Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A variable, opposite external potential \(\left(\mathrm{E}_{\text {ex }}\right.\) ) is applied to the cell \(\mathrm{Zn} \mathrm{Zn}^{2+}(1 \mathrm{M}) \| \mathrm{Cu}^{2+}(1 \mathrm{M}) \mid \mathrm{Cu}\), of potential \(1.1 \mathrm{~V}\). When \(\mathrm{E}_{\mathrm{ext}}<1.1 \mathrm{~V}\) and \(\mathrm{E}_{\text {ext }}>1.1 \mathrm{~V}\), respectively electrons flow from : [Main Online April 10, 2015] (a) anode to cathode in both cases (b) cathode to anode and anode to cathode (c) anode to cathode and cathode to anode (d) cathode to anode in both cases

Step-by-Step Solution

Answer

(c) anode to cathode and cathode to anode.

Step 1: Analyze Cell Potential

The given cell reaction is a standard galvanic cell reaction: \( \text{Zn} | \text{Zn}^{2+} \text{(1M)} \| \text{Cu}^{2+} \text{(1M)} | \text{Cu} \). The potential of this cell, \( E_{\text{cell}} \), is given as \( 1.1 \text{ V} \). This is the electromotive force (EMF) driving the electrons from the anode to the cathode.

Step 2: Apply External Potential Less Than Cell Potential

When an external potential \( E_{\text{ext}} < 1.1 \text{ V} \) is applied, the net potential will still be favorable for the galvanic cell reaction. Therefore, electrons will naturally flow from the anode to the cathode as the cell still maintains a driving potential for electron flow.

Step 3: Apply External Potential Greater Than Cell Potential

When \( E_{\text{ext}} > 1.1 \text{ V} \), the external potential overcomes the cell's potential. In this case, the electrons are forced to flow in the reverse direction: from cathode to anode, because the external voltage is doing work against the cell's natural potential.

Step 4: Determine Direction of Electron Flow for Both Cases

From the analysis: - For \( E_{\text{ext}} < 1.1 \text{ V} \), electrons flow from anode to cathode. - For \( E_{\text{ext}} > 1.1 \text{ V} \), electrons flow from cathode to anode.

Key Concepts

Galvanic Cell

A galvanic cell is a type of electrochemical cell that converts chemical energy into electrical energy through a spontaneous redox reaction. In these cells, two different metals are connected through a salt bridge, allowing ions to flow between them while electrons travel through an external circuit. This setup facilitates electron flow from the anode (where oxidation occurs) to the cathode (where reduction takes place).

• The anode is the negative terminal because it releases electrons.
• The cathode is the positive terminal where electrons are accepted.

In the example given, a zinc ( Zn ) electrode interacts with copper ions in a copper sulfate solution. Zinc loses electrons more readily than copper does, making it the anode.

Cell Potential

Cell potential, also known as electromotive force (EMF), is the measure of the energy difference per charge between two electrodes. It's represented in volts (V) and indicates how much electrical energy per unit of charge is provided by the conversion of chemical energy. For a setup like Zn | Zn^{2+} (1M) || Cu^{2+} (1M) | Cu , the cell potential is 1.1 V. This voltage is created by the difference in the reduction potentials of the two metal electrodes.

• Positive potential indicates a spontaneous reaction.
• Higher cell potential means greater ability to do work.

In this galvanic cell, the zinc metal supplies the electrons because it has a lower electrode potential compared to copper.

Electron Flow

Electron flow is a central concept in electrochemical cells, determining the directionality of current. In a galvanic cell under natural conditions (without external influence), electrons will flow from the anode to the cathode.

Effect of External Potentials

An external potential can alter this flow:

• If E_{ext} is less than cell potential, the natural electron flow is maintained from anode to cathode.
• If E_{ext} is greater than cell potential, the external force reverses the direction, pushing electrons from cathode to anode.

This reversal occurs because the external source surpasses the energy provided naturally by the cell's potential, forcing a non-spontaneous reaction.

External Potential

External potential refers to the voltage applied from an external source which can influence the behavior of an electrochemical cell by changing the direction and magnitude of electron flow. In the discussed cell example, if the external potential applied ( E_{ext}) is less than 1.1 V, it boosts the electron flow along its natural course from the anode to the cathode. However, when E_{ext} exceeds 1.1 V, this potential overpowers the cell's natural EMF, driving electrons in the opposite direction from the cathode to the anode. This is effectively proving external work against the cell, turning a galvanic cell into an electrolytic cell temporarily. Understanding the effect of varying external potentials is crucial for controlling electron flow in electrochemical applications, such as recharging batteries or electroplating.