Problem 1 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Given : \(\mathrm{Co}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Co}^{2+} ; \mathrm{E}^{\circ}=+1.81 \mathrm{~V}\) \(\mathrm{Pb}^{4+}+2 \mathrm{e}^{-} \rightarrow \mathrm{Pb}^{2+} ; \mathrm{E}^{0}=+1.67 \mathrm{~V}\) \(\mathrm{Ce}^{4+}+\mathrm{e}^{-} \rightarrow \mathrm{Ce}^{3+} ; \mathrm{E}^{0}=+1.61 \mathrm{~V}\) \(\mathrm{Bi}^{3+}+3 \mathrm{e}^{-} \rightarrow \mathrm{Bi} ; \mathrm{E}^{\circ}=+0.20 \mathrm{~V}\) oxidizing power of the species will increase in the order: (a) \(\mathrm{Ce}^{4+}<\mathrm{Pb}^{4+}<\mathrm{Bi}^{3+}<\mathrm{Co}^{3+}\) (b) \(\mathrm{Bi}^{3+}<\mathrm{Ce}^{4+}<\mathrm{Pb}^{4+}<\mathrm{Co}^{3+}\) (c) \(\mathrm{Co}^{3+}<\mathrm{Ce}^{4+}<\mathrm{Bi}^{3+}<\mathrm{Pb}^{4+}\) (d) \(\mathrm{Co}^{3+}<\mathrm{Pb}^{4+}<\mathrm{Ce}^{4+}<\mathrm{Bi}^{3+}\)

Step-by-Step Solution

Answer

Option (b) is correct: Bi³⁺ < Ce⁴⁺ < Pb⁴⁺ < Co³⁺.

Step 1: Understand Standard Reduction Potentials

The given standard reduction potentials indicate how easily a species will gain electrons. A higher positive value means a stronger oxidizing agent, as it is more likely to accept electrons.

Step 2: List the Given Reduction Potentials

List the reduction potentials in descending order based on their values: - Co⁺³: +1.81 V - Pb⁺⁴: +1.67 V - Ce⁺⁴: +1.61 V - Bi⁺³: +0.20 V

Step 3: Rank the Oxidizing Power

Since a higher reduction potential corresponds to stronger oxidizing power, order the species from highest to lowest based on their standard reduction potential values: 1. Co⁺³ 2. Pb⁺⁴ 3. Ce⁺⁴ 4. Bi⁺³

Step 4: Compare with Given Orderings

Compare the order derived in Step 3 with the options given in the problem. The derived order, from weakest to strongest oxidizing agent, is Bi⁺³ < Ce⁺⁴ < Pb⁺⁴ < Co⁺³.

Key Concepts

Standard Reduction Potential

In electrochemistry, the term "standard reduction potential" is crucial for understanding how substances react. It is a measure of the tendency of a chemical species to gain electrons and be reduced. The standard condition implies that concentrations are at 1 mol/L for aqueous solutions and the substances are at a pressure of 1 atm and at a temperature of 25°C (298 K). The potential is measured in volts (V), and a more positive standard reduction potential indicates a stronger tendency to gain electrons, meaning the species is a more powerful oxidizing agent.
For example, in the given data:

• Cobalt(III) ions (\( \mathrm{Co}^{3+} \) ) have a high standard reduction potential of +1.81 V, suggesting they are very likely to gain electrons.
• Lead(IV) ions (\( \mathrm{Pb}^{4+} \) ) follow closely with +1.67 V.
• Cerium(IV) ions (\( \mathrm{Ce}^{4+} \) ) have a +1.61 V reading, indicating a strong but slightly lesser potential than lead.
• Bismuth(III) ions (\( \mathrm{Bi}^{3+} \) ) show a much lower value at +0.20 V, indicating weaker oxidizing power.

Oxidizing Agents

Oxidizing agents are substances that gain electrons during a chemical reaction, allowing them to oxidize another substance. Their ability to oxidize other substances is directly linked to their standard reduction potential; the higher the standard reduction potential, the stronger oxidizing agent the species is. In essence, they "remove" electrons from other substances.
From what we learned about standard reduction potentials, we can rank the oxidizing agents in order of decreasing power. With the highest potential, \( \mathrm{Co}^{3+} \) is the strongest oxidizing agent, followed by \( \mathrm{Pb}^{4+} \), \( \mathrm{Ce}^{4+} \), and lastly \( \mathrm{Bi}^{3+} \), which is the weakest among those listed. This essentially means that if these ions were to compete for electrons, \( \mathrm{Co}^{3+} \) would win hands down.

Electron Transfer

Electron transfer is at the heart of all redox reactions. It involves the movement of electrons from a donor (the reducing agent) to an acceptor (the oxidizing agent). This process is fundamental in many natural and technological processes, including energy production in batteries and cellular respiration.
During this process, as one substance loses electrons, it undergoes oxidation, and another substance gains those electrons and thus, undergoes reduction. In our specific case:

• The \( \mathrm{Co}^{3+} \) ion receives an electron to become \( \mathrm{Co}^{2+} \), highlighting its role as an oxidizing agent in electron transfer.
• Similarly, the electron transfers lead \( \mathrm{Pb}^{4+} \) to \( \mathrm{Pb}^{2+} \) and \( \mathrm{Ce}^{4+} \) to \( \mathrm{Ce}^{3+} \), showcasing their ability to accept electrons.

These examples illustrate the concept of electron transfer in action, where the movement of electrons defines the change between oxidation states.

Redox Reactions

Redox reactions, the abbreviated term for reduction-oxidation reactions, are reactions where the transfer of electrons occurs between two reactants. These reactions are essential for chemical processes in various fields, from industrial applications to biological systems.
In any redox reaction, there will always be two parts: oxidation (loss of electrons) and reduction (gain of electrons). In what concerns us here:

• The reduction half-reaction involves the gaining of electrons by \( \mathrm{Co}^{3+} \), \( \mathrm{Pb}^{4+} \), \( \mathrm{Ce}^{4+} \), and \( \mathrm{Bi}^{3+} \). They are reduced to lower oxidation states, indicating they are reduced during the redox process.
• Simultaneously, there would be substances that must undergo oxidation to provide these electrons, though they are not specified in our examples.

Understanding redox reactions allows for insight into processes that involve electron transfer and plays a vital role in balancing chemical equations that describe these reactions.