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The screenshot of the slide I mentioned in the questionI'm undergrad student majoring in materials science and engineering. I faced this question while studying for a course named "surface engineering of materials".

This slide is a part of my study material. It's discussing about the reduction potential of coating materials. But while listing them, there's no mention of the solution the materials are dipped in.

Isn't the electrode potential dependent on ln(Kp) here? and if the reagents are changed, won't ln(Kp) and thus the electrode potential change?

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But while listing them, there's no mention of the solution the materials are dipped in.

Yes, you are correct. It depends on all the reactants and the solvent where these are. In my answer I expect that with solution you refer actually to the solvent. I will explain the dependencies of what you ask from:

  1. The table you have shown displays the standard oxidation potential $E^\Theta$ of several half-reactions .
  2. $E^\Theta$ will depend, easily said, on the standard chemical potential $\mu_i^\Theta$ of all the species participating.
  3. For a solid species $\mu_i^\Theta$ will be a function of: (1) pressure (generally $\pu{1 bar}$), (2) specified temperature $T^\Theta$, and (3) the identity of the species itself. For two different solids $i$ and $j$, in general we have $$ \mu_\pu{i}^\Theta(\pu{1 bar},T^\Theta) \neq \mu_\pu{j}^\Theta (\pu{1 bar},T^\Theta) $$ However, for all the solids in your list, these values are zero because they are elements in their most stable state, which happens to be the solid state.
  4. For species in solution you need to specify a scale. Once you select it, $\mu_i^\Theta$ will be a function of: (1) pressure (generally $\pu{1 bar}$), (2) specified temperature $T^\Theta$, (3) the identity of the species itself, and (4) the identity of the solvent. For example if you choose the molality scale, then the standard state is a hypothetical ideal $1$ molal solution of this solute $ i $ in a certain solvent, at the pressure of $\pu{1 bar}$ and a defined temperature $T^\Theta$.

For the same solvent, lets say water, then two ions have different standard chemical potentials (so $E^\Theta$ will change) $$ \mu_\ce{Na^+}^\Theta(\pu{1 bar},T^\Theta, \ce{water}) \neq \mu_\ce{Mg^2+}^\Theta (\pu{1 bar},T^\Theta, \ce{water}) $$

For different solvents, the same species will have different standard chemical potentials (so $E^\Theta$ will change) $$ \mu_\ce{Na^+}^\Theta(\pu{1 bar},T^\Theta, \ce{solvent I}) \neq \mu_\ce{Na^+}^\Theta (\pu{1 bar},T^\Theta, \ce{solvent II}) $$ This is why in the back of chemistry books, for charges species, they identify the identity of the solvent, e.g. putting between parentheses ($\ce{aq}$).

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