Problem 164 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following Column-I (a) \(\mathrm{Pt}\left|\mathrm{H}_{2}(1 \mathrm{~atm})\right| \mathrm{H}^{+}(1 \mathrm{M})\) (b) \(\mathrm{Pt}\left|\overrightarrow{\mathrm{Cl}}^{-}\right| \mathrm{Cl}_{2}\) (c) \(\mathrm{Pt}\left[\mathrm{H}_{2}(1 \mathrm{~atm}) \mid \mathrm{H}^{+}\left(\mathrm{C}_{1} \| \mathrm{H}^{+}\left(\mathrm{C}_{2}\right) \mathrm{H}_{2}(1 \mathrm{~atm}) \mid \mathrm{Pt}\right.\right.\) (d) \(\mathrm{Pt} \mathrm{H}_{2}\left(\mathrm{p}_{1} \mathrm{~atm}\right)\left[\mathrm{H}^{+}(1 \mathrm{M}) \| \mathrm{H}^{+}(1 \mathrm{M})\left|\mathrm{H}_{2}\left(\mathrm{p}_{2} \mathrm{~atm}\right)\right| \mathrm{Pt}\right.\) Column-II (p) Wrong representation (q) Concentration cell (r) Standard hydrogen electrode (s) \(\mathrm{E}^{\circ}=0\) (t) The cell may be commercially feasibly

Step-by-Step Solution

Answer

(a)-(r), (b)-(p), (c)-(q), (d)-(t)

Step 1: Identify the Standard Hydrogen Electrode

In Column-I, option (a) is \( \mathrm{Pt}\left|\mathrm{H}_{2}(1 \mathrm{~atm})\right| \mathrm{H}^{+}(1 \mathrm{M}) \). This setup is a standard hydrogen electrode, characterized by the use of pure hydrogen gas at 1 atm, in contact with 1M H⁺ ions. This corresponds to option (r) in Column-II.

Step 2: Identify the Gas Electrode Representation

In Column-I, option (b) is \( \mathrm{Pt}\left|\overrightarrow{\mathrm{Cl}}^{-}\right| \mathrm{Cl}_{2} \) which appears to be an incorrect representation for a gas electrode, as it doesn’t specify concentrations or partial pressures. This matches option (p) in Column-II indicating it is a wrong representation.

Step 3: Identify the Concentration Cell with Hydrogen

In Column-I, option (c) is \( \mathrm{Pt}\left[\mathrm{H}_{2}(1 \mathrm{~atm}) \mid \mathrm{H}^{+}\left(\mathrm{C}_{1} \| \mathrm{H}^{+}\left(\mathrm{C}_{2}\right) \mathrm{H}_{2}(1 \mathrm{~atm}) \mid \mathrm{Pt}\right.\right.\). This setup is characteristic of a concentration cell, as it has different concentrations \( C_1 \) and \( C_2 \). This corresponds to option (q) in Column-II.

Step 4: Identify the Hydrogen Concentration Cell

In Column-I, option (d) is \( \mathrm{Pt} \mathrm{H}_{2}\left(\mathrm{p}_{1} \mathrm{~atm}\right)\left[\mathrm{H}^{+}(1 \mathrm{M}) \| \mathrm{H}^{+}(1 \mathrm{M})\left|\mathrm{H}_{2}\left(\mathrm{p}_{2} \mathrm{~atm}\right)\right| \mathrm{Pt}\right. \). This is a concentration cell with different gas pressures \( p_1 \) and \( p_2 \) and the same concentration, typically used to generate electrical energy. This setup is best matched with option (t) indicating commercial feasibility.

Key Concepts

Standard Hydrogen Electrode

The standard hydrogen electrode (SHE) is a fundamental reference point for measuring electrode potential in electrochemical cells. It acts as the universal reference for electrode potentials and is crucial in determining the efficacy and behavior of electrochemical reactions. The SHE is composed of several key components:

• A platinum electrode, which is inert and acts as a surface for the hydrogen reaction to occur.
• Hydrogen gas at a pressure of 1 atm, ensuring that the hydrogen molecules are evenly distributed.
• 1 M H⁺ ions, which maintain a constant concentration to achieve equilibrium conditions.

This setup achieves a potential of 0 V by definition, making it the baseline for comparing all other electrode potentials. The SHE is crucial for: - Establishing a consistent reference point for measuring and comparing the electrode potentials of other half-cells. - Standardizing conditions in electrochemical experiments to ensure accuracy and reproducibility. By directly contacting the hydrogen gas with the solution of hydrogen ions, the standard hydrogen electrode helps in understanding the thermodynamics of half-cell reactions.

Concentration Cell

A concentration cell is an intriguing type of electrochemical cell that generates electrical energy from the chemical potential difference caused by varying concentrations of ions. Unlike typical galvanic cells, where the driving force is a redox reaction, the concentration cell relies on the principle that ions will naturally move from a region of higher concentration to one of lower concentration, striving for equilibrium. This ionic movement can be harnessed to generate an electric current. In the setup presented in the problem, the concentration cell makes use of:

• Different concentrations of hydrogen ions in two separate compartments.
• A uniform setup with hydrogen gas at a consistent pressure in both compartments.

The potential difference resulting from the concentration gradient is calculated using the Nernst equation: \[ E = E^0 - \frac{RT}{nF} \ln \left( \frac{[C_2]}{[C_1]} \right) \]where \(C_1\) and \(C_2\) represent the concentrations in the two compartments. The configuration shown in this exercise emphasizes the capacity to produce practical electrical energy by simply utilizing the natural tendency of ions to diffuse.

Gas Electrode Representation

Gas electrode representation is a method used to depict electrochemical cells involving gas-phase reactions on electrodes. Accurate representation is key to correct analysis and understanding of the reactions and processes occurring within the cell. In a properly represented gas electrode, several elements need to be specified:

• The identity of the gas involved, crucial for recognizing the chemical reactions taking place.
• The electrode material, often platinum, which must be inert to provide a durable surface for reaction without participating in it.
• Concentration or pressure conditions, which are necessary to understand the state of the gas and its interaction with the electrode.

In the exercise example, a misrepresented gas electrode highlights the importance of clear and correct notation. Accurate notation ensures that the electrochemical processes are well-understood and correctly quantified, thus preventing errors in scientific communication and experimentation.

Electrode Potential

Electrode potential, or reduction potential, is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. In electrochemical cells, this potential difference between two electrodes generates the capacity to do work —electric potential energy that can be converted into current. Essential factors influencing electrode potential include:

• The intrinsic properties of the substances involved in the half-cell reaction.
• Concentration of ions, which follows Le Chatelier's principle, affecting the equilibrium state and potential.
• Temperature and pressure conditions, relevant for reactions involving gases.

In practice, electrode potentials are measured relative to the standard hydrogen electrode (SHE), which is defined as having a potential of 0 V. The absolute value of an electrode potential can be positive or negative, indicating whether a reduction or oxidation reaction is favored under standard conditions. Accurately understanding and measuring electrode potential is vital for predicting how electrochemical cells will function and for designing efficient energy storage systems.