Problem 66 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following four electrodes (1) \(\mathrm{Cu}^{2+}(0.0001 \mathrm{M}) \mid \mathrm{Cu}(\mathrm{s})\) (2) \(\mathrm{Cu}^{2}(0.1 \mathrm{M}) \mid \mathrm{Cu}(\mathrm{s})\) (3) \(\mathrm{Cu}^{2}(0.0 \mathrm{lM}) \mid \mathrm{Cu}(\mathrm{s})\) (4) \(\mathrm{Cu}^{2+}(0.001 \mathrm{M}) \mid \mathrm{Cu}(\mathrm{s})\) If the standard reduction potential of \(\mathrm{Cu}^{2 \mathrm{\prime}} \mid \mathrm{Cu}\) is \(+0.34\) \(\mathrm{V}\), the reduction potentials (in volts) of the above electrodes following the order (a) \(1>4>3>2\) (b) \(1>2>3>4\) (c) \(3>4>2>1\) (d) \(2>3>4>1\)

Step-by-Step Solution

Answer

Option (d) is correct: 2 > 3 > 4 > 1.

Step 1: Identify Relevant Equation

The Nernst equation is used to calculate electrode potential based on concentration. For the half-cell standard copper reaction: \[ \mathrm{Cu}^{2+} + 2\mathrm{e}^- \rightarrow \mathrm{Cu} \] the Nernst equation is: \[ E = E^0 - \frac{RT}{nF} \ln \frac{1}{[\mathrm{Cu}^{2+}]} \] In standard conditions, this simplifies to: \[ E = E^0 - \frac{0.0592}{2} \log_{10} \frac{1}{[\mathrm{Cu}^{2+}]} \] where \( E^0 = +0.34 \, \mathrm{V} \) and \( n = 2 \).

Step 2: Calculate Potential for Electrode 1

Using the Nernst equation for \[ [\mathrm{Cu}^{2+}] = 0.0001 \, \mathrm{M} = 10^{-4} \, \mathrm{M} \] we find: \[ E_1 = +0.34 - \frac{0.0592}{2} \log_{10} \frac{1}{10^{-4}} \] \[ E_1 = +0.34 - 0.0296 \times 4 \]\[ E_1 = +0.34 - 0.1184 \] \[ E_1 = +0.2216 \, \mathrm{V} \]

Step 3: Calculate Potential for Electrode 2

For \[ [\mathrm{Cu}^{2+}] = 0.1 \, \mathrm{M} \], we use the Nernst equation:\[ E_2 = +0.34 - \frac{0.0592}{2} \log_{10} \frac{1}{0.1} \]\[ E_2 = +0.34 - 0.0296 \times 1 \]\[ E_2 = +0.34 - 0.0296 \]\[ E_2 = +0.3104 \, \mathrm{V} \]

Step 4: Calculate Potential for Electrode 3

For \[ [\mathrm{Cu}^{2+}] = 0.01 \, \mathrm{M} \], we apply the equation:\[ E_3 = +0.34 - \frac{0.0592}{2} \log_{10} \frac{1}{0.01} \]\[ E_3 = +0.34 - 0.0296 \times 2 \]\[ E_3 = +0.34 - 0.0592 \]\[ E_3 = +0.2808 \, \mathrm{V} \]

Step 5: Calculate Potential for Electrode 4

Given \[ [\mathrm{Cu}^{2+}] = 0.001 \, \mathrm{M} = 10^{-3} \, \mathrm{M} \], we calculate:\[ E_4 = +0.34 - \frac{0.0592}{2} \log_{10} \frac{1}{10^{-3}} \]\[ E_4 = +0.34 - 0.0296 \times 3 \]\[ E_4 = +0.34 - 0.0888 \]\[ E_4 = +0.2512 \, \mathrm{V} \]

Step 6: Rank Electrode Potentials

The calculated potentials are:\[ E_1 = 0.2216 \, \mathrm{V} \]\[ E_2 = 0.3104 \, \mathrm{V} \]\[ E_3 = 0.2808 \, \mathrm{V} \]\[ E_4 = 0.2512 \, \mathrm{V} \]Ranking them in order from highest to lowest gives: \[ E_2 > E_3 > E_4 > E_1 \]

Step 7: Select Correct Answer

Based on the ranking from highest to lowest potential (\( E_2 > E_3 > E_4 > E_1 \)), the correct answer matches option (d):\(2 > 3 > 4 > 1\).

Key Concepts

Electrode Potential

Electrode potential is an essential concept in electrochemistry that helps us understand how cells generate electricity. It refers to the voltage difference between an electrode and a reference point, usually another electrode, when the cell is at standard conditions. This potential is critical as it dictates how well the electrode can serve as a source or sink of electrons.
For any given electrode, like the copper (Cu) electrode, the potential depends significantly on the concentrations of the ions involved. The Nernst equation is often used to calculate this potential based on ionic concentrations. The higher the concentration of ions, the more positive the electrode potential tends to be. This relationship is crucial when determining how different electrodes will interact when part of an electrochemical cell.
In practical terms, understanding electrode potential allows us to predict the direction of electron flow, which is essential in designing batteries and other devices that rely on redox reactions. By mastering electrode potential, we can evaluate and optimize the efficiency of these processes, leading to better performance and reliability.

Standard Reduction Potential

The standard reduction potential is a key indicator of the tendency of a chemical species to gain electrons and undergo reduction. This potential is measured under standard conditions: 1 M concentration for each ion, a pressure of 1 atmosphere, and a temperature of 298 K (25°C). Standard conditions are important because they provide a consistent baseline for comparison.
Reduction potentials are usually given for half-reactions and reflect an element or compound's affinity for electrons. A more positive standard reduction potential indicates a greater likelihood of being reduced, whereas a more negative value suggests the opposite. For instance, the standard reduction potential of copper (Cu^{2+} | Cu) is +0.34 V, indicating copper ions (Cu^{2+}) have a good tendency to capture electrons and form copper metal (Cu).
These values are pivotal when predicting the direction of redox reactions in electrochemical cells. By comparing the standard reduction potentials of the half-reactions, we can determine which species will act as the oxidizing agent and which will be reduced. This understanding is indispensable for efficiently designing energy-generating systems and conducting predictive analyses regarding the behavior of chemical reactions.

Copper Electrode

The copper electrode is a common component in electrochemistry, particularly in the context of redox reactions and electrochemical cells. It is often used due to copper's good electrical conductivity and moderate oxidizing ability. In these systems, copper metal acts as either an anode or cathode depending on the setup of the electrochemical cell it is part of.
When in the cathode, the copper electrode will attract electrons and undergo a reduction reaction. Here, copper ions (Cu^{2+}) gain electrons to become copper metal (Cu). This process is crucial in applications like electroplating, where a metal is deposited on a surface. Conversely, as an anode, copper may lose electrons and oxidize, releasing copper ions into the solution.
The behavior of the copper electrode can be assessed using the Nernst equation, where the concentration of copper ions in the solution directly affects the electrode's potential. Adjusting these concentrations allows us to manipulate the cell's overall voltage and efficiency. Understanding the copper electrode's role in electrochemical processes is vital for advancing technologies in energy storage, metal refining, and corrosion prevention.