Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The standard reduction potentials of \(\mathrm{Cu}^{2+} \mid \mathrm{Cu}\) and \(\mathrm{Cu}^{2+} \mid \mathrm{Cu}^{+}\)are \(0.337\) \(\mathrm{V}\) and \(0.153\) respectively. The standard electrode potential of \(\mathrm{Cu}^{+} \mid \mathrm{Cu}\) half cell is [1997-1 Mark] (a) \(0.184 \mathrm{~V}\) (b) \(0.827 \mathrm{~V}\) (c) \(0.521 \mathrm{~V}\) (d) \(0.490 \mathrm{~V}\)

Step-by-Step Solution

Answer

The answer is option (a) 0.184 V.

Step 1: Identify the given reduction potentials

We are given the following standard reduction potentials: 1. For the half-cell reaction \( \mathrm{Cu}^{2+} + 2\mathrm{e}^- \rightarrow \mathrm{Cu} \), the reduction potential is \( E^0(Cu^{2+}/Cu) = 0.337 \text{ V} \).2. For the half-cell reaction \( \mathrm{Cu}^{2+} + \mathrm{e}^- \rightarrow \mathrm{Cu}^+ \), the reduction potential is \( E^0(Cu^{2+}/Cu^+) = 0.153 \text{ V} \).

Step 2: Express the equations based on standard reduction potentials

The standard electrode potential of a cell is given by the difference between the reduction potentials of the half-cells: \[ E^0_{\text{cell}} = E^0(\text{reduction}) - E^0(\text{oxidation}) \]

Step 3: Calculate standard electrode potential for \( \mathrm{Cu}^+ \mid \mathrm{Cu} \)

From the given data, two reactions can be combined:1. \( \mathrm{Cu}^{2+} + \mathrm{e}^- \rightarrow \mathrm{Cu}^+ \) with \( E^0 = 0.153 \text{ V} \)2. \( \mathrm{Cu}^{2+} + 2\mathrm{e}^- \rightarrow \mathrm{Cu} \) with \( E^0 = 0.337 \text{ V} \)For the reaction \( \mathrm{Cu}^+ + \mathrm{e}^- \rightarrow \mathrm{Cu} \):Use \( E^0(\mathrm{Cu}^{2+}/\mathrm{Cu}) = 0.337 \text{ V} \) and \( E^0(\mathrm{Cu}^{2+}/\mathrm{Cu}^+) = 0.153 \text{ V} \):\[ E^0(\mathrm{Cu}^+/\mathrm{Cu}) = E^0(\mathrm{Cu}^{2+}/\mathrm{Cu}) - E^0(\mathrm{Cu}^{2+}/\mathrm{Cu}^+) \]\[ E^0(\mathrm{Cu}^+/\mathrm{Cu}) = 0.337 \text{ V} - 0.153 \text{ V} = 0.184 \text{ V} \]

Step 4: Select the correct option

The calculated standard electrode potential for \( \mathrm{Cu}^+ \mid \mathrm{Cu} \) is \( 0.184 \text{ V} \), which corresponds to option \(a\).

Key Concepts

Standard Reduction Potentials

In the world of electrochemistry, the Standard Reduction Potential is a constant that tells us how easily a species can acquire electrons—that is, how strongly it wants to be reduced. Reduction is the process of gaining electrons, and it's crucial in many chemical reactions, especially those involved in generating electricity in batteries.
The Standard Reduction Potential is measured under standard conditions: a solute concentration of 1 M, a gas pressure of 1 atm, and a temperature of 25°C (298 K). These potentials are useful because they allow us to predict the direction and strength of redox reactions. By comparing the standard reduction potentials for two half-reactions, we can determine which species will be reduced and which will be oxidized in a redox reaction.

• A positive standard reduction potential means the species is more likely to be reduced.
• A negative potential indicates it prefers to be oxidized instead.

In a given electrochemical reaction, the difference in standard reduction potentials of the two half-cells will dictate the overall cell potential, which can then be used to do work, such as powering devices.

Electrochemical Cells

Electrochemical cells, often known as galvanic or voltaic cells, are fascinating devices that convert chemical energy into electrical energy. They're the heart of batteries that power countless devices in our daily lives, from flashlights to smartphones.
Each electrochemical cell consists of two half-cells, each containing a different chemical reaction, called redox reactions, that occurs at separate electrodes.

• One half-cell undergoes oxidation (loss of electrons), and the other undergoes reduction.
• The movement of electrons from the anode (oxidation site) to the cathode (reduction site) through an external circuit is what generates electricity.

A salt bridge or a porous membrane is often used to maintain the flow of ions between the two half-cells, keeping the charges balanced. The potential difference between the electrodes when no current is flowing is called the cell's electromotive force (emf) or cell potential.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are processes where electrons are transferred between entities, a fundamental concept in chemistry and electrochemistry.
Reduction refers to the gain of electrons, while oxidation is the loss of electrons. An easy way to remember this is the mnemonic "OIL RIG"—Oxidation Is Loss, Reduction Is Gain.
Taking a closer look at a redox reaction, it can be divided into two separate half-reactions:

• The oxidation half-reaction, where one species gives up electrons, and
• The reduction half-reaction, where another species gains those electrons.

Each of these half-reactions has its own standard reduction potential, which can be found in various tables. The overall redox reaction is balanced with respect to mass and charge, reflecting the conservation laws.
Understanding redox reactions is key to harnessing reactions for generating electrical power in electrochemical cells and countless applications in industrial processes.