Problem 13 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Given below are the half-cell reactions: $$ \begin{aligned} &\mathrm{Mn}^{2+}+2 \mathrm{e}^{-} \rightarrow \mathrm{Mn} ; \mathrm{E}^{\circ}=-1.18 \mathrm{~V} \\ &2\left(\mathrm{Mn}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+}\right) ; \mathrm{E}^{\circ}=+1.51 \mathrm{~V} \end{aligned} $$ The \(\mathrm{E}^{\circ}\) for \(3 \mathrm{Mn}^{2+} \rightarrow \mathrm{Mn}+2 \mathrm{Mn}^{3+}\) will be: (a) \(-2.69 \mathrm{~V} ;\) the reaction will not occur (b) \(-2.69 \mathrm{~V}\); the reaction will occur (c) \(-0.33 \mathrm{~V}\); the reaction will not occur (d) \(-0.33 \mathrm{~V}\); the reaction will occur

Step-by-Step Solution

Answer

(c) \(-0.33 \mathrm{~V}\); the reaction will not occur.

Step 1: Identify Half-cell Reactions

List the provided half-cell reactions. We have: \( \mathrm{Mn}^{2+} + 2 \mathrm{e}^{-} \rightarrow \mathrm{Mn} \) with \( E^{\circ} = -1.18 \mathrm{~V} \), and \( 2(\mathrm{Mn}^{3+} + \mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+}) \) with \( E^{\circ} = 1.51 \mathrm{~V} \).

Step 2: Balance and Combine Reactions

To find the cell potential for the complete reaction \( 3 \mathrm{Mn}^{2+} \rightarrow \mathrm{Mn} + 2 \mathrm{Mn}^{3+} \), balance the electrons in each half-reaction and combine them. The reaction becomes: \( 3 \mathrm{Mn}^{2+} + 2 \mathrm{Mn}^{3+} + 2 \mathrm{e}^{-} \rightarrow \mathrm{Mn} + 6 \mathrm{Mn}^{2+} \). Simplify this to \( 3\mathrm{Mn}^{2+} \rightarrow \mathrm{Mn} + 2\mathrm{Mn}^{3+} \).

Step 3: Calculate the Net Cell Potential

Apply the equation \( E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}} \). Identify the cathode reaction as \( \mathrm{Mn}^{2+} + 2 \mathrm{e}^{-} \rightarrow \mathrm{Mn} \) and the anode as \( \mathrm{Mn}^{2+} \rightarrow \mathrm{Mn}^{3+} + \mathrm{e}^{-} \). The cell potential \( E^{\circ}_{\text{cell}} \) is \(-1.18 - 1.51 = -0.33 \mathrm{~V} \).

Step 4: Determine Reaction Feasibility

An overall cell potential \( E^{\circ}_{\text{cell}} = -0.33 \mathrm{~V} \) indicates a non-spontaneous reaction since it is negative. Therefore, the reaction will not occur under standard conditions.

Key Concepts

Standard Electrode Potential

The standard electrode potential, denoted as \( E^{ ext{°}} \), is a fundamental concept in electrochemistry. It represents the inherent ability of a half-cell to gain or lose electrons when compared to the standard hydrogen electrode (SHE). By convention, the standard hydrogen electrode is assigned a potential of 0.00 V.
Each half-cell reaction has its own standard electrode potential, which is determined under standard conditions: 1 M concentration of solutions, 1 atm pressure for gases, and a temperature of 25°C or 298 K. These potentials help us understand which substances are more likely to undergo reduction (gain electrons) or oxidation (lose electrons).
In electrochemical cells, a more positive standard electrode potential means the half-cell has a greater tendency to gain electrons, marking it as a better oxidizing agent. Conversely, a more negative potential indicates a greater tendency to lose electrons, identifying it as a reduction agent. By comparing these potentials, we can predict the direction of electron flow in an electrochemical cell.

Electrochemical Cells

Electrochemical cells are devices that transform chemical energy into electrical energy or vice versa. They comprise two half-cells, each involving a redox reaction, connected by an external circuit and an ion-conducting solution, such as a salt bridge.
An electrochemical cell has two main parts: the anode and the cathode. The anode is where oxidation occurs, releasing electrons, while the cathode is the site of reduction, accepting electrons. When assembling a cell, it's vital to ensure that the electrons can flow freely from the anode to the cathode through the external circuit.
Understanding electrochemical cells also involves calculating the cell potential, \( E^{ ext{°}}_{ ext{cell}} \). The cell potential is the difference between the standard electrode potentials of the cathode and the anode. It is expressed by the equation:
\[ E^{ ext{°}}_{ ext{cell}} = E^{ ext{°}}_{ ext{cathode}} - E^{ ext{°}}_{ ext{anode}} \]
This potential helps us determine the feasibility of a reaction. When \( E^{ ext{°}}_{ ext{cell}} \) is positive, the reaction is spontaneous and can generate electrical energy. Conversely, a negative value implies a non-spontaneous process.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes where electrons are transferred between species. These reactions are central to electrochemistry and occur in all electrochemical cells.
In a redox reaction, one species undergoes oxidation, losing electrons, while another undergoes reduction, gaining electrons. The simultaneous occurrence of these processes is essential for sustaining the flow of electrons and producing electricity.
To balance redox reactions, you often need to ensure that the number of electrons lost in oxidation equals the number of electrons gained in reduction. This might involve adjusting coefficients and balancing additional elements, as necessary.
Redox reactions drive many important applications, such as batteries, fuel cells, and electroplating. By exploiting the natural tendency of these reactions to proceed, we can harness their energy to power devices or facilitate chemical transformations. Understanding redox principles allows chemists and engineers to design systems that are efficient, safe, and effective.