Question

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

Short answer

The potential of the hydrogen electrode dipped in the solution with a pH of 3 at 25°C is approximately -0.177 V. So the correct option is (c) -0.177 V.

Step-by-step solution

Understand the Nernst Equation

The Nernst equation is a formula that calculates the electric potential of a half-cell or full cell reaction in electrochemistry. Written for hydrogen it is \(E=E_{0}-\frac{2.303 RT}{nF} pH\). Here \(E\) is the electrode potential, \(E_{0}\) is the standard reduction potential of a half-cell reduction reaction (for hydrogen, \(E_0 = 0V\)), \(R\) is the ideal gas constant (use \(R=0.08V\), as we will be using voltage, temperature in Kelvin and mole), \(T\) is the temperature in kelvin, \(n\) is the number of moles of electrons per mole of the substance (for hydrogen, \(n = 1\)), \(F\) is the Faraday constant (\(F = 96485 C mol^{-1}\)), and \(pH\) is the acidity of the solution.

Plug the given values into the Nernst equation

Plug the given values into the formula, \(E=E_{0}-\frac{2.303 RT}{nF}pH\). As this is a hydrogen electrode, \(E_{0}\) equals 0. The temperature is given as \(25^{\circ} \mathrm{C}\), but for the Nernst equation we need to convert this to Kelvin by adding 273, so \(T = 298K\). The number of moles of electrons, \(n\), for hydrogen is 1. The standard gas constant, \(R\), is 0.08 and the Faraday constant, \(F\), is 96485. Lastly, the given pH of the solution is 3. Now you can plug in these values: \(E = 0 - \frac{2.303*0.08*298}{1*96485}*3\).

Calculate the potential of the cell

Perform the calculation in the equation to find \(E\). It should result in a cell potential of approximately -0.177 V

Key concepts

Hydrogen Electrode

A hydrogen electrode is an essential component in electrochemistry, often used as a reference point for measuring cell potentials. It consists of a platinum electrode in a solution where hydrogen gas is bubbled over it. This setup allows the electrode potential to be measured when connected to another electrode.
In a hydrogen electrode, hydrogen gas at a pressure of 1 atm is bubbled through an aqueous acid solution. At the electrode surface, the reaction occurring can be described as:

• Hydrogen ions in the solution gain electrons to form hydrogen gas: \[ \text{2H}^+ + 2e^- \rightarrow \text{H}_2\]

This redox reaction helps establish a potential difference that can be measured. The standard potential of a hydrogen electrode is defined to be 0 V at all temperatures, making it a perfect benchmark. Therefore, the hydrogen electrode serves as the foundation for determining the electromotive force (emf) of other cells by using the Nernst equation to adjust for non-standard conditions like pH and temperature differences.

Cell Potential

The cell potential, also called electromotive force (emf), is the measure of the voltage or electric potential difference between two electrodes in an electrochemical cell. It gives us insights into how much energy is available for chemical reactions and how efficiently a cell can generate electricity.
"The cell potential is influenced by several factors such as:

• Concentration of ions in the solution.
• Temperature of the system.
• Pressure of gases involved, especially in a hydrogen electrode setup.

To calculate the cell potential under non-standard conditions, the Nernst equation is used. This equation relates the concentration of ion species involved to the electrode potential. For example, in the case of a hydrogen electrode with a pH of 3, the Nernst equation helps adjust the standard electrode potential to reflect the acidity. By substituting the actual conditions into the equation, you can calculate the effective cell potential accurately, telling us how the cell would behave in reality."

Electrochemistry

Electrochemistry is the branch of chemistry that deals with the interplay between electrical energy and chemical reactions. This field primarily covers concepts related to electron transfer, the operation of batteries, and electrolysis. One core aspect is the study of redox reactions, where reduction and oxidation occur simultaneously.
In electrochemistry, understanding how ions interact with electrodes is crucial. This includes:

• The way electrons are transferred from one species to another.
• The role of electrolytes in conducting electricity within the cell.
• How potential differences arise and how they can be utilized.

One practical application of electrochemistry is in galvanic and electrolytic cells. These cells convert chemical energy into electrical energy and vice versa. The hydrogen electrode demonstrates electrochemical principles by showing how hydrogen ions can gain electrons, making it a classic example studied within this field to better grasp electron flow and potential energy changes across electrochemical cells."