) by H₂(g) spontaneous under standard conditions? What is E°cell?

12. Mn(III) can disproportionate (both oxidize and reduce itself) by means of the following half-reactions:

Mn³⁺(aq) + e⁻ → Mn²⁺(aq) E°=1.51 V

Mn³⁺(aq) + 2H₂O(l) → MnO₂(s) + 4H⁺(aq) + e⁻ E°=0.95 V

1. What is E° for the disproportionation reaction?
2. Is disproportionation more or less thermodynamically favored at low pH than at pH 7.0? Explain your answer.
3. How could you prevent the disproportionation reaction from occurring?

13. For the reduction of oxygen to water, E° = 1.23 V. What is the potential for this half-reaction at pH 7.00? What is the potential in a 0.85 M solution of NaOH?

14. The biological molecule abbreviated as NADH (reduced nicotinamide adenine dinucleotide) can be formed by reduction of NAD⁺ (nicotinamide adenine dinucleotide) via the half-reaction NAD⁺ + H⁺ + 2e⁻ → NADH; E° = −0.32 V.

1. Would NADH be able to reduce acetate to pyruvate?
2. Would NADH be able to reduce pyruvate to lactate?
3. What potential is needed to convert acetate to lactate?

acetate + CO₂ + 2H⁺ +2e⁻ → pyruvate +H₂O E° = −0.70 V

pyruvate + 2H⁺ + 2e⁻ → lactate E° = −0.185 V

15. Given the following biologically relevant half-reactions, will FAD (flavin adenine dinucleotide), a molecule used to transfer electrons whose reduced form is FADH₂, be an effective oxidant for the conversion of acetaldehyde to acetate at pH 4.00?

acetate + 2H⁺ +2e⁻ → acetaldehyde + H₂O E° = −0.58 V

FAD + 2H⁺ +2e⁻ → FADH₂ E° = −0.18 V

16. Ideally, any half-reaction with E° > 1.23 V will oxidize water as a result of the half-reaction O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l).

1. Will FeO₄2⁻ oxidize water if the half-reaction for the reduction of Fe(VI) → Fe(III) is FeO₄²⁻(aq) + 8H⁺(aq) + 3e⁻ → Fe³⁺(aq) + 4H₂O; E° = 1.9 V?
2. What is the highest pH at which this reaction will proceed spontaneously if [Fe³⁺] = [FeO₄²⁻] = 1.0 M and \(P_\mathrm{O_2}\)= 1.0 atm?

17. Under acidic conditions, ideally any half-reaction with E° > 1.23 V will oxidize water via the reaction O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l).

1. Will aqueous acidic KMnO₄ evolve oxygen with the formation of MnO₂?
2. At pH 14.00, what is E° for the oxidation of water by aqueous KMnO₄ (1 M) with the formation of MnO₂?
3. At pH 14.00, will water be oxidized if you are trying to form MnO₂ from MnO₄²⁻ via the reaction 2MnO₄²⁻(aq) + 2H₂O(l) → 2MnO₂(s) + O₂(g) + 4OH⁻(aq)?

18. Complexing agents can bind to metals and result in the net stabilization of the complexed species. What is the net thermodynamic stabilization energy that results from using CN⁻ as a complexing agent for Mn³⁺/Mn²⁺?

Mn³⁺(aq) + e⁻ → Mn²⁺(aq) E° = 1.51 V

Mn(CN)₆³⁻(aq) + e⁻ → Mn(CN)₆⁴⁻ E° = −0.24 V

19. You have constructed a cell with zinc and lead amalgam electrodes described by the cell diagram Zn(Hg)(s)∣Zn(NO₃)₂(aq)∥Pb(NO₃)₂(aq)∣Pb(Hg)(s). If you vary the concentration of Zn(NO₃)₂ and measure the potential at different concentrations, you obtain the following data:

Zn(NO3)2 (M)	Ecell (V)
0.0005	0.7398
0.002	0.7221
0.01	0.7014

1. Write the half-reactions that occur in this cell.
2. What is the overall redox reaction?
3. What is E°_cell? What is ΔG° for the overall reaction?
4. What is the equilibrium constant for this redox reaction?

20. Hydrogen gas reduces Ni²⁺ according to the following reaction: Ni²⁺(aq) + H₂(g) → Ni(s) + 2H⁺(aq); E°_cell = −0.25 V; ΔH = 54 kJ/mol.
    1. What is K for this redox reaction?
    2. Is this reaction likely to occur?
    3. What conditions can be changed to increase the likelihood that the reaction will occur as written?
    4. Is the reaction more likely to occur at higher or lower pH?

21. The silver–silver bromide electrode has a standard potential of 0.07133 V. What is K_sp of AgBr?

Numerical Answers

3. 6e⁻; E°_cell = 1.813 V; the reaction is spontaneous; ΔG° = −525 kJ/mol Al.

13. yes; E° = 0.40 V

17. 1. yes; E° = 0.45 V
    2. 0.194 V
    3. yes; E° = 0.20 V

20.4: Ecell as a Function of Concentrations

Conceptual Problems

1. What advantage is there to using an alkaline battery rather than a Leclanché dry cell?
2. Why does the density of the fluid in lead–acid batteries drop when the battery is discharged?
3. What type of battery would you use for each application and why?

1. powering an electric motor scooter
2. a backup battery for a smartphone
3. powering an iPod

4. Why are galvanic cells used as batteries and fuel cells? What is the difference between a battery and a fuel cell? What is the advantage to using highly concentrated or solid reactants in a battery?

Conceptual Answer

1. lead storage battery
2. lithium–iodine battery
3. NiCad, NiMH, or lithium ion battery (rechargeable)

Numerical Problem

1. This reaction is characteristic of a lead storage battery:

Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(l)

If you have a battery with an electrolyte that has a density of 1.15 g/cm³ and contains 30.0% sulfuric acid by mass, is the potential greater than or less than that of the standard cell?

Numerica Answer

1. [H₂SO₄] = 3.52 M; E > E°

20.5: Batteries: Producing Electricity Through Chemical Reactions

20.6: Corrosion: Unwanted Voltaic Cells

20.7: Electrolysis: Causing Nonspontaneous Reactions to Occur

Conceptual Problems

1. Why might an electrochemical reaction that is thermodynamically favored require an overvoltage to occur?
2. How could you use an electrolytic cell to make quantitative comparisons of the strengths of various oxidants and reductants?
3. Why are mixtures of molten salts, rather than a pure salt, generally used during electrolysis?
4. Two solutions, one containing Fe(NO₃)₂·6H₂O and the other containing the same molar concentration of Fe(NO₃)₃·6H₂O, were electrolyzed under identical conditions. Which solution produced the most metal? Justify your answer.

Numerical Problems

1. The electrolysis of molten salts is frequently used in industry to obtain pure metals. How many grams of metal are deposited from these salts for each mole of electrons?
   1. AlCl₃
   2. MgCl₂
   3. FeCl₃

2. Electrolysis is the most direct way of recovering a metal from its ores. However, the Na⁺(aq)/Na(s), Mg²⁺(aq)/Mg(s), and Al³⁺(aq)/Al(s) couples all have standard electrode potentials (E°) more negative than the reduction potential of water at pH 7.0 (−0.42 V), indicating that these metals can never be obtained by electrolysis of aqueous solutions of their salts. Why? What reaction would occur instead?

3. What volume of chlorine gas at standard temperature and pressure is evolved when a solution of MgCl₂ is electrolyzed using a current of 12.4 A for 1.0 h?

4. What mass of copper metal is deposited if a 5.12 A current is passed through a Cu(NO₃)₂ solution for 1.5 h.

5. What mass of PbO₂ is reduced when a current of 5.0 A is withdrawn over a period of 2.0 h from a lead storage battery?

6. Electrolysis of Cr³⁺(aq) produces Cr²⁺(aq). If you had 500 mL of a 0.15 M solution of Cr³⁺(aq), how long would it take to reduce the Cr³⁺ to Cr²⁺ using a 0.158 A current?

7. Predict the products obtained at each electrode when aqueous solutions of the following are electrolyzed.
   1. AgNO₃
   2. RbI

8. Predict the products obtained at each electrode when aqueous solutions of the following are electrolyzed.
   1. MgBr₂
   2. Hg(CH₃CO₂)₂
   3. Al₂(SO₄)₃

Answers

3. 5.2 L

1. cathode: Ag(s); anode: O₂(g);
2. cathode: H₂(g); anode: I₂(s)

20.8: Industrial Electrolysis Processes

True or False:

1. The main product of the chlor-alkali process is NaCl.
2. A diaphragm cell yields the purest concentration of NaOH.
3. In a diaphragm cell, the oxidation of Cl^- ions occurs at the anode and the reduction of Na⁺ occurs at the cathode.
4. H₂ gas is a byproduct of the chlor-alkali process.
5. Electrorefining for copper is effective because out of the all of the metals in an ore, only copper is oxidized at the anode at low voltages.
6. A mercury cell uses mercury liquid as the cathode.
7. The chlor-alkali process is spontaneous.
8. A mercury cell requires a higher voltage and more energy than a diaphragm cell.
9. In a membrane cell, all ions can freely be exchanged between the membrane.
10. The reaction between NaOH and Cl₂ gas is necessary for the chlor-alkali process.

Outside Links

• Electrolysis: Industrial Uses (Wikipedia)
• Industrial Electrolysis and Electrochemical Engineering (electrochem.org pdf)
• Wagenknecht, John H. "Industrial organic electrosynthesis (SOA-Electrochemistry)." J. Chem. Educ. 1983, 60, 271.

Check Your Understanding: Answers

1. False - The chlor-alkali process is the electrolysis of NaCl, not the electrosynthesis. NaCl is one of the main reactants of the chlor-alkali process
2. False - A diaphragm cell yields the most impure NaOH. The mercury cell yields purer NaOH, followed by the membrane cell with the purest.
3. False - Due to the high voltage required to reduce Na ions (meaning the large negative standard electrode reduction potential of sodium), the reduction of water occurs instead.
4. True - Yes, H₂ gas is produced at the cathode while Cl₂ gas is produced at the anode.
5. False - Though Au, Ag and Pt are not oxidized, Sb, Bi and Sn are oxidized but are precipitated as they form hydroxides and oxides. Fe, Ni, Co and Zn are oxidized as well, but they are dissolved in water. Thus, even though copper is the only pure metal solid we have left, other impurities are oxidized as well.
6. True - Liquid mercury at the bottom of the tank acts as the cathode. More mercury is constantly cycled back into the tank as amalgam is treated with water.
7. False - Electrosynthesis requires energy.
8. True - A mercury cell needs 3400 kWh/ton Cl₂ opposed to 2500 in a diaphragm cell.
9. False - In a membrane cell, only cations can pass through the membrane into the cathode. This explains why the NaOH on the cathode side has so little chlorine ion impurities.
10. False - If Cl₂ and NaOH come into contact, Cl₂ turns into ClO^-, ClO₃^-, Cl ions. This is not desirable, so the difference in solution levels is used to prevent backflow of NaOH into the anode side.