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 scenario (a) where \(P_{\text{H}_2} = 2 \text{ atm}\) and \([\text{H}^+] = 1.0 \text{ M}\).

Step 1: Understanding the Nernst Equation

The reduction potential of a half-cell, such as the hydrogen half-cell, can be calculated using the Nernst Equation: \[E = E^{0} - \frac{RT}{nF} \ln \left(\frac{P_\text{H}_2}{\left[\text{H}^+\right]^2}\right)\] where: - \(E^{0}\) is the standard reduction potential of the half-cell (0 V for the hydrogen electrode), - \(R\) is the universal gas constant, - \(T\) is the temperature in Kelvin, - \(n\) is the number of moles of electrons transferred in the reaction, - \(F\) is Faraday’s constant, - \(P_{\text{H}_2}\) is the partial pressure of hydrogen gas, - \(\left[\text{H}^+\right]\) is the hydrogen ion concentration. For simplicity in standard conditions at 298K, this simplifies to: \[E = 0 - 0.0591 \log \left(\frac{P_\text{H}_2}{\left[\text{H}^+\right]^2}\right)\]

Key Concepts

Electrochemical Cells

Electrochemical cells are fascinating components of chemistry that facilitate redox reactions between two distinct substances. These cells can transform chemical energy into electrical energy and vice versa. An electrochemical cell typically consists of two half-cells. Each half-cell contains an electrode and an electrolyte, which work together to conduct electricity.
The magic happens when the electrons transfer from one half-cell to another. This electron flow creates a current that can perform work or provide energy. In practical applications, electrochemical cells are vital for batteries, fuel cells, and electrolysis processes. Understanding how these cells function can help grasp complex chemical concepts, particularly when discussing reduction potential and standard conditions.

Reduction Potential

Reduction potential, denoted as \(E\), is an essential concept in electrochemistry. It measures the tendency of a chemical species to gain electrons and be reduced.
A higher reduction potential means a greater likelihood of gaining electrons. Reduction potentials are crucial because they help determine the direction of electron flow in electrochemical cells.
Each half-cell in an electrochemical cell has a distinct reduction potential. By comparing the potentials of two half-cells, one can predict which direction electrons will travel. The hydrogen half-cell, used as a standard reference, has a reduction potential of 0 volts under standard conditions. This reference point allows scientists to measure and compare the reduction potential of other half-cells more conveniently.

Standard Conditions

Standard conditions play a crucial role in simplifying and standardizing electrochemical measurements. These conditions typically refer to a temperature of 298 K (25°C), a pressure of 1 atm, and solutions with concentration of 1 M.
By adhering to these conditions, scientists can reliably compare electrochemical data without inconsistencies.
Electrochemical reactions, including those using the Nernst equation, become more predictable and manageable under standard conditions. With precise conditions, the calculations of reduction potential become straightforward and comparable across different reactions, enhancing the reliability of the data obtained.

Hydrogen Half-Cell

The hydrogen half-cell often serves as a standard in electrochemistry. It consists of a platinum electrode in contact with hydrogen gas and an acidic solution containing \( ext{H}^+\) ions.
The standard hydrogen electrode (SHE) sets the benchmark with a reduction potential of 0 volts. This reference point allows consistent measurement of other electrodes’ potentials.
Understanding its configuration and behavior is crucial in electrochemistry. This half-cell exemplifies the principles of cell potential calculations. By manipulating conditions such as pressure of \( ext{H}_2\) and concentration of \( ext{H}^+\), one can see shifts in potential, illustrating the dynamic nature of electrochemical systems. All these aspects make the hydrogen half-cell an invaluable tool for learning about redox reactions and potential measurement.