Chapter 18

How many coulombs of charge are needed to accomplish each of the following conversions by electrolysis? (a) Produce \(0.50 \mathrm{~mol} \mathrm{Al}\) by electrolysis of \(\mathrm{Al}_{2} \mathrm{O}_{3}\). (b) Reduce all of the \(\mathrm{Cu}^{2+}\) in \(100 \mathrm{~mL}\) of \(0.20 \mathrm{M}\) \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) (c) Make \(10.0 \mathrm{~g} \mathrm{Cl}_{2}\) by electrolysis of molten \(\mathrm{NaCl}\). (d) Deposit \(0.32 \mathrm{~g}\) silver from an aqueous \(\mathrm{AgNO}_{3}\) solution.

How many coulombs of charge are needed to accomplish each of the following conversions by electrolysis? (a) Form \(0.50 \mathrm{~mol} \mathrm{Ca}\) from \(\mathrm{CaCl}_{2}\). (b) Produce \(3.0 \mathrm{~g} \mathrm{Al}\) by electrolysis of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (c) Form \(0.52 \mathrm{~g} \mathrm{O}_{2}\) by electrolysis of an aqueous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) solution. (d) Make \(1.0 \mathrm{~L}\) of gaseous \(\mathrm{H}_{2}\) at standard temperature and pressure by electrolysis of water.

What mass of cadmium is deposited from a \(\mathrm{CdCl}_{2}\) solution by passing a current of \(1.50 \mathrm{~A}\) for 38.0 minutes?

Like zinc, sodium is a rather active metal. Would it be possible to use metallic sodium for cathodic protection of the iron hull of an ocean vessel? Explain.

The electrochemical processes that occur in the corrosion of iron are represented by the half-reactions $$ \begin{array}{l} \mathrm{Fe}(\mathrm{s}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \\ \mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{H}^{+}(\mathrm{aq})+4 \mathrm{e}^{-} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell) \end{array} $$ (a) Write the overall reaction. (b) What is the standard potential for the overall chemical reaction? (c) Natural water has a pH of about \(5.9,\) and air is 0.21 mol fraction oxygen. If the concentration of iron(II) in the water is \(5 \times 10^{-5} M\), what is the potential of the corrosion reaction in the presence of air and natural water at 1 atm pressure and \(298 \mathrm{~K} ?\)

An aluminum bulkhead in a swimming pool collapsed. Stainless steel (mostly iron) braces were bolted to the aluminum to strengthen the bulkhead. Within a few months, the bulkhead collapsed again and showed extreme corrosion of the aluminum close to the steel bolts. Explain the electrochemical processes that occurred in the reinforced bulkhead.

Assign the oxidation states of all elements in each of the following: (a) \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) (b) \(\mathrm{Ba}\left(\mathrm{ClO}_{4}\right)_{2}\) (c) \(\mathrm{T} 1^{3+}\)

Sphalerite is the naturally occurring mineral zinc sulfide, from which zinc metal is extracted. The ore is heated in oxygen to form zinc oxide and sulfur dioxide, followed by the reaction of metal oxide with elemental carbon to form CO. (a) Write a balanced equation for each of these reactions. (b) For each reaction, identify the element that is oxidized and the one that is reduced.

What is the reduction potential of the hydrogen electrode at \(298 \mathrm{~K}\) if the pressure of gaseous hydrogen is \(2.5 \mathrm{~atm}\) in a solution of \(\mathrm{pH} 6.00 ?\)

The standard free energy change at \(25^{\circ} \mathrm{C}, \Delta G^{\circ},\) is equal to \(-34.3 \mathrm{~kJ}\) for $$ 2 \mathrm{Fe}(\mathrm{CN})_{6}^{3-}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{Fe}(\mathrm{CN})_{6}^{4-}(\mathrm{aq})+\mathrm{I}_{2}(\mathrm{~s}) $$ Calculate the standard potential for this reaction.

The equilibrium constant at \(25^{\circ} \mathrm{C}\) is \(1.58 \times 10^{2}\) for $$\begin{aligned} 2 \mathrm{VO}^{2+}(\mathrm{aq})+\mathrm{Br}_{2}(\ell)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \\\& 2 \mathrm{VO}_{2}^{2+}(\mathrm{aq})+2 \mathrm{Br}^{-}(\mathrm{aq})+4 \mathrm{H}^{+}(\mathrm{aq}) \end{aligned} $$ Calculate \(\Delta G^{\circ}\) and \(E^{\circ}\) for this reaction.

Calculate the potential of the half-reaction $$ \mathrm{Fe}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+} $$ when the concentrations in solution are \(\left[\mathrm{Fe}^{3+}\right]=0.033 M\) and \(\left[\mathrm{Fe}^{2+}\right]=0.0025 M,\) and the temperature is \(298 \mathrm{~K}\).

Another type of battery is the al 71 in which the cell reaction is $$ \mathrm{Zn}(\mathrm{s})+\mathrm{HgO}(\mathrm{s}) \rightarrow \mathrm{Hg}(\ell)+\mathrm{ZnO}(\mathrm{s}) $$ \(E^{o}=+1.35 \mathrm{~V}\) (a) What is the standard free energy change for this reaction? (b) The standard free energy change in a voltaic cell is the maximum electrical energy that the cell can produce. If the reaction in a zinc-mercury cell consumes \(1.00 \mathrm{~g}\) mercury oxide, what is the standard free energy change? (c) For how many hours could a mercury cell produce a \(10-\mathrm{mA}\) current if the limiting reactant is \(3.50 \mathrm{~g}\) mercury oxide?

In the analytical technique called electrogravimetry, electrolysis is used to separate the analyte from a solution by depositing it on an inert electrode. The electrode is weighed before and after the experiment to find the mass of analyte deposited. A \(0.122-\mathrm{g}\) sample of a copper-zinc alloy was treated with concentrated sulfuric acid to produce a solution containing copper(II) and zinc(II) sulfates. The platinum cathode used in the electrolysis of this solution increased in mass by \(0.073 \mathrm{~g}\) after exhaustive electrolysis. (a) Which metal was deposited on the cathode during the electrolysis? Write the balanced equation for the electrolysis reaction. (b) What was the mass percentages of copper and zinc in the alloy sample?

At \(298 \mathrm{~K}\), the solubility product constant \(\mathrm{for} \mathrm{PbC}_{2} \mathrm{O}_{4}\) is \(8.5 \times 10^{-10}\), and the standard reduction potential of the \(\mathrm{Pb}^{2+}(\) aq \()\) to \(\mathrm{Pb}(\mathrm{s})\) is \(-0.126 \mathrm{~V}\). (a) Find the standard potential of the half-reaction $$ \mathrm{PbC}_{2} \mathrm{O}_{4}(\mathrm{~s})+2 \mathrm{e}^{-} \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(\mathrm{aq}) $$ (Hint: The desired half-reaction is the sum of the equations for the solubility product and the reduction of \(\mathrm{Pb}^{2+}\). Find \(\Delta G^{\circ}\) for these two reactions and add them to find \(\Delta G^{\circ}\) for their sum. Convert the \(\Delta G^{\infty}\) to the potential of the desired half-reaction.) (b) Calculate the potential of the \(\mathrm{Pb} / \mathrm{PbC}_{2} \mathrm{O}_{4}\) electrode in a \(0.025 M\) solution of \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\)

The acid-base titration curves discussed in Chapter 16 can be determined using a \(\mathrm{pH}\) meter, which measures the potential of a cell made up of a reference electrode and an indicating electrode that responds to the hydrogen ion concentration in solution. Assume that the cell potential, in volts, follows the equation \(E_{\text {cell }}=k-0.059 \mathrm{pH}\) The potential of the cell is \(135 \mathrm{mV}\) at the start of a titration of a \(0.032 \mathrm{MHCl}\) solution with \(\mathrm{NaOH}(\mathrm{aq}) . \mathrm{What}\) is the potential of this cell when the equivalence point is reached?

Calculate the rate of oxygen gas production at standard temperature and pressure, in units of milliliters per minute \((\mathrm{mL} / \mathrm{min}),\) by the electrolysis of water at a \(0.250-\mathrm{A}\) current

An electrolytic cell produces aluminum from \(\mathrm{Al}_{2} \mathrm{O}_{3}\) at the rate of \(10 \mathrm{~kg} /\) day. Assuming a yield of \(100 \%\), (a) how many moles of electrons must pass through the cell in one day? (b) how many coulombs are passing through the cell? (c) how many moles of oxygen \(\left(\mathrm{O}_{2}\right)\) are being produced simultaneously?

A At \(298 \mathrm{~K},\) the solubility product constant for solid \(\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2}\) is \(1.5 \times 10^{-9} .\) Use the standard reduction potential of \(\mathrm{Ba}^{2+}(\mathrm{aq})\) to find the standard potential for the half-reaction $$ \mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2}(\mathrm{~s})+2 \mathrm{e}^{-} \rightarrow \mathrm{Ba}(\mathrm{s})+2 \mathrm{IO}_{3}^{-}(\mathrm{aq}) $$ (Hint: Find \(\Delta G^{\circ}\) for both the solubility equilibrium and the reduction half-reaction for \(\mathrm{Ba}^{2+},\) and add the reactions. Use the \(\Delta G^{\infty}\) for the sum reaction to find \(E^{a}\).)

A Consider the standard reduction potentials of cesium and lithium. $$ \begin{array}{ll} \mathrm{Cs}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Cs}(\mathrm{s}) & E^{\circ}=-3.026 \mathrm{~V} \\\ \mathrm{Li}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Li}(\mathrm{s}) & E^{\circ}=-3.095 \mathrm{~V} \end{array} $$ The periodic trends in the properties of the element indicate that fluorine is the most chemically reactive nonmetal, so perhaps it is not surprising that the standard reduction potential of fluorine has the highest positive value for a nonmetallic element. However, periodic properties of the elements also indicate that cesium should be the most reactive metal. Comparison of the voltage of the cesium half-reaction with that of lithium shows that the standard reduction potential of lithium is less negative than that of cesium, indicating that lithium is a better oxidizer than is cesium. (a) Calculate the standard cell voltages of the voltaic cells based on the reaction $$ 2 \mathrm{M}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{M}^{+}(\mathrm{aq})+2 \mathrm{~F}^{-}(\mathrm{aq}) $$ where \(\mathrm{M}\) is \(\mathrm{Cs}\) and \(\mathrm{Li}\). (b) Assuming that the pressure of \(\mathrm{F}_{2}(\mathrm{~g})\) stays at \(1.00 \mathrm{~atm}\), what concentration does \(\mathrm{Li}^{+}(\mathrm{aq})\) have to be for the voltage of the \(\mathrm{Li} / \mathrm{F}_{2}\) voltaic cell to equal the standard voltage of the \(\mathrm{Cs} / \mathrm{F}_{2}\) voltaic cell? (c) Can you suggest a reason why the standard reduction potential of lithium is lower than that of cesium, even though periodic trends indicate that cesium is the more reactive metal? (d) Calculate \(\Delta G^{o}\) for both the \(\mathrm{Li} / \mathrm{F}_{2}\) and the \(\mathrm{Cs} / \mathrm{F}_{2}\) voltaic cells from their \(E^{\circ} \mathrm{s}\). Compare this with the Gibbs' free energies of formation of \(2 \mathrm{~mol} \mathrm{LiF}\) and CsF. Can you explain the difference? (e) Given the fact that alkali metals react rather violently with water, it would be unlikely that any voltaic cell can be constructed using Li(s) or \(\mathrm{Cs}(\mathrm{s})\) in the presence of water. A more likely scenario is that the voltaic cell would have no solvent, so that the voltaic cell reaction would be $$ 2 \mathrm{M}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{MF}(\mathrm{xtal}) $$ where \(\mathrm{M}\) is \(\mathrm{Cs}\) or \(\mathrm{Li}\). What would be the \(E^{\circ}\) s of the two different voltaic cells if this were the reaction? (Hint: See your answer to part d.)