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Chapter 20: Problem 6

Consider the following table of standard electrode potentials for a series of hypothetical reactions in aqueous solution: $$ \begin{array}{lr} \hline \text { Reduction Half-Reaction } & {E^{\circ}(\mathrm{V})} \\ \hline \mathrm{A}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{A}(s) & 1.33 \\\ \mathrm{~B}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{B}(s) & 0.87 \\\ \mathrm{C}^{3+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{C}^{2+}(a q) & -0.12 \\ \mathrm{D}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{D}(s) & -1.59 \\\ \hline \end{array} $$ (a) Which substance is the strongest oxidizing agent? Which is weakest? (b) Which substance is the strongest reducing agent? Which is weakest? (c) Which substance(s) can oxidize \(\mathrm{C}^{2+} ?\)

Short Answer

Expert verified
(a) Strongest oxidizing agent: A+, with an electrode potential of 1.33 V. Weakest oxidizing agent: D3+, with an electrode potential of -1.59 V. (b) Strongest reducing agent: D(s), with reverted electrode potential: 1.59 V. Weakest reducing agent: C2+ with reverted electrode potential: 0.12 V. (c) Only D(s) can oxidize C2+.

Step by step solution

01

a) Strongest and Weakest oxidizing agents

To determine the strongest and weakest oxidizing agents, we need to look at the electrode potentials in the given table since a more positive potential indicates a stronger oxidizing agent. The oxidation agents are the ones in the reduced form in the table. So, - Strongest oxidizing agent: A+, with an electrode potential of 1.33 V. - Weakest oxidizing agent: D3+, with an electrode potential of -1.59 V.
02

b) Strongest and Weakest reducing agents

To determine the strongest and weakest reducing agents, we need to look at the electrode potentials in the table. A more negative potential indicates a stronger reducing agent. The reducing agents are represented by the substances in their oxidized forms. To find the reducing agents, we need to change the half-reactions into their "opposite" form: 1. A(s) 鉄� A+(aq) + e鈦�, E = -1.33 V 2. B(s) 鉄� B2+(aq) + 2e鈦�, E = -0.87 V 3. C2+(aq) 鉄� C3+(aq) + e鈦�, E = 0.12 V 4. D(s) 鉄� D3+(aq) + 3e鈦�, E = 1.59 V So, - Strongest reducing agent: D(s), with reverted electrode potential: 1.59 V. - Weakest reducing agent: C2+ with reverted electrode potential: 0.12 V.
03

c) Substances that can oxidize C2+

Oxidizing C2+ means we need to find the substances that, when coupled with C2+, will have a positive overall cell potential (螖E > 0). In other words, C2+ needs to be the strongest reducing agent among the species being compared. From the calculations in part (b), we already know that C2+ has a reverted electrode potential of 0.12 V. For any species S with E(S), we need to check if E(S) + E(C2+) > 0. Comparing with the other reverted electrode potentials: 1. A(s), E = -1.33 V: -1.33 + 0.12 = -1.21 V 2. B(s), E = -0.87 V: -0.87 + 0.12 = -0.75 V 3. D(s), E = 1.59 V: 1.59 + 0.12 = 1.71 V The overall cell potential is positive only for D(s). So, only D(s) can oxidize C2+.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Oxidizing Agents
Oxidizing agents are substances that gain electrons during a chemical reaction. This action of gaining electrons causes them to oxidize another substance, hence the name "oxidizing agents." They are crucial in redox reactions, where one substance is oxidized, and another is reduced. The potential of an oxidizing agent to obtain electrons is indicated by its electrode potential value 鈥� the more positive this value, the stronger the oxidizing power. In our exercise, the strongest oxidizing agent is \( A^+ \), with a potential of 1.33 V, because it can readily accept electrons. On the flip side, the weakest oxidizing agent is \( D^{3+} \), at -1.59 V, indicating reluctance to gain electrons.
Examining Reducing Agents
Reducing agents are chemicals that donate electrons to another molecule in a redox reaction. When they donate electrons, they become oxidized themselves, but in this process, they reduce the other substance, earning their title "reducing agents." To identify the strength of a reducing agent, we must consider the reversed electrode potential from the standard table. Substances with more negative potentials make stronger reducing agents, showing they have a greater tendency to lose electrons. From the given table after reversing the reactions, \( D(s) \) is determined to be the strongest reducing agent with a potential of -1.59 V, and \( C^{2+} \) is the weakest with 0.12 V.
Decoding Redox Reactions
Redox reactions involve the transfer of electrons between two substances. This amalgamation of oxidation and reduction processes happens simultaneously, as one molecule's loss of electrons (oxidation) directly corresponds to another's electron gain (reduction). Redox reactions are pivotal in both natural and technological processes, from cellular respiration in our bodies to energy generation in batteries. In our exercise, to determine which substances can oxidize \( C^{2+} \), we need to compare the electrode potentials of other candidates in reversed reactions with \( C^{2+} \)'s potential. Here, \( D(s) \) with a potential of -1.59 V in its reversed form is the only substance capable of oxidizing \( C^{2+} \), as it meets the criterion of a positive overall cell potential.

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Most popular questions from this chapter

The purification process of silicon involves the reaction of silicon tetrachloride vapor \(\left(\mathrm{SiCl}_{4}(g)\right)\) with hydrogen to \(1250^{\circ} \mathrm{C}\) to form solid silicon and hydrogen chloride. \((\mathbf{a})\) Write a balanced equation for this reaction. (b) What is being oxidized, and what is being reduced? (c) Which substance is the reductant, and which is the oxidant?

Metallic gold is collected from below the anode when a mixture of copper and gold metals is refined by electrolysis. Explain this behavior.

Some years ago a unique proposal was made to raise the Titanic. The plan involved placing pontoons within the ship using a surface-controlled submarine-type vessel. The pontoons would contain cathodes and would be filled with hydrogen gas formed by the electrolysis of water. It has been estimated that it would require about \(7 \times 10^{8} \mathrm{~mol}\) of \(\mathrm{H}_{2}\) to provide the buoyancy to lift the ship (J. Chem. Educ., 1973, Vol. 50, 61). (a) How many coulombs of electrical charge would be required? (b) What is the minimum voltage required to generate \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) if the pressure on the gases at the depth of the wreckage \((3 \mathrm{~km})\) is \(30 \mathrm{MPa} ?(\mathbf{c})\) What is the minimum electrical energy required to raise the Titanic by electrolysis? (d) What is the minimum cost of the electrical energy required to generate the necessary \(\mathrm{H}_{2}\) if the electricity costs 85 cents per kilowatt-hour to generate at the site?

(a) How many coulombs are required to plate a layer of chromium metal \(0.15 \mathrm{~mm}\) thick on an auto bumper with a total area of \(0.40 \mathrm{~m}^{2}\) from a solution containing \(\mathrm{CrO}_{4}^{2-}\) ? The density of chromium metal is \(7.20 \mathrm{~g} / \mathrm{cm}^{3}\). (b) What current flow is required for this electroplating if the bumper is to be plated in \(20.0 \mathrm{~s} ?(\mathbf{c})\) If the external source has an emf of \(+5.5 \mathrm{~V}\) and the electrolytic cell is \(60 \%\) efficient, how much electrical energy is expended to electroplate the bumper?

Heart pacemakers are often powered by lithium-silver chromate "button" batteries. The overall cell reaction is $$ 2 \mathrm{Li}(s)+\mathrm{Ag}_{2} \mathrm{CrO}_{4}(s) \longrightarrow \mathrm{Li}_{2} \mathrm{CrO}_{4}(s)+2 \mathrm{Ag}(s) $$ (a) Lithium metal is the reactant at one of the electrodes of the battery. Is it the anode or the cathode? (b) Choose the two half-reactions from Appendix \(\mathrm{E}\) that most closely approximate the reactions that occur in the battery. What standard emf would be generated by a voltaic cell based on these half-reactions? (c) The battery generates an emf of \(+3.5 \mathrm{~V}\). How close is this value to the one calculated in part (b)? (d) Calculate the emf that would be generated at body temperature, \(37^{\circ} \mathrm{C}\). How does this compare to the emf you calculated in part (b)?
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