786 CHAPTER 19 Electrochemistry

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Applying What You've Learned The pain caused by having aluminum foil contact a dental filling results from the filling being made the cathode in an electrochemical cell. Another type of discomfort can result from the filling being made the anode in an electrochemical cell. This occurs when the filling touches a metal with a greater reduction potential than the components of the amalgam, such as gold. When an amalgam filling comes into contact with a gold inlay, the tin in the filling (the most easily oxidized of the major amalgam components) is oxidized creating an unpleasant metallic taste in the mouth. A simplified, unbalanced equation for the redox reaction that takes place is

Problems:

•

Gold inlay I

",,) + 4H+(aq) + 4e- • 2H20(l)

_. SnLT

filling

Gold inlay touching amalgam dental filling I

a) Balance (in acidic medium) the equation for the oxidation of tin from an amalgam filling. [ ~. Sample Problem 19.1]

b) Calculate the standard cell potential for the reaction in part (a). [ ~. Sample Problem 19.2]

c) Which of the components of dental amalgam (mercury, silver, tin, copper, or zinc) would be oxidized when a filling is brought into contact with lead? [ ~. Sample Problem 19.3]

d) Calculate the standard free-energy change for the reaction in part (a). [ ~. Sample Problem 19.4]

e) Calculate the equilibrium constant at 25°C for the reaction in part (a). [ ~. Sample Problem 19 .5]

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CHAPTER SUMMARY

Section 19.1

o Redox reactions are those in which oxidation numbers change. Half­reactions are the separated oxidation and reduction reactions that make up the overall redox reaction.

o Redox equations can be balanced via the half-reaction method, which allows for the addition of H20 to balance 0, H+ to balance H, and OH- for reactions taking place in basic solution.

Section 19.2

o An electrochemical cell in which a spontaneous chemical reaction generates a flow of electrons through a wire is called a galvanic cell.

o Half-reactions in a galvanic cell take place in separate compartments called half-cells. Half-cells contain electrodes in solutions and are connected via an external wire and by a salt bridge.

o The electrode at which reduction occurs is called the cathode; the electrode at which oxidation occurs is called the anode.

o The difference in electric potential between the cathode and the anode is the cell potential (Ecell)'

Section 19.3

o We use standard reduction potentials (EO) to calculate the standard cell voltage or standard cell potential (E~eID.

o Half-cell potentials are measured relative to the standard hydrogen electrode (SHE), the half-reaction for which has an arbitrarily defined standard reduction potential of zero.

Section 19.4

o E~ell is related to the standard free-energy change (C:..GO) and to the equilibrium constant, K. A positive E~ell corresponds to a negative (C:..GO) value and a large K value.

Section 19.5

o Ecell under other than standard-state conditions is determined from E~ell and the reaction quotient, Q, using the Nerizst equation.

I(EyWORDS

Anode, 763

Battery, 777

Cathode, 763

Cell potential (Ecell)' 764

Concentration cell, 775

Corrosion, 784

Electrode, 763

Electrolysis, 780

Electrolytic cell, 780

Fuel cell, 778

KEY WORDS 787

o A concentration cell has the same type of electrode and the same ion in solution (at different concentrations) in the anode and C8 ihode compartments.

Section 19.6

Batteries are portable, self-contained sources of electric energy consisting of galvanic cells or series of galvanic cells.

o Fuel cells are not really batteries but also supply electric energy via a spontaneous redox reaction. Reactants must be supplied constantly for a fuel cell to operate.

Section 19.7

o Electrolysis is the use of electric energy to drive a nonspontaneous redox reaction. An electrochemical cell used for this purpose is called an electrolytic cell.

o The voltage that must actually be supplied to drive a nonspontaneous redox reaction is greater than the calculated amount because of overvoltage.

o Electrolysis is used to recharge lead storage batteries, separate compounds into their constituent elements, and separate and purify metals.

o We can calculate the amount of a substance produced in electrolysis if we know the current applied to the cell and the length of time for which it is applied.

Section 19.8

o Corrosion is the undesirable oxidation of metals.

o Corrosion can be prevented by coating the metal surface with paint, a less easily oxidized metal, or a more easily oxidized metal such as

• ZlllC.

o The use of a more easily oxidized metal is known as cathodic protection, wherein the metal being protected is made the cathode in a galvanic cell. Galvanization is the cathodic protection of iron or steel

. . USlllg zmc.

Galvanic cell, 763

Galvanization, 785

Half-cell, 763

Half-reaction, 760

Nemst equation, 774 •

Overvoltage, 782

Salt bridge, 763

Standard hydrogen electrode (SHE), 765

Standard reduction potential (EO), 765

788 CHAPTER 19 Electrochemistry

KEY EQUATIONS

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19.1

19.2

19.3

19.4

E O - EO E O cell - cathode - anode

I::..G = -nFEceli

I::..Go = -nFE~ell

EO II = RT In K ce nF

19 5 E o = 0.0592 V I ct K . cell n °b

19.6

19.7

E = EO - RT In Q nF

E = EO _ 0.0592 V log Q n

QUESTIONS AND PROBLEMS

Section 19.1: Balancing Redox Equations

Problems

19.1

19.2

Balance the following redox equations by the half-reaction method:

(a) H20 2 + Fe2+ • Fe3+ + H20 (in acidic solution) (b) Cu + HN03 • Cu2+ + NO + H20 (in acidic solution) (c) CN- + Mn04 • CNO- + Mn02 (in basic solution) (d) Br2 • BrO} + Br - (in basic solution) (e) S20~- + 12 • 1- + S40~- (in acidic sol ution)

Balance the following redox equations by the half-reaction method:

(a) Mn2+ + H20 2 --.... Mn02 + H20 (i n basic solution) (b) Bi(OH)3 + SnOi- • SnO~- + Bi (in basic solution) (c) Cr20~- + C20~- • Cr3+ + CO2 (in acidic solution) (d) CIO} + Cl- • Cl2 + CI02 (in acidic solution) (e) Mn2+ + BiO} • Bi3+ + Mn04 (in acidic solution)

Section 19.2: Galvanic Cells \

Review Questions I

19.3 Define the following terms: anode, cathode, cell voltage, electromotive jorce, standard reduction potential.

19.4

19.5

19.6

19.7

Describe the basic features of a gal vanic cell. Why are the two components of the cell separated from each other?

What is the function of a salt bridge? What kind of electrolyte should be used in a salt bridge?

What is a cell diagram? Write the cell diagram for a galvanic cell consisting of an Al electrode placed in a I M Al(N0 3)3 solution and an Ag electrode placed in aIM AgN03 solution.

What is the difference between the half-reactions discussed in redox processes in Chapter 4 and the half-cell reactions discussed in Section 19.2?

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Section 19.3: Standard Reduction Potentials

Review Questions

19.8 Discuss the spontaneity of an electrochemical reaction in terms of its standard emf (E~cll) '

19.9 After operating a Daniell cell (see Figure 19.1) for a few minutes, a student notices that the cell emf begins to drop. Why?

Problems

19.10 Calculate the standard emf of a cell that uses the Mg/Mg2+ and Cu/Cu2+ half-cell reactions at 25°C. Write the equation for the cell reaction that occurs under standard-state conditions.

19.11

19.1?

Calculate the standard emf of a cell that uses Ag/ Ag + and All AI3+ half-cell reactions. Write the cell reaction that occurs . under standard-state conditions.

Predict whether Fe3+ can oxidize 1- to 12 under standard-state conditions.

19.13 Which of the following reagents can oxidize H20 to 0 2(g) under standard-state conditions: H +(aq) , Cl-(aq), CI2(g), Cu2+ (aq), Pb2+ (aq), Mn04 (aq) (in acid)?

19.14 Consider the following half-reactions:

Mn04 (aq) + .8H+(aq) + 5e - -_. Mn2+ (aq) + 4H20(I)

NO } (aq) + 4H+(aq) + 3e - • NO(g) + 2H20(l)

Predict whether NO} ions will oxidize Mn2+ to Mn04 under standard-state conditions.

19.15 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) + Cd2+(aq) • Ca2+ (aq) + Cd(s) (b) 2Br-(aq) + Sn2+ (aq) • Br2(l) + Sn(s) (c) 2Ag(s) + Ni2 +(aq) • 2Ag+(aq) + Ni(s) (d) Cu+(aq) + Fe3+ (aq) • Cu2+(aq) + Fe2+ (aq)

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19.16 Which species in each pair is a better oxidizing agent under standard-state conditions: (a) Br2 or AuH , (b) H2 or Ag +, (c) Cd2+ or CrH , (d) O2 in acidic media or O2 in basic media?

19.17 Which species in each pair is a better reducing agent under standard-state conditions: (a) Na or Li, (b) H2 or 12> (c) Fe2+ or Ag, (d) Br- or Co2+ ?

Section 19.4: Spontaneity of Redox Reactions Under Standard-State Conditions

Review Questions

19.18 Use the information in Table 2.1, and calculate the Faraday constant.

19.19 Write the equations relating I1Go and Kto the standard emf of a cell. Define all the terms.

19.20 Compare the ease of measuring the equilibrium constant electrochemically with that by chemical means [see Equation (1 8.15)] .

Problems

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

Mg(s) + Zn2+(aq) -.:. =:!:' Mg2+ (aq) + Zn(s)

19.22 The equilibrium constant for the reaction

Sr(s) + Mg2+(aq). ' Sr2+(aq) + Mg(s)

is 2.69 X 1012 at 25°C. Calculate EO for a cell made up of Sr1Sr2+

and Mg/Mg2+ half-cells.

19.23 Use the standard reduction potentials to find the equilibrium constant for each of the following reactions at 2YC:

(a) Brz(l) + 21-(aq) • ' 2Br- (aq) + 12(s) (b) 2Ce4+(aq) + 2Cqaq) • • CI2(g) + 2Ce3+(aq) (c) 5Fe2+(aq) + Mn04(aq) + 8H +(aq). ' Mn2+(aq) + 4H20 + 5FeH (aq)

19.24 Calculate I1Go and Kc fo r the following reactions at 25°C:

(a) Mg(s) + Pb2+(aq) • • Mg2+ (aq) + Pb(s)

(b) 0 2(g) + 4H+(aq) + 4Fe2+(aq) . ' 2H20 (l) + 4FeH (aq)

(c) 2AI(s) + 3lz(s) • ' 2AIH (aq) + 6r-(aq)

19.25 Under standard-state conditions, what spontaneous reaction will . I . h ' C 4 + C H F 3+ d occur 1n aqueous so ulion among t e IOns e , e' , e , an

Fe2+? Calculate I1Go and Kc for the reaction.

19.26 Given that EO = 0.52 V for the reduction Cu +(aq) + e - • Cu(s), calculate EO, I1Go, and K for the following reaction at 25°C:

Section 19.5: Spontaneity of Redox Reactions Under Conditions Other Than Standard State

Review Questions

19.27 Write the Nernst equation, and explain all the terms.

19.28 Write the Nernst equation for the following processes at some I temperature T

(a) Mg(s) + Sn2+(aq). • Mg2+(aq) + Sn(s) (b) 2Cr(s) + 3Pb2+ (aq) • • 2CrH(aq) + 3Pb(s)

QUESTIONS AND PROBLEMS 789

Problems

19.29 What is the potential of a cell made up of Z n/Zn2+ and ClLCU:­half-ce lls at 25°C if [Zn2+ ] = 0.25 M and [Cu2+] = 0.1 5 ,\f'?

19.30 Calculate EO, E, and I1G for the following cell reactions.

(a) Mg(s) + Sn2+(aq) . • Mg2+(aq) + Sn(s) [Mg2+] = 0.045 M, [Sn2+] = 0.035 M

(b) 3Zn(s) + 2CrH (aq) . • 3Zn2+ (aq) + 2Cr(s) [CrH ] = 0.010 M, [Zn2+] = 0.0085 M

19.31 Calculate the standard potential of the cell consisting of the ZnlZn2+ half-cell and the SHE. What will the emf of the cell be if [Zn2+] = 0.45 M, PH = 2.0 atm, and [H+] = 1.8 M?

2

19.32 What is the emf of a cell consisting of a Pb2+/Pb half-cell and a PtlH+ 1H2 half-cell if [Pb2+] = 0.10 M, [H] = 0.050 M, and PH = 1.0 atm?

2

19.33 Refening to the anangement in Figure 19.1, calculate the [Cu2+]/[Zn2+] ratio at which the following reaction is spontaneous at 25°C:

Cu(s) + Zn2+ (aq) • Cu2+ (aq) + Zn(s)

19.34 Calculate the emf of the following concentration cell:

Mg(s) I Mg2+(0.24 M) II Mg2 +(0.53 M) I Mg(s)

Section 19.6: Batteries

Review Questions

19.35 What is a battery? Describe several types of batteries.

19.36 Explain the differences between a primary galvanic cell-one that is not rechargeable-and a storage cell (for example, the lead storage battery), which is rechargeable.

19.37 Discuss the advantages and disadvantages of fuel cells over conventional power plants in producing electricity.

Problems

19.38 The hydrogen-oxygen fuel cell is described in Section 19.6. (a) What volume of H ig), stored at 25°C at a pressure of 155 atm , would be needed to run an electric motor drawing a cunent of 8.5 A for 3.0 h? (b) What volume (in 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 Oz is consumed in the cel!. The other components of air do not affect the fuel-cell reactions. Assume ideal gas behavior.

19.39 Calculate the standard emf of the propane fuel cell discussed on page 779 at 2YC, given that I1G 'f for propane is - 23.5 kJ/mo!.

Section 19.7: Electrolysis

Review Questions

19.40 What is the difference be een a galvanic cell (such as a Daniell . cell) and an electrolytic cell?

19.41 What is Faraday's contribution to quantitative electrolysis?

19.42 Define the term over voltage. How does overvoltage affect electrolytic processes?

790 CHAPTER 19 Electrochemistry

Problems

19.43 The half-reaction at an electrode is

19.44

. 19.45

19.46

Mg2+ (molten) + 2e- --~. Mg(s)

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

Consider the electrolysis of molten barium chloride (BaCI2) .

(a) Write the half-reactions. (b) How many grams of barium metal can be produced by supplying 0.50 A for 30 min?

• Considering only the cost of electricity, would it be cheaper to produce a ton of sodium or a ton of aluminum by electrolysis?

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, and (c) 50.0 tons of calcium?

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

2H20(l) • 0 2(g) + 4H+ (aq) + 4e -

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

19.48 How many faradays of electricity are required to produce (a) 0.84 L of O2 at exactly 1 atm and 25°C from aqueous H2S0 4 solution, (b) 1.50 L of Cl2 at 750 mmHg and 20°C from molten NaCl, and (c) 6.0 g of Sn from molten SnCI2?

19.49 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.

19.50 In the electrolysis of an aqueous AgN03 solution, 0.67 g of Ag is deposited after a certain period of time. (a) Write the half-reaction for the reduction of Ag +. (b) What is the probable oxidation half-reaction? (c) Calculate the quantity of electricity used (in coulombs).

19.51 A steady current was passed through molten CoS04 until 2.35 g of metallic cobalt was produced. Calculate the number of coulombs of electricity used.

19.52 A constant electric current flows for 3.75 h through two electrolytic cells connected in series. One contains a solution of AgN03 and the second a solution of CuCI2. During this time, 2.00 g of silver is deposited in the first cell. (a) How many grams of copper are deposited in the second cell? (b) What is the current flowing (in amperes)?

19.53 What is the hourly production rate of chlorine gas (in kg) from an electrolytic cell using aqueous NaCI electrolyte and carrying a current of 1.500 X 103 A? The anode efficiency for the oxidation of Cl- is 93.0 percent.

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

How long (in hours) would it take to apply a chromium plating 1.0 X 10-2 mm thick to a car bumper with a surface area of 0.25 m2 in an electrolytic cell carrying a current of 25.0 A? (The density of chromium is 7 .1 9 g/cm3

.)

19.55 The passage of a current of 0.750 A for 25.0 min deposited 0.369 g of copper from a CUS04 solution. From this information, calculate the molar mass of copper.

19.56 A quantity of 0.300 g of copper was deposited from a CUS04 solution by passing a current of 3.00 A through the solution for 304 s. Calculate the value of the Faraday constant.

19.57

19.58

In a certain electrolysis experiment, 1.44 g of Ag were deposited in one cell (containing an aqueous AgN03 solution), while 0.120 g of an unknown metal X was deposited in another cell (containing an aqueous XCl3 solution) in series with the AgN03

cell. Calculate the molar mass of X.

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

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

Section 19.8: Corrosion

Review Questions

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

19.60 "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.

19.61 Tarnished silver contains Ag2S. The tarnish can be removed by placing silverware in an aluminum pan containing an inert electrolyte solution, such as NaCI. Explain the electrochemical principle for this procedure. [The standard reduction potential for the half-cell reaction Ag2S(s) + 2e- • 2Ag(s) + S2-(aq) is -0.71 V.]

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

Additional Problems

19.63 For each of the following redox reactions, (i) write the half­reactions, (ii) write a balanced equation for the whole reaction, (iii) determine in which direction the reaction will proceed spontaneously under standard-state conditions:

(a) H2(g) + Ne+(aq) • H +(aq) + Ni(s) (b) Mn04 (aq) + Cl - (aq) • Mn2+(aq) + CI2(g) (in acid

solution) (c) Cr(s) + Zn2+(aq) --+. CrH(aq) + Zn(s)

19.64 The oxidation of 25.0 mL of a solution containing Fe2+ requires 26.0 mL of 0.0250 M K2Cr207 in acidic solution. Balance the following equation, and calculate the molar concentration of Fe2+:

19.65 The S02 present in air is mainly responsible for the phenomenon of acid rain. The concentration of S02 can be determined by titrating against a standard permanganate solution as follows:

5S02 + 2Mn04 +2H20 • 5S0~- + 2Mn2+ + 4H+

Calculate the number of grams of S02 in a sample of air if 7.37 mL of 0.00800 M KMn04 solution is required for the titration .

19.66 A sample of iron ore weighing 0.2792 g was dissolved in an

excess of a dilute acid solution. All the iron was first converted to Fe(II) ions. The solution then required 23.30 mL of 0.0194 M KMn04 for oxidation to Fe(III) ions. Calculate the percent by mass of iron in the ore.

19.67 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 unbalanced equation:

(a) Balance this equation. (b) If 36.44 mL of a 0.01652 M KMn04 solution is required to completely oxidize 25.00 mL of an H20 2 solution, calculate the molarity of the H20 2 solution.

19.68 Oxalic acid (H2C20 4) is present in many plants and vegetables. (a) Balance the following equation in acid solution:

Mn04 + C20~- • Mn2+ + CO2

(b) If a 1.00-g sample of plant matter requires 24.0 mL of 0.0100 M KMn04 solution to reach the equivalence point, what is the percent by mass of H2C20 4 in the sample?

19.69 Calcium oxalate (CaC20 4) is insoluble in water. This property has been used to determine the amount of Ca2+ ions in blood. The calcium oxalate isolated from blood is dissolved in acid and titrated against a standardized KMn04 solution as described in Problem 19.68. In one test it is found that the calcium oxalate isolated from a 1O.0-mL sample of blood requires 24.2 mL of 9.56 X 10- 4 M KMn04 for titration. Calculate the number of milligrams of calcium per milliliter of blood.

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

19.71

E D.G Cell Reaction > 0

> 0 =0

From the following information, calculate the solubility product of AgBr:

Ag+(aq) + e- -_. Ag(s)

AgBr(s) + e - • Ag(s) + Br - (aq)

eo = 0.80V

EO = 0.07V

19.72 Consider a galvanic cell composed of the SHE and a half-cell using the reaction Ag + (aq) + e - • 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 [H+] in the hydrogen electrode is changed to (i) 1.0 X

10- 2 M and (ii) 1.0 X 10-5 M, all other reagents being held at standard-state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter.

19.73 A galvanic cell consists of a silver electrode in contact with 346 mL of 0.100 M AgN03 solution and a magnesium electrode in contact with 288 mL of 0.100 M Mg(N03h solution. (a) Calculate E for the cell at 25°C. (b) A current is drawn from the cell until 1.20 g of silver has been deposited at the silver electrode. Calculate E for the cell at this stage of operation.

19.74 Explain why chlorine gas can be prepared by electrolyzing an aqueous solution of NaCI but fluorine gas cannot be prepared by electrolyzing an aqueous solution of NaF.

QUESTIONS AND PROBLEMS 791

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

Cu(s) I Cu2+ (0.080 M) II Cu2+ (1.2 M) I Cu(s)

19.76 The cathode reaction in the Leclanche cell is given by

2Mn02(S) + Zn2+ (aq) + 2e- • ZnMn204(S)

If a Leclanche cell produces a current of 0.0050 A, calculate how many hours this current supply will last if there is initially 4.0 g of Mn02 present in the cell. Assume that there is an excess of Zn2+ ions.

19.77 For a number of years, it was not clear whether mercury(I) ions existed in solution as Hg + or as Hg~+ . To distinguish between these two possibilities, we could set up the following system:

Hg(l) I soln A II soln B I Hg(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 Vat 18°C, what can you deduce about the nature of the mercury(I) ions?

19.78 An aqueous KI solution to which a few drops of phenolphthalein 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 soluble in water, but in the presence of r ions, it forms the brown color of 1:3 ions. See Problem 13.114.)

19.79 A piece of magnesium metal weighing 1.56 g is placed in 100.0 mL of 0.100 M AgN03 at 25°C. Calculate [Mg2+] and [Ag +] in solution at equilibrium. What is the mass of the magnesium left? The volume remains constant.

19.80 Describe an experiment that would enable you to detennine which is the cathode and which is the anode in a galvanic cell using copper and zinc electrodes.

19.81 An acidified solution was electrolyzed using copper electrodes. A constant current of 1.18 A caused the anode to lose 0.584 g after 1.52 X 103 s. (a) What is the gas produced at the cathode, and what is its volume at STP? (b) Given that the charge of an electron is 1.6022 X 10- 19 C, calculate Avogadro's number. Assume that copper is oxidized to Cu2+ ions.

19.82 In a certain electrolysis experiment involving AI3+ ions, 60.2 g of AI is recovered when a current of 0.352 A is used. How many minutes did the electrolysis last?

19.83 Consider the oxidation of ammonia:

(a) Calculate the D.Go for the reaction. (b) If this reaction were used in a fuel cell , what would the standard cell potential be?

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792 CHAPTER 19 Electrochemistry

19.84 When an aqueous solution contairting 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, calculate 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?

19.85 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, the student finds that 2 .64 & of Ag and 1.61 g of Au are deposited at the cathodes. What is the oxidation state of gold in the gold salt?

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

19.87 Given that

19.88

19.89

19.90

2Hg2+(aq) + 2e- ------. Hg~+ (aq)

Hg~+(aq) + 2e- • 2Hg(l)

EO = 0.92 V

EO = 0.85 V

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

Hg~+ (aq) • Hg2+(aq) + Hg(l)

(The precedi ng reaction is an example of a disproportionation reaction in which an element in one oxidation state is both oxidized and reduced. )

Fluorine (F2) is obtained by the electrolysis of liquid hydrogen fluoride (HF) containing potassium fluoride (KF). (a) Write the half-cell reactions and the overall reaction for the process. (b) What is the purpose 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.

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

Industrially, copper is purified by electrolysis . The impure copper acts as the anode, and the cathode is made of pure copper. The electrodes are immersed in a CUS04 solution. During electrolysis, copper at the anode enters the solution as Cu2+ while Cu2+ ions are reduced at the cathode. (a) Write half-cell reactions and the overall reaction for the electrol ytic process . (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?

19.91 An aqueous solution of a platinum salt is electrolyzed at a current of 2.50 A for 2.00 h. As a result, 9.09 g of metallic Pt is formed at the cathode. Calculate the charge on the Pt ions in this solution.

19.92 Consider a galvanic cell consisting of a magnesium electrode in contact with 1.0 M Mg(N03)2 and a cadmium electrode in contact with 1.0 M Cd(N0 3h Calculate EO for the cell, and draw a diagram showing the cathode, anode, and direction of electron flow.

19.93 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.

19.94 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 HN03 and three parts HCI by volume), called aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are HAuCl4 and NOz.) (b) What is the function of HCl?

19.95 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?

19.96 A silver rod and a SHE are dipped into a saturated aqueous solution of si lver oxalate (Ag2C20 4), at 25°C. The measured potential difference between the rod and the SHE is 0.589 V, the rod being positive. Calculate the solubility product constant for silver oxalate.

19.97 Zinc is an amphoteric metal; that is, it reacts with both acids and bases. The standard reduction potential is -1.36 V for the reaction

Calculate the formation constant (Kr) for the reaction

Z n2+ (aq) + 40W(aq)' • Zn(OH)~-(aq)

19.98 Use the data in Table 19.1 to determine whether or not hydrogen peroxide will undergo disproportionation in an acid medium:

19.99

19.100

2HzOz • 2HzO + Oz·

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

y 2+ + 2e- __ ~. Y

X2+ + 2e - ---+. X

I EO 1= 0.34 V

I EO I = 0.25 V

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

A galvanic cell is constructed as follows. One half-cell consists of a platinum wire immersed in a solution containing 1.0 M Sn2+ and 1.0 M SnH

; the other half-cell has a thallium rod immersed in a solution of 1.0 M TI + (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 TI + concentration is increased 10-fo1d? (EOTtm = -0.34 V)

19.101 Given the standard reduction potential for Au3+ in Table 19.1 and

Au + (aq) + e- • Au(s) EO = 1.69 V

answer the fo llowing questions. (a) Why does gold not tarnish in air? (b) Will the following disproportionation occur spontaneously?

3Au+(aq) • Au3+ (aq) + 2Au(s)

(c) Predict the reaction between gold and fluorine gas.

19.102 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?

19.103

19.104

19.105

19.106

When 25.0 mL of a solution containing both Fe2 + and Fe3+ ions is titrated with 23.0 mL of 0.0200 M KMn04 (in dilute sulfuric acid), all the Fe2+ ions are oxidized to Fe3+ ions. Next, the solution is treated with Zn metal to convert all the Fe3+ ions to Fe2+ ions. Finally, 40.0 mL of the same KMn04 solution is added to the solution in order to oxidize the Fe2+ ions to Fe3+ . Calculate the molar concentrations of Fe2+ and Fe3+ in the original solution.

Consider the Daniell cell in Figure 19.1. When viewed externally, the anode appears negative and the cathode positive (electrons are flowing from the anode to the cathode). Yet in solution anions are moving toward the anode, which means that it must appear positive to the anions. Because the anode cannot simultaneously be negative and positive, give an explanation for this apparently contradictory situation .

Use the data in Table 19.1 to show that the decomposition of H20i (a disproportionation reaction) is spontaneous at 25°C:

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 = 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 original sulfuric acid concentration using a current of 22.4 A?

19.107 Consider a Daniell cell operating under non-standard-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) EO, (c) Q, (d) In Q, (e) n?

19.108 A spoon was silver-plated electrolytically in an AgN03 solution . (a) Sketch a diagram for the process. (b) If 0.884 g of Ag was deposited on the spoon at a constant cunent of 18.5 rnA, how long (in min) did the electrolysis take?

19.109 Comment on whether F2 will become a stronger oxidizing agent with increasing H+ concentration.

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

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

Pb(s) + 2H+(aq). > Pb2+ (aq) + Hi g)

given that [Pb2+] = 0.035 M and the solution is buffered at pH 1.60.

19.112 A piece of magnesium ribbon and a copper wire are partially immersed in a 0.1 M HCI 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 occuning at the metals. (b) What visual evidence would you seek to show that Cu is not oxidized to Cu2+ ? (c) At some stage, NaOH solution is added to the beaker to neutralize the HCI acid. Upon further addition of NaOH, a white precipitate form s. What is it?

QUESTIONS AND PROBLEMS 793

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

·r?1 Air cathode 1<

20H- H2O I

/ -Zinc anode

Zn • Zn(OH)1 • ZnO -

The net transformation is Zn(s) + ~ 02(g) > 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 I kg of the metal) of the zinc electrode? (d) If a CUlTent of 2.1 X 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? Assume that the temperature is 25°C and the partial pressure of oxygen is 0.21 atm.

19.114 Calculate EO for the reactions of mercury with (a) 1 M HCI

19.115

19.116

19.117

19.118

and (b) I M HN03. Which acid will oxidize Hg to Hg~+ under standard-state conditions? Can you identify which pictured test tube contains HN03 and Hg and which contains HCI and Hg?

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 hypothetical reaction:

Li+(aq) + m ig) > Li(s) + H +(aq)

Using the appropriate equation presented in this chapter and the thermodynamic data in Appendix 2, calculate EO for Li+(aq) + e > Li(s) at 298 K. Use 96,485 .338 C/mol e - for the Faraday constant. Compare your result with that listed in Table 19.1.

A galvanic cell using Mg/Mg2+ and Cu/Cu2+ 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 [Cu2+ ] remaining?

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

• 2H+(aq) + 2e- ---+> H2(g)

2H20 (l ) + 2e- • H 2(g ) + 20W(aq)

EO = O.OOV

EO = -0.83 V

Compare the pros and cons of a fuel cell, such as the hydrogen­oxygen fuel cell, and a coal-fired power station for generating electricity.

794 CHAPTER 19 Electrochemistry

19.119 Lead storage batteries are rated by ampere-hours, that is, the number of amperes they can deliver in an hour. (a) Show that 1 Ah = 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 the lead will be used up in the electrochemical reaction, and refer to the electrode reactions on page 777.) (c) Calculate E~ell and AGO for the battery.

19.120 Use Equations 18.11 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 thermodynamic data in Appendix 2.)

19.121 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 first passing an iron sheet of appropriate dimensions through an electrolytic cell containing Zn2+ ions, using 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 efficiency of the process is 95 percent? The electricity rate is $0.12 per kilowatt hour (kWh), where 1 W = 1 l is and the density of Zn is 7.1 4 g/cm3

19.122 A 9.00 X 102 mL amount of 0.200 M MgI2 solution was electrolyzed. As a result, hydrogen gas was generated at the cathode and iodine was formed at the anode. The volume of hydrogen collected at 26°C and 779 mmHg was 1.22 X 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? Assume the volume of the solution was constant.

19.123

19.124

19.125

19.126

Based on the following standard reduction potentials,

Fe2+(aq) + 2e- • Fe(s) E'l = -0.44 V

E~ = 0.77 V

calculate the standard reduction potential for the half-reaction

FeH (aq) + 3e- • Fe(s) E '3 =?

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 filled with water so the spoon was totally immersed. Next, she added a few tablespoonfuls of baking soda (sodium bicarbonate), which readily dissolved. Finally, she placed some aluminum foil at the bottom of the pan in contact with the spoon and then heated the solution to about 80°C. After a few minutes, the spoon was removed and rinsed with cold water. The tarnish was gone, and the spoon regained its original shiny appearance. (a) Describe with equations the electrochemical basis for the procedure. (b) Adding N aCI instead of N aHC03 would also work because both compounds are strong electrolytes. What is the added advantage of using NaHC03? (Hint: Consider the pH of the solution.) (c) What is the purpose of heating the solution? (d) Some commercial tarnish removers contain a fluid (or paste) that is a dilute HCI solution. Rubbing the spoon with the fluid will also remove the tarnish. Name two disadvantages of using this procedure compared to the one described previously.

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

Zn(s) + Cu2+(aq) +.==' Zn2+(aq) + Cu(s)

Cytochrome-c is a protein involved in biological electron transfer processes. The redox half-reaction is shown by the reduction of the Fe3+ ion to the Fe2+ ion:

cyt c(Fe3+) + e - --+. cyt c(Fe2+) EO = 0.254 V

Calculate the number of moles of cyt c(FeH) formed from cyt

c(Fe2+) with the Gibbs free energy derived from the oxidation of I mole of glucose.

PRE-PROFESSIONAL PRACTICE EXAM PROBLEMS: PHYSICAL AND BIOLOGICAL SCIENCES

A galvanic cell is constructed by immersing a piece of copper wire in 25 .0 mL of a 0.20 M CUS04 solution and a zinc strip in 25.0 mL of a 0 .20 M ZnS04 solution. Cu2+ ions react with aqueous NH3 to form the complex ion Cu(NH3)~+:

Cu2+ (aq) + 4NH3(aq) --+. Cu(NH3)~+

1. U si ng the eq uati on

E = EO _ 0.0592 V lou Q n b

calculate the emf of the cell at 25°C.

a) 0.0 V b) 1.10 V c) 0.90 V d) 1.30 V

2. What would happen if a small amount of concentrated NH3 solution were added to the CUS04 solution?

a) Nothing. b) Emf would increase. c) Emf would decrease. d) Not enough information to determine.

3. What would happen if a small amount of concentrated NH3 solution were added to the ZnS04 solution?

a) Nothing. b) Emf would increase. c) Emf would decrease. d) Not enough information to determine.

4. In a separate experiment, 25.0 mL of 3.00 M NH3 is added to the CUS04 solution . If the emf of the cell is 0.68 V at equilibrium, calculate the formation constant (K r) of Cu(NH3)~+ '

a) 9.4 X 1022

b) 1.1 X 10- 23

c) 1.5 X 10- 14

d) 1.5 X 1014

ANSWERS TO IN-CHAPTER MATERIALS 795

ANSWERS TO IN-CHAPTER MATERIALS

Answers to Practice Problems 19.1A Mn04 + 5Fe2+ + 8H+ • Mn2+ + 5Fe3+ + 4H20. 19.1B 2Mn04 + H20 + 3CN- • 2Mn02 + 20H- + 3CNO-. 19.2A Cd + Pb2+ • Cd2+ + Pb, E~ell = 0.27 V. 19.2B 2Al + 3Cu2+ • 2AI3+ + 3Cu, E~ell = 2.00 V. 19.3A (a) No reaction, (b) 2H+ + Pb • H2 + PbH 19.3B (a) No reaction, (b) 2H+ + Zn • H2 + Zn2+. 19.4A - 411 kJ/mol. 19.4B 23.2 kJ/mol. 19.5A 1 X 10-42. 19.5B 3 X 10-45. 19.6A Yes, the reaction is spontaneous. 19.6B 2.2 M. 19.7A 7.44 g Mg. 19.7B 0.96 A.

Answers to Checkpoints 19.1.1 a, c, e. 19.1.2 c. 19.3.1 d. 19.3.2 c. 19.3.3 b. 19.3.4 e. 19.4.1 b. 19.4.2 b. 19.5.1 b. 19.5.2 b. 19.7.1 a. 19.7.2 e.

Answers to Applying What You've Learned a) 2Sn + O2 + 4H+ • 2Sn2+ + 2H20 . b) 1.37 V. c) Tin and zinc. d) - 5.3 X 102 kJ/mol. e) 4 X 1092

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