Use the following half-reactions to write three spontaneous reactions, calculate \(E_{\text {cell }}^{\circ}\) for each reaction, and rank the strengths of the oxidizing and reducing agents: (1) \(\mathrm{Al}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(s) \quad E^{\circ}=-1.66 \mathrm{~V}\) (2) \(\mathrm{N}_{2} \mathrm{O}_{4}(g)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{NO}_{2}^{-}(a q) \quad E^{\circ}=0.867 \mathrm{~V}\) (3) \(\mathrm{SO}_{4}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(I)+2 \mathrm{e}^{-} \longrightarrow \mathrm{SO}_{3}^{2-}(a q)+2 \mathrm{OH}^{-}(a q)\) \(E^{\circ}=0.93 \mathrm{~V}\)

In electrochemistry, a redox reaction can be broken down into two half-reactions: an oxidation half-reaction and a reduction half-reaction. Each half-reaction shows either the loss of electrons (oxidation) or the gain of electrons (reduction). For example, in the given exercise, we have the following half-reactions:

• Aluminum: \( \text{Al}^{3+}(aq) + 3 \text{e}^{-} \rightarrow \text{Al}(s) \)
• Nitrogen dioxide: \( \text{N}_2\text{O}_4(g) + 2 \text{e}^{-} \rightarrow 2 \text{NO}_2^{-}(aq) \)
• Sulfate to sulfite: \( \text{SO}_4^{2-}(aq) + \text{H}_2\text{O}(l) + 2 \text{e}^{-} \rightarrow \text{SO}_3^{2-}(aq) + 2 \text{OH}^{-}(aq) \)

These half-reactions are foundational in understanding how electrons are transferred in a redox reaction. By balancing these half-reactions, we can combine them to form a complete redox reaction with identifiable oxidation and reduction parts.

Standard reduction potentials \( (E^{\text{°}}) \) indicate the tendency of a species to gain electrons and be reduced. These values are measured under standard conditions (1M concentration, 1 atm pressure, and 25°C). The more positive the reduction potential, the stronger the species is as an oxidizing agent. In this exercise, we consider the following standard reduction potentials:

• Aluminum: \( E^{\text{°}} = -1.66 \text{ V} \)
• Nitrogen dioxide: \( E^{\text{°}} = 0.867 \text{ V} \)
• Sulfate to sulfite: \( E^{\text{°}} = 0.93 \text{ V} \)

By comparing these values, we can determine which species will act as the reducing or oxidizing agent when they react.

Oxidizing agents are substances that gain electrons and are reduced in a redox reaction. They help oxidize another substance by taking its electrons. A strong oxidizing agent has a high standard reduction potential. From the exercise, we ranked the oxidizing agents based on their reduction potentials:

• \( \text{SO}_4^{2-} \) (strongest oxidizing agent)
• \( \text{N}_2\text{O}_4 \)
• \( \text{Al}^{3+} \)

This ranking helps us predict how readily each species will gain electrons and thus how they will behave in various redox reactions.

Reducing agents are substances that lose electrons and are oxidized in a redox reaction. They help reduce another substance by donating electrons. A strong reducing agent has a low or negative standard reduction potential. From our exercise, the reducing agents are ranked as follows based on their tendency to lose electrons:

• \( \text{Al} \) (strongest reducing agent)
• \( \text{NO}_2^{-} \)
• \( \text{SO}_3^{2-} \)

Knowing the strength of a reducing agent helps us understand how easily it will lose electrons to another substance in a redox reaction.

Electrochemical cells convert chemical energy into electrical energy through redox reactions. They consist of two half-cells, each containing a different half-reaction. In these cells, electrons flow from the reducing agent at the anode to the oxidizing agent at the cathode. The standard cell potential \( (E_{\text{cell}}^{\text{°}}) \) for the overall reaction can be calculated by summing the standard reduction potentials of the reduction and oxidation half-reactions. As seen in our exercise, this is how we calculate \( E_{\text{cell}}^{\text{°}} \) for different reaction combinations:

• Combination of Al and N₂O₄: \( E_{\text{cell}}^{\text{°}} = 2.527 \text{ V} \)
• Combination of Al and SO₄^2-: \( E_{\text{cell}}^{\text{°}} = 2.59 \text{ V} \)
• Combination of NO₂^- and SO₄^2-: \( E_{\text{cell}}^{\text{°}} = 0.063 \text{ V} \)

A positive \( E_{\text{cell}}^{\text{°}} \) value indicates that the reaction is spontaneous and the electrochemical cell will generate electrical energy.