Problem 32 - Chemistry The Molecular Science

Question

Consider these half-reactions: $$ \begin{array}{lr} \hline \text { Half-reaction } & E^{\circ}(\mathrm{V}) \\ \hline \mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au}(\mathrm{s}) & 1.52 \\ \mathrm{Pt}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt}(\mathrm{s}) & 1.118 \\ \mathrm{Co}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Co}(\mathrm{s}) & -0.277 \\ \mathrm{Mn}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{Mn}(\mathrm{s}) & -1.18 \\ \hline \end{array} $$ (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 \(\mathrm{Co}(\mathrm{s})\) reduce \(\mathrm{Pt}^{2+}(\mathrm{aq})\) to \(\mathrm{Pt}(\mathrm{s})\) ? (f) Will \(\mathrm{Pt}(\mathrm{s})\) reduce \(\mathrm{Co}^{2+}(\mathrm{aq})\) to \(\mathrm{Co}(\mathrm{s})\) ? (g) Which ions can be reduced by Co(s)?

Step-by-Step Solution

Answer

(a) Mn^{2+}, (b) Au^{3+}, (c) Mn, (d) Au, (e) Yes, (f) No, (g) Au^{3+} and Pt^{2+}.

Step 1: Understanding Standard Reduction Potentials

The standard reduction potential, denoted by \(E^{ ext{°}}\), indicates how readily a chemical species gains electrons (is reduced). A higher \(E^{ ext{°}}\) value means the species is a stronger oxidizing agent because it more readily accepts electrons.

Step 2: Identifying Oxidizing Agents

An oxidizing agent is reduced in a redox reaction. Therefore, the strongest oxidizing agent will be the one with the highest \(E^{ ext{°}}\), and the weakest will have the lowest. By examining the half-reactions, the highest \(E^{ ext{°}}\) is for \(\mathrm{Au}^{3+}/\mathrm{Au}\) (1.52 V) and the lowest among positive values is \(\mathrm{Co}^{2+}/\mathrm{Co}\) (-0.277 V). Thus, \(\mathrm{Au}^{3+}\) is the strongest oxidizing agent and \(\mathrm{Mn}^{2+}/\mathrm{Mn}\) (since it has the most negative \(E^{\circ}\)) is the weakest.

Step 3: Identifying Reducing Agents

A reducing agent loses electrons (is oxidized) in a reaction. The stronger a reducing agent, the weaker its oxidizing counterpart. Since \(\mathrm{Mn}^{2+}/\mathrm{Mn}\) has the most negative \(E^{\circ}\), \(\mathrm{Mn}(s)\) is the strongest reducing agent. Conversely, \(\mathrm{Au}(s)\) is the weakest reducing agent because its oxidized form is the strongest oxidizing agent.

Step 4: Evaluating Redox Reactions for Specific Questions

To see if \(\mathrm{Co}(s)\) reduces \(\mathrm{Pt}^{2+}(aq)\), the reduction potential of \(\mathrm{Pt}^{2+}/\mathrm{Pt}\) (1.118 V) needs to be greater than the oxidation potential of \(\mathrm{Co}/\mathrm{Co}^{2+}\) inverse (-(-0.277V)=0.277V). Since 1.118V > 0.277V, \(\mathrm{Co}(s)\) can reduce \(\mathrm{Pt}^{2+}(aq)\). To check if \(\mathrm{Pt}(s)\) reduces \(\mathrm{Co}^{2+}(aq)\), compare \(\mathrm{Co}^{2+}/\mathrm{Co}\) (-0.277V) and \(\mathrm{Pt}/\mathrm{Pt}^{2+}\) inverse (-1.118V). Since -1.118V < -0.277V, \(\mathrm{Pt}(s)\) cannot reduce \(\mathrm{Co}^{2+}(aq)\).

Step 5: Identifying Ions Reduced by Co(s)

\(\mathrm{Co}(s)\) can reduce ions with higher reduction potentials than that of \(\mathrm{Co}^{2+}/\mathrm{Co}\). In the table, \(\mathrm{Au}^{3+}/\mathrm{Au}\) (1.52 V) and \(\mathrm{Pt}^{2+}/\mathrm{Pt}\) (1.118 V) are greater than \(\mathrm{Co}^{2+}/\mathrm{Co}\) (-0.277 V). Thus, \(\mathrm{Au}^{3+}(aq)\) and \(\mathrm{Pt}^{2+}(aq)\) can be reduced by \(\mathrm{Co}(s)\).

Key Concepts

Standard Reduction Potentials

When you delve into the world of redox reactions, the concept of standard reduction potentials becomes a key player. Essentially, the standard reduction potential, often represented as \(E^{\circ}\), is a measure of the tendency of a chemical species to gain electrons and thereby be reduced. This value is crucial because it provides insights into how different substances will behave during electron transfer processes.

A higher \(E^{\circ}\) indicates a stronger affinity for electrons, translating to a stronger oxidizing capability. In simple terms, if a species has a higher standard reduction potential, it means it's more "eager" to grab electrons during a reaction.

• High \(E^{\circ}\) = Stronger oxidizing agent (likes to gain electrons)
• Low \(E^{\circ}\) = Weaker oxidizing agent

In practical terms, when comparing the standard reduction potentials of different half-reactions, the one with the highest potential will act as the strongest oxidizing agent. Conversely, a negative \(E^{\circ}\) indicates a reluctancy to gain electrons, thus making it a weaker oxidizing agent. Remember that these potentials can be used to predict which direction reactions will proceed spontaneously.

Oxidizing Agents

Oxidizing agents play a central role in redox reactions. As these agents help oxidize other substances, they themselves get reduced. This means they gain electrons from the substance they are oxidizing.

The strength of an oxidizing agent is directly linked to its standard reduction potential. Generally, the species with the higher \(E^{\circ}\) value in a set of half-reactions acts as the strongest oxidizing agent because it is more ready to accept electrons.

• Strong oxidizing agents have high \(E^{\circ}\)
• They gain electrons quickly

For example, based on the data from the exercise, \(\mathrm{Au}^{3+}\) is the strongest oxidizing agent because it has the highest standard reduction potential of \(1.52 \ \text{V}\). Understanding which species acts as a strong oxidizing agent allows us to predict chemical reactions and manipulate them to our advantage in various applications.

Reducing Agents

In contrast to oxidizing agents, reducing agents give up electrons in redox reactions. While oxidizing agents accept electrons and are reduced, reducing agents are oxidized during the process.

A good rule of thumb is that the stronger the reducing agent, the more negative its standard reduction potential. This is because a more negative \(E^{\circ}\) indicates a species that doesn't hold onto its electrons tightly, making it more willing to donate them.

• Strong reducing agents have low or negative \(E^{\circ}\)
• They easily lose electrons

Using the half-reactions provided, \(\mathrm{Mn}(s)\) stands out as the strongest reducing agent, with its half-reaction having the most negative potential at \(-1.18 \ \text{V}\). Understanding reducing agents and their strengths is vital for designing chemical reactions, especially where electron transfer is essential, such as in batteries or metallurgical processes.