Problem 8 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

What is the standard reduction potential \(\left(\mathrm{E}^{\circ}\right)\) for \(\mathrm{Fe}^{3+} \rightarrow \mathrm{Fe}\) ? Given that : [Main Online April 8, 2017] \(\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \rightarrow \mathrm{Fe} ; \mathrm{E}_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{\circ}=-0.47 \mathrm{~V}\) \(\mathrm{Fe}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+} ; \mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}=+0.77 \mathrm{~V}\) (a) \(-0.057 \mathrm{~V}\) (b) \(+0.057 \mathrm{~V}\) (c) \(+0.30 \mathrm{~V}\) (d) \(-0.30 \mathrm{~V}\)

Step-by-Step Solution

Answer

The standard reduction potential for \(\mathrm{Fe}^{3+} \rightarrow \mathrm{Fe}\) is \(+0.30 \mathrm{~V}\). Answer: (c) \(+0.30 \mathrm{~V}\).

Step 1: Write Half Reactions

Identify and write the given half-reactions based on the provided information:1. \( \text{Fe}^{3+} + e^{-} \rightarrow \text{Fe}^{2+} \); \( E^\circ = +0.77 \text{ V} \)2. \( \text{Fe}^{2+} + 2e^{-} \rightarrow \text{Fe} \); \( E^\circ = -0.47 \text{ V} \)

Step 2: Determine Target Reaction

Determine the overall reaction to find by combining the given reactions:We want to find \( \text{Fe}^{3+} \rightarrow \text{Fe} \).

Step 3: Combine Reactions

Combine the given half-reactions to find the desired half-reaction:- Reverse the second reaction to match the electrons.- Adding the reactions:\( \text{Fe}^{3+} + e^{-} \rightarrow \text{Fe}^{2+} \) and \( \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^{-} \) gives \( \text{Fe}^{3+} \rightarrow \text{Fe} \) (net 3e- transfer).

Step 4: Calculate Overall E°

Use the standard cell potential formula:\( E^\circ_{\text{overall}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}} \)Here,\( E^\circ_{\text{reduction}} = +0.77 \text{ V} \)\( E^\circ_{\text{oxidation}} = -0.47 \text{ V} \)Therefore,\( E^\circ = +0.77 \text{ V} - (-0.47 \text{ V}) = +0.30 \text{ V} \)

Step 5: Conclusion

The calculated standard reduction potential for the reaction \( \text{Fe}^{3+} \rightarrow \text{Fe} \) is \( +0.30 \text{ V} \), so the correct answer is (c) \(+0.30 \text{ V}\).

Key Concepts

Electrochemistry

Electrochemistry is a fascinating branch of chemistry that studies the interactions between electricity and chemical reactions. Essentially, it deals with reactions where electrons are transferred, also known as redox (reduction-oxidation) reactions. In this field, we explore how electrical energy can bring about chemical changes and vice versa.
Understanding electrochemistry is crucial because it applies to numerous real-world applications, from batteries and fuel cells to electroplating and corrosion prevention. The fundamental principles of electrochemistry involve the movement of electrons across different substances, which is key in these processes.
One of the core components of electrochemistry is the concept of electrochemical cells. These are devices that convert chemical energy into electrical energy, or the reverse. They consist of two electrodes submerged in electrolytic solutions. Each electrode has a different potential, and the difference between these potentials is known as the cell potential. This concept is vital in understanding how batteries produce electricity.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are processes that involve the transfer of electrons between two species. These reactions are central in electrochemistry as they power many of the applications such as batteries and energy storage systems.
In a redox reaction, one species loses electrons, undergoing oxidation, while another species gains those electrons, undergoing reduction. Oxidation and reduction always occur together, hence the term 'redox.'
Understanding which species gets oxidized and which gets reduced can be determined through oxidation states or half-reactions. To predict the direction and feasibility of redox reactions, chemists use standard reduction potentials, which are inherently linked to the ability of a species to gain electrons. By referencing a standard table, one can determine which species will undergo oxidation and which will be reduced.

Half-Reactions

Half-reactions are a way to simplify and analyze redox reactions by breaking them down into two parts: the oxidation half and the reduction half. This is essential for understanding the full redox process and calculating cell potentials in electrochemistry.
Each half-reaction shows either the loss of electrons (oxidation) or the gain of electrons (reduction). For instance, in the reactions involving iron species, we have:

• The reduction half-reaction: \( \text{Fe}^{3+} + e^{-} \rightarrow \text{Fe}^{2+} \) with \( E^\circ = +0.77 \text{ V} \).
• The oxidation half-reaction: \( \text{Fe}^{2+} + 2e^{-} \rightarrow \text{Fe} \) but needs to be flipped to \( \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^{-} \).

By analyzing both half-reactions, we can determine the direction of electron flow and combine them to form overall reactions. Through balancing these half-reactions, chemists gain insights into electron exchange and energy changes within chemical reactions.

Cell Potential Calculation

Calculating the cell potential of an electrochemical cell is crucial for determining the voltage that the cell can provide. The cell potential, denoted as \( E^\circ \), is calculated using the standard reduction potentials of the involved half-reactions.
The formula to calculate the overall cell potential is:\[ E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}} \]In the case of the iron reactions, let's examine the two reactions:

• \( \text{Fe}^{3+} + e^{-} \rightarrow \text{Fe}^{2+} \) has \( E^\circ = +0.77 \text{ V} \)
• \( \text{Fe}^{2+} + 2e^{-} \rightarrow \text{Fe} \) when reversed becomes \( \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^{-} \) with \( E^\circ = -0.47 \text{ V} \)

By substituting into the formula, we find the cell potential:\[ E^\circ = +0.77 \text{ V} - (-0.47 \text{ V}) = +0.30 \text{ V} \]This calculated potential helps predict whether a reaction will occur spontaneously and is a foundational concept in designing and understanding electrochemical cells.