Consider a Daniell cell operating under nonstandard- state

Balancing Redox Equations Problems Balance the following redox equations by the ion electron method: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}\) (in acidic solution) (b) \(\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) (in acidic solution) (c) \(\mathrm{CN}^{-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{CNO}^{-}+\mathrm{MnO}_{2}\) (in basic solution) (d) \(\mathrm{Br}_{2} \longrightarrow \mathrm{BrO}_{3}^{-}+\mathrm{Br}^{-}\) (in basic solution) (e) \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{2} \longrightarrow \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}\) (in acidic solution)

Balance the following equation for the reaction in an acidic medium by the ion-electron method: \(\mathrm{Fe}^{2+}+\mathrm{MnO}_{4}^{-} \ \longrightarrow \ \mathrm{Fe}^{3+}+\mathrm{Mn}^{2+}\)

Which of the following metals will react with (that is, be oxidized by) \(\mathrm{HNO}_{3}\), but not with HCl: Cu, Zn, Ag?

Balancing Redox Equations Problems Balance the following redox equations by the ion electron method: (a) \(\mathrm{Mn}^{2+}+\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{MnO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (in basic solution) (b) \(\mathrm{Bi}(\mathrm{OH})_{3}+\mathrm{SnO}_{2}^{2-} \longrightarrow \mathrm{SnO}_{3}^{2-}+\mathrm{Bi}\) (in basic solution) (c) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Cr}^{3+}+\mathrm{CO}_{2}\) (in acidic solution) (d) \(\mathrm{ClO}_{3}^{-}+\mathrm{Cl}^{-} \longrightarrow \mathrm{Cl}_{2}+\mathrm{ClO}_{2}\) (in acidic solution)

Can \(Sn\) reduce \(\mathrm{Zn}^{2+}(a q)\) under standard-state conditions?

Compare the ease of measuring the equilibrium constant of a reaction electrochemically with that by chemical means in general [see Equation (17.14)].

Galvanic Cells and Standard Emfs Review Questions Define the following terms: anode, cathode, cell voltage, electromotive force, standard reduction potential.

What is the standard emf of a galvanic cell made of a Cd electrode in a \(1.0 \ \mathrm{M} \ \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\) solution and a Cr electrode in a \(1.0 \ \mathrm{M} \ \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\) solution at \(25^{\circ} \mathrm{C}\)?

Consider the following cell diagram: \(\mathrm{Mg}(s)\left|\mathrm{MgSO}_{4}(0.40 M) \| \operatorname{NiSO}_{4}(0.60 M)\right| \mathrm{Ni}(s)\) Calculate the cell voltage at \(25^{\circ} \mathrm{C}\). How does the cell voltage change when (a) \(\left[\mathrm{Mg}^{2+}\right]\) is decreased by a factor of 4 and (b) \(\left[\mathrm{Ni}^{2+}\right]\) is decreased by a factor of 3?

Galvanic Cells and Standard Emfs Review Questions Describe the basic features of a galvanic cell. Why are the two components of the cell separated from each other?

Calculate the equilibrium constant for the following reaction at \(25^{\circ} \mathrm{C}\): \(\mathrm{Fe}^{2+}(a q)+2 \mathrm{Ag}(s) \rightleftharpoons \mathrm{Fe}(s)+2 \mathrm{Ag}^{+}(a q)\)

Which of the following metals can act as a sacrificial anode to protect iron? Sr, Ni, Pb, Co.

Galvanic Cells and Standard Emfs Review Questions What is the function of a salt bridge? What kind of electrolyte should be used in a salt bridge?

Calculate \(\Delta G^{\circ}\) for the following reaction at \(25^{\circ} \mathrm{C}\): \(2 \mathrm{Al}^{3+}(a q)+3 \mathrm{Mg}(s) \rightleftharpoons 2 \mathrm{Al}(s)+3 \mathrm{Mg}^{2+}(a q)\)

What is the minimum voltage needed for the electrolytic process shown above?

Galvanic Cells and Standard Emfs Review Questions What is a cell diagram? Write the cell diagram for a galvanic cell consisting of an Al electrode placed in a \(1 \ M \ \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) solution and a \(Ag\) electrode placed in a \(1 \ M \ \mathrm{AgNO}_{3}\) solution.

Will the following reaction occur spontaneously at \(25^{\circ} \mathrm{C}\), given that \(\left[\mathrm{Fe}^{2+}\right]=0.60 M\) and \(\left[\mathrm{Cd}^{2+}\right]=0.010 \mathrm{M}\)? \(\mathrm{Cd}(s)+\mathrm{Fe}^{2+}(a q) \longrightarrow \mathrm{Cd}^{2+}(a q)+\mathrm{Fe}(s)\)

Complete the following electrolytic cell by labeling the electrodes and showing the half-cell reactions. Explain why the signs of the anode and cathode are opposite to those in a galvanic cell.

Galvanic Cells and Standard Emfs Review Questions What is the difference between the half-reactions discussed in redox processes in Chapter 4 and the half-cell reactions discussed in Section 18.2?

What is the emf of a galvanic cell consisting of a \(\mathrm{Cd}^{2+} / \mathrm{Cd}\) half-cell and a \(\mathrm{Pt} / \mathrm{H}^{+} / \mathrm{H}_{2}\) half-cell if \(\left[\mathrm{Cd}^{2+}\right]=0.20 \mathrm{M}\), \(\left[\mathrm{H}^{+}\right]=0.16 M\), and \(P_{\mathrm{H}_{2}}=0.80\) atm?

Problem 8P After operating a Daniell cell (see Figure 18.1) for a few minutes, a student notices that the cell emf begins to drop. Why?

An aqueous solution of \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) is electrolyzed. What are the gaseous products at the anode and cathode?

Galvanic Cells and Standard Emfs Review Questions Use the information in Table 2.1, and calculate the Faraday constant.

A constant current is passed through an electrolytic cell containing molten \(\mathrm{MgCl}_{2}\) for 18 \(h\). If \(4.8 \times 10^{5} \ \mathrm{g}\) of \(\mathrm{Cl}_{2}\) are obtained, what is the current in amperes?

Galvanic Cells and Standard Emfs Review Questions Discuss the spontaneity of an electrochemical reaction in terms of its standard emf \(\left(E_{\text {cell }}^{\circ}\right)\).

Calculate the standard emf of a cell that uses the \(\mathrm{Mg} / \mathrm{Mg}^{2+}\) and \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) half-cell reactions at \(25^{\circ} \mathrm{C}\). Write the equation for the cell reaction that occurs under standard-state conditions.

Predict whether \(\mathrm{Fe}^{3+}\) can oxidize \(\mathrm{I}^{-}\) to \(\mathrm{I}_{2}\), under standard-state conditions.

Consider the following half-reactions: \(\begin{array}{l} \mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q)+5 e^{-} \underset{\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)}{\longrightarrow}\\ \mathrm{NO}_{3}^{-}(a q)+4 \mathrm{H}^{+}(a q)+3 e^{-} \longrightarrow \mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \end{array}\) Predict whether \(\mathrm{NO}_{3}^{-}\) ions will oxidize \(\mathrm{Mn}^{2+}\) to \(\mathrm{MnO}_{4}^{-}\) under standard-state conditions.

Predict whether the following reactions would occur spontaneously in aqueous solution at \(25^{\circ} \mathrm{C}\). Assume that the initial concentrations of dissolved species are all 1.0 \(M\). (a) \(\mathrm{Ca}(s)+\mathrm{Cd}^{2+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{Cd}(s)\) (b) \(2 \mathrm{Br}^{-}(a q)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Br}_{2}(l)+\operatorname{Sn}(s)\) (c) \(2 \mathrm{Ag}(s)+\mathrm{Ni}^{2+}(a q) \longrightarrow 2 \mathrm{Ag}^{+}(a q)+\mathrm{Ni}(s)\) (d) \(\mathrm{Cu}^{+}(a q)+\mathrm{Fe}^{3+}(a q) \underset{\mathrm{Cu}^{2+}(a q)+\mathrm{Fe}^{2+}(a q)}{\longrightarrow}\)

Which species in each pair is a better oxidizing agent under standard-state conditions? (a) \(\mathrm{Br}_{2} \text { or } \mathrm{Au}^{3+}\), (b) \(\mathrm{H}_{2} \text { or } \mathrm{Ag}^{+}\), (c) \(\mathrm{Cd}^{2+} \text { or } \mathrm{Cr}^{3+}\), (d) \(\mathrm{O}_{2}\), in acidic media or \(\mathrm{O}_{2}\) in basic media.

Which species in each pair is a better reducing agent under standard-state conditions? (a) Na or Li, (b) \(\mathrm{H}_{2}\) or \(\mathrm{I}_{2}\), (c) \(\mathrm{Fe}^{2+} \text { or } \mathrm{Ag}\), (d) \(\mathrm{Br}^{-} \text {or } \mathrm{Co}^{2+}\).

The \(E_{\text {cell }}^{\circ}\) for the following cell is 1.54 V at \(25^{\circ} \mathrm{C}\) \(\mathrm{U}(s)\left|\mathrm{U}^{3+}(a q) \| \mathrm{Ni}^{2+}(a q)\right| \mathrm{Ni}(s)\) Calculate the standard reduction potential for the \(\mathrm{U}^{3+} / \mathrm{U}\) half-cell.

Spontaneity of Redox Reactions Write the equations relating \(\Delta G^{\circ}\) and \(K\) to the standard emf of a cell. Define all the terms.

The equilibrium constant for the reaction \(\operatorname{Sr}(s)+\mathrm{Mg}^{2+}(a q) \rightleftharpoons \mathrm{Sr}^{2+}(a q)+\mathrm{Mg}(s)\) is \(2.69 \times 10^{12}\) at \(25^ {\circ} \mathrm{C}\). Calculate \(E^{\circ}\) for a cell made up of \(\mathrm{Sr} / \mathrm{Sr}^{2+}\) and \(\mathrm{Mg} / \mathrm{Mg}^{2+}\) half-cells.

Calculate \(\Delta G^{\circ}\) and \(K_{\mathrm{c}}\). for the following reactions at \(25^{\circ} \mathrm{C}\): (a) \(\mathrm{Mg}(s)+\mathrm{Pb}^{2+}(a q) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{Pb}(s)\) (b) \(\mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)\) (c) \(\begin{aligned}\mathrm{O}_2(g)+4\mathrm{H}^+(aq)+4 \mathrm{Fe}^{2+}(aq) & \rightleftharpoons\\ \left(2\mathrm{H}_2\mathrm{O}(l)+4\mathrm{Fe}^{3+}(aq\right) & \end{aligned}\) (d) \(2 \mathrm{Al}(s)+3 \mathrm{I}_{2}(s) \rightleftharpoons 2 \mathrm{Al}^{3+}(a q)+6 \mathrm{I}^{-}(a q)\)

Given that \(E^{\circ}=0.52 \ \mathrm{V}\) for the reduction \(\mathrm{Cu}^{+}(a q)+e^{-} \rightarrow \mathrm{Cu}(s)\), calculate \(E^{\circ}\), \(\Delta G^{\circ}\), and \(K\) for the following reaction at \(25^{\circ} \mathrm{C}\): \(2 \mathrm{Cu}^{+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{Cu}(s)\)

Write the Nernst equation and explain all the terms.

Write the Nernst equation for the following processes at some temperature \(T\): (a) \(\mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Sn}(s)\) (b) \(2 \mathrm{Cr}(s)+3 \mathrm{Pb}^{2+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+3 \mathrm{Pb}(s)\)

What is the potential of a cell made up of \(\mathrm{Zn} / \mathrm{Zn}^{2+}\) and \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) half-cells at \(25^{\circ} \mathrm{C} \text { if }\left[\mathrm{Zn}^{2+}\right]=0.25 M\) and \(\left[\mathrm{Cu}^{2+}\right]=0.15 \mathrm{M}\)?

Calculate \(E^{\circ}\), \(E\), and \(\Delta G\) for the following cell reactions. (a) \(\begin{array}{l} \mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\operatorname{Sn}(s) \\ {\left[\mathrm{Mg}^{2+}\right]=0.045 \mathrm{M},\left[\mathrm{Sn}^{2+}\right]=0.035 \mathrm{M}} \end{array}\) (b) \(\begin{array}{l} 3 \mathrm{Zn}(s)+2 \mathrm{Cr}^{3+}(a q) \longrightarrow 3 \mathrm{Zn}^{2+}(a q)+2 \mathrm{Cr}(s) \\ {\left[\mathrm{Cr}^{3+}\right]=0.010 M,\left[\mathrm{Zn}^{2+}\right]=0.0085 M} \end{array}\)

Calculate the standard potential of the cell consisting of the \(\mathrm{Zn} / \mathrm{Zn}^{2+}\) half-cell and the SHE. What will the emf of the cell be if \(\left[\mathrm{Zn}{ }^{2+}\right]=0.45 \mathrm{M}, P_{\mathrm{H}_2}=2.0\) atm, and \(\left[\mathrm{H}^{+}\right]=1.8 \mathrm{M}\)?

What is the emf of a cell consisting of a \(\mathrm{Pb}^{2+} / \mathrm{Pb}\) half-cell and a \(\mathrm{Pt} / \mathrm{H}^{+} / \mathrm{H}_{2}\) half-cell if \(\left[\mathrm{Pb}^{2+}\right]=0.10\mathrm{\ M}\) , \(\left[\mathrm{H}^+\right]=0.050\mathrm{\ M}\) , and \(P_{H_2}=1.0\mathrm{\ atm}\) ?

Referring to the arrangement in Figure 18.1, calculate the \(\left[\mathrm{Cu}^{2+}\right] /\left[\mathrm{Zn}^{2+}\right]\) ratio at which the following reaction is spontaneous at \(25^{\circ} \mathrm{C}\) : \(\mathrm{Cu}(s)+\mathrm{Zn}^{2+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{Zn}(s)\) Text Transcription: [Cu^2+]/[Zn^2+] 25^circ C Cu (s)+Zn^2+(aq) longrightarrow Cu^2+(aq)+Zn(s)

Calculate the emf of the following concentration cell: \(\operatorname{Mg}(s)\left|\mathrm{Mg}^{2+}(0.24 M) \| \mathrm{Mg}^{2+}(0.53 M)\right| \mathrm{Mg}(s)\) Text Transcription: Mg(s)|Mg^2+(0.24 M)||Mg^2+(0.53 M)|Mg(s)

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.

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

Calculate the standard emf of the propane fuel cell discussed on p. 838 at \(25^{\circ} \mathrm{C}\), given that \(\Delta G_{\mathrm{f}}^{\circ}\) for propane is \(-23.5 \mathrm{~kJ} / \mathrm{mol}\).

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

"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.

Tarnished silver contains \(\mathrm{Ag}_2 \mathrm{~S}\). The tarnish can be removed by placing silverware in an aluminum pan containing an inert electrolyte solution, such as \(\mathrm{NaCl}\). Explain the electrochemical principle for this procedure. [The standard reduction potential for the half-cell reaction \(\mathrm{Ag}_2 \mathrm{~S}(s)+2 e^{-} \rightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)\) is \(-0.71 \mathrm{~V}\)].

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

Describe the electrolysis of an aqueous solution of \(\mathrm{KNO}_3\).

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

The half-reaction at an electrode is \(\mathrm{Mg}^{2+} \text { (molten) }+2 e^{-} \longrightarrow \operatorname{Mg}(s)\) Calculate the number of grams of magnesium that can be produced by supplying 1.00 F to the electrode. Text Transcription: Mg^2 (molten)+2e^-longrightarrow Mg(s)

Consider the electrolysis of molten barium chloride, \(\mathrm{BaCl}_{2}\). (a) Write the half-reactions. (b) How many grams of barium metal can be produced by supplying 0.50 A for 30 min? Text Transcription: BaCl_2

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

One of the half-reactions for the electrolysis of water is \(2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 e^{-}\) If 0.076 L of \(\mathrm{O}_{2}\) is collected at \(25^{\circ} \mathrm{C}\) and 755 mmHg, how many moles of electrons had to pass through the solution? Text Transcription: 2H_2 O(l)longrightarrow O_2(g)+4H^+(aq)+4e^- O_2 25^circ C

How many moles of electrons are required to produce (a) 0.84 L of \(\mathrm{O}_{2}\) at exactly 1 atm and \(25^{\circ} \mathrm{C}\) from aqueous \(\mathrm{H}_{2} \mathrm{SO}_{4}\) solution; (b) 150 L of \(\mathrm{Cl}_{2}\) at 750 mmHg and \(20^{\circ} \mathrm{C}\) from molten NaCl; (c) 6.0 g of Sn from molten \(\mathrm{SnCl}_{2}\) ? Text Transcription: O_2 25^circ C H_2SO_4 Cl_2 20^circ C SnCl_2

Calculate the amounts of Cu and \(\mathrm{Br}_{2}\) produced in 1.0 h at inert electrodes in a solution of \(\mathrm{CuBr}_{2}\) by a current of 4.50 A. Text Transcription: Br_2 CuBr_2

In the electrolysis of an aqueous \(\mathrm{AgNO}_{3}\) solution, 0.67 g of Ag is deposited after a certain period of time. (a) Write the half-reaction for the reduction of \(\mathrm{Ag}^{+}\). (b) What is the probable oxidation halfreaction? (c) Calculate the quantity of electricity used, in coulombs. Text Transcription: AgNO_3 Ag^+

A steady current was passed through molten \(\mathrm{CoSO}_{4}\) until 2.35 g of metallic cobalt was produced. Calculate the number of coulombs of electricity used. Text Transcription: CoSO_4

A constant electric current flows for 3.75 h through two electrolytic cells connected in series. One contains a solution of \(\mathrm{AgNO}_{3}\) and the second a solution of \(\mathrm{CuCl}_{2}\). During this time 2.00 g of silver are 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? Text Transcription: AgNO_3 CuCl_2

What is the hourly production rate of chlorine gas (in kg ) from an electrolytic cell using aqueous NaCl electrolyte and carrying a current of \(1.500 \times 10^{3} \mathrm{~A}\) ? The anode efficiency for the oxidation of \(\mathrm{Cl}^{-}\) is 93.0 percent. Text Transcription: 1.500 x 10^3 A Cl^-

Chromium plating is applied by electrolysis to objects suspended in a dichromate solution, according to the following (unbalanced) half-reaction: \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+e^{-}+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cr}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) How long (in hours) would it take to apply a chromium plating \(1.0 \times 10^{-2} \mathrm{~mm}\) thick to a car bumper with a surface area of \(0.25 \mathrm{~m}^{2}\) in an electrolytic cell carrying a current of 25.0 A ? (The density of chromium is \(7.19 \mathrm{~g} / \mathrm{cm}^{3}\).) Text Transcription: Cr_2O^2-_7(aq)+e^-+H^-(aq)longrightarrow Cr(s)+H_2O(l) 1.0 x 10^-2 0.25m^2 7.19 g/cm^3

The passage of a current of 0.750 A for 25.0 min deposited 0.369 g of copper from a \(\mathrm{CuSO}_4\) solution. From this information, calculate the molar mass of copper.

A quantity of 0300 g of copper was deposited from a \(\mathrm{CuSO}_{4}\) solution by passing a current of 3.00 A through the solution for 304 s. Calculate the value of the Faraday constant. Text Transcription: CuSO_4

In a certain electrolysis experiment, 1.44 g of Ag were deposited in one cell (containing an aqueous \(\mathrm{AgNO}_{3}\) solution), while 0.120 g of an unknown metal \(X\) was deposited in another cell (containing an aqueous \(\mathrm{XCl}_{3}\) solution) in series with the \(\mathrm{AgNO}_{3}\) cell. Calculate the molar mass of \(X\). Text Transcription: AgNO_3 X XCl_3

One of the half-reactions for the electrolysis of water is \(2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{H}_2(g)\) If 0.845 L of \(\mathrm{H}_2\) is collected at \(25^{\circ} \mathrm{C}\) and 782 mmHg, how many moles of electrons had to pass through the solution?

A steady current of 10.0 A is passed through three electrolytic cells for 10.0 min. Calculate the mass of the metals formed if the solutions are \(0.10 \ \mathrm{M} \ \mathrm{AgNO}_{3}, 0.10 \ \mathrm{M} \ \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\), and \(0.10 \ \mathrm{M} \ \mathrm{Au}\left(\mathrm{NO}_{3}\right)_{3}\). Text Transcription: 0.10 M AgNO_3, 0.10 M Cu(NO_3)_2 0.10 M Au(NO_3)_3

Industrially, copper metal can be purified electrolytically according to the following arrangement. The anode is made of the impure Cu electrode and the cathode is the pure Cu electrode. The electrodes are immersed in a \(\mathrm{CuSO}_{4}\) solution. (a) Write the half-cell reactions at the electrodes. (b) Calculate the mass (in g) of Cu purified after passing a current of 20 A for 10 h. (c) Explain why impurities such as Zn, Fe, Au, and Ag are not deposited at the electrodes. Text Transcription: CuSO_4

A Daniell cell consists of a zinc electrode in 1.00 L of \(1.00 \ M \ \mathrm{ZnSO}_{4}\) and a Cu electrode in 1.00 L of \(1.00 \ \mathrm{M} \ \mathrm{CuSO}_{4}\) at \(25^{\circ} \mathrm{C}\). A steady current of 10.0 A is drawn from the cell. Calculate the \(E_{\text {cell }}\) after 1.00 h. Assume volumes to remain constant. Text Transcription: 1.00 M ZnSO_4 1.00 M CuSO_4 25^circ C E_cell

A concentration cell is constructed having Cu electrodes in two \(\mathrm{CuSO}_{4}\) solutions A and B. At \(25^{\circ} \mathrm{C}\), the osmotic pressures of the two solutions are 48.9 atm and 4.89 atm, respectively. Calculate the \(E_{\text {cell }}\), assuming no ion-pair formation. Text Transcription: CuSO_4 25^circ C E_cell

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 direction the reaction will proceed spontaneously under standard-state conditions: (a) \(\mathrm{H}_{2}(g)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Ni}(s)\) (b) \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow\) \(\mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(g)\) (in acid solution) (c) \(\mathrm{Cr}(s)+\mathrm{Zn}^{2+}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{Zn}(s)\) Text Transcription: H_2g+Ni^2+(aq)longrightarrow H^+Ni(s) MnO^-_4(aq)+Cl^-(aq)longrightarrow Mn^2+(aq)+Cl_2(g) Cr(s)+Zn^2+(aq)longrightarrow Cr^3+(aq)+Zn(s)

The oxidation of 25.0 mL of a solution containing \(\mathrm{Fe}^{2+}\) requires 26.0 mL of \(0.0250 \ M \ \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) in acidic solution. Balance the following equation and calculate the molar concentration of \(\mathrm{Fe}^{2+}\) : \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{Fe}^{2+}+\mathrm{H}^{+} \longrightarrow \mathrm{Cr}^{3+}+\mathrm{Fe}^{3+}\) Text Transcription: Fe^2+ 0.0250 M K_2Cr_2O_7 Cr_2O^2-_7 +Fe^+H^+longrightarrow Cr_3+Fe^3+

The \(\mathrm{SO}_{2}\) present in air is mainly responsible for the phenomenon of acid rain. The concentration of \(\mathrm{SO}_{2}\) can be determined by titrating against a standard permanganate solution as follows: \(5 \mathrm{SO}_{2}+2 \mathrm{MnO}_{4}^{-}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow\) \(5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+4 \mathrm{H}^{+}\) Calculate the number of grams of \(\mathrm{SO}_{2}\) in a sample of air if 7.37 mL of \(0.00800 \ \mathrm{M} \ \mathrm{KMnO} \mathrm{KM}_{4}\) solution are required for the titration. Text Transcription: SO_2 5SO_2+2MnO^-_4+2H_2O longrightarrow 5SO^2-_4+2Mn^2+ +4H^+ 0.00800 M KMO_4

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 \(0.0194 \ M \ \mathrm{KMnO}_{4}\) for oxidation to Fe (III) ions. Calculate the percent by mass of iron in the ore. Text Transcription: 0.0194 M KMnO_4

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

From the following information, calculate the solubility product of \(\mathrm{AgBr}\) : \(\mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \mathrm{Ag}(s)\) \(E^{\circ}=0.80 \mathrm{~V}\) \(\mathrm{AgBr}(s)+e^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q)\) \(E^{\circ}=0.07 \mathrm{~V}\)

Consider a galvanic cell composed of the SHE and a half-cell using the reaction \(\mathrm{Ag}^{+}(a q)+e^{-} \rightarrow \mathrm{Ag}(s)\). (a) Calculate the standard cell potential. (b) What is the spontaneous cell reaction under standard-state conditions? (c) Calculate the cell potential when \(\left[\mathrm{H}^{+}\right]\) in the hydrogen electrode is changed to (i) \(1.0 \times 10^{-2} \ \mathrm{M}\) and (ii) \(1.0 \times 10^{-5} \ \mathrm{M}\), all other reagents being held at standard-state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter. Text Transcription: Ag^+(aq)+e^- rightarrow Ag(s) [H^+] 1.0 x 10^-2 M 1.0 x 10^-5 M

Calculate the emf of the following concentration cell at \(25^{\circ} \mathrm{C}\) : \(\mathrm{Cu}(s)\left|\mathrm{Cu}^{2+}(0.080 M) \| \mathrm{Cu}^{2+}(1.2 M)\right| \mathrm{Cu}(s)\)

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 \(\mathrm{I}^{-}\) ions, it forms the brown color of \(\mathrm{I}_{3}^{-}\) ions. See Problem 12.102.) Text Transcription: I^- I^-_3

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

An acidified solution was electrolyzed using copper electrodes. A constant current of 1.18 A caused the anode to lose 0.584 g after \(1.52 \times 10^{3} \mathrm{~s}\). (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 \(1.6022 \times 10^{-19} \mathrm{C}\), calculate Avogadro's number. Assume that copper is oxidized to \(\mathrm{Cu}^{2+}\) ions. Text Transcription: 1.52 x 10^3 s 1.6022 x 10^-19 C Cu^2+

In a certain electrolysis experiment involving \(\mathrm{Al}^{3+}\) ions, 60.2 g of Al is recovered when a current of 0.352 A is used. How many minutes did the electrolysis last? Text Transcription: Al^3+

Consider the oxidation of ammonia: \(4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) (a) Calculate the \(\Delta G^{\circ}\) for the reaction. (b) If this reaction were used in a fuel cell, what would the standard cell potential be? Text Transcription: 4NH_3(g)+3O_2(g) longrightarrow 2 N_2(g)+6H_2O(l) DeltaG^circ

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, calculate the volume (in liters) of \(\mathrm{O}_{2}\) generated at \(23^{\circ} \mathrm{C}\) and 747 mmHg. (b) What is the current used if the electrolytic process took 2.00 h ? Text Transcription: O_2 23^circ C

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 finds 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?

Given that \(2 \mathrm{Hg}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Hg}_{2}^{2+}(a q) \quad E^{\circ}=0.92 \mathrm{~V}\) \(\mathrm{Hg}_{2}^{2+}(a q)+2 e^{-} \longrightarrow 2 \mathrm{Hg}(l) \quad E^{\circ}=0.85 \mathrm{~V}\) calculate \(\Delta G^{\circ}\) and \(K\) for the following process at \(25^{\circ} \mathrm{C}\) : \(\mathrm{Hg}_{2}^{2+}(a q) \longrightarrow \mathrm{Hg}^{2+}(a q)+\mathrm{Hg}(l)\) (The preceding reaction is an example of a disproportionation reaction in which an element in one oxidation state is both oxidized and reduced.)

A galvanic cell with \(E_{\text {cell }}^{\circ}=0.30 \mathrm{~V}\) can be constructed using an Fe electrode in a \(1.0 \ \mathrm{M} \ \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}\) solution, and either a Sn electrode in a \(1.0 \ \mathrm{M} \ \mathrm{Sn}\left(\mathrm{NO}_{3}\right)_{2}\) solution, or a Cr electrode in a \(1.0 \ \mathrm{M} \ \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\) solution, even though \(\mathrm{Sn}^{2+} / \mathrm{Sn}\) and \(\mathrm{Cr}^{3+} / \mathrm{Cr}\) have different standard reduction potentials. Explain.

Shown here is a galvanic cell connected to an electrolytic cell. Label the electrodes (anodes and cathodes) and show the movement of electrons along the wires and cations and anions in solution. For simplicity, the salt bridge is not shown for the galvanic cell.

Fluorine \(\left(\mathrm{F}_{2}\right)\) 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 \(\mathrm{F}_{2}\) (in liters) collected at \(24.0^{\circ} \mathrm{C}\) and 1.2 atm after electrolyzing the solution for 15 h at a current of 502 A.

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 \(\mathrm{CuSO}_{4}\) solution. During electrolysis, copper at the anode enters the solution as \(\mathrm{Cu}^{2+}\) while \(\mathrm{Cu}^{2+}\) ions are reduced at the cathode. (a) Write half-cell reactions and the overall reaction for the electrolytic 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 ?

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 are formed at the cathode. Calculate the charge on the Pt ions in this solution.

Consider a galvanic cell consisting of a magnesium electrode in contact with \(1.0 \ \mathrm{M} \ \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) and a cadmium electrode in contact with \(1.0 \ \mathrm{M} \ \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}\). Calculate \(E^{\circ}\) for the cell, and draw a diagram showing the cathode, anode, and direction of electron flow.

A current of 6.00 A passes through an electrolytic cell containing dilute sulfuric acid for 3.40 h. If the volume of \(\mathrm{O}_{2}\) gas generated at the anode is 4.26 L (at STP), calculate the charge (in coulombs) on an electron.

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?

The table here shows the standard reduction potentials of several half-reactions: \(\text { Half-Reactions } \quad \quad \quad \quad \boldsymbol{E}^{\circ}(\mathbf{V})\) ______________________________ \(\mathrm{A}^{2+}+2 e^{-} \longrightarrow \mathrm{A} \quad \quad \quad-1.46\) \(\mathrm{~B}_{2}+2 e^{-} \longrightarrow 2 \mathrm{~B}^{-} \quad \quad \quad \ 0.33\) \(\mathrm{C}^{3+}+3 e^{-} \longrightarrow \mathrm{C} \quad \quad \quad \quad 1.13 \\\) \(\mathrm{D}^{+}+e^{-} \longrightarrow \mathrm{D} \quad \quad \quad \ \ -0.87\) _______________________________ (a) Which is the strongest oxidizing agent and which is the strongest reducing agent? (b) Which substances can be oxidized by \(\mathbf{B}_{2}\)? (c) Which substances can be reduced by \(\mathrm{B}^{-}\)? (d) Write the overall equation for a cell that delivers a voltage of 2.59 V under standard-state conditions.

Consider a concentration cell made of the following two compartments: \(\mathrm{Cl}_{2}(0.20 \mathrm{~atm}) \mid \mathrm{Cl}^{-}(1.0 \mathrm{M})\) and \(\mathrm{Cl}_{2}(2.0 \mathrm{~atm}) \mid \mathrm{Cl}^{-}(1.0 \mathrm{M})\). Platinum is used as the inert electrodes. Draw a cell diagram for the cell and calculate the emf of the cell at \(25^{\circ} \mathrm{C}\).

A silver rod and a SHE are dipped into a saturated aqueous solution of silver oxalate, \(\mathrm{Ag}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\), at \(25^{\circ} \mathrm{C}\). 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.

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 \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q)+2 e^{-} \longrightarrow \mathrm{Zn}(s)+4 \mathrm{OH}^{-}(a q)\) Calculate the formation constant \(\left(K_{\mathrm{f}}\right)\) for the reaction \(\mathrm{Zn}^{2+}(a q)+4 \mathrm{OH}^{-}(a q) \rightleftharpoons \mathrm{Zn}(\mathrm{OH})_{4}^{2-}(a q)\)

Use the data in Table 18.1 to determine whether or not hydrogen peroxide will undergo disproportionation in an acid medium: \(2 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\).

The magnitudes (but not the signs) of the standard reduction potentials of two metals \(\mathrm{X}\) and \(\mathrm{Y}\) are \(\mathrm{Y}^{2+}+2 e^{-} \longrightarrow \mathrm{Y} \left|E^{\circ}\right|=0.34 \mathrm{~V}\) \(\mathrm{X}^{2+}+2 e^{-} \longrightarrow \mathrm{X} \left|E^{\circ}\right|=0.25 \mathrm{~V}\) where the || notation denotes that only the magnitude (but not the sign) of the \(E^{\circ}\) value is shown. When the half-cells of \(\mathrm{X}\) and \(\mathrm{Y}\) are connected, electrons flow from \(\mathrm{X}\) to \(\mathrm{Y}\). When \(\mathrm{X}\) is connected to a SHE, electrons flow from \(\mathrm{X}\) to SHE. (a) Are the \(E^{\circ}\) values of the half-reactions positive or negative? (b) What is the standard emf of a cell made up of \(\mathrm{X}\) and \(\mathrm{Y}\)?

A galvanic cell is constructed as follows. One halfcell consists of a platinum wire immersed in a solution containing \(1.0 \ \mathrm{M} \ \mathrm{Sn}^{2+}\) and \(1.0 \ \mathrm{M} \ \mathrm{Sn}^{4+}\); the other half-cell has a thallium rod immersed in a solution of \(1.0 \ \mathrm{M} \ \mathrm{Tl}^{+}\). (a) Write the half-cell reactions and the overall reaction. (b) What is the equilibrium constant at \(25^{\circ} \mathrm{C}\)? (c) What is the cell voltage if the \(\mathrm{T1}^{+}\)concentration is increased tenfold? \(\left(E_{\mathrm{T} 1^{+} / \mathrm{Tl}}^{\circ}=-0.34 \mathrm{~V}_{.}\right)\)

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?

When 25.0 mL of a solution containing both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) ions is titrated with 23.0 mL of \(0.0200 \ \mathrm{M} \ \mathrm{KMnO}_{4}\) (in dilute sulfuric acid), all of the \(\mathrm{Fe}^{2+}\) ions are oxidized to \(\mathrm{Fe}^{3+}\) ions. Next, the solution is treated with Zn metal to convert all of the \(\mathrm{Fe}^{3+}\) ions to \(\mathrm{Fe}^{2+}\) ions. Finally, 40.0 mL of the same \(\mathrm{KMnO}_{4}\) solution are added to the solution in order to oxidize the \(\mathrm{Fe}^{2+}\) ions to \(\mathrm{Fe}^{3+}\). Calculate the molar concentrations of \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) in the original solution.

Consider the Daniell cell in Figure 18.1. 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 18.1 to show that the decomposition of \(\mathrm{H}_{2} \mathrm{O}_{2}\) (a disproportionation reaction) is spontaneous at \(25^{\circ} \mathrm{C}\) : \(2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\)

Consider two electrolytic cells A and B. Cell A contains a \(0.20 \ \mathrm{M} \ \mathrm{CoSO}_{4}\) solution and platinum electrodes. Cell B differs from cell A only in that cobalt metals are used as electrodes. In each case, a current of 0.20 A is passed through the cell for 1.0 h. (a) Write equations for the half-cell and overall cell reactions for these cells. (b) Calculate the products formed (in grams) at the anode and cathode in each case.

A galvanic cell consists of a Mg electrode in a \(1 \ \mathrm{M} \ \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) solution and another metal electrode \(\mathrm{X}\) in a \(1 \mathrm{MX}\left(\mathrm{NO}_{3}\right)_{2}\) solution. Listed here are the \(E_{\text {cell }}^{\circ}\) values of four such galvanic cells. In each case, identify \(\mathrm{X}\) from Table 18.1. (a) \(E_{\text {cell }}^{\circ}=2.12 \mathrm{~V}\), (b) \(E_{\text {cell }}^{\circ}=2.24 \mathrm{~V}\), (c) \(E_{\text {cell }}^{\circ}=1.61 \mathrm{~V}\), (d) \(E_{\text {cell }}^{\circ}=1.93 \mathrm{~V}\).

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 amperes?

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) \(E^{\circ}\), (c) \(Q\), (d) ln \(Q\), and (e) \(n\)?

Comment on whether \(\mathrm{F}_{2}\) will become a stronger oxidizing agent with increasing \(\mathrm{H}^{+}\) concentration.

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.

Calculate the pressure of \(\mathrm{H}_{2}\) (in atm) required to maintain equilibrium with respect to the following reaction at \(25^{\circ} \mathrm{C}\) : \(\mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g)\) Given that \(\left[\mathrm{Pb}^{2+}\right]=0.035 \ M\) and the solution is buffered at pH 1.60.

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 \(\mathrm{Cu}^{2+}\) ? (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?

The zinc-air battery shows much promise for electric cars because it is lightweight and rechargeable: The net transformation is \(\mathrm{Zn}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{ZnO}(s)\). (a) Write the half-reactions at the zinc-air electrodes and calculate the standard emf of the battery at \(25^{\circ} \mathrm{C}\). (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 current of \(2.1 \times 10^{5} \mathrm{~A}\) 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 \(25^{\circ} \mathrm{C}\) and the partial pressure of oxygen is 0.21 atm.

Calculate \(E^{\circ}\) for the reactions of mercury with (a) 1 M HCl and (b) \(1 \ M \ \mathrm{HNO}_{3}\). Which acid will oxidize Hg to \(\mathrm{Hg}_{2}^{2+}\) under standard-state conditions? Can you identify which test tube shown contains \(\mathrm{HNO}_{3}\) and Hg and which contains HCl 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 \(\mathrm{Li}^{+}(a q)+\frac{1}{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{Li}(s)+\mathrm{H}^{+}(a q)\) Using the appropriate equation presented in this chapter and the thermodynamic data in Appendix 3 , calculate \(E^{\circ}\) for \(\mathrm{Li}^{+}(a q)+e^{-} \rightarrow \mathrm{Li}(s)\) at 298 K. Compare your result with that listed in Table 18.1. (See back endpaper for the Faraday constant.)

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 \(\mathrm{Li}^{+}(a q)+\frac{1}{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{Li}(s)+\mathrm{H}^{+}(a q)\) Using the appropriate equation presented in this chapter and the thermodynamic data in Appendix 3 , calculate \(E^{\circ}\) for \(\mathrm{Li}^{+}(a q)+e^{-} \rightarrow \mathrm{Li}(s)\) at 298 K. Compare your result with that listed in Table 18.1. (See back endpaper for the Faraday constant.)

A galvanic cell using \(\mathrm{Mg} / \mathrm{Mg}^{2+}\) and \(\mathrm{Cu} / \mathrm{Cu}^{2+}\) halfcells operates under standard-state conditions at \(25^{\circ} \mathrm{C}\) 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 \(\left[\mathrm{Cu}^{2+}\right]\) remaining?

Given the following standard reduction potentials, calculate the ion-product, \(K_{\mathrm{w}}\), for water at \(25^{\circ} \mathrm{C}\) : \(2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g) \quad \quad E^{\circ}=0.00 \mathrm{~V}\) \(2 \mathrm{H}_{2} \mathrm{O}(l)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q)\) \(E^{\circ}=-0.83 \mathrm{~V}\)

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

Use Equations (17.10) and (18.3) to calculate the emf values of the Daniell cell at \(25^{\circ} \mathrm{C}\) and \(80^{\circ} \mathrm{C}\). Comment on your results. What assumptions are used in the derivation? (Hint: You need the thermodynamic data in Appendix 3.)

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 \(\mathrm{Zn}^{2+}\) 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 J/s and the density of Zn is \(7.14 \mathrm{~g} / \mathrm{cm}^{3}\).

Based on the following standard reduction potentials: \(\mathrm{Fe}^{2+}(aq)+2e^-\longrightarrow\mathrm{Fe}(s)\ \ \ \ \ \ \ \ \ \ \ \quad E_1^{\circ}=-0.44\mathrm{\ V}\) \(\mathrm{Fe}^{3+}(aq)+e^-\longrightarrow\mathrm{Fe}^{2+}(aq)\quad\ \ \ \ \ \ \ E_2^{\circ}=0.77\mathrm{\ V}\) calculate the standard reduction potential for the half-reaction \(\mathrm{Fe}^{3+}(aq)+3e^-\longrightarrow\mathrm{Fe}(s)\quad\ \ \ \ \ \ \ \ \ E_3^{\circ}=?\)

Calculate the equilibrium constant for the following reaction at 298 K: \(\mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+\mathrm{Cu}(s)\)

The nitrite ion \(\left(\mathrm{NO}_{2}^{-}\right)\) in soil is oxidized to nitrate ion \(\left(\mathrm{NO}_{3}^{-}\right)\) by the bacteria Nitrobacter agilis in the presence of oxygen. The half-reduction reactions are \(\mathrm{NO}_3^-+2\mathrm{H}^++2e^-\longrightarrow\mathrm{NO}_2^-+\mathrm{H}_2\mathrm{O}\ \ \ E^{\circ}=0.42\mathrm{\ V}\) \(\mathrm{O}_2+4\mathrm{H}^++4e^-\longrightarrow2\mathrm{H}_2\mathrm{O}\quad\ \ \ \ \ \ \ \ \ \ E^{\circ}=1.23\mathrm{\ V}\) Calculate the yield of ATP synthesis per mole of nitrite oxidized. (Hint: See Section 17.7.)

Fluorine is a highly reactive gas that attacks water to form \(\mathrm{HF}\) and other products. Follow the procedure in Problem 18.126 to show how you can determine indirectly the standard reduction for fluorine as shown in Table 18.1.

Show a sketch of a galvanic concentration cell. Each compartment consists of a \(\mathrm{Co}\) electrode in a \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) solution. The concentrations in the compartments are 2.0 M and 0.10 M, respectively. Label the anode and cathode compartments. Show the direction of electron flow. (a) Calculate the \(E_{\text {cell }}\) at \(25^{\circ} \mathrm{C}\). (b) What are the concentrations in the compartments when the \(E_{\text {cell }}\) drops to 0.020 V? Assume volumes to remain constant at 1.00 L in each compartment.

The emf of galvanic cells varies with temperature (either increases or decreases). Starting with Equation (18.3), derive an equation that expresses \(E_{\text {cell }}^{\circ}\) in terms of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\). Predict whether \(E_{\text {cell }}^{\circ}\) will increase or decrease if the temperature of a Daniell cell increases. Assume both \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) to be temperature independent.

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 concentrations? Explain.

It has been suggested that a car can be powered from the hydrogen generated by reacting aluminum soda cans with a solution of lye (sodium hydroxide) according to the following reaction: \(2\mathrm{Al}(s)+2\mathrm{OH}^-(aq)+6\mathrm{H}_2\mathrm{O}(l)\ \longrightarrow\ 2\mathrm{\ Al}(\mathrm{OH})_4^-(aq)+3\mathrm{H}_2(g)\) How many aluminum soda cans would be required to generate the same amount of chemical energy as contained in one tank of gasoline? Read the Chemistry in Action on aluminum recycling in Chapter 21 (p. 952), and comment on the cost and environmental impact of powering a car with aluminum cans.

Estimate how long it would take to electroplate a teaspoon with silver from a solution of \(\mathrm{AgNO}_{3}\), assuming a constant current of \(2 \ \mathrm{A}\).

The potential for a cell based on the standard hydrogen electrode and the half-reaction \(\mathbf{M}^{n+}(a q)+n e^{-} \longrightarrow \mathbf{M}(s)\) was measured at several concentrations of \(\mathbf{M}^{n+}(a q)\), giving the following plot. What is the value of \(n\) in the half-reaction?

Calculate the standard emf of a cell that uses \(\mathrm{Ag} / \mathrm{Ag}^{+}\) and \(\mathrm{Al} / \mathrm{Al}^{3}\) half-cell reactions. Write the cell reaction that occurs under standard-state conditions.

Which of the following reagents can oxidize \(\mathrm{H}_{2} \mathrm{O}\) to \(\mathrm{O}_{2}(g)\) under standard-state conditions? \(\mathrm{H}^{+}(a q)\), \(\mathrm{Cl}^{-}(a q), \ \mathrm{Cl}_{2}(g), \ \mathrm{Cu}^{2+}(a q), \ \mathrm{Pb}^{2+}(a q), \ \mathrm{MnO}_{4}^{-}(a q)\) (in acid).

Consider the electrochemical reaction \(\mathrm{Sn}^{2+}+\mathrm{X} \rightarrow \mathrm{Sn}+\mathrm{X}^{2+}\). Given that \(E_{\text {cell }}^{\circ}=0.14 \ \mathrm{V}\), what is the \(E^{\circ}\) for the \(\mathrm{X}^{2+} / \mathrm{X}\) half-reaction?

Spontaneity of Redox Reactions The \(E^{\circ}\) value of one cell reaction is positive and that of another cell reaction is negative. Which cell reaction will proceed toward the formation of more products at equilibrium?

What is the equilibrium constant for the following reaction at \(25^ {\circ} \mathrm{C}\)? \(\mathrm{Mg}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{Zn}(s)\)

Use the standard reduction potentials to find the equilibrium constant for each of the following reactions at \(25^ {\circ} \mathrm{C}\): (a) \(\mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)\) (b) \(2 \mathrm{Ce}^{4+}(a q)+2 \mathrm{Cl}^{-}(a q) \underset{\mathrm{Cl}_{2}(g)+2 \mathrm{Ce}^{3+}(a q)}{\rightleftharpoons}\) (c) \(5 \mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q) \underset{\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)+5 \mathrm{Fe}^{3+}(a q)}{\rightleftharpoons}\)

Under standard-state conditions, what spontaneous reaction will occur in aqueous solution among the ions \(\mathrm{Ce}^{4+}\), \(\mathrm{Ce}^{3+}\), \(\mathrm{Fe}^{3+}\), and \(\mathrm{Fe}^{2+}\)? Calculate \(\Delta G^{\circ}\) and \(K_{\mathrm{c}}\) for the reaction.

The hydrogen-oxygen fuel cell is described in Section 18.6. (a) What volume of \(\mathrm{H}_2(\mathrm{~g})\), stored at \(25^{\circ} \mathrm{C}\) at a pressure of 155 atm, would be needed to run electric motor drawing a current of 8.5 A for 3.0 h? (b) What volume (liters) of air at \(25^{\circ} \mathrm{C}\) and 1.00 atm will have to pass into the cell per minute to run the motor? Assume that air is 20 percent \(\mathrm{O}_2\) by volume and that all the \(\mathrm{O}_2\) is consumed in the cell. The other components of air do not affect the fuel-cell reactions. Assume ideal gas behavior.

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?

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: \(\mathrm{MnO}_4^{-}+\mathrm{H}_2 \mathrm{O}_2 \longrightarrow \mathrm{O}_2+\mathrm{Mn}^{2+}\) (a) Balance the above equation. (b) If \(36.44 \mathrm{~mL}\) of a \(0.01652 \mathrm{M} \mathrm{KMnO}_4\) solution are required to completely oxidize \(25.00 \mathrm{~mL}\) of a \(\mathrm{H}_2 \mathrm{O}_2\) solution, calculate the molarity of the \(\mathrm{H}_2 \mathrm{O}_2\) solution.

Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is present in many plants and vegetables. (a) Balance the following equation in acid solution: \(\mathrm{MnO}_{4}^{-}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Mn}^{2+}+\mathrm{CO}_{2}\) (b) If a 1.00-g sample of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) requires 24.0 mL of \(0.0100 \ \mathrm{M} \ \mathrm{} \mathrm{KMnO}_{4}\) solution to reach the equivalence point, what is the percent by mass of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) in the sample?

Calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) is insoluble in water. This property has been used to determine the amount of \(\mathrm{Ca}^{2+}\) ions in blood. The calcium oxalate isolated from blood is dissolved in acid and titrated against a standardized \(\mathrm{KMnO}_{4}\) solution as described in Problem 18.72. In one test, it is found that the calcium oxalate isolated from a 10.0 mL sample of blood requires 24.2 mL of \(9.56 \times 10^{-4} \ M \ \mathrm{KMnO}_{4}\) for titration. Calculate the number of milligrams of calcium per milliliter of blood. Text Transcription: (CaC_2O_4) Ca^2+ KMnO_4 9.56 x 10^-4 M KMnO_4

A galvanic cell consists of a silver electrode in contact with \(346 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNOAN} 3\) solution and a magnesium electrode in contact with 288 mL of \(0.100 \mathrm{M} \mathrm{Mg}\left(\mathrm{NO}_3\right)_2\) solution. (a) Calculate E for the cell at \(25^{\circ} \mathrm{C}\). (b) A current is drawn from the cell until \(1.20 \mathrm{~g}\) of silver have been deposited at the silver electrode. Calculate E for the cell at this stage of operation.

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

The cathode reaction in the Leclanché cell is given by \(2 \mathrm{MnO}_{2}(s)+\mathrm{Zn}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{ZnMn}_{2} \mathrm{O}_{4}(s)\) 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 \(\mathrm{MnO}_{2}\) present in the cell. Assume that there is an excess of \(\mathrm{Zn}^{2+}\) ions.

Suppose you are asked to verify experimentally the electrode reactions shown in Example 18.8. In addition 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.

For a number of years it was not clear whether mercury(I) ions existed in solution as \(\mathrm{Hg}^{+}\) or as \(\mathrm{Hg}_2^{2+}\). To distinguish between these two possibilities, we could set up the following system: \(\mathrm{Hg}(l)|\operatorname{soln} \mathrm{A} \| \operatorname{soln} \mathrm{B}| \mathrm{Hg}(l)\) 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 V at \(18^{\circ} \mathrm{C}\), what can you deduce about the nature of the mercury(I) ions?

A piece of magnesium metal weighing 1.56 g is placed in 100.0 mL of \(0.100 \ M \ \mathrm{AgNO}_{3}\) at \(25^{\circ} \mathrm{C}\). Calculate \(\left[\mathrm{Mg}^{2+}\right]\) and \(\left[\mathrm{Ag}^{+}\right]\)in solution at equilibrium. What is the mass of the magnesium left? The volume remains constant. Text Transcription: 0.100 M AgNO_3 25^circ C [Mg^2+] [Ag^+]

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?

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.

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 \(\mathrm{HNO}_3\) and three parts HCl by volume), called aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are \(\mathrm{HAuCl}_4\) and \(\mathrm{NO}_2\).) (b) What is the function of HCl?

Given the standard reduction potential for \(\mathrm{Au}^{3+}\) in Table 18.1 and \(\mathrm{Au}^{+}(a q)+e^{-} \longrightarrow \mathrm{Au}(s) \quad E^{\circ}=1.69 \mathrm{~V}\) answer the following questions. (a) Why does gold not tarnish in air? (b) Will the following disproportionation occur spontaneously? \(3 \mathrm{Au}^{+}(a q) \longrightarrow \mathrm{Au}^{3+}(a q)+2 \mathrm{Au}(s)\) (c) Predict the reaction between gold and fluorine gas.

An electrolysis cell was constructed similar to the one shown in Figure 18.18, except \(0.1 \ \mathrm{M} \ \mathrm{MgCl}_{2}(a q)\) was used as the electrolyte solution. Under these conditions, a clear gas was formed at one electrode and a very pale green gas was formed at the other electrode in roughly equal volumes. (a) What gases are formed at these electrodes? (b) Write balanced half-reactions for each electrode. Account for any deviation from the normally expected results.

Lead storage batteries are rated by ampere hours, that is, the number of amperes they can deliver in an hour. (a) Show that \(1 \ \mathrm{~A} \ \cdot \ \mathrm{h}=3600 \ \mathrm{C}\). (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. 835.) (c) Calculate \(E_{\text {cell }}^{\circ}\) and \(\Delta G^{\circ}\) for the battery.

A \(9.00 \times 10^2-\mathrm{mL} 0.200 \mathrm{MMgI}_2\) 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 \(26^{\circ} \mathrm{C}\) and 779 mmHg was \(1.22 \times 10^3 \mathrm{~mL}\). (a) Calculate the charge in coulombs consumed in the process. (b) How long (in min) did the volume of the solution was constant.

A galvanic cell is constructed by immersing a piece of copper wire in 25.0 mL of a \(0.20 \mathrm{M} \mathrm{CuSO}_4\) solution and a zinc strip in 25.0 mL of a 0.20 M ZnSO solution. (a) Calculate the emf of the cell at \(25^{\circ} \mathrm{C}\) and predict what would happen if a small amount of concentrated \(\mathrm{NH}_3\) solution were added to (i) the CuSO \({ }_4\) solution and (ii) the \(\mathrm{ZnSO}_4\) solution. Assume that the volume in each compartment remains constant at 25.0 mL. (b) In a separate experiment, 25.0 mL of 3.00 M \(\mathrm{NH}_3\) are added to the \(\mathrm{CuSO}_4\) solution. If the emf of the cell is 0.68 V, calculate the formation constant \(\left(K_f\right)\) of \(\mathrm{Cu}\left(\mathrm{NH}_3\right)_4^{2+}\)

To remove the tarnish \(\left(\mathrm{Ag}_2 \mathrm{~S}\right)\) 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 tablespoonful 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 \(80^{\circ} \mathrm{C}\). 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 NaCl instead of \(\mathrm{NaHCO}_3\) would also work because both compounds are strong electrolytes. What is the added advantage of using \(\mathrm{NaHCO}_3\) ? (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 HCl solution. Rubbing the spoon with the fluid will also remove the tarnish. Name two disadvantages of using this procedure compared to the one described above.

The diagram here shows an electrolytic cell consisting of a \(\mathrm{Co}\) electrode in a 2.0 M \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) solution and a \(\mathrm{Mg}\) electrode in a 2.0 M \(\mathrm{Co}\left(\mathrm{Mg}_{3}\right)_{2}\) solution. (a) Label the anode and cathode and show the half-cell reactions. Also label the signs (\(+\) or \(-\)) on the battery terminals. (b) What is the minimum voltage to drive the reaction? (c) After the passage of 10.0 A for 2.00 h the battery is replaced with a voltmeter and the electrolytic cell now becomes a galvanic cell. Calculate \(E_{\text {cell }}\). Assume volumes to remain constant at 1.00 L in each compartment.