Problem 33 - Chemistry The Molecular Science

Question

Consider these half-reactions: $$ \begin{array}{lr} \hline \text { Half-reaction } & E^{\circ}(\mathrm{V}) \\ \hline \mathrm{Ce}^{4+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{Ce}^{3+}(\mathrm{aq}) & 1.72 \\ \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(\mathrm{s}) & 0.80 \\ \mathrm{Hg}_{2}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Hg}(\ell) & 0.80 \\ \mathrm{Sn}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Sn}(\mathrm{s}) & -0.14 \\ \mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Ni}(\mathrm{s}) & -0.25 \\ \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{s}) & -1.68 \\ \hline \end{array} $$ (a) Which is the weakest oxidizing agent? (b) Which is the strongest oxidizing agent? (c) Which is the strongest reducing agent? (d) Which is the weakest reducing agent? (e) Will \(\mathrm{Sn}(\mathrm{s})\) reduce \(\mathrm{Ag}^{+}(\mathrm{aq})\) to \(\mathrm{Ag}(\mathrm{s}) ?\) (f) Will \(\mathrm{Hg}(\ell)\) reduce \(\mathrm{Sn}^{2+}(\mathrm{aq})\) to \(\mathrm{Sn}(\mathrm{s}) ?\) (g) Name the ions that can be reduced by \(\operatorname{Sn}(\mathrm{s})\). (h) Which metals can be oxidized by \(\mathrm{Ag}^{+}(\mathrm{aq}) ?\)

Step-by-Step Solution

Answer

(a) \(\mathrm{Al}^{3+}\); (b) \(\mathrm{Ce}^{4+}\); (c) \(\mathrm{Al}(s)\); (d) \(\mathrm{Ce}^{3+}\); (e) Yes; (f) No; (g) \(\mathrm{Ag}^{+}\), \(\mathrm{Hg}_{2}^{2+}\); (h) \(\mathrm{Sn}\), \(\mathrm{Ni}\),\(\mathrm{Al}\).

Step 1: Understanding Oxidizing and Reducing Agents

Oxidizing agents gain electrons and are reduced in a reaction, while reducing agents lose electrons and are oxidized. The effectiveness of an agent is determined by the standard electrode potential, \(E^\circ \). A more positive \(E^\circ \) indicates a stronger oxidizing agent, and a less positive or more negative \(E^\circ \) indicates a stronger reducing agent.

Step 2: Identify Weakest Oxidizing Agent

The weakest oxidizing agent has the most negative standard electrode potential among all half reactions. From the given data:- \(\mathrm{Al}^{3+} + 3e^- \rightarrow \mathrm{Al}, E^\circ = -1.68\text{ V}\)It is the least positive (most negative) potential, making \(\mathrm{Al}^{3+}(\mathrm{aq})\) the weakest oxidizing agent.

Step 3: Identify Strongest Oxidizing Agent

The strongest oxidizing agent has the most positive standard electrode potential. From the given data:- \(\mathrm{Ce}^{4+} + e^- \rightarrow \mathrm{Ce}^{3+}, E^\circ = 1.72\text{ V}\)This is the most positive potential, making \(\mathrm{Ce}^{4+}(\mathrm{aq})\) the strongest oxidizing agent.

Step 4: Identify Strongest Reducing Agent

The strongest reducing agent has the most negative standard electrode potential (opposite sign of oxidation potential). From the data, \(\mathrm{Al}(\mathrm{s})\) has:- \(\mathrm{Al}^{3+} + 3e^- \rightarrow \mathrm{Al}, E^\circ = -1.68\text{ V}\)Thus, \(\mathrm{Al}(\mathrm{s})\) is the strongest reducing agent.

Step 5: Identify Weakest Reducing Agent

The weakest reducing agent corresponds to the least negative or most positive potential. From the data, \(\mathrm{Ce}^{3+}(\mathrm{aq})\) converts to \(\mathrm{Ce}^{4+}(\mathrm{aq})\) most weakly with:- \(\mathrm{Ce}^{4+} + e^- \rightarrow \mathrm{Ce}^{3+}, E^\circ = 1.72\text{ V}\)Thus, \(\mathrm{Ce}^{3+}(\mathrm{aq})\) is the weakest reducing agent.

Step 6: Determine if Sn(s) will reduce Ag+(aq)

To determine if \(\mathrm{Sn}(\mathrm{s})\) can reduce \(\mathrm{Ag}^{+}(\mathrm{aq})\), compare their \(E^\circ\) values. \(\mathrm{Sn}^{2+}/\mathrm{Sn}\) is \(-0.14\text{ V}\) and \(\mathrm{Ag}^{+}/\mathrm{Ag}\) is \(0.80\text{ V}\). \(\mathrm{Sn}(\mathrm{s})\) can reduce \(\mathrm{Ag}^{+}(\mathrm{aq})\) because \(-0.14\text{ V}\) is less than \(0.80\text{ V}\).

Step 7: Determine if Hg(l) will reduce Sn2+(aq)

Check if \(\mathrm{Hg}(\ell)\) can reduce \(\mathrm{Sn}^{2+}(\mathrm{aq})\). The \(E^\circ\) for \(\mathrm{Sn}^{2+/Sn}\) is \(-0.14\text{ V}\) and \(\mathrm{Hg}^{2+/Hg}\) is also \(0.80\text{ V}\). Since \(\mathrm{Hg}(\ell)\) has \(0.80\text{ V}\) and cannot exceed the \(0.80\text{ V}\) threshold of \(\mathrm{Sn}(\mathrm{s})\), \(\mathrm{Hg}(\ell)\) cannot reduce \(\mathrm{Sn}^{2+}(\mathrm{aq})\).

Step 8: Identify ions reducible by Sn(s)

\(\mathrm{Sn}(\mathrm{s})\) can reduce ions with \(E^\circ\) higher (more positive) than \(-0.14\text{ V}\). From the data, the ions are:- \(\mathrm{Ag}^{+}(\mathrm{aq})\) with \(E^\circ = 0.80\text{ V}\)- \(\mathrm{Hg}_{2}^{2+}(\mathrm{aq})\) with \(E^\circ = 0.80\text{ V}\)

Step 9: Identify metals oxidizable by Ag+(aq)

\(\mathrm{Ag}^{+}(\mathrm{aq})\) can oxidize metals with \(E^\circ\) less than \(0.80\text{ V}\). From the breakdown:- \(\mathrm{Sn}(\mathrm{s})\) with \(E^\circ = -0.14\text{ V}\)- \(\mathrm{Ni}(\mathrm{s})\) with \(E^\circ = -0.25\text{ V}\)- \(\mathrm{Al}(\mathrm{s})\) with \(E^\circ = -1.68\text{ V}\)

Key Concepts

Oxidizing Agents

Oxidizing agents are substances that gain electrons and, as a result, are themselves reduced during a chemical reaction. Their primary role is to cause another substance to lose electrons, thus acting as the oxidizer in the reaction process.

When evaluating oxidizing agents, the standard electrode potential, often denoted as \( E^{\circ} \), becomes an instrumental factor. An oxidizing agent with a more positive \( E^{\circ} \) value is stronger because it has a higher tendency to gain electrons. For example, in the exercise provided, \( \mathrm{Ce}^{4+} \) has the highest \( E^{\circ} \) value of 1.72 V, making it the strongest oxidizing agent.

Key characteristics of oxidizing agents include:

• Causing oxidation (loss of electrons) in other substances.
• Being reduced themselves (gain of electrons during the reaction).
• Typically having higher positive electrode potentials.

These agents are essential in various chemical processes from industrial applications to biological systems.

Reducing Agents

Reducing agents are substances that donate electrons to another species, leading to its reduction. In this process, the reducing agents themselves are oxidized. They are essentially the electron providers in redox (reduction-oxidation) reactions.

The effectiveness of a reducing agent can be measured by its standard electrode potential. Contrary to oxidizing agents, a more negative \( E^{\circ} \) value indicates a stronger reducing agent, as they readily give up electrons. For instance, in the exercise, \( \mathrm{Al} \) being converted to \( \mathrm{Al}^{3+} \) has an \( E^{\circ} \) value of -1.68 V, making it a strong reducing agent.

Important aspects of reducing agents include:

• Donating electrons to other substances, thus reducing them.
• Undergoing oxidation themselves in the process (loss of electrons).
• Typically having more negative electrode potentials.
• Participating in processes ranging from battery operations to metabolic pathways.

Understanding their behavior is crucial for predicting the outcomes of chemical reactions.

Standard Electrode Potential

Standard electrode potential (\( E^{\circ} \)) is a measure of the individual potential of a reversible electrode at standard state conditions, which usually include a concentration of 1 M, a pressure of 1 atm, and a temperature of 25°C (298 K). This value is crucial in determining the direction and feasibility of redox reactions.

An electrode potential is reflective of the tendency of a chemical species to be reduced. A positive \( E^{\circ} \) suggests a good oxidizing tendency, while a negative \( E^{\circ} \) indicates a good reducing tendency. This metric helps chemists predict which metals can oxidize or reduce other substances. For example, any species with lower standard potential than \( \/mathrm{Ag}^{+} \) is capable of being oxidized by it.

Key features of \( E^{\circ} \):

• It provides a quantitative measure of the redox-reaction spontaneity.
• Helps in identifying how metals interact with each other in terms of electron exchange.
• Is used to construct electrochemical cells.

Understanding \( E^{\circ} \) values is essential for applications like electroplating, corrosion prevention, and energy generation.