Question

For the generic reaction \(\mathrm{A}(a q)+\mathrm{B}(a q) \longrightarrow\) \(\mathrm{A}^{-}(a q)+\mathrm{B}^{+}(a q)\) for which \(E^{\circ}\) is a positive number, answer the following questions: (a) What is being oxidized, and what is being reduced? (b) If you made a voltaic cell out of this reaction, what half-reaction would be occurring at the cathode, and what half-reaction would be occurring at the anode? (c) Which half-reaction from (b) is higher in potential energy? (d) What is the sign of the free energy change for the reaction? [Sections \(20.4\) and \(20.5]\)

Short answer

(a) A is being oxidized, and B is being reduced. (b) Cathode half-reaction: B(aq) + e^- -> B^(+)(aq); Anode half-reaction: A(aq) -> A^-(aq) + e^-. (c) The cathode half-reaction (B(aq) + e^- -> B^(+)(aq)) has a higher potential energy. (d) The sign of the free energy change for the reaction is Negative.

Step-by-step solution

(a) Identify oxidation and reduction

In the given redox reaction, A(aq) + B(aq) -> A^-(aq) + B^(+)(aq), we can observe that A loses an electron and becomes A^-, and B gains an electron and becomes B^+. Oxidation is the loss of electrons. Therefore, A is being oxidized. Reduction is the gain of electrons. Therefore, B is being reduced.

(b) Half-reactions at cathode and anode in the voltaic cell

In a voltaic cell, the reduction occurs at the cathode and the oxidation takes place at the anode. So, at the cathode, the half-reaction is B(aq) + e^- -> B^+(aq) And at the anode, the half-reaction is A(aq) -> A^-(aq) + e^-

(c) Which half-reaction has higher potential energy

We know that the standard reduction potential, E^0, is a positive number for the given reaction. Since the reduction occurs at the cathode and E^0 is positive, the half-reaction at the cathode (B(aq) + e^- -> B^+(aq)) has a higher potential energy.

(d) Sign of the free energy change for the given reaction

As per the relation between Gibbs free energy change and cell potential, ΔG = -nFE, where n is the number of electrons transferred, F is Faraday's constant, and E is the cell potential. Since E^0 is a positive number for the given reaction, the free energy change, ΔG, will be negative as per the equation. So, the sign of the free energy change for the given reaction is Negative.

Key concepts

Oxidation and Reduction

In chemistry, redox reactions are fundamental processes that involve the transfer of electrons between chemical species. These are characterized by two main types of reactions: oxidation and reduction.

• Oxidation: This occurs when a substance loses electrons. In the process detailed in the exercise, species A is oxidized, as it loses an electron and transforms into A^-.
• Reduction: This process involves the gaining of electrons by a chemical species. In the reaction, B is reduced as it gains an electron to form B⁺.

Always remember, oxidation and reduction occur simultaneously in these reactions; you can't have one without the other. In other words, as electron donors give up electrons (oxidation), electron acceptors gain them (reduction). This simultaneous process is why these reactions are often referred to as "redox" reactions.

Voltaic Cell

A voltaic cell is a device that harnesses redox reactions to generate electrical energy. In these cells, the overall redox reaction is split into two half-reactions, each occurring in separate compartments.

• Anode: Here, oxidation takes place. It's the source of liberated electrons. For the reaction A(aq) -> A^-(aq) + e^-, A is oxidized at the anode.
• Cathode: Reduction occurs at this electrode, consuming the electrons supplied by the anode. In our reaction, B(aq) + e^- -> B⁺(aq) takes place at the cathode.

The process of electron flow from the anode to the cathode through an external circuit is what produces electricity. The separation of these half-reactions in a voltaic cell enables this electron flow, making such cells powerful energy sources.

Half-Reactions

Half-reactions are a way of representing the separate processes of oxidation and reduction in the overall redox reaction. They provide insight into the electron transfer process.

• Anodic Reaction: This is where oxidation occurs. For our case, the half-reaction is A(aq) -> A^-(aq) + e^-.
• Cathodic Reaction: This half-reaction deals with the reduction process, given as B(aq) + e^- -> B⁺(aq).

Analyzing these helps us understand not only how the electrons are shifted between substances but also the energetic changes involved. Each half-reaction has its associated electrode potential, which can inform us about the feasibility and spontaneity of the reaction occurring in a voltaic cell.

Free Energy Change

The free energy change, \(\Delta G\), in a chemical reaction determines its spontaneity. The relation with electrical work in redox reactions is key as shown by the equation: \(\Delta G = -nFE\), where:

• \(n\) is the number of moles of electrons exchanged
• \(F\) is Faraday's constant (approximately 96,485 C mol^-1)
• \(E\) is the cell potential

In the textbook solution, \(E^0\) is positive. This means that \(\Delta G\), the Gibbs free energy change, must be negative. A negative \(\Delta G\) indicates that the reaction is spontaneous and capable of performing work under standard conditions. This concept is crucial for understanding why certain reactions are thermodynamically favorable and can be harnessed in practical applications like voltaic cells.