Chapter 17

Methane can serve as the fuel for electric cars powered by fuel cells. Carbon dioxide is a product of the fuel cell reaction. All cars powered by internal combustion engines burning natural gas (mostly methane) produce \(\mathrm{CO}_{2}\). Why are electric vehicles powered by fuel cells likely to produce less \(\mathrm{CO}_{2}\) per mile?

To make the refueling of fuel cells easier, several manufacturers are developing converters that turn readily available fuels- -such as natural gas, propane, and methanol-into \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\). Although vehicles with such power systems are not truly "zero emission," they still offer significant environmental benefits over vehicles powered by internal combustion engines. Describe a few of these benefits.

To inhibit corrosion of steel structures in contact with seawater, pieces of other metals (often zinc) are attached to the structures to serve as "sacrificial anodes." Explain how these attached pieces of metal might protect the structures, and describe which properties of zinc make it a good selection.

Lithium-Sulfur Dioxide Batteries The U.S. military uses batteries based on the reduction of liquid sulfur dioxide at a carbon cathode in certain communications equipment. Lithium metal is used as the anode. The overall cell reaction is $$ 2 \mathrm{Li}(s)+2 \mathrm{SO}_{2}(\ell) \rightarrow \mathrm{Li}_{2} \mathrm{S}_{2} \mathrm{O}_{4}(s) $$ a. Write half-reactions for the anode and cathode reactions. b. How many electrons are transferred in the cell reaction? c. Draw a Lewis structure for the \(\mathrm{S}_{2} \mathrm{O}_{4}^{2-}\) anion.

A concentration cell can be constructed by using the same half-reaction for both the cathode and anode. What is the value of \(E_{\text {cell }}\) of a concentration cell that combines copper electrodes in contact with \(0.25 M\) copper (11) nitrate and \(0.00075 M\) copper (11) nitrate solutions?

Lithium-lon Batteries Scientists at the University of Texas, Austin, and at MIT developed a cathode material for lithium-ion batteries based on \(\mathrm{LiFePO}_{4},\) which is the composition of the cathode when the battery is fully discharged. Batteries with this cathode are more powerful than those of the same mass with LiCoO \(_{2}\) cathodes. They are also more stable at high temperatures. a. What is the formula of the LiFePO, cathode when the battery is fully charged? b. Is Fe oxidized or reduced as the battery discharges? c. Is the cell potential of a lithium-ion battery with an iron phosphate cathode likely to differ from one with a cobalt oxide cathode? Explain your answer.

Starting with Equation \(14.19\left(\Delta G=\Delta G^{*}+R T \ln Q\right)\) and \(\Delta G_{\text {cll }}^{n}=-n F E_{\text {call }}^{\circ}\) derive an cquation relating \(E_{\text {cell and }}\) the equilibrium constant ( \(K\) ) of an electrochemical cell reaction. Hint: Recall that \(Q=K\) and \(\Delta G=0\) in a reaction mixture at chemical equilibrium.

In a NiMH battery, what are the oxidation states of (a) \(\mathrm{Ni}\) in \(\mathrm{NiO}(\mathrm{OH}),\) (b) \(\mathrm{H}\) in \(\mathrm{MH},(\mathrm{c}) \mathrm{M}\) in \(\mathrm{MH},\) and \((\mathrm{d}) \mathrm{H}\) in \(\mathrm{H}_{2} \mathrm{O}\)

A magnesium battery can be constructed from an anode of magnesium metal and a cathode of molybdenum sulfide, Mo \(_{3} \mathrm{S}_{4}\). The half-reactions are Anode: \(\mathrm{Mg}(\mathrm{s}) \rightarrow \mathrm{Mg}^{2+}(a q)+2 \mathrm{e}^{-} \quad E_{\text {anode }}^{\circ}=2.37 \mathrm{V}\) Cathode: \(\mathrm{Mg}^{2+}(a q)+\mathrm{Mo}_{3} \mathrm{S}_{4}(s)+2 \mathrm{e}^{-} \rightarrow \mathrm{MgMo}_{3} \mathrm{S}_{4}(s)\) $$ E_{\text {cathode }}^{\circ}=? $$ If the standard cell potential for the battery is \(1.50 \mathrm{V}\) what is the value of \(E^{\circ}\) for the reduction of \(\mathrm{Mo}_{3} \mathrm{S}_{4} ?\) b. What are the apparent oxidation states and electron configurations of Mo in \(\mathrm{Mo}_{3} \mathrm{S}_{4}\) and in \(\mathrm{Mg} \mathrm{Mo}_{3} \mathrm{S}_{4} ?\) "c. The electrolyte in the battery contains a complex magnesium salt, \(\mathrm{Mg}\left(\mathrm{AlCl}_{3} \mathrm{CH}_{3}\right)_{2}\). Why is it necessary to include \(\mathrm{Mg}^{2+}\) ions in the electrolyte?

The element fluorine, \(\mathrm{F}_{2},\) was first produced in 1886 by the electrolysis of HF. Chemical syntheses of \(\mathrm{F}_{2}\) did not happen until 1986 when Karl O. Christe successfully prepared \(\mathrm{F}_{2}\) by the following reaction: \(\mathrm{K}_{2} \mathrm{MnF}_{6}(s)+2 \mathrm{SbF}_{5}(\ell) \rightarrow\) $$ 2 \mathrm{KSbF}_{6}(s)+\mathrm{MnF}_{3}(s)+\frac{1}{2} \mathrm{F}_{2}(g) $$ a. Assign oxidation numbers to the clements in each compound and determine the number of electrons involved in the process. b. Using the following \(\Delta H_{\mathrm{f}}^{\text {t }}\) values, calculate \(\Delta H^{\circ}\) for the reaction. \(\Delta H_{f_{\mathrm{f}, \mathrm{B}}^{*} \mathrm{b}, d(\theta)}=-1324 \mathrm{k} \mathrm{J} / \mathrm{mol} \quad \Delta H_{\left(\mathrm{X}, \mathrm{M}_{\mathrm{h}} \mathrm{F}_{\mathscr{Q}}\right)}^{\circ}=-2435 \mathrm{k} \mathrm{J} / \mathrm{mol}\) $$ \Delta H_{(\mathrm{Mn} \mathrm{F}, \mathrm{G})}^{\mathrm{o}}=-1579 \mathrm{kJ} / \mathrm{mol} \quad \Delta H_{\mathrm{EKSH}, \mathrm{S}_{0}}=-2080 \mathrm{kJ} / \mathrm{mol} $$ c. If we assume that \(\Delta S\) is relatively small, such that \(\Delta G \approx \Delta H,\) cstimate \(E^{\circ}\) for this reaction. d. If \(\Delta S\) for the reaction is greater than zero, is our value for \(E^{\circ}\) in part (c) too high or too low? e. The electrochemical synthesis of \(\mathrm{F}_{2}\) is described by the following clectrolytic cell reaction: $$ 2 \mathrm{KHF}_{2}(\ell) \rightarrow 2 \mathrm{KF}(\ell)+\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) $$ Assign oxidation numbers and determine the number of electrons involved in this process.

Corrosion of Copper Pipes The copper pipes frequently used in household plumbing may corrode and eventually leak. The corrosion reaction is believed to involve the formation of copper( 1 ) chloride: $$ 2 \mathrm{Cu}(s)+\mathrm{Cl}_{2}(a q) \rightarrow 2 \mathrm{CuCl}(s) $$ a. Write balanced cquations for the half-reactions in this redox reaction. b. Calculate \(E_{\text {ran }}^{\circ}\) and \(\Delta G_{\text {rxn }}^{a}\) for the reaction.

Elemental uranium may be produced from uranium dioxide by the following two- step process: $$ \begin{aligned} \mathrm{UO}_{2}(s)+4 \mathrm{HF}(g) & \rightarrow \mathrm{UF}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \\ \mathrm{UF}_{4}(s)+2 \mathrm{Mg}(s) & \rightarrow \mathrm{U}(s)+2 \mathrm{MgF}_{2}(a q) \end{aligned} $$ a. Identify the reducing agent. b. Identify the element that is reduced. c. Using data from the table of standard reduction potentials in Appendix \(6,\) find the maximum \(E^{*}\) value for the reduction of UF \(_{4}\) for the second reaction. d. Will \(1.00 \mathrm{g}\) of \(\mathrm{Mg}(s)\) be sufficicnt to produce \(1.00 \mathrm{g}\) of uranium?

Sodium-Sulfur Batteries The low cost of sodium and sulfur relative to lithium makes voltaic cells based on sodium attractive to electric vehicle manufacturers, provided the technological hurdles of managing a battery that operates at \(300^{\circ} \mathrm{C}\) can be overcome. The overall cell reaction is $$ 2 \mathrm{Na}(s)+3 \mathrm{S}(\ell) \rightarrow \mathrm{Na}_{2} \mathrm{S}_{3}(s) \quad E_{\mathrm{cell}}^{\circ}=2.076 \mathrm{V} $$ a. Which element is oxidized and which is reduced? b. How many electrons are transferred in the overall cell reaction? c. What is the value of \(\Delta G^{\circ}\) for the reaction? d. If a battery containing \(5.25 \mathrm{kg} \mathrm{Na}\) is \(50 \%\) discharged when it is connected to a charger with an output of 200 A, how long does it take to recharge the battery? e. Draw a Lewis structure for the \(\mathrm{S}_{3}^{2-}\) anion.

Electrolysis of Seawater Magnesium metal is obtained by the electrolysis of molten \(\mathrm{Mg}^{2+}\) salts obtained from evaporated seawater. a. Does elemental Mg form at the cathode or anode? b. Do you think the principal ingredient in sea salt (NaCl) needs to be separated from the Mg \(^{2+}\) salts before electrolysis? Explain your answer. c. Would electrolysis of an aqueous solution of \(\mathrm{Mg} \mathrm{Cl}_{2}\) also produce elemental Mg? d. If your answer to part (c) was no, what would the products of electrolysis be?

Silverware Tarnish Low concentrations of hydrogen sulfide in air react with silver to form \(\mathrm{Ag}_{2} \mathrm{S}\), more familiar to us as tarnish. Silver polish contains aluminum metal powder in a basic suspension. a. Write a balanced net ionic equation for the redox reaction between \(\mathrm{Ag}_{2} \mathrm{S}\) and \(\mathrm{A} 1\) metal that produces \(\mathrm{Ag}\) metal and \(\mathrm{Al}(\mathrm{OH})_{3}\) b. Calculate \(E^{\circ}\) for the reaction. Hint: Derive \(E^{\circ}\) values for the half-reactions in which \(\mathrm{Ag}_{2} \mathrm{S}\) is reduced to Ag metal and \(\mathrm{Al}(\mathrm{OH})\), is reduced to Al metal. Then replace the \(\left[\mathrm{Ag}^{+}\right]\) and \(\left[\mathrm{Al}^{3+}\right]\) terms in the Nernst cquations for these two half-reactions with terms based on the \(K_{* p}\) values of \(\mathrm{Ag}_{2} \mathrm{S}\) and \(\mathrm{Al}(\mathrm{OH})_{3}\) and the concentrations of sulfide and hydroxide ions (both of which are equal to one molar under standard conditions).