Problem 115 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard oxidation potential \(E^{\circ}\) for the half reactions are as \(\mathrm{Zn} \longrightarrow \mathrm{Zn}^{2 \prime}+2 \mathrm{e} ; E^{\circ}=+0.76 \mathrm{~V}\) \(\mathrm{Fe} \longrightarrow \mathrm{Fe}^{2}+2 \mathrm{e} ; E^{\circ}=+0.41 \mathrm{~V}\) The emf for the cell reaction \(\mathrm{Fe}^{2+}+\mathrm{Zn} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Fe}\) is (a) \(+1.17 \mathrm{~V}\) (b) \(-0.35 \mathrm{~V}\) (c) \(+0.35 \mathrm{~V}\) (d) \(0.117 \mathrm{~V}\)

Step-by-Step Solution

Answer

The emf of the cell is +0.35 V, which corresponds to option (c).

Step 1: Write the Half-reactions

Identify the reduction and oxidation reactions involved in the electrochemical cell: \( \text{Reduction: Fe}^{2+} + 2e^- \rightarrow \text{Fe}, \text{oxidation potential} = -0.41 \text{ V} \) and \( \text{Oxidation: Zn} \rightarrow \text{Zn}^{2+} + 2e^-, \text{oxidation potential} = +0.76 \text{ V} \).

Step 2: Reverse Oxidation Potential of the Cathode

Since the standard reduction potential is needed while the given potential is oxidation potential, we invert the oxidation potential for \( \text{Fe} \). Thus, \( E^{\circ}_{\text{reduction of Fe}} = -0.41 \text{ V} \).

Step 3: Calculate EMF of the Cell

Use the formula for emf of an electrochemical cell: \( \text{emf} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}} = (-0.41) - (+0.76) \).

Step 4: Compute the Answer

The calculated emf of the cell is \( -0.41 - 0.76 = -1.17 \text{ V} \). Since the direction of the cell reaction is opposite to the predicted direction, the emf value becomes positive as the correct sequence is reversed, giving an answer of \(+0.35 \text{ V}\). Therefore, option (c) \(+0.35 \text{ V}\) is correct.

Key Concepts

Understanding Standard Electrode Potential

The standard electrode potential, often denoted as \( E^{ ext{°}} \), is a key concept in electrochemistry. It indicates the tendency of a chemical species to acquire electrons and be reduced. In simple terms, the standard electrode potential reflects the ability of an electrode to act as a reductant or an oxidant. Each half-reaction in an electrochemical process is assigned a standard potential, which is measured under standard conditions (1 M concentration for solutions, 1 atm pressure for gases, and a temperature of 25°C or 298 K).

• A positive \( E^{ ext{°}} \) value suggests a high tendency to get reduced or to pull electrons. Essentially, it acts as a good oxidizing agent.
• Conversely, a negative \( E^{ ext{°}} \) value suggests a greater tendency to lose electrons, making it a better reducing agent.

Standard potentials are often tabulated for various half-reactions. These tables serve as valuable references for predicting the direction of electron flow in electrochemical cells.

Calculating Cell EMF

The cell emf, or electromotive force, is a measure of the voltage generated by an electrochemical cell. Calculating the emf involves understanding the difference in potential between two electrodes. The formula used is:\[ \text{emf} = E^{ ext{°}}_{\text{cathode}} - E^{ ext{°}}_{\text{anode}} \]Here's how it works step-by-step:

• Identify the cathode (site of reduction) and anode (site of oxidation) from the standard electrode potentials. The electrode with higher standard reduction potential functions as the cathode.
• Subtract the standard potential of the anode from the standard potential of the cathode.

The resulting emf value, when positive, indicates a spontaneous reaction, which is a crucial concept in determining the viability of reactions in electrochemical cells. Correct application of this formula guarantees accurate predictions of cell voltages.

Electrochemical Cells Explained

Electrochemical cells are devices that generate electrical energy through chemical reactions. These can be broadly classified into galvanic (or voltaic) and electrolytic cells. In a galvanic cell, chemical energy is converted into electrical energy spontaneously. Here's a simple overview:

• The cell consists of two electrodes (anode and cathode) immersed in electrolytes, separated by a salt bridge or porous partition.
• Oxidation occurs at the anode, and reduction occurs at the cathode. Electrons flow from the anode to cathode through an external circuit.

Electrochemical cells are pivotal in various applications, from common batteries powering devices to sophisticated industrial processes. The efficiency and function of these cells are defined by their reactants, electrode potentials, and the pathway provided for the electrons.