The percent efficiency of a fuel cell is defined as ΔG°/ΔH° × 100. If hydrogen gas were distributed for domestic and industrial use from a central electrolysis facility, the gas could be piped to consumers much as methane is piped today. Conventional nuclear power stations have an efficiency of 25%–30%. Use tabulated data to calculate the efficiency of a fuel cell in which the reaction H₂(g) + 1/2O₂(g) → H₂O(g) occurs under standard conditions.

♦ You are about to run an organic reaction and need a strong oxidant. Although you have BrO₃⁻ at your disposal, you prefer to use MnO₄⁻. You notice you also have MnO₂ in the lab.

1. Predict whether you will be able to synthesize MnO₄⁻ using the materials available to you.
2. Write the overall reaction for the synthesis of MnO₄⁻.
3. What is ΔG° for this reaction?
4. What is the equilibrium constant?

It is possible to construct a galvanic cell using amalgams as electrodes, each containing different concentrations of the same metal. One example is the Pb(Hg)(a₁)∣PbSO₄(soln)∣Pb(Hg)(a₂) cell, in which a₁ and a₂ represent the concentrations of lead in the amalgams. No chemical change occurs; rather, the reaction transfers lead from one amalgam to the other, thus altering the Pb concentration in both amalgams. Write an equation for E for such a cell.

♦ The oldest known metallurgical artifacts are beads made from alloys of copper, produced in Egypt, Mesopotamia, and the Indus Valley around 3000 BC. To determine the copper content of alloys such as brass, a sample is dissolved in nitric acid to obtain Cu²⁺(aq), and then the pH is adjusted to 7.0. Excess KI is used to reduce the Cu²⁺ to Cu⁺ with concomitant oxidation of I⁻ to I₂. The iodine that is produced is then titrated with thiosulfate solution to determine the amount of Cu²⁺ in the original solution. The following reactions are involved in the procedure:

1. Cu²⁺(aq) + I⁻(aq) + e⁻ → CuI(s); E° = 0.86 V
2. S₄O₆²⁻(aq) + 2e⁻ → 2S₂O₃²⁻(aq); E° = 0.08 V
3. NO₃⁻(aq) + 2H⁺(aq) + 2e⁻ → NO₂⁻(aq) + H₂O(l); E° = 0.94 V
4. I₂(s) + 2e⁻ → 2I⁻(aq); E° = 0.54 V

1. Write a balanced chemical equation for the reaction between nitric acid and Cu(s).
2. What is E°_cell for this reaction?
3. What is E°_cell for the reaction between thiosulfate and iodine?
4. When the pH of the copper(ll) solution is adjusted to 7.0, what is E for reduction of nitrate?
5. Why is it necessary to adjust the pH of the copper(II) solution before adding KI?
6. Use tabulated data to explain why rust (Fe₂O₃) is a contaminant that renders this method useless in determining Cu concentrations.

The biological electron transport chain provides for an orderly, stepwise transfer of electrons. Both NADH (reduced nicotinamide adenine dinucleotide) and FADH₂ (reduced flavin adenine dinucleotide) are energy-rich molecules that liberate a large amount of energy during oxidation. Free energy released during the transfer of electrons from either of these molecules to oxygen drives the synthesis of ATP (adenosine triphosphate) formed during respiratory metabolism. The reactions are as follows:

$$\begin{array}{cccc}\hfill \text{NADH}+{\text{H}}^{+}+\frac{1}{2}{\text{O}}_2& \to {\text{NAD}}^{+}+{\text{H}}_2\text{O}& \Delta G°\prime & =-52.6\text{ kcal/mol}\hfill \\ \hfill {\text{FADH}}_2+\frac{1}{2}{\text{O}}_2& \to \text{FAD}+{\text{H}}_2\text{O}& \Delta G°\prime & =-43.4\text{ kcal/mol}\hfill \end{array}$$

The standard potential (E°′) for a biological process is defined at pH = 7.0.

1. What is E°′_cell for each reaction?
2. What is the reduction potential of NAD⁺ at pH 7.0?
3. What is the reduction potential of FAD at pH 7.0?

While working at a nuclear reactor site, you have been put in charge of reprocessing spent nuclear fuel elements. Your specific task is to reduce Pu(VI) to elemental Pu without reducing U(VI) to elemental U. You have the following information at your disposal:

$$\begin{array}{cccccc}\hfill E°& {\text{UO}}_2{}^{2+}& \stackrel{0.05}{\to }{\text{UO}}_2{}^{+}& \stackrel{0.62}{\to }{\text{U}}^{4+}& \stackrel{-0.61}{\to }{\text{U}}^{3+}& \stackrel{-1.85}{\to }\text{U}\\ \hfill E°& {\text{PuO}}_2{}^{2+}& \stackrel{0.91}{\to }{\text{PuO}}_2{}^{+}& \stackrel{1.17}{\to }{\text{Pu}}^{4+}& \stackrel{0.98}{\to }{\text{Pu}}^{3+}& \stackrel{-2.03}{\to }\text{Pu}\end{array}$$

Use tabulated data to decide what reductant will accomplish your task in an acidic solution containing 1.0 M concentrations of both UO₂²⁺ and PuO₂²⁺.

Stainless steels typically contain 11% Cr and are resistant to corrosion because of the formation of an oxide layer that can be approximately described as FeCr₂O₄, where the iron is Fe(II). The protective layer forms when Cr(II) is oxidized to Cr(III) and Fe is oxidized to Fe(II). Explain how this film prevents the corrosion of Fe to rust, which has the formula Fe₂O₃.

♦ Ion-selective electrodes are powerful tools for measuring specific concentrations of ions in solution. For example, they are used to measure iodide in milk, copper-ion levels in drinking water, fluoride concentrations in toothpastes, and the silver-ion concentration in photographic emulsions and spent fixing solutions. Describe how ion-selective electrodes work and then propose a design for an ion-selective electrode that can be used for measuring water hardness (Ca²⁺, Mg²⁺) in water-conditioning systems.

♦ Enzymes are proteins that catalyze a specific reaction with a high degree of specificity. An example is the hydrolysis of urea by urease:

$${\text{NH}}_{\text{2}}{\text{CONH}}_{\text{2}}+{\text{2H}}_{\text{2}}\text{O}+{\text{H}}^{+}\stackrel{\text{urease}}{\to }{\text{2NH}}_{\text{4}}{}^{+}+{\text{HCO}}_{\text{3}}{}^{-}$$

An enzyme electrode for measuring urea concentrations can be made by coating the surface of a glass electrode with a gel that contains urease.

1. Explain what occurs when the electrode is placed in contact with a solution that contains urea.
2. What species diffuses through the gel?
3. What would be an effective reference electrode?

Gas-sensing electrodes can be constructed using a combination electrode that is surrounded by a gas-permeable membrane. For example, to measure CO₂, a pH electrode and a reference electrode are placed in solution on the “inner” side of a CO₂-permeable membrane, and the sample solution is placed on the “external” side. As CO₂ diffuses through the membrane, the pH of the internal solution changes due to the reaction CO₂(g) + H₂O(l) → HCO₃⁻(aq) + H⁺(aq). Thus the pH of the internal solution varies directly with the CO₂ pressure in the external sample. Ammonia electrodes operate in the same manner. Describe an electrode that would test for ammonia levels in seawater.

US submarines that are not nuclear powered use a combination of batteries and diesel engines for their power. When submerged, they are battery driven; when on the surface, they are diesel driven. Why are batteries not used when submarines are on the surface?

List some practical considerations in designing a battery to power an electric car.

♦ It is possible to run a digital clock using the power supplied by two potatoes. The clock is connected to two wires: one is attached to a copper plate, and the other is attached to a zinc plate. Each plate is pushed into a different potato; when a wire connects the two potatoes, the clock begins to run as if it were connected to a battery.

1. Draw a cell diagram of the potato clock.
2. Explain why the clock runs.

♦ The silver–zinc battery has the highest energy density of any rechargeable battery available today. Its use is presently limited to military applications, primarily in portable communications, aerospace, and torpedo-propulsion systems. The disadvantages of these cells are their limited life (they typically last no more than about 2 yr) and their high cost, which restricts their use to situations in which cost is only a minor factor. The generally accepted equations representing this type of battery are as follows:

$$2\text{AgO(s)}+\text{Zn(s)}+{\text{H}}_{\text{2}}\text{O(l)}\to {\text{Ag}}_{\text{2}}\text{O(s)}+{\text{Zn(OH)}}_{\text{2}}\text{(aq)}E°=1.85\text{ V}$$ $${\text{Ag}}_2\text{O(s)}+\text{Zn(s)}+{\text{H}}_{\text{2}}\text{O(l)}\to 2\text{Ag(s)}+{\text{Zn(OH)}}_{\text{2}}\text{(aq)}E°=1.59\text{ V}$$

1. Write the overall cell reaction and calculate E°_cell.
2. If the cell is 75% efficient, what is the maximum amount of work that can be generated from this type of battery?
3. Use tabulated data to calculate the maximum work that can be generated by a lead storage cell. If a silver–zinc battery is operating at 100% efficiency, how do the two batteries compare?

All metals used in boats and ships are subject to corrosion, particularly when the vessels are operated in salt water, which is a good electrolyte. Based on the data in the following table, where potentials are measured using a glass electrode, explain why

1. iron or steel should not be used in bolts in a lead ballast keel.
2. ordinary brass should not be used as a structural fastening, particularly below the waterline.
3. an aluminum hull should not be painted with a copper-based antifouling paint.
4. magnesium sacrificial anodes are preferred over zinc when a vessel is kept in fresh water.
5. Monel (an alloy that contains mostly nickel and copper) is preferred over stainless steel for freshwater tanks.

Parents often coat a baby’s first shoes with copper to preserve them for posterity. A conducting powder, such as graphite, is rubbed on the shoe, and then copper is electroplated on the shoe. How much copper is deposited on a shoe if the electrolytic process is run for 60 min at 1.2 A from a 1.0 M solution of CuSO₄?

Before 1886, metallic aluminum was so rare that a bar of it was displayed next to the Crown Jewels at the Paris Exposition of 1855. Today, aluminum is obtained commercially from aluminum oxide by the Hall–Heroult process, an electrolytic process that uses molten Al₂O₃ and cryolite (Na₃AlF₆). As the operation proceeds, molten Al sinks to the bottom of the cell. The overall reaction is 2Al₂O₃(l) + 3C(s) → 4Al(l) + 3CO₂(g); however, the process is only approximately 90% efficient.

1. Why is cryolite added to the Al₂O₃?
2. How much aluminum is deposited if electrodeposition occurs for 24 h at 1.8 A?

♦ One of the most important electrolytic processes used in industry is the electrolytic reduction of acrylonitrile (CH₂CHCN) to adiponitrile [NC(CH₂)₄CN]. The product is then hydrogenated to hexamethylenediamine [H₂N(CH₂)₆NH₂], a key component of one form of nylon. Using this process, Monsanto produces about 200,000 metric tons of adiponitrile annually. The cathode reaction in the electrochemical cell is as follows:

2CH₂CHCN + 2H⁺ + 2e⁻ → NC(CH₂)₄CN

The cost of electricity makes this an expensive process. Calculate the total number of kilowatt-hours of electricity used by Monsanto each year in this process, assuming a continuous applied potential of 5.0 V and an electrochemical efficiency of 50%. (One kilowatt-hour equals 3.6 × 10³ kJ.)

♦ Compact discs (CDs) are manufactured by electroplating. Information is stored on a CD master in a pattern of “pits” (depressions, which correspond to an audio track) and “lands” (the raised areas between depressions). A laser beam cuts the pits into a plastic or glass material. The material is cleaned, sprayed with [Ag(NH₃)₂]⁺, and then washed with a formaldehyde solution that reduces the complex and leaves a thin silver coating. Nickel is electrodeposited on the disk and then peeled away to produce a master disk, which is used to stamp copies.

1. Write the half-reactions that correspond to the electrodeposition reaction.
2. If a CD has a radius of 12 cm and an interior hole with a diameter of 2.5 cm, how long does it take to deposit a 50 µm layer of nickel on one side of the CD using a 1.0 M solution of NiSO₄ and a current of 0.80 A?

♦ Calculate the total amount of energy consumed in the electrolysis reaction used to make the 16 × 10⁶ metric tons of aluminum produced annually worldwide, assuming a continuous applied potential of 5.0 V and an efficiency of 50%. Express your answer in kilojoules and in kilowatt-hours. (See Problem 19 for the conversion between kilowatt-hours and kilojoules.)