The e.m.f. of a cell corresponding to the reaction : $$ \begin{aligned} \mathrm{Zn}(s)+2 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Zn}^{2+}+& \mathrm{H}_{2}(\mathrm{~g}) \\ (0.1 \mathrm{M}) &(1 \mathrm{~atm}) \end{aligned} $$ is \(0.28 \mathrm{~V}\) at \(25^{\circ} \mathrm{C}\) and \(E_{\mathrm{Zn} / \mathrm{Zn}^{2+}}^{\circ}=0.76 \mathrm{~V}\) (i) Write half cell reactions. (ii) Calculate \(\mathrm{pH}\) of the solution at \(\mathrm{H}\) electrode.

An electrochemical cell is a device capable of generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy. Electrochemical cells are fundamental to the fields of electrochemistry and are traditionally divided into two categories: galvanic cells (or voltaic cells) and electrolytic cells.

In a galvanic cell, a spontaneous chemical reaction generates electrical energy, and this is the setup typically involved in the study of the Nernst Equation. The cell consists of two half-cells, each containing an electrode (a conductor like a metal) and an electrolyte (a substance that contains ions that can move). One half-cell undergoes oxidation, the other reduction.

The key relevance of an electrochemical cell in our exercise, lays in its ability to establish an electrical circuit that allows for the movement of ions and free electrons. For the given reaction involving zinc and hydrogen ions, zinc acts as the anode where oxidation takes place and the hydrogen ions are reduced at the cathode, forming hydrogen gas. The flow of electrons from the anode to the cathode through an external circuit is what generates electric current and thereby a measureable potential difference, or electromotive force (emf).

In chemistry, the pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. pH calculation is fundamental in the study of electrochemical reactions, particularly in determining the concentration of hydrogen ions, \( [\text{H}^+] \) in a solution. The pH scale typically ranges from 0 to 14, with 7 being neutral. Values less than 7 indicate acidity, while values greater than 7 indicate basicity.

The relationship between pH and hydrogen ion concentration is given by the formula:\[ pH = -\log([\text{H}^+]) \]In the context of our exercise, the pH calculation is utilized in conjunction with the Nernst Equation to deduce the acidity in the environment of the hydrogen electrode. The Nernst Equation ties in the emf of the electrochemical cell to the concentration of the reacting species, making pH calculations an integral step in comprehensively analyzing cell reactions.

It is noteworthy that accuracy is paramount when utilizing logarithmic calculations. As noted in the given solution, an error in calculating the pH, such as obtaining a negative value, suggests a miscalculation, since pH cannot be negative when dealing with concentrations of real substances. Ensuring the correct interpretation of logarithmic values is essential in providing valid results.

The standard electrode potential, denoted as \( E^\circ \), is an intrinsic chemical property that represents the tendency of a chemical species to be reduced and is measured under standard conditions: a 1 molar concentration for each aqueous species involved, a partial pressure of 1 atmosphere for any gases in the reaction, and a temperature of 25°C.

Comparing Electrode Potentials

By comparing the standard electrode potentials of two half-reactions, one can predict the direction of electron flow when these half-cells are connected. For instance, in our exercise, the standard electrode potential for the \( \text{Zn}/\text{Zn}^{2+} \) couple is 0.76 V. This indicates the ease at which zinc metal can lose electrons compared to the hydrogen ions gaining electrons.

Impact on Cell Potential

The standard electrode potential is critical in determining the cell potential, which is the net potential difference between electrodes when no current is flowing. In the given problem, this value helps to establish the foundational electromotive force before any concentration or pressure variations are considered using the Nernst Equation.

Incorporating the standard electrode potential into the Nernst Equation is essential for calculating the actual emf under non-standard conditions, and the deviation from the standard electrode potential is what allows us to explore the effects of concentration (such as pH) on the electrochemical cell's behavior.