Problem 114 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard reduction potential for \(\mathrm{Fe}^{2+} / \mathrm{Fe}\) and \(\mathrm{Sn}^{2+} /\) Sn electrodes are \(-0.44\) and \(-0.14\) volts respectively. For the cell reaction \(\mathrm{Fe}^{2 i}+\mathrm{Sn} \longrightarrow \mathrm{Fe}+\mathrm{Sn}^{2}\) The standard emf is (a) \(+0.30 \mathrm{~V}\) (b) \(-0.58 \mathrm{~V}\) (c) \(+0.58 \mathrm{~V}\) (d) \(-0.300 \mathrm{~V}\)

Step-by-Step Solution

Answer

The standard emf is (b) \(-0.58 \mathrm{~V}\).

Step 1: Identify the cell reaction

The cell reaction given is \( \mathrm{Fe}^{2+} + \mathrm{Sn} \rightarrow \mathrm{Fe} + \mathrm{Sn}^{2+} \). This means \( \mathrm{Fe}^{2+} \) is being reduced to \( \mathrm{Fe} \) and \( \mathrm{Sn} \) is being oxidized to \( \mathrm{Sn}^{2+} \).

Step 2: Determine half-reactions and potentials

For the reduction of \( \mathrm{Fe}^{2+} \), we use the standard reduction potential \( E^0_{(\mathrm{Fe}^{2+}/\mathrm{Fe})} = -0.44 \mathrm{~V} \). For the oxidation of \( \mathrm{Sn} \) to \( \mathrm{Sn}^{2+} \), we need to reverse the reaction, changing the sign of the standard potential for \( \mathrm{Sn}^{2+}/\mathrm{Sn} \), so it becomes \( E^0_{(\mathrm{Sn}/\mathrm{Sn}^{2+})} = +0.14 \mathrm{~V} \).

Step 3: Calculate the standard emf (E°cell)

The standard emf \( (E^0_{cell}) \) for the cell is calculated using the equation:\[E^0_{cell} = E^0_{cathode} - E^0_{anode}\]The cathode is where reduction occurs (\( \mathrm{Fe}^{2+} \to \mathrm{Fe} \)) and the anode is where oxidation occurs (\( \mathrm{Sn} \to \mathrm{Sn}^{2+} \)). Thus,\[E^0_{cell} = (-0.44 \mathrm{~V}) - (+0.14 \mathrm{~V}) = -0.58 \mathrm{~V}\]

Step 4: Determine the correct answer choice

Compare the calculated emf \( -0.58 \mathrm{~V} \) to the given options. The correct answer is (b) \(-0.58 \mathrm{~V}\).

Key Concepts

Electrochemistry

Electrochemistry is a branch of chemistry that deals with the relationship between electrical energy and chemical reactions. It covers processes where electrons move between molecules, ions, or atoms, often resulting in the generation or use of electricity.
Electrochemistry encompasses a variety of phenomena such as:

• Galvanic Cells: These are devices that convert chemical energy into electrical energy via spontaneous redox reactions.


• Electrolytic Cells: In these cells, electrical energy drives non-spontaneous chemical reactions.


• Standard Electrode Potentials: These potentials measure the tendency of a chemical species to be reduced. They are usually measured in volts.

During a typical electrochemical reaction, two electrodes are involved – an anode and a cathode. At the anode, oxidation occurs, and at the cathode, reduction takes place. Understanding how electrochemistry works forms the foundation for analyzing redox reactions and calculating cell potentials.

Redox Reactions

Redox reactions, or reduction-oxidation reactions, entail the transfer of electrons between chemical species. These reactions are fundamental to electrochemistry and are characterized by the change in oxidation states of the molecules involved.
In a redox reaction:

• The species that loses electrons gets oxidized, which occurs at the anode.


• The species that gains electrons gets reduced, which happens at the cathode.


• Each half-reaction either consists of oxidation or reduction.

Analyzing redox reactions involves breaking them down into their respective half-reactions and calculating the standard electrode potentials. By doing so, you can determine the overall cell potential, which is necessary for evaluating the feasibility of electrochemical processes.
For instance, in the given exercise, the reaction involves oxidizing tin (Sn to Sn^{2+}) and reducing iron ions (Fe^{2+} to Fe). By determining the potentials, you can understand how redox reactions power electrochemical cells.

Nernst Equation

The Nernst equation is vital in electrochemistry because it calculates the electromotive force (emf) of an electrochemical cell under non-standard conditions. While the standard emf is calculated under specific conditions, actual lab conditions may differ.
Mathematically, it's expressed as:\[E = E^0_{cell} - \frac{RT}{nF} \ln Q\]Here:

• E: represents the cell potential under non-standard conditions.


• E^0_{cell}: is the standard cell potential.


• R: the universal gas constant (8.314 J mol^{-1} K^{-1}).


• T: is the temperature in Kelvin.


• n: number of moles of electrons transferred in the reaction.


• F: Faraday's constant (96485 C mol^{-1}).


• Q: the reaction quotient.

The Nernst equation is especially useful for evaluating how cell voltage responds to varying concentrations and pressure conditions.
In practice, understanding and applying the Nernst equation helps predict and control the performance of batteries, sensors, and other electrochemical devices in different environments.