Problem 3 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The standard reduction potential for the process: \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+\mathrm{e}^{-} \rightarrow\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is \(1.8 \mathrm{~V}\). The standard reduction potential for the process: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}+\mathrm{e}^{-}\) \(\rightarrow\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) is \(0.1 \mathrm{~V} .\) Which of the complex ion, \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) or \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) can be oxidized to the corresponding cobalt (III) complex, by oxygen, in basic medium, under standard condition? \(\left[\right.\) Given: \(\left.E_{\mathrm{O}_{2} / \mathrm{OH}^{-}}^{\circ}=0.4 \mathrm{~V}\right]\) (a) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (b) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) (c) both (d) none of these

Step-by-Step Solution

Answer

\([\mathrm{Co}(\mathrm{NH}_{3})_{6}]^{2+}\) can be oxidized to the corresponding cobalt (III) complex by oxygen in basic medium under standard condition.

Step 1: Understanding Standard Reduction Potentials

The standard reduction potential of a half-cell is a measure of the tendency of reagents to gain electrons and be reduced. The higher the standard reduction potential, the greater the substance's affinity for electrons and the stronger the oxidizing agent.

Step 2: Comparing Standard Reduction Potentials

To determine which complex ion can be oxidized by oxygen in a basic medium, compare the standard reduction potentials of the given complexes with the potential for the O2/OH- couple. In a spontaneous reaction, the substance with the lower reduction potential gets oxidized (loses electrons), and the one with the higher reduction potential gets reduced (gains electrons).

Step 3: Identifying the Oxidizable Complex

Look at the given standard reduction potentials. For \([\mathrm{Co}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\), it is 1.8 V, and \([\mathrm{Co}(\mathrm{NH}_{3})_{6}]^{3+}\) is 0.1 V. Since the standard reduction potential of the O2/OH- couple is 0.4 V, this means that a complex ion with a standard reduction potential lower than 0.4 V can be oxidized by oxygen under standard conditions. Hence, the \([\mathrm{Co}(\mathrm{NH}_{3})_{6}]^{2+}\) complex with a standard reduction potential of 0.1 V can be oxidized by oxygen, as it is less than 0.4 V. The \([\mathrm{Co}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\) cannot be oxidized since its potential is much higher than 0.4 V.

Key Concepts

Oxidation and Reduction

In chemistry, oxidation and reduction are processes that involve the transfer of electrons between chemical species.

Oxidation is the loss of electrons from a molecule, atom, or ion, resulting in an increase in its oxidation state. Conversely, reduction is the gain of electrons with a corresponding decrease in oxidation state. These two processes always occur simultaneously; when one species is oxidized, another is reduced. This is because electrons cannot exist freely in a reaction—they must be transferred from one species to another.

Take for instance the process described in the exercise, where cobalt complexes are involved in redox reactions. The cobalt ion in \( \left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{3+} \) is reduced to \( \left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+} \) when it gains an electron. As for the comprehension improvement advice, it's crucial to understand that the substance that has a stronger tendency to gain electrons (higher reduction potential) will facilitate the oxidation of the other substance involved in the reaction.

Electrochemistry

The field of electrochemistry is concerned with the study of chemical reactions which involve the movement of electrons. These reactions can cause a flow of electric current and are harnessed in various technologies, such as batteries, fuel cells, and electrolysis processes.

The standard reduction potential plays a fundamental role in electrochemistry. It is essentially a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. The higher the standard reduction potential, the more likely it is for the species to gain electrons when it is connected to another species in a redox reaction. This value is important as it helps predict the direction of electron flow in an electrochemical cell.

When dealing with electrochemical reactions, as in the provided exercise, comparing the standard reduction potentials of different species allows us to predict which species will be oxidized and which will be reduced in a given reaction.

Chemical Spontaneity

The concept of chemical spontaneity indicates whether a reaction can occur on its own without the need for additional energy. Spontaneous reactions are driven by factors such as enthalpy, entropy, and the Gibbs free energy.

In the context of redox reactions and electrochemistry, the spontaneity is often assessed using standard reduction potentials—the more positive the standard reduction potential, the more likely a substance is to gain electrons and be reduced. For a reaction to be spontaneous, the oxidizing agent must have a higher reduction potential than the reducing agent.

Referencing the exercise, the oxygen in its \( O_2/OH^- \) form as an oxidizing agent has a standard reduction potential of 0.4 V. This potential is higher than that of the \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \) complex (0.1 V) but lower than that of the \( \left[\mathrm{Co}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+} \) complex (1.8 V). As a result, only the \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} \) complex can be oxidized by oxygen under standard conditions in a basic medium because its potential is below the potential of the oxygen, which aligns with the rule for chemical spontaneity.