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The Nernst equation is a fundamental tool in electrochemistry that allows you to calculate the electrode potential of a cell. It relates the concentration (or activity) of ions in the solution to the potential across the electrode. For a monovalent cation like lithium ion \[E = E^0 + \frac{RT}{F} \ln \left( a_{\mathrm{Li}^+} + K_{\mathrm{Li}^+, \mathrm{H}^+}^{\mathrm{Pot}} \cdot a_{\mathrm{H}^+} \right)\]

• \(E^0\): Standard electrode potential.
• \(R\): Universal gas constant, 8.314 J/(mol路K).
• \(T\): Temperature in Kelvin.
• \(F\): Faraday's constant, 96485 C/mol.
• \(a_{\mathrm{Li}^+}\): Activity of lithium ions in solution.
• \(a_{\mathrm{H}^+}\): Activity of hydrogen ions, related to pH.

The Nernst equation highlights how even small changes in ion concentrations can substantially alter the electrode potential, which is vital for understanding how sensors and electrodes function in various chemical environments.

pH is a measure of the acidity or basicity of a solution; it directly influences the activity of hydrogen ions \((a_{\mathrm{H}^+})\) in the Nernst equation. When the pH changes, it affects the ion activity and thus, the electrode potential. The formula \(a_{\mathrm{H}^+} = 10^{-\text{pH}}\) shows us the relationship between pH and hydrogen ion activity.
In the context of ion-selective electrodes, a shift in pH can change the potential reading significantly, especially if the electrode has some sensitivity to hydrogen ions. As seen in the problem, decreasing the pH from 7.2 to 1.1 markedly increases the hydrogen ion activity, which affects the measured potential. Thus, pH control or compensation may be necessary for accurate measurements in analytical chemistry.

The selectivity coefficient \((K_{\mathrm{Li}^+, \mathrm{H}^+}^{\mathrm{Pot}})\) is a parameter that quantifies how much more an ion-selective electrode responds to its primary ion over interfering ions, such as hydrogen ions. For the lithium ion (\(Li^+\)) electrode, a low selectivity coefficient means that it has a high preference for lithium ions and minimal interference from hydrogen ions.
This is crucial in contexts where the solution includes different ions, as it affects the accuracy of measurements. A lower selectivity coefficient indicates that the electrode is more selective to \(Li^+\) and less affected by the presence of \(H^+\). In our exercise, the selectivity coefficient of \(4 \times 10^{-4}\) illustrates some degree of interference by hydrogen ions, influencing how the potential changes as pH varies.

Electrode potential calculation involves substituting known values into the Nernst equation to determine the overall potential of the electrode under specified conditions. For the problem at hand, the potential was calculated for a lithium-ion electrode when the pH was altered.
This process starts by determining the activities of the ions involved, utilizing both given concentrations and mathematical expressions for the activities, such as \(a_{\mathrm{H}^+} = 10^{-\text{pH}}\). Then, these activities and constants (\(R, T, F\)) are plugged into the Nernst equation to solve for the new potential \(E\).
The step-by-step substitution of these values allowed the calculation to yield a potential of approximately \(-0.397 \mathrm{~V}\), illustrating the impact of changing pH on electrode readings.