Question

You are given these three reducing agents: \(\mathrm{Zn}(\mathrm{s})\) \(\mathrm{Sn}^{2+}(\mathrm{aq}),\) and \(\mathrm{I}^{-}(\mathrm{aq}) .\) Use data from Appendix \(\mathrm{D}\) to determine which of them can, under standard-state conditions in acidic solution, reduce (a) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})\) to \(\mathrm{Cr}^{3+}(\mathrm{aq})\) (b) \(\mathrm{Cr}^{3+}(\text { aq })\) to \(\mathrm{Cr}^{2+}(\mathrm{aq})\) (c) \(\mathrm{SO}_{4}^{2-}(\text { aq })\) to \(\mathrm{SO}_{2}(\mathrm{g})\)

Short answer

The actual agents that may perform the reduction will depend on the E0 values found in Appendix D. If the E0 value of the reducing agent is lower than that of the oxidizing agent, then it can perform the reduction. Without the actual values, no specific agents can be specified.

Step-by-step solution

Identify the E0 values

First, refer to Appendix D to find the standard reduction potentials (E0) for the agents. Remember, a higher E0 value denotes a stronger oxidizing agent, and a lower E0 value (i.e., a more negative or less positive value) indicates a stronger reducing agent.

Predict the redox reactions

For Part (a), compare the E0 values of \(\mathrm{Zn}(\mathrm{s})\), \(\mathrm{Sn}^{2+}(\mathrm{aq}),\) and \(\mathrm{I}^{-}(\mathrm{aq})\), with that of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})\). The effective reducing agents are the ones whose E0 values are lower. Repeat this step for parts (b) and (c).

Conclude

State which of the reducing agents (if any) can reduce the oxidizing agents in each part of the question.

Key concepts

Reduction Potentials

When it comes to understanding redox reactions, reduction potentials are key. Each substance involved in a redox reaction has a reduction potential value. This value indicates its willingness to gain electrons and be reduced.

• A positive reduction potential suggests that a substance readily accepts electrons, making it a good oxidizing agent.
• A negative reduction potential indicates that a substance does not easily gain electrons and is instead a strong reducing agent.

The standard reduction potentials (\( E^0 \)) are measured under standard conditions—usually 1 molar concentration, 1 bar of pressure, and 25 degrees Celsius.

Using Reduction Potentials

When identifying which substances will act as oxidizing or reducing agents in a reaction, you compare their reduction potentials. A higher\( E^0 \) value means a stronger oxidizing agent while a lower—or more negative—\( E^0 \) indicates a stronger reducing agent. This helps predict which direction the reaction will proceed.

Reducing Agents

Reducing agents are substances that donate electrons in a chemical reaction, essentially causing another substance to be reduced. Reducing agents themselves get oxidized in the process.

• Good reducing agents have low or negative reduction potentials.
• They often contain atoms with a low oxidation state, willing to increase their oxidation number by losing electrons.

In the original exercise, substances like \( \mathrm{Zn}(\mathrm{s}) \) or \( \mathrm{I}^{-}(\mathrm{aq}) \) act as reducing agents. By donating electrons, they can reduce other compounds, such as \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \) to \( \mathrm{Cr}^{3+}(\mathrm{aq}) \), if their reduction potential is lower than that of the oxidizing agent. The ability of reducing agents to cause a reduction is central to many chemical processes, including biological systems and industrial applications.

Oxidizing Agents

Oxidizing agents are the opposite of reducing agents. They accept electrons in a chemical reaction, causing another substance to be oxidized. In doing so, oxidizing agents become reduced.

• Oxidizing agents typically have high reduction potentials, making them eager to accept electrons.
• They often contain atoms with high oxidation states that they seek to lower by gaining electrons.

For instance, in the original problem, \( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \) serves as an oxidizing agent that can be reduced to \( \mathrm{Cr}^{3+}(\mathrm{aq}) \) if a suitable reducing agent is present. Identifying oxidizing agents is crucial in both lab and real-world applications, such as detoxifying pollutants or in batteries where they help generate power through controlled redox reactions. Understanding the interplay between oxidizing and reducing agents enables chemists to harness redox reactions for energy, synthesis, and biochemistry.