Standard Electrodes: Pressure & Half Cell Potential Impact

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Maintaining a pressure of 1 atmosphere in standard electrodes, particularly in standard hydrogen electrodes, is crucial because the potential of a half-cell is indeed influenced by pressure. The relationship between gas pressure and concentration is governed by Henry's law, which states that the concentration of a dissolved gas is proportional to its partial pressure above the solution. This means that as pressure increases, the concentration of dissolved hydrogen also increases, affecting the electrode potential. Using pressure as a standard state simplifies calculations and aligns with the convention of defining standard conditions, just as a 1M concentration is used for ions. Therefore, standardizing at 1 atm ensures consistency in measurements and comparisons of electrode potentials across different systems.
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In standard electrodes, why it is necessary to maintain the pressure as 1 atmosphere, is the potential of an half cell depends on pressure too? If yes then how the potential of an half cell depends upon pressure?

Say for example, i know that in standard hydrogen electrodes we maintain the concentration and temperature as 1M and temperature 25°C since the potential depends upon temperature and concentration of the electrolyte.but why should we maintain the pressure as and1 atmosphere? If the potential depends upon pressure, how come they are related i didn't get the logic!
 
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Note that the concentration of the dissolved gaseous hydrogen is directly proportional to the pressure of the gas over the solution (even heard about Henry's law?). But dealing with the concentration is inconvenient, it is easier to express the gas presence using its pressure. And just like we assume 1M solution is the standard state for an ion, we assume 1 atm is a standard state for the gas.
 
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