The standard electrode potentials E^∘ in the earlier literature are based on a standard state pr

step 1 Calculate the standard free energy change for the given reaction. The half reactions and the cor

The standard electrode potentials E^∘ in the earlier...

The standard electrode potentials $E^{\circ}$ in the earlier literature are based on a standard state pressure of 1 atm. Show that when the bar is used as the standard state pressure, standard electrode potentials $E^{\circ}(\mathrm{atm})$ need to be corrected to $E^{\circ}(\mathrm{bar})$ using \[ E^{\circ}(\mathrm{bar})=E^{\circ}(\mathrm{atm})+(0.000169 \mathrm{V}) \Delta \nu \] where $\Delta \nu$ is the increase in the number of gaseous molecules as the cell reaction (including hydrogen) proceeds as written.

The standard electrode potentials $E^{\circ}$ in the earlier literature are based on a standard state pressure of 1 atm. Show that when the bar is used as the standard state pressure, standard electrode potentials $E^{\circ}(\mathrm{atm})$ need to be corrected to $E^{\circ}(\mathrm{bar})$ using
\[
E^{\circ}(\mathrm{bar})=E^{\circ}(\mathrm{atm})+(0.000169 \mathrm{V}) \Delta \nu
\]
where $\Delta \nu$ is the increase in the number of gaseous molecules as the cell reaction (including hydrogen) proceeds as written.

Key Concepts

Stoichiometry of Gaseous Molecules

In the context of electrode potential corrections, the reaction stoichiometry, specifically the change in the number of moles of gas (??), is crucial. An increase in gaseous molecules during the reaction results in an additional pressure-volume work term, which in turn necessitates the adjustment of the standard electrode potential when shifting from the traditional 1 atm to 1 bar pressure condition.

Pressure Corrections in Electrochemistry

When the standard pressure is altered from 1 atm to 1 bar, a correction must be applied to the standard electrode potentials due to the slight difference in the thermodynamic scale. This correction accounts for the change in the free energy of the system as pressure-dependent terms, particularly for gases, are modified according to the ideal gas law.

Gibbs Free Energy and Its Relation to Electrode Potential

The relationship between the Gibbs free energy change and the electrode potential is fundamental in electrochemistry, as it connects the thermodynamic favorability of a reaction with its electrical work output. Changes in pressure alter the Gibbs energy of gaseous reactants or products, thereby affecting the measured electrode potentials.

Standard State

The standard state defines the conditions (such as temperature, pressure, and concentration) under which thermodynamic measurements, including electrode potentials, are made. Traditionally, a pressure of 1 atm was used, but the use of 1 bar as the standard state requires minor corrections, particularly in reactions involving gases.

Standard Electrode Potential

This is the measure of the intrinsic tendency of a chemical species to acquire electrons and thereby be reduced under standard conditions. It is determined under defined reference conditions and serves as a benchmark for comparing the reactivity of different redox couples in electrochemical cells.

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