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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{tabular}{lr} \hline Reduction Half-Reaction & \(E^{+}(\mathrm{V})\) \\ \hline\(A^{+}(a q)+\mathrm{c}^{-} \longrightarrow \mathrm{A}(\mathrm{s})\) & \(1.33\) \\ \(\mathrm{~B}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{B}(s)\) & \(0.87\) \\ \(\mathrm{C}^{3+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{C}^{2+}(a q)\) & \(-0.12\) \\ \(\mathrm{D}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{D}(s)\) & \(-1.59\) \\ \hline \end{tabular} (a) Which substance is the strongest oxidixing agent? Which is weakest? (b) Which substance is the strongest reducing agent? Which is weakest? (c) Which substance(s) can oxidize \(C^{24}\) ? [Sections 20.4 and 20.5]

Short Answer

Expert verified
The strongest oxidizing agent is \(A^+\) and the weakest oxidizing agent is \(D^{3+}\). The strongest reducing agent is \(D\) and the weakest reducing agent is \(A\). The substances that can oxidize \(C^{2+}\) are \(A^+\) and \(B^{2+}\).

Step by step solution

01

Identify the strongest and weakest oxidizing agents

The strongest oxidizing agent corresponds to the reaction with the highest standard electrode potential (E潞). In contrast, the weakest oxidizing agent corresponds to the reaction with the lowest standard electrode potential. Looking at the given table: - Strongest oxidizing agent: Reaction with highest E潞 = \(A^{+}(aq) + e^{-}\rightarrow A(s)\), E潞 = 1.33 V - Weakest oxidizing agent: Reaction with lowest E潞 = \(D^{3+}(aq) + 3e^{-}\rightarrow D(s)\), E潞 = -1.59 V So, the strongest oxidizing agent is \(A^+\) and the weakest oxidizing agent is \(D^{3+}\).
02

Identify the strongest and weakest reducing agents

A reducing agent is a substance that loses electrons while helping another substance to gain electrons or be reduced. The strongest reducing agent corresponds to the reduction half-reaction that has the lowest standard electrode potential when written as an oxidation half-reaction. In contrast, the weakest reducing agent corresponds to the reduction half-reaction that has the highest standard electrode potential when written as an oxidation half-reaction. For reduction half-reaction: \(A^{+}(aq)+e^{-}\rightarrow A(s)\), E潞 = 1.33 V Oxidation half-reaction: \(A(s)\rightarrow A^{+}(aq)+e^{-}\), E潞 = -1.33 V For reduction half-reaction: \(B^{2+}(aq)+2e^{-}\rightarrow B(s)\), E潞 = 0.87 V Oxidation half-reaction: \(B(s)\rightarrow B^{2+}(aq)+2e^{-}\), E潞 = -0.87 V For reduction half-reaction: \(C^{3+}(aq)+ e^{-}\rightarrow C^{2+}(aq)\), E潞 = -0.12 V Oxidation half-reaction: \(C^{2+}(aq)\rightarrow C^{3+}(aq) + e^{-}\), E潞 = 0.12 V For reduction half-reaction: \(D^{3+}(aq)+3 e^{-}\rightarrow D(s)\), E潞 = -1.59 V Oxidation half-reaction: \(D(s)\rightarrow D^{3+}(aq)+3 e^{-}\), E潞 = 1.59 V Strongest reducing agent: Reaction with lowest E潞 (oxidation half-reaction) = \(D(s) \rightarrow D^{3+}(aq) + 3 e^{-}\), E潞 = 1.59 V Weakest reducing agent: Reaction with highest E潞 (oxidation half-reaction) = \(A(s) \rightarrow A^{+}(aq) + e^{-}\), E潞 = -1.33 V So, the strongest reducing agent is \(D\) and the weakest reducing agent is \(A\).
03

Identify which substance(s) can oxidize C^{2+}

The substance(s) that can oxidize \(C^{2+}\) is/are the ones where the reduction potential of their half-reaction is greater than the oxidation potential of the half-reaction involving \(C^{2+}\). The oxidation half-reaction for \(C^{2+}\) is: \(C^{2+}(aq) \rightarrow C^{3+}(aq) + e^{-}\) with E潞 = 0.12 V. Given reduction half-reactions: 1. \(A^{+}(aq) + e^{-} \rightarrow A(s)\) with E潞 = 1.33 V 2. \(B^{2+}(aq) + 2e^{-} \rightarrow B(s)\) with E潞 = 0.87 V 3. \(D^{3+}(aq) + 3e^{-} \rightarrow D(s)\) with E潞 = -1.59 V If E潞 (given reaction) > E潞 (\(C^{2+}\) oxidation half-reaction), then the given reaction can oxidize \(C^{2+}\). 1. E潞 (1.33 V) > E潞 (0.12 V), so \(A^{+}\) can oxidize \(C^{2+}\). 2. E潞 (0.87 V) > E潞 (0.12 V), so \(B^{2+}\) can oxidize \(C^{2+}\). 3. E潞 (-1.59 V) < E潞 (0.12 V), so \(D^{3+}\) cannot oxidize \(C^{2+}\). Thus, the substances that can oxidize \(C^{2+}\) are \(A^+\) and \(B^{2+}\).

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Key Concepts

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

Oxidizing Agent
An oxidizing agent is a substance that gains electrons and, in the process, causes other substances to lose electrons鈥攅ssentially oxidizing them. In an electrochemical cell, the substance with the greater tendency to gain electrons, typically at the cathode, is the stronger oxidizing agent.

For instance, if we refer to the standard electrode potentials for the hypothetical reactions provided in your exercise, we see that the substance with the highest electrode potential, which is 1.33 volts for the reaction involving A+, is the strongest oxidizing agent. This high potential indicates that A+ has a strong affinity for electrons. On the other hand, the substance with the lowest electrode potential of -1.59 volts involving D3+ is the weakest oxidizing agent.

As part of our exercise improvement advice, we should note that understanding the role of oxidizing agents is crucial in predicting the direction of redox reactions and identifying which substances can be oxidized.
Reducing Agent
Conversely, a reducing agent is a substance that donates electrons to another species and is itself oxidized in the process. To identify the strongest and weakest reducing agents from a series of reactions, we need to consider the standard electrode potentials when the reactions are written as oxidation reactions.

The substance D, which has the highest positive potential of 1.59 volts when written as an oxidation reaction, is the strongest reducing agent because it has the greatest tendency to lose electrons. Meanwhile, A, which has an oxidation potential of -1.33 volts, demonstrates the least tendency to lose electrons, making it the weakest reducing agent. This evaluation helps us to predict and explain how different substances behave in redox reactions.
Electrochemical Reduction-Oxidation Reactions
Electrochemical reduction-oxidation reactions, commonly referred to as redox reactions, involve the transfer of electrons from one species to another. These reactions have two halves鈥攖he reduction half and the oxidation half.

In the standard electrode potential table provided, each pair of species that undergoes an electron transfer represents a half-reaction. Combining two such half-reactions, where one species gets reduced and another gets oxidized, makes a complete redox reaction. The potential differences between the half-reactions are what drive the electron transfer. The ability to predict which substances can undergo oxidation or reduction by comparing their standard electrode potentials is essential for understanding and predicting redox reactions.
Standard Reduction Potential
The standard reduction potential (E潞) is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. It is measured in volts (V) at standard conditions, which include a temperature of 298 K (25 掳C), a 1 M concentration for each ion participating in the reaction, and a pressure of 1 atmosphere for any gases involved.

When analyzing standard reduction potentials, remember that a higher positive value indicates a greater tendency to be reduced (function as an oxidizing agent), while a more negative value indicates a reduced likelihood of gaining electrons (function as a reducing agent). This concept is crucial in the problem at hand as it guides us in determining the strongest and weakest oxidizing and reducing agents by comparing standard reduction potential values.

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Most popular questions from this chapter

A voltaic cell similar to that shown in Figure \(20.5\) is constructed. One electrode half-cell consists of a silver strip placed in a solution of \(\mathrm{AgNO}_{\mathrm{g}}\) and the other has an iron strip placed in a solution of \(\mathrm{FeCl}_{2}\). The overall cell reaction is $$ \mathrm{Fe}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{Ag}(s) $$ (a) What is being oxidized, and what is being reduced? (b) Write the half-reactions that occur in the two half-cells. (c) Which electrode is the anode, and which is the cathode? (d) Indicate the signs of the electrodes. (e) Do electrons flow from the silver electrode to the iron electrode or from the iron to the silver? (f) In which directions do the cations and anions migrate through the solution?

From each of the following pairs of substances, use data in Appendix E to choose the one that is the stronger oxidizing agent: (a) \(\mathrm{Cl}_{2}(g)\) or \(\mathrm{Br}_{2}(l)\) (b) \(\mathrm{Zn}^{2+}(a q)\) or \(\operatorname{Cd}^{2+}(a q)\) (c) \(\mathrm{Cl}^{-}(a q)\) or \(\mathrm{ClO}_{3}^{-}(a q)\) (d) \(\mathrm{H}_{2} \mathrm{O}_{2}(a q)\) or \(\mathrm{O}_{2}(\mathrm{~g})\)

Hydrogen gas has the potential for use as a clean fuel in reaction with oxygen. The relevant reaction is $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I) $$ Consider two possible ways of utilizing this reaction as an electrical energy source: (i) Hydrogen and oxygen gases are combusted and used to drive a generator, much as coal is currently used in the electric power industry; (ii) hydrogen and oxygen gases are used to generate electricity directly by using fuel cells that operate at \(85^{\circ} \mathrm{C}\). (a) Use data in Appendix C to calculate \(\Delta H^{t}\) and \(\Delta S^{\circ}\) for the reaction. We will assume that these values do not change appreciably with temperature. (b) Based on the values from part (a), what trend would you expect for the magnitude of \(\Delta G\) for the reaction as the temperature increases? (c) What is the significance of the change in the magnitude of \(\Delta G\) with temperature with respect to the utility of hydrogen as a fuel? (d) Based on the analysis here, would it be more efficient to use the combustion method or the fuel-cell method to generate electrical energy from hydrogen?

If the equilibrium constant for a two-electron redox reaction at \(298 \mathrm{~K}\) is \(1.5 \times 10^{-4}\), calculate the corresponding \(\Delta G^{\text {t }}\) and \(E_{\text {red }}\)

(a) A voltaic cell is constructed with all reactants and products in their standard states. Will the concentration of the reactants increase, decrease, or remain the same as the cell operates? (b) What happens to the emf of a cell if the concentrations of the products are increased?
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