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) \(-0.177 \mathrm{~V}\).

Electrode potential is the measure of the electrical potential difference between an electrode and a reference electrode. In the context of the Nernst equation, it is a way to quantify the driving force behind the flow of ions between the electrode and the electrolyte. When an electrode is dipped in an electrolyte solution, an electrochemical reaction occurs, and the potential that develops is based on the specific chemistry of the electrode material and the ions present.
The Nernst equation, written as \( E = E^0 - \frac{2.303 RT}{F} \times \text{pH} \), is central to the calculation of this potential. In an exercise where the pH of the solution and the temperature are known, we can calculate the electrode potential by substituting these values into the equation.
For example, when a hydrogen electrode is dipped in an acidic solution with pH 3 at 25 degrees Celsius, we can determine its potential by taking the temperature into account (which affects the value of \( RT/F \) ), the pH value, and considering that for the hydrogen electrode, \( E^0 = 0 \). The computation is straightforward, allowing us to immediately find the potential at these given conditions.

Chemical thermodynamics is the study of the interrelation between heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. In the context of the Nernst equation, it helps us understand how the properties of the system, including temperature, pressure, and concentration of the constituents, affect the electrode potential.
The universal gas constant (R) and the temperature (T) from the equation are thermodynamic parameters. At the standard conditions (298 K or 25 degrees Celsius), using constants for R and Faraday's (F), we can calculate the potential change for the hydrogen electrode using the given pH value.
By factoring in these thermodynamics concepts when using the Nernst equation, we can predict the feasibility and the direction of the electrochemical reactions. This is essential for students who are not just looking for the right answer to a textbook problem but aiming to understand the principles that govern physical chemistry.

The impact of pH on electrode potential is notable because pH is a measure of the hydrogen ion concentration in a solution. Since the hydrogen electrode involves hydrogen ions directly (either producing or consuming them depending on the direction of reaction), any change in their concentration will affect the electrode potential.
In the Nernst equation, the pH appears explicitly, which shows the linear relationship between the hydrogen ion concentration and the potential. An increase in pH, indicating a decrease in hydrogen ion concentration, will result in a decrease in the electrode potential, affecting the cell's ability to do electrical work.
Therefore, by understanding the role of pH in the Nernst equation, students can predict how changes in acidity or alkalinity could alter the overall cell potential of electrochemical cells, which is crucial in applications like batteries, corrosion, and electroplating.

The Standard Hydrogen Electrode (SHE) is a reference electrode which is assigned a potential of 0 volts, and it is used in measuring electrode potentials. It is a fundamental component in electrochemical cell design because it provides a consistent comparison point for other electrode potentials.
When using the SHE in calculations with the Nernst equation, the electrode potential of the SHE is taken as \( E^0 = 0 \) volts. In practice, this means that any potential measured is solely due to the other half-cell in the electrochemical cell setup. This simplifies calculations and allows us to isolate the chemical behavior of the electrode of interest.
By referencing the SHE, students can better understand the concept of reduction potentials and how they are applicable in real-world scenarios, such as determining the direction of electron flow in an electrochemical reaction or configuring the setup of voltaic cells.