Chapter 19

Balance the following redox equations by the halfreaction 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 redox equations by the half-reaction 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) (e) \(\mathrm{Mn}^{2+}+\mathrm{BiO}_{3}^{-} \longrightarrow \mathrm{Bi}^{3+}+\mathrm{MnO}_{4}^{-}\) (in acidic solution)

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

Describe the basic features of a galvanic 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 \(1 \mathrm{M} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) solution and an Ag electrode placed in a \(1 \mathrm{M} \mathrm{AgNO}_{3}\) solution.

Discuss the spontaneity of an electrochemical reaction in terms of its standard emf \(\left(E_{\mathrm{cell}}^{\circ}\right)\).

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 the following reactions would occur spontaneously in aqueous solution at \(25^{\circ} \mathrm{C}\). Assume that the initial concentrations of dissolved species are all \(1.0 \mathrm{M}\). (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) \(\mathrm{Cu}^{+}(a q)+\mathrm{Fe}^{3+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{Fe}^{2+}(a q)\)

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.

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

Write the Nernst equation, and explain all the terms.

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

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 \(\left[\mathrm{Zn}^{2+}\right]=0.45 \mathrm{M}, P_{\mathrm{H}_{2}}=2.0 \mathrm{~atm},\) and \(\left[\mathrm{H}^{+}\right]=1.8 M ?\)

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 \(\left[\mathrm{Pb}^{2+}\right]=0.10 \mathrm{M},\) \([\mathrm{H}]=0.050 M,\) and \(P_{\mathrm{H}}=1.0 \mathrm{~atm} ?\)

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

What is a battery? Describe several types of batteries.

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

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

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

What is Faraday's contribution to quantitative electrolysis?

Define the term overvoltage. How does overvoltage affect electrolytic processes?

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

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

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 \(0.076 \mathrm{~L}\) of \(\mathrm{O}_{2}\) is collected at \(25^{\circ} \mathrm{C}\) and \(755 \mathrm{mmHg}\), how many faradays of electricity had to pass through the solution? \(?\)

How many faradays of electricity are required to produce (a) \(0.84 \mathrm{~L}\) of \(\mathrm{O}_{2}\) at exactly 1 atm and \(25^{\circ} \mathrm{C}\) from aqueous \(\mathrm{H}_{2} \mathrm{SO}_{4}\) solution, (b) \(1.50 \mathrm{~L}\) of \(\mathrm{Cl}_{2}\) at \(750 \mathrm{mmHg}\) and \(20^{\circ} \mathrm{C}\) from molten \(\mathrm{NaCl}\), and (c) \(6.0 \mathrm{~g}\) of Sn from molten \(\mathrm{SnCl}_{2}\) ?

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

In the electrolysis of an aqueous \(\mathrm{AgNO}_{3}\) solution, \(0.67 \mathrm{~g}\) 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 half-reaction? (c) Calculate the quantity of electricity used (in coulombs).

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

What is the hourly production rate of chlorine gas (in \(\mathrm{kg})\) from an electrolytic cell using aqueous \(\mathrm{NaCl}\) 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.

A quantity of \(0.300 \mathrm{~g}\) of copper was deposited from a \(\mathrm{CuSO}_{4}\) solution by passing a current of \(3.00 \mathrm{~A}\) through the solution for 304 s. Calculate the value of the Faraday constant.

In a certain electrolysis experiment, \(1.44 \mathrm{~g}\) of Ag were deposited in one cell (containing an aqueous \(\mathrm{AgNO}_{3}\) solution), while \(0.120 \mathrm{~g}\) of an unknown metal \(\mathrm{X}\) 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 \(\mathrm{X}\).

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

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 \(\mathrm{Ag}_{2} \mathrm{~S}(s)+2 e^{-} \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)\) is \(\left.-0.71 \mathrm{~V} .\right]\)

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

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

As discussed in Section \(19.5,\) the potential of \(\mathrm{a}\) concentration cell diminishes as the cell operates and the concentrations in the two compartments approach each other. When the concentrations in both compartments are the same, the cell ceases to operate. At this stage, is it possible to generate a cell potential by adjusting a parameter other than concentration? Explain.

A sample of iron ore weighing \(0.2792 \mathrm{~g}\) was dissolved in an excess of a dilute acid solution. All the iron was first converted to Fe(II) ions. The solution then required \(23.30 \mathrm{~mL}\) of \(0.0194 \mathrm{M} \mathrm{KMnO}_{4}\) for oxidation to Fe(III) ions. Calculate the percent by mass of iron in the ore.

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 this equation. (b) If \(36.44 \mathrm{~mL}\) of a 0.01652 \(M \mathrm{KMnO}_{4}\) solution is required to completely oxidize \(25.00 \mathrm{~mL}\) of an \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution, calculate the molarity of the \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution.

Based on the following standard reduction potentials: $$\begin{aligned}\mathrm{Fe}^{2+}(a q)+2 e^{-} & \longrightarrow \mathrm{Fe}(s) & & E_{1}^{\circ}=-0.44 \mathrm{~V} \\ \mathrm{Fe}^{3+}(a q)+e^{-} \longrightarrow \mathrm{Fe}^{2+}(a q) & E_{2}^{\circ} &=0.77 \mathrm{~V} \end{aligned}$$ calculate the standard reduction potential for the halfreaction:$$\mathrm{Fe}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Fe}(s) \quad E_{3}^{\circ}=?$$

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

Consider a galvanic cell composed of the SHE and a half-cell using the reaction \(\mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \mathrm{Ag}(s)\). (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) \(1.0 \times 10^{-2} M\) and (ii) \(1.0 \times 10^{-5} M\), all other reagents being held at standard- state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter.

A galvanic cell consists of a silver electrode in contact with \(346 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) solution and a magnesium electrode in contact with \(288 \mathrm{~mL}\) 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 has been deposited at the silver electrode. Calculate \(E\) for the cell at this stage of operation.

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

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 \(0.0050 \mathrm{~A}\), calculate how many hours this current supply will last if there is initially \(4.0 \mathrm{~g}\) of \(\mathrm{MnO}_{2}\) present in the cell. Assume that there is an excess of \(\mathrm{Zn}^{2+}\) ions.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 \(0.0050 \mathrm{~A}\), calculate how many hours this current supply will last if there is initially \(4.0 \mathrm{~g}\) of \(\mathrm{MnO}_{2}\) present in the cell. Assume that there is an excess of \(\mathrm{Zn}^{2+}\) ions.

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: $$ \operatorname{Hg}(l) \mid \text { soln } \mathrm{A} \| \operatorname{soln} \mathrm{B} \mid \operatorname{Hg}(l)$$ where soln A contained 0.263 g mercury(I) nitrate per liter and soln B contained \(2.63 \mathrm{~g}\) mercury(I) nitrate per liter. If the measured emf of such a cell is \(0.0289 \mathrm{~V}\) at \(18^{\circ} \mathrm{C},\) what can you deduce about the nature of the mercury(I) ions?

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.