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Chapter 20: Problem 117

If a chemical reaction is carried out in a fuel cell, the maximum amount of useful work that can be obtained is (a) \(\Delta G ;\) (b) \(\Delta H ;\) (c) \(\Delta G / \Delta H ;\) (d) \(T \Delta S\).

Short Answer

Expert verified
The correct answer is (a) \(\Delta G\). The maximum work other than expansion work that can be achieved from a chemical reaction (at constant temperature and pressure) is equivalent to the Gibbs Free Energy change.

Step by step solution

01

Evaluate each option

Examine each provided choice: \(\Delta G\), \(\Delta H\), \(\Delta G / \Delta H\), and \(T \Delta S\). These represent different thermodynamic properties. \(\Delta G\) is the change in Gibbs Free Energy, \(\Delta H\) is the change in enthalpy, \(\Delta G / \Delta H\) is a ratio of these two changes, and \(T \Delta S\) denotes the change in entropy times the absolute temperature. However, the maximum amount of useful work that can be obtained from a chemical reaction is given by the Gibbs Free Energy Change, not by the Enthalpy change, their ratio or the term related to entropy.

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Most popular questions from this chapter

Describe in words how you would calculate the standard potential of the \(\mathrm{Fe}^{2+} / \mathrm{Fe}(\mathrm{s})\) couple from those of \(\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+} / \mathrm{Fe}(\mathrm{s})\).

Use the Nernst equation and data from Appendix D to calculate \(E_{\text {rell for each of the following cells. }}\) (a) \(\operatorname{Mn}(\mathrm{s}) | \mathrm{Mn}^{2+}(0.40 \mathrm{M}) \| \mathrm{Cr}^{3+}(0.35 \mathrm{M})\) \(\mathrm{Cr}^{2+}(0.25 \mathrm{M}) | \mathrm{Pt}(\mathrm{s})\) (b) \(\operatorname{Mg}\left(\text { s) } | \operatorname{Mg}^{2+}(0.016 \mathrm{M}) \|\left[\mathrm{Al}(\mathrm{OH})_{4}\right]^{-}(0.25 \mathrm{M})\right.\) \(\mathrm{OH}^{-}(0.042 \mathrm{M}) | \mathrm{Al}(\mathrm{s})\)

A solution containing both \(\mathrm{Ag}^{+}\) and \(\mathrm{Cu}^{2+}\) ions is subjected to electrolysis. (a) Which metal should plate out first? (b) Plating out is finished after a current of \(0.75 \mathrm{A}\) is passed through the solution for 2.50 hours. If the total mass of metal is \(3.50 \mathrm{g},\) what is the mass percent of silver in the product?

Consider the reaction \(\operatorname{Co}(\mathrm{s})+\mathrm{Ni}^{2+}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Co}^{2+}(\mathrm{aq})+\mathrm{Ni}(\mathrm{s}), \quad\) with \(\quad E_{\mathrm{cell}}^{\circ}=0.02 \mathrm{V} . \quad\) If \(\quad \mathrm{Co}(\mathrm{s}) \quad\) is added to a solution with \(\left[\mathrm{Ni}^{2+}\right]=1 \mathrm{M},\) should the reaction go to completion? Explain.

In each of the following examples, sketch a voltaic cell that uses the given reaction. Label the anode and cathode; indicate the direction of electron flow; write a balanced equation for the cell reaction; and calculate \(E_{\mathrm{cell}}^{\circ}\). (a) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Fe}^{3+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Fe}^{2+}(\mathrm{aq})\) (b) \(\mathrm{Pb}^{2+}(\mathrm{aq})\) is displaced from solution by \(\mathrm{Al}(\mathrm{s})\) (c) \(\mathrm{Cl}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g})+\mathrm{H}^{+}(\mathrm{aq})\) (d) \(\mathrm{Zn}(\mathrm{s})+\mathrm{H}^{+}+\mathrm{NO}_{3}^{-} \longrightarrow \mathrm{Zn}^{2+}+\) \(\mathrm{H}_{2} \mathrm{O}(1)+\mathrm{NO}(\mathrm{g})\)
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