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 reduced and B is being oxidized. (b) Cathode: \(\mathrm{A}(aq) + e^- \rightarrow \mathrm{A}^{-}(aq)\); Anode: \(\mathrm{B}(aq) \rightarrow \mathrm{B}^{+}(aq) + e^-\) (c) The reduction half-reaction (\(A + e^- \rightarrow A^-\)) has a higher potential energy. (d) The sign of the free energy change for the reaction is negative.

Step-by-step solution

(a) Identifying the species being oxidized and reduced

In a redox reaction, the species being oxidized loses electrons and the species being reduced gains electrons. Here, A and B are initially neutral and become A⁻ and B⁺ after the reaction, so A gains an electron and becomes reduced, while B loses an electron and becomes oxidized.

(b) Half-reactions in a voltaic cell

In a voltaic cell, the reduction half-reaction occurs at the cathode and the oxidation half-reaction occurs at the anode. In this case, A is reduced (gains an electron) and B is oxidized (loses an electron). Thus, the half-reactions are: Cathode: \(\mathrm{A}(aq) + e^- \rightarrow \mathrm{A}^{-}(aq)\) Anode: \(\mathrm{B}(aq) \rightarrow \mathrm{B}^{+}(aq) + e^-\)

(c) Determining the half-reaction with higher potential energy

Since the standard cell potential, \(E^{\circ}\), is positive, the overall reaction is spontaneous in the given direction. In a spontaneous reaction, the half-reaction with a higher reduction potential occurs at the cathode, and the half-reaction with the lower reduction potential occurs at the anode. Thus, the reduction half-reaction (\(A + e^- \rightarrow A^-\)) has a higher potential energy.

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

The free energy change of the reaction, \(\Delta G\), can be related to the standard cell potential by the following equation: \[\Delta G = -nFE^{\circ}\] where \(n\) is the number of electrons transferred (in this case, 1), \(F\) is the Faraday's constant, and \(E^{\circ}\) is the standard cell potential. Since \(E^{\circ}\) is positive, the free energy change, \(\Delta G\), will be negative. Therefore, the sign of the free energy change for the reaction is negative.

Key concepts

Redox Reaction

Redox reactions are fundamental to understanding electrochemistry. In a redox reaction, two simultaneous processes occur: oxidation and reduction. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. In the context of our exercise, species A gains an electron during the reaction, becoming A⁻, which means A is reduced. Conversely, species B loses an electron, becoming B⁺, making it oxidized.
To identify which species undergoes oxidation or reduction, observe changes in electron configuration or oxidation states of the reactants and products. Remember:

• Oxidation is Losing (OIL) electrons.
• Reduction is Gaining (RIG) electrons.

By following these steps, you can classify the roles of substances in redox reactions clearly.

Voltaic Cell

A voltaic cell, also known as a galvanic cell, is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It is composed of two half-cells, each containing a different electrode where specific half-reactions occur. In our exercise example, the reduction half-reaction occurs at the cathode, while the oxidation happens at the anode.
In practical terms:

• The cathode is the site of reduction where A⁻ is formed from A + an electron.
• The anode is the site of oxidation where B⁺ results from B losing an electron.

Connecting these electrodes with a wire allows the electrons to flow, producing an electric current that can be harnessed for work.

Standard Cell Potential

The standard cell potential, symbolized as \(E^{ ext{°}}\), is a measure of the voltage or electrical potential difference of a cell under standard conditions (1 M concentration, 25°C, and 1 atm pressure). A positive \(E^{ ext{°}}\) implies that the reaction is spontaneous and the cell can produce electricity.
The value of \(E^{ ext{°}}\) is determined by the difference between the reduction potentials of the cathode and the anode.

• Cathode reaction (reduction potential) contributes positively to \(E^{ ext{°}}\).
• Anode reaction (oxidation potential) contributes negatively to \(E^{ ext{°}}\).

In our example, a positive \(E^{ ext{°}}\) indicates that electrons prefer to flow from the anode to the cathode, demonstrating the reaction's favorable direction.

Free Energy Change

Free energy change, represented by \(\Delta G\), links the concept of energy readiness in a reaction with the capacity to perform work. It is closely associated with the standard cell potential through the equation:\[\Delta G = -nFE^{\text{°}}\]Where:

• \(n\) is the number of moles of electrons transferred, which in our case is 1.
• \(F\) is Faraday's constant, approximately 96485 C/mol.
• \(E^{\text{°}}\) is the standard cell potential.

Because our cell has a positive \(E^{\text{°}}\), \(\Delta G\) turns out to be negative, indicating that the reaction is spontaneous in nature. A negative free energy change confirms that energy is released, making it a thermodynamically favorable process.

Half-Reactions

Half-reactions are the core processes within electrochemical cells, breaking down the overall redox reaction into oxidation and reduction processes. By examining each half-reaction separately, we can better understand which species is gaining or losing electrons.
In a voltaic cell:

• The reduction half-reaction occurs at the cathode: \(\mathrm{A}(aq) + e^- \rightarrow \mathrm{A}^-(aq)\).
• The oxidation half-reaction occurs at the anode: \(\mathrm{B}(aq) \rightarrow \mathrm{B}^+(aq) + e^-\).

The separation into half-reactions not only clarifies the electron transfer mechanisms but also assists in calculating the standard cell potential and planning practical applications such as energy harvesting.