Problem 202 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard reduction potentials for \(\mathrm{Zn}^{2+} / \mathrm{Zn}, \mathrm{Ni}^{2+} / \mathrm{Ni}\), and \(\mathrm{Fe}^{2+} / \mathrm{Fe}\) are \(-0.76,-0.23\) and \(-0.44 \mathrm{~V}\) respectively. The reaction \(\mathrm{X}+\mathrm{Y}^{2+} \rightarrow \mathrm{X}^{2+}+\mathrm{Y}\) will be spontaneous when (a) \(\mathrm{X}=\mathrm{Fe}, \mathrm{Y}=\mathrm{Zn}\) (b) \(\mathrm{X}=\mathrm{Ni}, \mathrm{Y}=\mathrm{Zn}\) (c) \(\mathrm{X}=\mathrm{Ni}, \mathrm{Y}=\mathrm{Fe}\) (d) \(\mathrm{X}=\mathrm{Zn}, \mathrm{Y}=\mathrm{Ni}\)

Step-by-Step Solution

Answer

Option (d) is spontaneous since it has a positive cell potential.

Step 1: Understand Reduction Potentials

When comparing standard reduction potentials, the element or ion with the higher (less negative) potential will be reduced, and the lower potential will be oxidized. In a spontaneous redox reaction, the overall cell potential must be positive, meaning electrons flow from the lower to the higher potential.

Step 2: Calculate Reaction Potentials

Let's calculate the cell potential for each case by subtracting the reduction potential of the species being oxidized from that of the species being reduced: - (a) Fe + Zn²⁺ → Fe²⁺ + Zn: Potential = E(Zn²⁺/Zn) - E(Fe²⁺/Fe) = -0.76 - (-0.44) = -0.32 V - (b) Ni + Zn²⁺ → Ni²⁺ + Zn: Potential = E(Zn²⁺/Zn) - E(Ni²⁺/Ni) = -0.76 - (-0.23) = -0.53 V - (c) Ni + Fe²⁺ → Ni²⁺ + Fe: Potential = E(Fe²⁺/Fe) - E(Ni²⁺/Ni) = -0.44 - (-0.23) = -0.21 V - (d) Zn + Ni²⁺ → Zn²⁺ + Ni: Potential = E(Ni²⁺/Ni) - E(Zn²⁺/Zn) = -0.23 - (-0.76) = +0.53 V.

Step 3: Identify Spontaneous Reaction

A spontaneous reaction has a positive cell potential. From our calculations, option (d) Zn + Ni²⁺ → Zn²⁺ + Ni is the only reaction with a positive cell potential of +0.53 V.

Key Concepts

Standard Reduction Potentials

When it comes to understanding redox reactions, standard reduction potentials are crucial. These potentials indicate how likely a substance is to gain electrons, or be reduced, compared to the hydrogen electrode. The measurement is in volts, and each compound has a unique reduction potential.

In the context of redox reactions, there are a few key points to remember:

• A more positive standard reduction potential means a greater tendency to be reduced.
• A more negative potential suggests a greater tendency to lose electrons, or oxidize.
• The comparison of these potentials helps determine which species will be oxidized or reduced in a reaction.

Knowing the reduction potentials allows us to predict the flow of electrons between different substances, which is essential in determining how a reaction will proceed.

Electrochemistry

Electrochemistry is the study of chemical processes that cause electrons to move. This movement of electrons is what we refer to as electricity. When we talk about electrochemical reactions, redox reactions are typically involved. They involve the transfer of electrons between species.

The electrochemical cell is a key concept here. There are two types of cells:

• Galvanic (Voltaic) Cells: These cells host spontaneous reactions that generate electrical energy.
• Electrolytic Cells: In these, electrical energy is used to drive non-spontaneous reactions.

Understanding electrochemistry allows us to harness chemical reactions in batteries, fuel cells, and other technologies.

Spontaneous Reactions

A spontaneous reaction in the context of electrochemistry refers to a reaction that proceeds without needing external energy. The term "spontaneous" doesn't necessarily mean immediate, but indicates that once started, the reaction can maintain itself.

In redox reactions, whether or not a reaction is spontaneous is often determined by the cell potential:

• A positive cell potential indicates a spontaneous reaction. This means the electrons are naturally inclined to move in the direction of the reaction.
• A negative cell potential usually means the reaction is non-spontaneous and would require energy input to proceed.

Recognizing if a reaction is spontaneous has practical implications in designing batteries and other electrochemical devices.

Cell Potential Calculations

Calculating the cell potential is vital in predicting the behavior of redox reactions. The cell potential is derived by subtracting the reduction potential of the half-reaction where oxidation occurs from the reduction potential where reduction occurs.

To calculate:

• Identify which species is being reduced and which is oxidized.
• Use the formula: \[ E_{cell} = E_{reduction} - E_{oxidation} \]
• Ensure that you are subtracting the potential of the oxidized species from that of the reduced species.

For instance, if calculating the cell potential for a reaction, a positive result indicates that the reaction can occur spontaneously under standard conditions. Accurately calculating the cell potential can guide whether a redox reaction will proceed on its own or if it requires energy input.