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) \(2 \mathrm{HClO}(a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(I)\) \(E^{\circ}=1.63 \mathrm{~V}\) (2) \(\mathrm{Pt}^{2+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt}(s) \quad E^{\circ}=1.20 \mathrm{~V}\) (3) \(\mathrm{PbSO}_{4}(s)+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pb}(s)+\mathrm{SO}_{4}^{2-}(a q) \quad E^{\circ}=-0.31 \mathrm{~V}\)

In electrochemistry, a half-reaction is a chemical equation that shows either the reduction or oxidation process in an electrochemical cell. These reactions are essential for balancing the overall equation and determining the cell potential. Each half-reaction involves the transfer of electrons.
For instance, consider the half-reactions given in the exercise:

1. \(2 \text{HClO}(aq) + 2 \text{H}^{+}(aq) + 2e^- \rightarrow \text{Cl}_2(g) + 2 \text{H}_2O(l)\hspace{10}E^{\circ} = 1.63 \text{V}\)
2. \(\text{Pt}^{2+}(aq) + 2e^- \rightarrow \text{Pt}(s)\hspace{10}E^{\circ} = 1.20 \text{V}\)
3. \(\text{PbSO}_4(s) + 2e^- \rightarrow \text{Pb}(s) + \text{SO}_4^{2-}(aq)\hspace{10}E^{\circ} = -0.31 \text{V}\)

Half-reactions are used to calculate possible combinations for spontaneous reactions.

Cell potential (\(E_{\text{cell}}^{\circ}\)) is a measure of the voltage or electrical potential difference between two half-cells in an electrochemical cell. It's calculated based on the reduction potentials of the half-reactions. A positive \(E_{\text{cell}}^{\circ}\) indicates a spontaneous reaction.

To determine the overall cell potential, combine the half-reactions:

\(E_{\text{cell}}^{\circ} = E_{\text{cathode}}^{\circ} - E_{\text{anode}}^{\circ}\)

For example, combining the first and second half-reactions, the overall reaction is:

\(2 \text{HClO}(aq) + 2 \text{H}^{+}(aq) + \text{Pt}(s) \rightarrow \text{Cl}_2(g) + 2 \text{H}_2O(l) + \text{Pt}^{2+}(aq)\)
\(E_{\text{cell}}^{\circ} = 1.63 \text{V} - 1.20 \text{V} = 0.43 \text{V}\)

This positive value confirms the reaction is spontaneous.

Oxidizing agents are substances that gain electrons during a reaction and, in the process, they oxidize other substances. They are reduced themselves. The strength of oxidizing agents can be ranked based on their standard reduction potentials.

In the given exercise, the oxidizing agents are:

• \(HClO\) with \(E^{\circ} = 1.63 \text{V}\)
• \(\text{Pt}^{2+}\) with \(E^{\circ} = 1.20 \text{V}\)
• \(\text{PbSO}_4\) with \(E^{\circ} = -0.31 \text{V}\)

The most positive value indicates the strongest oxidizing agent. Thus, the ranking is:
\(\text{HClO} > \text{Pt}^{2+} > \text{PbSO}_4\)

Reducing agents are substances that lose electrons during a reaction, causing another substance to be reduced. They are oxidized themselves. The strength of reducing agents is inversely related to their standard reduction potentials.

From the exercise, the reducing agents are:

• \(\text{Pb}\)
• \(\text{Pt}\)
• \(\text{Cl}_2\)

The species involved in the half-reaction with the most negative potential are the strongest reducing agents. Thus, the ranking is:
\(\text{Pb} > \text{Pt} > \text{Cl}_2\)

Spontaneous reactions in electrochemistry occur when the cell potential (\(E_{\text{cell}}^{\circ}\)) is positive. This means the Gibbs free energy (\( \Delta G \) is negative.

To find if a reaction is spontaneous, we look at the combined cell potential:

For example:

• \(2 \text{HClO}(aq) + 2 \text{H}^{+}(aq) + \text{Pt}(s) \rightarrow \text{Cl}_2(g) + 2 \text{H}_2O(l) + \text{Pt}^{2+}(aq)\) with
  \(E_{\text{cell}}^{\circ} = 0.43 \text{V}\)
  
• \(2 \text{HClO}(aq) + 2 \text{H}^{+}(aq) + \text{Pb}(s) \rightarrow \text{Cl}_2(g) + 2 \text{H}_2O(l) + \text{PbSO}_4(s)\) with
  \(E_{\text{cell}}^{\circ} = 1.94 \text{V}\)
  
• \( \text{Pt}^{2+}(aq) + \text{Pb}(s) \rightarrow \text{Pt}(s) + \text{PbSO}_4(s)\)with
  \(E_{\text{cell}}^{\circ} = 1.51 \text{V}\)
  

Since all the cell potentials are positive, these reactions are spontaneous.