Problem 6 - Chemistry: The Central Science in SI Units, Global Edition

Question

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 \(\mathrm{C}^{2+} ?\)

Step-by-Step Solution

Answer

(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 1: 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.

Step 2: 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) ⟶ A+(aq) + e⁻, E = -1.33 V 2. B(s) ⟶ B2+(aq) + 2e⁻, E = -0.87 V 3. C2+(aq) ⟶ C3+(aq) + e⁻, E = 0.12 V 4. D(s) ⟶ D3+(aq) + 3e⁻, 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.

Step 3: 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 (ΔE > 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+.

Key Concepts

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 – 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.