Problems

19.11 Calculate the standard emf of a cell that uses the Mg/Mg21and Cu/Cu21 half-cell reactions at 25°C. Write the equation for the cell reaction that occurs under standard-state conditions.

19.12 Calculate the standard emf of a cell that uses Ag/Ag1 and Al/Al31 half-cell reactions. Write the cell reaction that occurs under standard-state conditions.

19.13 Predict whether Fe31 can oxidize I2 to I2 under standard-state conditions.

19.14 Which of the following reagents can oxidize H2O to O2(g) under standard-state conditions? H1(aq),

19.16 Predict whether the following reactions would occur spontaneously in aqueous solution at 25°C. Assume that the initial concentrations of dissolved species are all 1.0 M.

(a) Ca(s) 1 Cd21(aq) ¡ Ca21(aq) 1 Cd(s)

(b) 2Br2(aq) 1 Sn21(aq) ¡ Br2(l) 1 Sn(s)

(c) 2Ag(s) 1 Ni21(aq) ¡ 2Ag1(aq) 1 Ni(s)

(d) Cu1(aq) 1 Fe31(aq) ¡Cu21(aq) 1 Fe21(aq)

19.17 Which species in each pair is a better oxidizing agent under standard-state conditions? (a) Br2 or Au31, (b) H2 or Ag1, (c) Cd21 or Cr31, (d) O2 in acidic media or O2 in basic media.

19.18 Which species in each pair is a better reducing agent under standard-state conditions? (a) Na or Li, (b) H2 or I2, (c) Fe21 or Ag, (d) Br2 or Co21.

19.21 What is the equilibrium constant for the following reaction at 25°C?

Mg(s) 1 Zn21(aq) Δ Mg21(aq) 1 Zn(s)

19.22 The equilibrium constant for the reaction

Sr(s) 1 Mg21(aq) Δ Sr21(aq) 1 Mg(s)

is 2.69 3 1012 at 25°C. Calculate E° for a cell made up of Sr/Sr21 and Mg/Mg21 half-cells.

19.23 Use the standard reduction potentials to fi nd the equilibrium constant for each of the following reac-tions at 25°C:

(a) Br2(l) 1 2I2(aq) Δ 2Br2(aq) 1 I2(s)

(b) 2Ce41(aq) 1 2Cl2(aq) ΔCl2(g 2 1 2Ce31(aq)

(c) 5Fe21(aq) 1 MnO42(aq) 1 8H1(aq) Δ

Mn21(aq) 1 4H2O(l2 1 5Fe31(aq)

19.24 Calculate DG° and Kc for the following reactions at 25°C:

(a) Mg(s) 1 Pb21(aq) Δ Mg21(aq) 1 Pb(s)

(b) Br2(l2 1 2I2(aq) Δ 2Br2(aq) 1 I2(s)

(c) O2(g 2 1 4H1(aq) 1 4Fe21(aq) Δ2H2O(l) 1 4Fe31(aq)

(d) 2Al(s) 1 3I2(s) Δ 2Al31(aq) 1 6I2(aq)

19.25 Under standard-state conditions, what spontaneous reaction will occur in aqueous solution among the ions Ce41, Ce31, Fe31, and Fe21? Calculate DG° and Kc for the reaction.

19.26 Given that E° 5 0.52 V for the reduction Cu1(aq) 1 e2S Cu(s), calculate E°, DG°, and K for the fol-lowing reaction at 25°C:

2Cu1(aq) ¡ Cu21(aq) 1 Cu(s)

19.29 What is the potential of a cell made up of Zn/Zn21 and Cu/Cu21 half-cells at 25°C if [Zn21] 5 0.25 M and [Cu21] 5 0.15 M?

19.30 Calculate E°, E, and DG for the following cell reactions.

(a) Mg(s) 1 Sn21(aq) ¡ Mg21(aq) 1 Sn(s)[Mg21] 5 0.045 M, [Sn21] 5 0.035 M

(b) 3Zn(s) 1 2Cr31(aq) ¡ 3Zn21(aq) 1 2Cr(s)[Cr31] 5 0.010 M, [Zn21] 5 0.0085 M

19.31 Calculate the standard potential of the cell consisting of the Zn/Zn21 half-cell and the SHE. What will the emf of the cell be if [Zn21] 5 0.45 M, PH2

5 2.0 atm, and [H1] 5 1.8 M?

19.32 What is the emf of a cell consisting of a Pb21/Pb half-cell and a Pt/H1/H2 half-cell if [Pb21] 5 0.10 M, [H1] 5 0.050 M, and PH2

5 1.0 atm?

19.33 Referring to the arrangement in Figure 19.1, calcu-late the [Cu21]/[Zn21] ratio at which the following reaction is spontaneous at 25°C:

Cu(s) 1 Zn21(aq) ¡ Cu21(aq) 1 Zn(s)

19.34 Calculate the emf of the following concentration cell:

Mg(s) 0Mg21 (0.24 M) 0 0 Mg21 (0.53 M) 0Mg(s)

19.37 The hydrogen-oxygen fuel cell is described in Sec-tion 19.6. (a) What volume of H2(g), stored at 25°C at a pressure of 155 atm, would be needed to run an electric motor drawing a current of 8.5 A for 3.0 h? (b) What volume (liters) of air at 25°C and 1.00 atm will have to pass into the cell per minute to run the motor? Assume that air is 20 percent O2 by volume and that all the O2 is consumed in the cell. The other components of air do not affect the fuel-cell reac-tions. Assume ideal gas behavior.

19.38 Calculate the standard emf of the propane fuel cell discussed on p. 862 at 25°C, given that DG°f for propane is 223.5 kJ/mol.

CorrosionReview Questions

19.39 Steel hardware, including nuts and bolts, is often coated with a thin plating of cadmium. Explain the function of the cadmium layer.

19.40 “Galvanized iron” is steel sheet that has been coated with zinc; “tin” cans are made of steel sheet coated with tin. Discuss the functions of these coatings and the electrochemistry of the corrosion reactions that occur if an electrolyte contacts the scratched surface of a galvanized iron sheet or a tin can.

19.41 Tarnished silver contains Ag2S. The tarnish can be removed by placing silverware in an aluminum pan containing an inert electrolyte solution, such as NaCl. Explain the electrochemical principle for this procedure. [The standard reduction potential for the half-cell reaction Ag2S(s) 1 2e2S 2Ag(s) 1 S22(aq) is 20.71 V.]

19.42 How does the tendency of iron to rust depend on the pH of solution?

ElectrolysisReview Questions

19.43 What is the difference between a galvanic cell (such as a Daniell cell) and an electrolytic cell?

19.44 Describe the electrolysis of an aqueous solution of KNO3.

Problems

19.45 The half-reaction at an electrode is

Mg21(molten) 1 2e2 ¡ Mg(s)

Calculate the number of grams of magnesium that can be produced by supplying 1.00 F to the electrode.

19.46 Consider the electrolysis of molten barium chloride, BaCl2. (a) Write the half-reactions. (b) How many grams of barium metal can be produced by supplying 0.50 A for 30 min?

19.47 Considering only the cost of electricity, would it be cheaper to produce a ton of sodium or a ton of alumi-num by electrolysis?

19.48 If the cost of electricity to produce magnesium by the electrolysis of molten magnesium chloride is $155 per ton of metal, what is the cost (in dollars) of the electricity necessary to produce (a) 10.0 tons of aluminum, (b) 30.0 tons of sodium, (c) 50.0 tons of calcium?

19.49 One of the half-reactions for the electrolysis of water is

2H2O (l) ¡ O2(g) 1 4H1(aq) 1 4e2

If 0.076 L of O2 is collected at 25°C and 755 mmHg, how many moles of electrons had to pass through the solution?

19.50 How many moles of electrons are required to pro-duce (a) 0.84 L of O2 at exactly 1 atm and 25°C from aqueous H2SO4 solution; (b) 1.50 L of Cl2 at 750 mmHg and 20°C from molten NaCl; (c) 6.0 g of Sn from molten SnCl2?

19.51 Calculate the amounts of Cu and Br2 produced in 1.0 h at inert electrodes in a solution of CuBr2 by a current of 4.50 A.

19.52 In the electrolysis of an aqueous AgNO3 solution, 0.67 g of Ag is deposited after a certain period of time. (a) Write the half-reaction for the reduction of Ag1. (b) What is the probable oxidation half-reaction? (c) Calculate the quantity of electricity used, in coulombs.

19.53 A steady current was passed through molten CoSO4 until 2.35 g of metallic cobalt was produced. Calcu-late the number of coulombs of electricity used.

19.54 A constant electric current fl ows for 3.75 h through two electrolytic cells connected in series. One con-tains a solution of AgNO3 and the second a solution of CuCl2. During this time 2.00 g of silver are depos-ited in the fi rst cell. (a) How many grams of copper are deposited in the second cell? (b) What is the cur-rent fl owing, in amperes?

19.55 What is the hourly production rate of chlorine gas (in kg) from an electrolytic cell using aqueous NaCl electrolyte and carrying a current of 1.500 3 103A?

The anode effi ciency for the oxidation of Cl2 is 93.0 percent.

19.56 Chromium plating is applied by electrolysis to ob-jects suspended in a dichromate solution, according to the following (unbalanced) half-reaction:

Cr2O722(aq) 1 e2 1 H1(aq) ¡ Cr(s) 1 H2O(l)

How long (in hours) would it take to apply a chromium plating 1.0 3 1022 mm thick to a car bumper with a surface area of 0.25 m2 in an elec-trolytic cell carrying a current of 25.0 A? (The den-sity of chromium is 7.19 g/cm3.)

19.57 The passage of a current of 0.750 A for 25.0 min de-posited 0.369 g of copper from a CuSO4 solution. From this information, calculate the molar mass of copper.

19.58 A quantity of 0.300 g of copper was deposited from a CuSO4 solution by passing a current of 3.00 A through the solution for 304 s. Calculate the value of the Faraday constant.

19.59 In a certain electrolysis experiment, 1.44 g of Ag were deposited in one cell (containing an aqueous AgNO3 solution), while 0.120 g of an unknown metal X was deposited in another cell (containing an aqueous XCl3 solution) in series with the AgNO3 cell. Calculate the molar mass of X.

19.60 One of the half-reactions for the electrolysis of water is

2H1(aq) 1 2e2 ¡ H2(g)

If 0.845 L of H2 is collected at 25°C and 782 mmHg, how many moles of electrons had to pass through the solution?

Additional Problems19.61 For each of the following redox reactions, (i) write

the half-reactions; (ii) write a balanced equation for the whole reaction, (iii) determine in which direc-tion the reaction will proceed spontaneously under standard-state conditions:

(a) H2(g) 1 Ni21(aq) ¡ H1(aq) 1 Ni(s)

(b) MnO42(aq) 1 Cl2(aq) ¡

Mn21(aq) 1 Cl2(g) (in acid solution)

(c) Cr(s) 1 Zn21(aq) ¡ Cr31(aq) 1 Zn(s)

19.62 The oxidation of 25.0 mL of a solution containing Fe21 requires 26.0 mL of 0.0250 M K2Cr2O7 in acidic solution. Balance the following equation and calculate the molar concentration of Fe21:

Cr2O722 1 Fe21 1 H1 ¡ Cr31 1 Fe31

19.63 The SO2 present in air is mainly responsible for the phenomenon of acid rain. The concentration of SO2

can be determined by titrating against a standard permanganate solution as follows:

5SO2 1 2MnO42 1 2H2O ¡

5SO422 1 2Mn21 1 4H1

Calculate the number of grams of SO2 in a sample of air if 7.37 mL of 0.00800 M KMnO4 solution are re-quired for the titration.

19.64 A sample of iron ore weighing 0.2792 g was dis-solved in an excess of a dilute acid solution. All the iron was fi rst converted to Fe(II) ions. The solution then required 23.30 mL of 0.0194 M KMnO4 for oxidation to Fe(III) ions. Calculate the percent by mass of iron in the ore.

19.65 The concentration of a hydrogen peroxide solution can be conveniently determined by titration against a standardized potassium permanganate solution in an acidic medium according to the following unbal-anced equation:

MnO42 1 H2O2 ¡ O2 1 Mn21

(a) Balance the above equation. (b) If 36.44 mL of a 0.01652 M KMnO4 solution are required to com-pletely oxidize 25.00 mL of a H2O2 solution, calcu-late the molarity of the H2O2 solution.

19.66 Oxalic acid (H2C2O4) is present in many plants and vegetables. (a) Balance the following equation in acid solution:

MnO42 1 C2O4

22 ¡ Mn21 1 CO2

(b) If a 1.00-g sample of H2C2O4 requires 24.0 mL of 0.0100 M KMnO4 solution to reach the equivalence point, what is the percent by mass of H2C2O4 in the sample?

19.67 Complete the following table. State whether the cell reaction is spontaneous, nonspontaneous, or at equilibrium.

E DG Cell Reaction

. 0

. 0

5 0

19.68 Calcium oxalate (CaC2O4) is insoluble in water. This property has been used to determine the amount of Ca21 ions in blood. The calcium oxalate isolated from blood is dissolved in acid and titrated against a standardized KMnO4 solution as described in Prob-lem 19.66. In one test it is found that the calcium oxalate isolated from a 10.0-mL sample of blood re-quires 24.2 mL of 9.56 3 1024 M KMnO4 for titra-tion. Calculate the number of milligrams of calcium per milliliter of blood.

19.69 From the following information, calculate the solu-bility product of AgBr:

Ag1(aq) 1 e2 ¡ Ag(s) E° 5 0.80 V

AgBr(s) 1 e2 ¡ Ag(s) 1 Br2(aq) E° 5 0.07 V

19.70 Consider a galvanic cell composed of the SHE and a half-cell using the reaction Ag1(aq) 1 e2S Ag(s). (a) Calculate the standard cell potential. (b) What is the spontaneous cell reaction under standard-state conditions? (c) Calculate the cell potential when [H1] in the hydrogen electrode is changed to (i) 1.0 3 1022 M and (ii) 1.0 3 1025 M, all other reagents being held at standard-state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter.

19.71 A galvanic cell consists of a silver electrode in contact with 346 mL of 0.100 M AgNO3 solution and a mag-nesium electrode in contact with 288 mL of 0.100 M Mg(NO3)2 solution. (a) Calculate E for the cell at 25°C. (b) A current is drawn from the cell until 1.20 g of silver have been deposited at the sil ver electrode. Calculate E for the cell at this stage of operation.

19.72 Explain why chlorine gas can be prepared by elec-trolyzing an aqueous solution of NaCl but fl uorine gas cannot be prepared by electrolyzing an aqueous solution of NaF.

19.73 Calculate the emf of the following concentration cell at 25°C:

Cu(s) 0 Cu21 (0.080 M) 0 0 Cu21 (1.2 M) 0 Cu(s)

19.74 The cathode reaction in the Leclanché cell is given by

2MnO2(s) 1 Zn21(aq) 1 2e2 ¡ ZnMn2O4(s)

If a Leclanché cell produces a current of 0.0050 A, calculate how many hours this current supply will last if there are initially 4.0 g of MnO2 present in the cell. Assume that there is an excess of Zn21 ions.

19.75 Suppose you are asked to verify experimentally the electrode reactions shown in Example 19.8. In addi-tion to the apparatus and the solution, you are also given two pieces of litmus paper, one blue and the other red. Describe what steps you would take in this experiment.

19.76 For a number of years it was not clear whether mercury(I) ions existed in solution as Hg1 or as Hg2

21. To distinguish between these two possibili-ties, we could set up the following system:

Hg(l) 0 soln A 0 0 soln B 0Hg(l)

where soln A contained 0.263 g mercury(I) nitrate per liter and soln B contained 2.63 g mercury(I) nitrate per liter. If the measured emf of such a cell is 0.0289 V at 18°C, what can you deduce about the nature of the mercury(I) ions?

19.77 An aqueous KI solution to which a few drops of phe-nolphthalein have been added is electrolyzed using an apparatus like the one shown here:

Describe what you would observe at the anode and the cathode. (Hint: Molecular iodine is only slightly solu-ble in water, but in the presence of I2 ions, it forms the brown color of I3

2 ions. See Problem 12.98.)

19.78 A piece of magnesium metal weighing 1.56 g is placed in 100.0 mL of 0.100 M AgNO3 at 25°C. Calculate [Mg21] and [Ag1] in solution at equilib-rium. What is the mass of the magnesium left? The volume remains constant.

19.79 Describe an experiment that would enable you to de-termine which is the cathode and which is the anode in a galvanic cell using copper and zinc electrodes.

19.80 An acidifi ed solution was electrolyzed using copper electrodes. A constant current of 1.18 A caused the anode to lose 0.584 g after 1.52 3 103 s. (a) What is the gas produced at the cathode and what is its vol-ume at STP? (b) Given that the charge of an electron is 1.6022 3 10219 C, calculate Avogadro’s number. Assume that copper is oxidized to Cu21 ions.

19.81 In a certain electrolysis experiment involving Al31 ions, 60.2 g of Al is recovered when a current of 0.352 A is used. How many minutes did the elec-trolysis last?

19.82 Consider the oxidation of ammonia:

4NH3(g) 1 3O2(g) ¡ 2N2(g) 1 6H2O(l)

(a) Calculate the DG° for the reaction. (b) If this re-action were used in a fuel cell, what would the stan-dard cell potential be?

19.83 When an aqueous solution containing gold(III) salt is electrolyzed, metallic gold is deposited at the cathode and oxygen gas is generated at the anode. (a) If 9.26 g of Au is deposited at the cathode, calcu-late the volume (in liters) of O2 generated at 23°C and 747 mmHg. (b) What is the current used if the electrolytic process took 2.00 h?

19.84 In an electrolysis experiment, a student passes the same quantity of electricity through two electrolytic cells, one containing a silver salt and the other a gold salt. Over a certain period of time, she fi nds that 2.64 g

of Ag and 1.61 g of Au are deposited at the cathodes. What is the oxidation state of gold in the gold salt?

19.85 People living in cold-climate countries where there is plenty of snow are advised not to heat their ga-rages in the winter. What is the electrochemical basis for this recommendation?

19.86 Given that

2Hg21(aq) 1 2e2 ¡ Hg221(aq) E° 5 0.92 V

Hg221(aq) 1 2e2 ¡ 2Hg(l) E° 5 0.85 V

calculate DG° and K for the following process at 25°C:

Hg221(aq) ¡ Hg21(aq) 1 Hg(l)

(The preceding reaction is an example of a dispro-portionation reaction in which an element in one oxidation state is both oxidized and reduced.)

19.87 Fluorine (F2) is obtained by the electrolysis of liquid hydrogen fl uoride (HF) containing potassium fl uo-ride (KF). (a) Write the half-cell reactions and the overall reaction for the process. (b) What is the pur-pose of KF? (c) Calculate the volume of F2 (in liters) collected at 24.0°C and 1.2 atm after electrolyzing the solution for 15 h at a current of 502 A.

19.88 A 300-mL solution of NaCl was electrolyzed for 6.00 min. If the pH of the fi nal solution was 12.24, calculate the average current used.

19.89 Industrially, copper is purifi ed by electrolysis. The impure copper acts as the anode, and the cathode is made of pure copper. The electrodes are immersed in a CuSO4 solution. During electrolysis, copper at the anode enters the solution as Cu21 while Cu21 ions are reduced at the cathode. (a) Write half-cell reac-tions and the overall reaction for the electrolytic pro-cess. (b) Suppose the anode was contaminated with Zn and Ag. Explain what happens to these impurities during electrolysis. (c) How many hours will it take to obtain 1.00 kg of Cu at a current of 18.9 A?

19.90 An aqueous solution of a platinum salt is elec-trolyzed at a current of 2.50 A for 2.00 h. As a result, 9.09 g of metallic Pt are formed at the cathode. Cal-culate the charge on the Pt ions in this solution.

19.91 Consider a galvanic cell consisting of a magnesium electrode in contact with 1.0 M Mg(NO3)2 and a cad-mium electrode in contact with 1.0 M Cd(NO3)2. Cal-culate E° for the cell, and draw a diagram showing the cathode, anode, and direction of electron fl ow.

19.92 A current of 6.00 A passes through an electrolytic cell containing dilute sulfuric acid for 3.40 h. If the volume of O2 gas generated at the anode is 4.26 L (at STP), calculate the charge (in coulombs) on an electron.

19.93 Gold will not dissolve in either concentrated nitric acid or concentrated hydrochloric acid. However, the metal does dissolve in a mixture of the acids (one part HNO3 and three parts HCl by volume), called

aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are HAuCl4 and NO2.) (b) What is the function of HCl?

19.94 Explain why most useful galvanic cells give voltages of no more than 1.5 to 2.5 V. What are the prospects for developing practical galvanic cells with voltages of 5 V or more?

19.95 A silver rod and a SHE are dipped into a saturated aqueous solution of silver oxalate, Ag2C2O4, at 25°C. The measured potential difference between the rod and the SHE is 0.589 V, the rod being positive. Calcu-late the solubility product constant for silver oxalate.

19.96 Zinc is an amphoteric metal; that is, it reacts with both acids and bases. The standard reduction poten-tial is 21.36 V for the reaction

Zn(OH)422(aq) 1 2e2 ¡ Zn(s) 1 4OH2(aq)

Calculate the formation constant (Kf) for the reaction

Zn21(aq) 1 4OH2(aq) Δ Zn1OH2422(aq)

19.97 Use the data in Table 19.1 to determine whether or not hydrogen peroxide will undergo disproportion-ation in an acid medium: 2H2O2S 2H2O 1 O2.

19.98 The magnitudes (but not the signs) of the standard reduction potentials of two metals X and Y are

Y21 1 2e2 ¡ Y 0E° 0 5 0.34 V

X21 1 2e2 ¡ X 0E° 0 5 0.25 V

where the 0 0 notation denotes that only the magnitude (but not the sign) of the E° value is shown. When the half-cells of X and Y are connected, electrons fl ow from X to Y. When X is connected to a SHE, ele c-trons fl ow from X to SHE. (a) Are the E° values of the half-reactions positive or negative? (b) What is the standard emf of a cell made up of X and Y?

19.99 A galvanic cell is constructed as follows. One half-cell consists of a platinum wire immersed in a solu-tion containing 1.0 M Sn21 and 1.0 M Sn41; the other half-cell has a thallium rod immersed in a solution of 1.0 M Tl1. (a) Write the half-cell reactions and the overall reaction. (b) What is the equilibrium constant at 25°C? (c) What is the cell voltage if the T11 con-centration is increased tenfold? (E°Tl1/Tl 5 20.34 V.)

19.100 Given the standard reduction potential for Au31 in Table 19.1 and

Au1(aq) 1 e2 ¡ Au(s) E° 5 1.69 V

answer the following questions. (a) Why does gold not tarnish in air? (b) Will the following dispropor-tionation occur spontaneously?

3Au1(aq) ¡ Au31(aq) 1 2Au(s)

(c) Predict the reaction between gold and fl uorine gas.

19.101 The ingestion of a very small quantity of mercury is not considered too harmful. Would this statement

still hold if the gastric juice in your stomach were mostly nitric acid instead of hydrochloric acid?

19.102 When 25.0 mL of a solution containing both Fe21 and Fe31 ions is titrated with 23.0 mL of 0.0200 M KMnO4 (in dilute sulfuric acid), all of the Fe21 ions are oxidized to Fe31 ions. Next, the solution is treated with Zn metal to convert all of the Fe31 ions to Fe21 ions. Finally, 40.0 mL of the same KMnO4 solution are added to the solution in order to oxidize the Fe21 ions to Fe31. Calculate the molar concentrations of Fe21 and Fe31 in the original solution.

19.103 Consider the Daniell cell in Figure 19.1. When viewed externally, the anode appears negative and the cathode positive (electrons are fl owing from the an-ode to the cathode). Yet in solution anions are mov-ing toward the anode, which means that it must appear positive to the anions. Because the anode cannot simultaneously be negative and positive, give an ex-planation for this apparently contradictory situation.

19.104 Use the data in Table 19.1 to show that the decompo-sition of H2O2 (a disproportionation reaction) is spontaneous at 25°C:

2H2O2(aq) ¡ 2H2O(l) 1 O2(g)

19.105 The concentration of sulfuric acid in the lead-storage battery of an automobile over a period of time has decreased from 38.0 percent by mass (density 5 1.29 g/mL) to 26.0 percent by mass (1.19 g/mL). Assume the volume of the acid remains constant at 724 mL. (a) Calculate the total charge in coulombs supplied by the battery. (b) How long (in hours) will it take to recharge the battery back to the origi-nal sulfu ric acid concentration using a current of 22.4 amperes?

19.106 Consider a Daniell cell operating under nonstandard-state conditions. Suppose that the cell’s reaction is multiplied by 2. What effect does this have on each of the following quantities in the Nernst equation? (a) E, (b) E°, (c) Q, (d) ln Q, and (e) n?

19.107 A spoon was silver-plated electrolytically in a AgNO3 solution. (a) Sketch a diagram for the pro-cess. (b) If 0.884 g of Ag was deposited on the spoon at a constant current of 18.5 mA, how long (in min-utes) did the electrolysis take?

19.108 Comment on whether F2 will become a stronger ox-idizing agent with increasing H1 concentration.

19.109 In recent years there has been much interest in elec-tric cars. List some advantages and disadvantages of electric cars compared to automobiles with internal combustion engines.

19.110 Calculate the pressure of H2 (in atm) required to maintain equilibrium with respect to the following reaction at 25°C:

Pb(s) 1 2H1(aq) Δ Pb21(aq) 1 H2(g)

Given that [Pb21] 5 0.035 M and the solution is buffered at pH 1.60.

19.111 A piece of magnesium ribbon and a copper wire are partially immersed in a 0.1 M HCl solution in a beaker. The metals are joined externally by another piece of metal wire. Bubbles are seen to evolve at both the Mg and Cu surfaces. (a) Write equations representing the reactions occurring at the metals. (b) What visual evidence would you seek to show that Cu is not oxidized to Cu21? (c) At some stage, NaOH solution is added to the beaker to neutralize the HCl acid. Upon further addition of NaOH, a white precipitate forms. What is it?

19.112 The zinc-air battery shows much promise for electric cars because it is lightweight and rechargeable:

The net transformation is Zn(s) 1 12O2(g)S ZnO(s).

(a) Write the half-reactions at the zinc-air electrodes and calculate the standard emf of the battery at 25°C. (b) Calculate the emf under actual operating conditions when the partial pressure of oxygen is 0.21 atm. (c) What is the energy density (measured as the energy in kilojoules that can be obtained from 1 kg of the metal) of the zinc electrode? (d) If a cur-rent of 2.1 3 105 A is to be drawn from a zinc-air battery system, what volume of air (in liters) would need to be supplied to the battery every second? As-sume that the temperature is 25°C and the partial pressure of oxygen is 0.21 atm.

19.113 Calculate E° for the reactions of mercury with (a) 1 M HCl and (b) 1 M HNO3. Which acid will oxidize Hg to Hg2

21 under standard-state conditions? Can you identify which test tube below contains HNO3 and Hg and which contains HCl and Hg?

19.114 Because all alkali metals react with water, it is not possible to measure the standard reduction potentials of these metals directly as in the case of, say, zinc. An indirect method is to consider the following hy-pothetical reaction

Li1(aq) 1 12H2(g) ¡ Li(s) 1 H1(aq)

Use the appropriate equation presented in this chap-ter and the thermodynamic data in Appendix 3, cal-culate E° for Li1(aq) 1 e2S Li(s) at 298 K. Compare your result with that listed in Table 19.1. (See back endpaper for the Faraday constant.)

19.115 A galvanic cell using Mg/Mg21 and Cu/Cu21 half-cells operates under standard-state conditions at 25°C and each compartment has a volume of 218 mL. The cell delivers 0.22 A for 31.6 h. (a) How many grams of Cu are deposited? (b) What is the [Cu21] remaining?

19.116 Given the following standard reduction potentials, calculate the ion-product, Kw, for water at 25°C:

2H1(aq) 1 2e2 ¡ H2(g) E° 5 0.00 V

2H2O(l) 1 2e2 ¡ H2(g) 1 2OH2(aq)

E° 5 20.83 V

Special Problems

19.117 Compare the pros and cons of a fuel cell, such as the hydrogen-oxygen fuel cell, and a coal-fi red power station for generating electricity.

19.118 Lead storage batteries are rated by ampere hours, that is, the number of amperes they can deliver in an hour. (a) Show that 1 A ? h 5 3600 C. (b) The lead anodes of a certain lead-storage battery have a total mass of 406 g. Calculate the maximum theoretical capacity of the battery in ampere hours. Explain why in practice we can never extract this much energy from the battery. (Hint: Assume all of the lead will

be used up in the electrochemical reaction and refer to the electrode reactions on p. 858.) (c) Calculate E°cell and DG° for the battery.

19.119 Use Equations (18.10) and (19.3) to calculate the emf values of the Daniell cell at 25°C and 80°C. Comment on your results. What assumptions are used in the derivation? (Hint: You need the thermody-namic data in Appendix 3.)

19.120 A construction company is installing an iron culvert (a long cylindrical tube) that is 40.0 m long with a radius of 0.900 m. To prevent corrosion, the culvert

must be galvanized. This process is carried out by fi rst passing an iron sheet of appropriate dimensions through an electrolytic cell containing Zn21 ions, us-ing graphite as the anode and the iron sheet as the cathode. If the voltage is 3.26 V, what is the cost of electricity for depositing a layer 0.200 mm thick if the effi ciency of the process is 95 percent? The elec-tricity rate is $0.12 per kilowatt hour (kWh), where 1 W 5 1 J/s and the density of Zn is 7.14 g/cm3.

19.121 A 9.00 3 102-mL 0.200 M MgI2 was electrolyzed. As a result, hydrogen gas was generated at the cath-ode and iodine was formed at the anode. The volume of hydrogen collected at 26°C and 779 mmHg was 1.22 3 103 mL. (a) Calculate the charge in coulombs consumed in the process. (b) How long (in min) did the electrolysis last if a current of 7.55 A was used? (c) A white precipitate was formed in the process. What was it and what was its mass in grams? As-sume the volume of the solution was constant.

19.122 Based on the following standard reduction poten-tials:

Fe21(aq) 1 2e2 ¡ Fe(s) E°1 5 20.44 V

Fe31(aq) 1 e2 ¡ Fe21(aq) E°2 5 0.77 V

calculate the standard reduction potential for the half-reaction

Fe31(aq) 1 3e2 ¡ Fe(s) E°3 5 ?

19.123 A galvanic cell is constructed by immersing a piece of copper wire in 25.0 mL of a 0.20 M CuSO4 solu-tion and a zinc strip in 25.0 mL of a 0.20 M ZnSO4 solution. (a) Calculate the emf of the cell at 25°C and predict what would happen if a small amount of concentrated NH3 solution were added to (i) the CuSO4 solution and (ii) the ZnSO4 solution. Assume that the volume in each compartment remains con-stant at 25.0 mL. (b) In a separate experiment, 25.0 mL of 3.00 M NH3 are added to the CuSO4 so-lution. If the emf of the cell is 0.68 V, calculate the formation constant (Kf) of Cu(NH3)4

21.

19.124 Calculate the equilibrium constant for the following reaction at 298 K:

Zn(s) 1 Cu21(aq) ¡ Zn21(aq) 1 Cu(s)

19.125 To remove the tarnish (Ag2S) on a silver spoon, a student carried out the following steps. First, she placed the spoon in a large pan fi lled with water so the spoon was totally immersed. Next, she added a few tablespoonful of baking soda (sodium bicar-bonate), which readily dissolved. Finally, she placed some aluminum foil at the bottom of the pan in contact with the spoon and then heated the solu-tion to about 80°C. After a few minutes, the spoon was removed and rinsed with cold water. The tar-nish was gone and the spoon regained its original shiny appearance. (a) Describe with equations the electrochemical basis for the procedure. (b) Adding NaCl instead of NaHCO3 would also work because both compounds are strong electrolytes. What is the added advantage of using NaHCO3? (Hint: Con-sider the pH of the solution.) (c) What is the pur-pose of heating the solution? (d) Some commercial tarnish removers containing a fl uid (or paste) that is a dilute HCl solution. Rubbing the spoon with the fl uid will also remove the tarnish. Name two disad-vantages of using this procedure compared to the one described above.

19.126 The nitrite ion (NO22) in soil is oxidized to nitrate ion

(NO32) by the bacteria Nitrobacter agilis in the pres-

ence of oxygen. The half-reduction reactions are

NO32 1 2H1 1 2e2 ¡ NO2

2 1 H2O E° 5 0.42 V

O2 1 4H1 1 4e2 ¡ 2H2O E° 5 1.23 V

Calculate the yield of ATP synthesis per mole of nitrite oxidized. (Hint: See Section 18.7.)

19.127 Fluorine is a highly reactive gas that attacks water to form HF and other products. Follow the procedure in Problem 19.114 to show how you can determine in-directly the standard reduction for fl uorine as shown in Table 19.1.

19.128 As mentioned on p. 856, a concentration cell ceases to operate when the concentrations of the two cell compartments are equal. At this stage, is it possible to generate an emf from the cell by adjusting another parameter without changing the concentra-tions? Explain.

Answers to Practice Exercises

19.1 5Fe21 1 MnO42 1 8H1 S 5Fe31 1 Mn21 1 4H2O.

19.2 No. 19.3 0.34 V. 19.4 1 3 10242.19.5 DG° 5 24.1 3 102 kJ/mol. 19.6 Yes, E 5 10.01 V.19.7 0.38 V. 19.8 Anode, O2; cathode, H2.19.9 2.0 3 104 A.