Problem 16 - Chemistry: Principles and Reactions

Question

For the following half-reactions, answer the questions below. $$ \begin{array}{cc} \mathrm{Co}^{3+}(a q)+e^{-} \longrightarrow \mathrm{Co}^{2+}(a q) & E^{\circ}=+1.953 \mathrm{~V} \\ \mathrm{Fe}^{3+}(a q)+e^{-} \longrightarrow \mathrm{Fe}^{2+}(a q) & E^{\circ}=+0.769 \mathrm{~V} \\ \mathrm{I}_{2}(a q)+2 e^{-} \longrightarrow 2 \mathrm{I}^{-}(a q) & E^{o}=+0.534 \mathrm{~V} \\ \mathrm{~Pb}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Pb}(s) & E^{\circ}=-0.127 \mathrm{~V} \\ \mathrm{Cd}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Cd}(s) & E^{\circ}=-0.402 \mathrm{~V} \\ \mathrm{Mn}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Mn}(s) & E^{\circ}=-1.182 \mathrm{~V} \end{array} $$ (a) Which is the weakest reducing agent? (b) Which is the strongest reducing agent? (c) Which is the strongest oxidizing agent? (d) Which is the weakest oxidizing agent? (e) Will \(\mathrm{Pb}(s)\) reduce \(\mathrm{Fe}^{3+}(a q)\) to \(\mathrm{Fe}^{2+}(a q) ?\) (f) Will \(\mathrm{I}^{-}(a q)\) reduce \(\mathrm{Pb}^{2+}(a q)\) to \(\mathrm{Pb}(s) ?\) (g) Which ion(s) can be reduced by \(\mathrm{Pb}(s)\) ? (h) Which if any metal(s) can be oxidized by \(\mathrm{Fe}^{3+}(a q)\) ?

Step-by-Step Solution

Answer

Answer: Co^3+(aq) is the weakest reducing agent.

Step 1: (a) Weakest reducing agent

The weakest reducing agent will have the highest standard reduction potential. In this case, Co redution potential is +1.953 V, which is the highest among the given half-reactions. Therefore, Co^3+(aq) is the weakest reducing agent.

Step 2: (b) Strongest reducing agent

The strongest reducing agent will have the lowest standard reduction potential. In this case, Mn's reduction potential is -1.182 V, which is the lowest among the given half-reactions. Therefore, Mn^2+(aq) is the strongest reducing agent.

Step 3: (c) Strongest oxidizing agent

The strongest oxidizing agent will have the highest standard reduction potential. As determined in part (a), it is the Co^3+(aq) with a standard reduction potential of +1.953 V.

Step 4: (d) Weakest oxidizing agent

The weakest oxidizing agent will have the lowest standard reduction potential. As determined in part (b), it is the Mn^2+(aq) with a standard reduction potential of -1.182 V.

Step 5: (e) Will Pb(s) reduce Fe^3+(aq) to Fe^2+(aq)?

To determine if Pb(s) will spontaneously reduce Fe^3+(aq) to Fe^2+(aq), compare the standard reduction potentials of both half-reactions. Pb's reduction potential is -0.127 V, while Fe^3+'s is +0.769 V. Since Pb's potential is lower than Fe^3+'s, Pb(s) will spontaneously reduce Fe^3+(aq) to Fe^2+(aq).

Step 6: (f) Will I^-(aq) reduce Pb^2+(aq) to Pb(s)?

In order to determine if I^-(aq) will spontaneously reduce Pb^2+(aq) to Pb(s), compare the standard reduction potentials of both half-reactions. I₂ reduction potential is +0.534 V, while Pb^2+'s is -0.127 V. Since I₂'s potential is higher than Pb^2+'s, I^-(aq) will not spontaneously reduce Pb^2+(aq) to Pb(s).

Step 7: (g) Which ions can be reduced by Pb(s)?

To determine which ions can be reduced by Pb(s), compare Pb's standard reduction potential (-0.127 V) with other ions. Pb(s) can reduce ions with a higher reduction potential, which includes: Fe^3+(aq) with a potential of +0.769 V and Co^3+(aq) with a potential of +1.953 V.

Step 8: (h) Which metals can be oxidized by Fe^3+(aq)?

To determine which metals can be oxidized by Fe^3+(aq), compare its standard reduction potential (+0.769 V) with other metals. Fe^3+(aq) can oxidize metals with a lower reduction potential, which includes: Pb(s) with a potential of -0.127 V, Cd(s) with a potential of -0.402 V, and Mn(s) with a potential of -1.182 V.

Key Concepts

Oxidizing Agents

An oxidizing agent is a substance that gains electrons during a chemical reaction and, in the process, is reduced.
It effectively "oxidizes" another substance by causing it to lose electrons.
Oxidizing agents are crucial in redox reactions, serving as the counterpart to reducing agents.
In the list of half-reactions provided, you can determine the strongest oxidizing agent by looking at the standard reduction potentials.

• The higher the standard reduction potential, the stronger the oxidizing agent.
• For instance, in the provided exercise, Co³⁺(aq), with a standard reduction potential of +1.953 V, is the strongest oxidizing agent.

Understanding oxidizing agents is essential when predicting the direction and spontaneity of redox reactions.

Reducing Agents

A reducing agent is the opposite of an oxidizing agent.
It donates electrons to another substance in a redox reaction and is, in turn, oxidized.
Reducing agents "reduce" other substances by providing them with electrons.
To identify the best reducing agent from the list, look for the lowest standard reduction potential.

• In our exercise, Mn²⁺(aq) has the lowest potential of -1.182 V, making it the strongest reducing agent.
• Conversely, Co³⁺(aq) is the weakest reducing agent because it has the highest standard reduction potential.

These concepts help predict which substances will lose electrons more readily in a redox reaction.

Standard Reduction Potential

The standard reduction potential is a measure of the tendency of a chemical species to acquire electrons and be reduced.
These potentials are measured under standard conditions: 25°C, 1 bar pressure, and 1 M concentration for every species in solution.
Standard Conditions:

• Measured in volts (V)
• Helps predict the direction of redox reactions
• Species with more positive potentials are stronger oxidizing agents
• Species with more negative potentials are stronger reducing agents

The concept is central to understanding how different substances interact in redox reactions.
For example, knowing that Fe³⁺ has a standard reduction potential of +0.769 V can help determine how it will behave in reactions with other elements.

Half-Reactions

Half-reactions are part of the broader redox reaction concept, focusing on the transfer of electrons.
Each half-reaction shows either the oxidation or reduction process separately.

In a Redox Reaction:

• Oxidation half-reaction: Shows the loss of electrons
• Reduction half-reaction: Shows the gain of electrons

By separating reactions into half-reactions, it's easier to understand which species lose electrons and which gain them.
This separation also allows us to use standard reduction potentials to predict reaction outcomes and perform stoichiometric calculations more easily.
By analyzing the given half-reactions in the exercise, we can make informed conclusions about the direction and spontaneity of the reactions.