When a hydrogen electrode and a normal calomel electrode are...

When a hydrogen electrode and a normal calomel electrode are immersed in a solution at $25^{\circ} \mathrm{C},$ a potential of 0.664 $\mathrm{V}$ is obtained. Calculate $(a)$ the $\mathrm{pH}$ and $(b)$ the hydrogen ion activity.

Key Concepts

Electrochemical Cells and Cell Potentials

This concept involves measuring the potential difference between two electrodes immersed in solutions. The cell potential is determined by the difference in the individual electrode potentials, and it serves as a driving force for the electrochemical reaction. An understanding of these potentials allows one to deduce properties of the solution, such as acidity or ion activity.

Standard Electrode Potentials

Standard electrode potentials are reference values measured under standard conditions (typically at 1 M concentration and 25°C) and are used to quantify the tendency of an electrode to gain or lose electrons. They provide a baseline for comparing different electrode reactions and are essential in determining cell potentials when one electrode is a standard reference, such as the standard hydrogen electrode (SHE) or a calomel electrode.

The Nernst Equation

The Nernst equation links the electrode potential to the concentrations (or more precisely, the activities) of the redox-active species involved in the half-cell reaction. It illustrates how deviations from standard conditions affect potential, and is indispensable for calculating parameters like hydrogen ion activity or pH in an electrochemical cell.

Hydrogen Electrode (Standard Hydrogen Electrode - SHE)

The hydrogen electrode, often taken as the standard hydrogen electrode, is a reference electrode with a defined potential of zero under standard conditions. It involves the equilibrium between hydrogen gas and hydrogen ions in solution, with its potential being directly influenced by the hydrogen ion activity, making it a key tool in determining pH in electrochemical measurements.

pH and Hydrogen Ion Activity

pH is defined as the negative logarithm of the hydrogen ion activity in a solution, which reflects the effective concentration of hydrogen ions involved in chemical reactions. Understanding the relationship between pH and hydrogen ion activity is crucial for interpreting electrochemical measurements and for calculating the acidity of the solution using the Nernst equation.

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