Problem 47 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Assuming standard conditions, arrange the following in order of increasing strength as oxidizing agents in acidic solution: \(\mathrm{MnO}_{4}^{-}(a q), \mathrm{O}_{3}(g), \mathrm{HSO}_{4}^{-}(a q), \mathrm{O}_{2}(g), \mathrm{HClO}(a q)\) (b) Arrange the following in order of increasing strength as reducing agents in basic solution: \(\mathrm{Cr}(\mathrm{OH})_{3}(s), \mathrm{Fe}(s), \mathrm{Ca}(s),\) \(\mathrm{H}_{2}(g), \mathrm{Mn}(s)\)

Step-by-Step Solution

Answer

(a) The order of increasing strength as oxidizing agents in acidic solution is: \(\mathrm{O}_{2}(g) < \mathrm{HSO}_{4}^{-}(a q) < \mathrm{MnO}_{4}^{-}(a q) < \mathrm{HClO}(a q) < \mathrm{O}_{3}(g)\) (b) The order of increasing strength as reducing agents in basic solution is: \(\mathrm{H}_{2}(g) < \mathrm{Fe}(s) < \mathrm{Cr}(\mathrm{OH})_{3}(s) < \mathrm{Mn}(s) < \mathrm{Ca}(s)\)

Step 1: Look up the standard half-cell potentials for each of the given species: \(\mathrm{MnO}_{4}^{-}(a q)\), \(\mathrm{O}_{3}(g)\), \(\mathrm{HSO}_{4}^{-}(a q)\), \(\mathrm{O}_{2}(g)\), and \(\mathrm{HClO}(a q)\). These values can be found in standard reduction potential tables. Step 2: Compare the half-cell potentials

Rank the species by their standard half-cell potential from smallest to largest. Step 3: Order of increasing strength as oxidizing agents

Step 2: The order of increasing strength as oxidizing agents in acidic solution will correspond to increasing half-cell potentials, as higher half-cell potential values indicate stronger oxidizing agents. List them in the order of their increasing half-cell potentials. Answers: The standard half-cell potentials for the given species in the acidic solution are as follows: \(\mathrm{MnO}_{4}^{-}(a q)\): \( +1.51 \, V \) \(\mathrm{O}_{3}(g)\): \( +2.07 \, V \) \(\mathrm{HSO}_{4}^{-}(a q)\): \( +1.24 \, V \) \(\mathrm{O}_{2}(g)\): \( +1.23 \, V \) \(\mathrm{HClO}(a q)\): \( +1.63 \, V \) Therefore, the order of increasing strength as oxidizing agents in the acidic solution is: \(\mathrm{O}_{2}(g) < \mathrm{HSO}_{4}^{-}(a q) < \mathrm{MnO}_{4}^{-}(a q) < \mathrm{HClO}(a q) < \mathrm{O}_{3}(g)\) #b) Reducing agents in basic solution# Step 1: Find the half-cell potentials of the species

Look up the standard half-cell potentials for each of the given species in basic solution: \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\), \(\mathrm{Fe}(s)\), \(\mathrm{Ca}(s)\), \(\mathrm{H}_{2}(g)\), and \(\mathrm{Mn}(s)\). These values can be found in standard reduction potential tables. Step 2: Compare the half-cell potentials

Step 3: Rank the species by their standard half-cell potential from largest to smallest. Step 3: Order of increasing strength as reducing agents

The order of increasing strength as reducing agents in basic solution corresponds to the decreasing half-cell potentials, as lower half-cell potential values indicate stronger reducing agents. List them in the order of their decreasing half-cell potentials. Answers: The standard half-cell potentials for the given species in the basic solution are as follows: \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\): \( -0.74 \, V \) \(\mathrm{Fe}(s)\): \( -0.45 \, V \) \(\mathrm{Ca}(s)\): \( -2.87 \, V \) \(\mathrm{H}_{2}(g)\): \( 0.00 \, V \) \(\mathrm{Mn}(s)\): \( -1.18 \, V \) Therefore, the order of increasing strength as reducing agents in the basic solution is: \(\mathrm{H}_{2}(g) < \mathrm{Fe}(s) < \mathrm{Cr}(\mathrm{OH})_{3}(s) < \mathrm{Mn}(s) < \mathrm{Ca}(s)\)

Key Concepts

Oxidizing Agents

An oxidizing agent is a chemical substance that readily accepts electrons from other molecules. This acceptance of electrons allows it to oxidize other substances. In simpler terms, an oxidizing agent helps other components lose electrons and thus is reduced in the process.

• The effectiveness of an oxidizing agent is often determined by its standard reduction potential.
• A higher standard reduction potential indicates a stronger oxidizing agent.

For example, in an acidic solution, different species such as permanganate ion (\(\mathrm{MnO}_{4}^{-}(a q)\)), ozone (\(\mathrm{O}_{3}(g)\)), and other components have various capabilities of acting as oxidizing agents. When ranked by their strength in accepting electrons, those with larger positive reduction potentials will be stronger oxidants.
Thus, in a list with the following potentials:

• \(\mathrm{O}_{2}(g)\): +1.23V
• \(\mathrm{HSO}_{4}^{-}(a q)\): +1.24V
• \(\mathrm{MnO}_{4}^{-}(a q)\): +1.51V
• \(\mathrm{HClO}(a q)\): +1.63V
• \(\mathrm{O}_{3}(g)\): +2.07V

The agent with the highest potential, \(\mathrm{O}_{3}(g)\), would be regarded as the strongest oxidizing agent.

Reducing Agents

A reducing agent, in contrast to an oxidizing agent, is a substance that donates electrons to another chemical species. As it gives up electrons, it itself becomes oxidized. In essence, a reducing agent helps another substance to gain electrons.

• The effectiveness as a reducing agent is inversely related to its standard reduction potential.
• A lower (or more negative) potential signifies a stronger reducing agent.

Within a basic solution, various metals like calcium (\(\mathrm{Ca}(s)\)), iron (\(\mathrm{Fe}(s)\)), and others can act as reducing agents. Determining strength involves analyzing their ability to donate electrons, ranked by increasingly negative potentials:
For instance:

• \(\mathrm{H}_{2}(g)\): 0.00V
• \(\mathrm{Fe}(s)\): -0.45V
• \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\): -0.74V
• \(\mathrm{Mn}(s)\): -1.18V
• \(\mathrm{Ca}(s)\): -2.87V

Here, the most electronegative component, \(\mathrm{Ca}(s)\), demonstrates the strongest reducing power.

Electrochemical Series

The electrochemical series, also known as the activity series, is a comprehensive list of elements and their standard electrode potentials. This series is a fundamental tool in electrochemistry and provides valuable insight into the behavior of substances as oxidizing and reducing agents.

• Substances at the top of the series, with more positive standard potentials, are good oxidizing agents.
• Conversely, substances lower down the series are typically stronger reducing agents.

Standard reduction potentials are measured under standard conditions, which include a concentration of 1 M, a pressure of 1 atm, and a temperature of 25°C (298 K).
The electrochemical series is crucial for predicting the feasibility of redox reactions. When encountering a redox reaction, referencing these potentials helps us understand which substances will be oxidized or reduced based on their placement and values in the series. If using the series:

• Reactions where the oxidizing agent has a higher potential than the reducing agent are generally spontaneous.
• Reactions with a negative difference are non-spontaneous under standard conditions.

Therefore, the electrochemical series is a key guide in determining the strength and effectiveness of oxidizing and reducing agents within various chemical processes.