Chapter 18

Describe three factors limiting widespread use of cars powered by fuel cells.

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 offer converters that turn readily available fuels--such as natural gas, propane, and methanol-into \(\mathrm{H}_{2}\) for the fuel cells 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 those benefits.

A direct methanol fuel cell uses the oxidation of methanol by oxygen to generate electrical energy. The overall reaction, which is given below, has a \(\Delta G^{\circ}\) value of -702.4 kJ/mol of methanol oxidized. What is the standard cell potential for this fuel cell? $$\mathrm{CH}_{3} \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell)$$

Calculate the \(E_{\text {cell value at } 298} \mathrm{K}\) for the cell based on the reaction $$ mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q) \rightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s)$$ when \(\left[\mathrm{Ag}^{+}\right]=2.56 \times 10^{-3} \mathrm{Mand}\left[\mathrm{Cu}^{2+}\right]=8.25 \times 10^{-4} \mathrm{M}\)

Using the appropriate standard potentials in Appendix 6, determine the equilibrium constant for the following reaction at \(298 \mathrm{K}\) $$\mathrm{Fe}^{3+}(a q)+\mathrm{Cr}^{2+}(a q) \rightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Cr}^{3+}(a q)$$

Using the appropriate standard potentials in Appendix 6, determine the equilibrium constant at \(298 \mathrm{K}\) for the following reaction between \(\mathrm{MnO}_{2}\) and \(\mathrm{Fe}^{2+}\) in acid solution: \(4 \mathrm{H}^{+}(a q)+\mathrm{MnO}_{2}(s)+2 \mathrm{Fe}^{2+}(a q) \rightarrow\) $$\mathrm{Mn}^{2+}(a q)+2 \mathrm{Fe}^{3+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell)$$

Electrolysis of Seawater Magnesium metal is obtained by the electrolysis of molten \(\mathrm{Mg}^{2+}\) salts from evaporated seawater. a. Would elemental Mg form at the cathode or anode? b. Do you think the principal ingredient in sea salt (NaCl) would need to be separated from the \(\mathrm{Mg}^{2+}\) 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 be the products of electrolysis?

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 \(\mathrm{Al}\) metal that produces \(\mathrm{Ag}\) metal and \(\mathrm{Al}(\mathrm{OH})_{3}\) b. Calculate \(E^{\circ}\) for the reaction.

A magnesium battery can be constructed from an anode of magnesium metal and a cathode of molybdenum sulfide, \(\mathrm{Mo}_{3} \mathrm{S}_{4} .\) The standard reduction potentials of the electrode half-reactions are $$\mathrm{Mg}^{2+}(a q)+2 \mathrm{e}^{-} \rightarrow \mathrm{Mg}(s) \quad E^{\circ}=-2.37 \mathrm{V}$$ \(\mathrm{Mg}^{2+}(a q)+\mathrm{Mo}_{3} \mathrm{S}_{4}(s)+2 \mathrm{e}^{-} \rightarrow \mathrm{MgMo}_{3} \mathrm{S}_{4}(s) \quad E^{\circ}=?\) a. 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 of Mo in \(\mathrm{Mo}_{3} \mathrm{S}_{4}\) and in \(\mathrm{MgMo}_{3} \mathrm{S}_{4} ?\) "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?