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 V, which is option (d).

Step 1: Identify the Nernst Equation for pH

The Nernst equation for a hydrogen electrode in a solution is given by \[ E = E^0 - \frac{2.303RT}{F} \times \text{pH} \]where \( E^0 \) is the standard electrode potential of the hydrogen electrode, which is 0 V at 25°C.

Step 2: Substitute Given Values Into the Equation

We substitute the given values into the Nernst equation:\[ E = 0 - 0.059 \times 3 \]

Step 3: Calculate the Potential

Simplify the equation:\[ E = -0.177 \text{ V} \]

Step 4: Match the Result with Options

Compare the calculated value to the options given in the exercise:The calculated potential \(-0.177 \text{ V}\) matches option (d).

Key Concepts

Hydrogen Electrode

The hydrogen electrode is a crucial reference electrode used in electrochemistry. It serves as a standard measurement for electrode potentials. A typical hydrogen electrode consists of a platinum electrode in the presence of hydrogen gas at 1 atm pressure. It is immersed in an acidic solution where the concentration of hydrogen ions is known. The potential it generates is considered to be 0 V at standard temperature conditions, which is typically 25°C.

Using hydrogen electrodes, we can determine the pH of solutions through their potential in comparison to a standard electrode. This makes them invaluable in experiments where pH does not only affect chemical reactions but also electrochemical processes. The hydrogen electrode helps ensure that the comparisons across different systems are accurate and consistent.

Electrode Potential

Electrode potential refers to the voltage developed between an electrode and its surrounding electrolyte. It is influenced by the type of electrode, the concentration of ions in solution, and environmental conditions such as temperature. The hydrogen electrode, with its potential set at 0 V, serves as the baseline for measuring other electrodes' potential, allowing them to be expressed in relation to the standard hydrogen electrode (SHE).

The measurement of electrode potential is essential in predicting the direction of redox reactions. By knowing which potential is higher or lower, scientists can determine the tendency of a chemical species to gain or lose electrons. This assessment can help in applications like electroplating, corrosion prevention, and battery design.

pH Calculation

pH is a scale used to specify the acidity or basicity of an aqueous solution. It is calculated from the concentration of hydrogen ions in the solution. The relationship of pH with potential is described via the Nernst equation, which helps us understand how pH affects electrical potential.

For a hydrogen electrode immersed in a solution, the Nernst equation can be rearranged to find the potential resulting from different pH levels. The formula is \[ E = E^0 - \frac{2.303RT}{F} \times \text{pH} \] At 25°C, the constant \( \frac{2.303RT}{F} \) is approximately 0.059 V, simplifying calculations. If you dip a hydrogen electrode into a solution with a known pH, using this equation allows for the determination of the potential difference generated by changes in pH.

Temperature Effects on Potential

Temperature plays a significant role in electrochemical reactions and their potentials. It affects the energies between the electrode and its electrolyte. The Nernst equation takes temperature into account through the term \( \frac{RT}{F} \). As temperature changes, so does this term, altering the calculated potential.

An increase in temperature typically increases the rate of kinetic activity, which may lead to higher electron movement resulting in a change in potential. Conversely, a lower temperature can slow down reactions. Understanding these effects is vital for accurately predicting the behavior of electrochemical cells under different conditions. This knowledge is especially crucial in processes like batteries' efficiency management and industrial electrochemical applications.