Problem 201 - A Complete Resource Book in Chemistry for JEE Main

Question

The reduction potential of hydrogen half-cell will be negative if: (a) \(\mathrm{p}\left(\mathrm{H}_{2}\right)=2 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\) (b) \(\mathrm{p}\left(\mathrm{H}_{2}\right)=1 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=1.0 \mathrm{M}\) (c) \(\mathrm{p}\left(\mathrm{H}_{2}\right)=1 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}\) (d) \(\mathrm{p}\left(\mathrm{H}_{2}\right)=2 \mathrm{~atm}\) and \(\left[\mathrm{H}^{+}\right]=2.0 \mathrm{M}\)

Step-by-Step Solution

Answer

The reduction potential is negative in cases (c) and (d).

Step 1: Understanding the Nernst Equation

To determine the reduction potential of the hydrogen half-cell, we use the Nernst equation: \[ E = E^0 - \frac{RT}{nF} \ln \left( \frac{[H^+]^2}{p(H_2)} \right) \].For the hydrogen half-cell at standard conditions, \( E^0 = 0 \) V.

Step 2: Simplifying the Nernst Equation for Hydrogen

Given \( E^0 = 0 \) V and the simplicity of natural constants, we simplify for the hydrogen half-cell at 298 K:\[ E = - \frac{0.059}{2} \log \left( \frac{[H^+]^2}{p(H_2)} \right) \].This becomes:\[ E = -0.059 \log \left( \frac{[H^+]^2}{p(H_2)} \right) \].

Step 3: Analyzing Each Case

- **Case (a)**: \( \left[H^+\right] = 1.0 \) M, \( p(H_2) = 2.0 \) atm. \[ E = -0.059 \log \left( \frac{1^2}{2} \right) \] results in a positive potential since log term is negative.- **Case (b)**: \( \left[H^+\right] = 1.0 \) M, \( p(H_2) = 1.0 \) atm. \[ E = -0.059 \log \left( \frac{1^2}{1} \right) \] results in exact zero potential.- **Case (c)**: \( \left[H^+\right] = 2.0 \) M, \( p(H_2) = 1.0 \) atm. \[ E = -0.059 \log \left( \frac{2^2}{1} \right) \] results in negative potential.- **Case (d)**: \( \left[H^+\right] = 2.0 \) M, \( p(H_2) = 2.0 \) atm. \[ E = -0.059 \log \left( \frac{2^2}{2} \right) \] results in slightly negative potential.

Step 4: Conclusion of Cases

From analyzing each case, we find that cases (c) and (d) yield negative reduction potentials because the logarithmic terms result in positive values, which are then negated.

Key Concepts

Reduction Potential

Reduction potential is a measure of the tendency of a chemical species to acquire electrons and be reduced. In electrochemistry, it helps to determine how freely electrons are transferred during a redox reaction. When we talk about reduction potential, we often reference it under standard conditions. This means that measurements are taken at 25°C, 1 M concentration for solutions, and 1 atm pressure for gases.
In the case of the hydrogen half-cell, if the reduction potential is zero, it acts as a reference for measuring potentials of other electrodes. However, in varied conditions, such as changing the concentration of hydrogen ions or the pressure of the hydrogen gas, the reduction potential can become negative or positive. A negative reduction potential indicates a lesser tendency to gain electrons when compared to the standard hydrogen electrode, implying a weaker oxidizing agent.
The Nernst equation is often used to calculate non-standard reduction potentials, taking into account the changes in concentrations and pressures.

Hydrogen Half-Cell

The hydrogen half-cell is a crucial standard in electrochemistry used to compare and measure the reduction potentials of other electrodes. It consists of a platinum electrode in a solution with protons (H⁺ ions) and hydrogen gas (), typically at 1 M concentration for H⁺ and 1 atm pressure for . This setup, under standard conditions, has an assigned potential of 0 V, making it ideal for referencing purposes.
In scenarios where conditions differ from the standard, such as  at 2 atm or [H⁺] at 2 M, we need to adjust the measured potential using the Nernst equation. This equation takes into the account the logarithmic relationship between concentration and pressure to compute the potential under non-standard conditions.
The hydrogen half-cell is not only fundamental for comparison purposes, but it also plays a pivotal role in setting the zero point for the electrochemical series.

Electrochemistry

Electrochemistry is the scientific field that studies the relationship between electricity and chemical change. It focuses heavily on redox reactions, where oxidation and reduction occur simultaneously, transferring electrons between substances.
A cornerstone concept in electrochemistry is the electrochemical cell, which can generate electrical energy from chemical reactions or facilitate chemical reactions through the introduction of electric energy. These cells are divided into two electrode types: anode (where oxidation occurs) and cathode (where reduction occurs).
The hydrogen half-cell is an example of an electrochemical system used to measure the electrode potentials. This understanding is crucial for applications like batteries, electroplating, and corrosion prevention.
Through the lens of electrochemistry, we understand how electrochemical processes can be optimized and controlled through careful manipulation of potentials and reactions, reflected in the precision of the Nernst equation for calculating non-standard cell potentials.