Problem 99 - A Complete Resource Book in Chemistry for JEE Main

Question

The hydrogen electrode is dipped in a solution of \(\mathrm{pH}\) 3 at \(25^{\circ} \mathrm{C}\). The potential would be (the value of \(2.303\) \(\mathrm{RT} / F\) is \(0.059 \mathrm{~V})\) (a) \(0.177 \mathrm{~V}\) (b) \(0.087 \mathrm{~V}\) (c) \(0.059 \mathrm{~V}\) (d) \(-0.177 \mathrm{~V}\).

Step-by-Step Solution

Answer

The potential is \(0.177\, \text{V}\) (option a).

Step 1: Understanding the Nernst Equation

The Nernst equation can be used to find the electrode potential of a half-cell. It is given by \( E = E^{\circ} - \frac{0.059}{n} \log [H^+] \), where \( E^{\circ} \) is the standard electrode potential, \( n \) is the number of moles of electrons, and \([H^+]\) is the concentration of hydrogen ions.

Step 2: Setting Up Equation with Given Values

For the standard hydrogen electrode, the standard electrode potential \( E^{\circ} \) is \( 0 \) V. The hydrogen ion concentration can be determined from pH: \([H^+] = 10^{-\mathrm{pH}} \), which at pH 3 gives \([H^+] = 10^{-3} \). Substitute these values into the Nernst equation.

Step 3: Calculating the Potential

Substitute \( n = 1 \), since there is one electron involved in the hydrogen reaction, into the equation: \[ E = 0 - (0.059 \times \log [10^{-3}]) = 0 + (0.059 \times 3) = 0.177 \text{ V} \]

Step 4: Comparing with Multiple Choices

The calculated potential \(0.177\, \text{V}\) matches option (a) exactly. Thus, \(0.177\, \text{V}\) is the correct answer.

Key Concepts

Hydrogen Electrode

The hydrogen electrode is a fundamental concept in electrochemistry. It acts as a reference half-cell against which all other electrodes are measured. The standard hydrogen electrode (SHE) consists of a platinum electrode in a solution where hydrogen gas is bubbled through at a pressure of 1 atmosphere. The platinum acts as an inert conductor, facilitating the electron exchange between the hydrogen gas and ions without participating in the reaction itself.

To maintain standard conditions, the concentration of hydrogen ions in the solution should be 1 M. This standard setup defines the electrode potential of the SHE as exactly 0 V at 25°C, making it a baseline for measuring the electrode potentials of other half-cells.

Understanding the construction and function of the hydrogen electrode is vital, as it provides a consistent reference point in electrochemical cells. This ensures accurate measurement and comparison of electrode potentials across different scenarios.

Electrode Potential

Electrode potential refers to the voltage developed across a cell's electrode caused by the redox reaction occurring at the electrode surface. It is crucial in determining how much work a cell can perform.

The electrode potential is influenced by:

• The nature of the electrode material and the substances involved in the reaction.
• The concentrations of ions in the solution.
• The temperature of the system.

For any half-cell, the potential can be calculated using the Nernst Equation. This equation accounts for variables like ion concentration and temperature, thus providing a quantifiable potential in any given condition.

The Nernst equation for a general half-cell is expressed as:\[ E = E^{\circ} - \frac{0.059}{n} \log [oxidation/reduction] \] where:

• \( E^{\circ} \) is the standard electrode potential.
• \( n \) is the number of moles of electrons exchanged in the reaction.

Electrode potential is the driving force that directs the flow of electrons in an electrochemical cell, critical in applications ranging from batteries to electrolysis.

pH Concentration

pH is a numeric scale used to determine the acidity or basicity of a solution, expressed as the negative logarithm of the hydrogen ion concentration.

In formula: \[ \text{pH} = -\log [H^+] \]This relationship allows you to convert pH values into ion concentrations and vice versa. For example, a solution with a pH of 3 has a hydrogen ion concentration of \( [H^+] = 10^{-3} \; M \).

The pH concentration significantly affects the electrode potential of a half-cell, as seen through the Nernst equation. Lower pH values correspond to higher hydrogen ion concentrations, which impacts the voltage developed across the electrode.

Understanding the interplay between pH and hydrogen ion concentration is crucial for accurately determining electrode potentials and studying electrochemical reactions in varied conditions.

Standard Electrode Potential

Standard electrode potential \( (E^{\circ}) \) is a vital thermodynamic quantity. It represents the measure of the potential developed by a half-cell under standard conditions, which includes a concentration of 1 M for all ionic species in solution, a gas pressure of 1 atm, and a temperature of 25°C.

These conditions ensure that the potential measurements are consistent and comparable between different systems. The standard electrode potential for every half-cell can be found in electrochemical tables.

In SHE, the standard potential is assigned a value of exactly zero. Other electrode potentials are then compared to this baseline value. This allows the calculation of cell potentials for electrochemical cells using the equation: \[ E_{cell} = E_{cathode}^{\circ} - E_{anode}^{\circ} \]Standard electrode potentials are instrumental in predicting the direction of redox reactions and calculating the electromotive force (emf) of electrochemical cells, making them central to studies in electrochemistry.