I am having trouble understanding the concept of the electrochemical potential $\mu$. In my textbook the electrochemical potential is defined as $\mu=\frac{\partial G}{\partial n}$. It seems to me as an arbitrary equation that I cannot understand which simply defines the partial derivative of $G$ as "electrochemical potential". I know that this is obviously false but I am searching for an intuitive explanation of the equation above. I am also interested in the uses that this quantity has other than the prediction of a concentration equilibrium. Any help is really appreciated.
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Very loosely it is the change in (free) energy of the system when you add one additional particle. – Marius Ladegård Meyer Feb 20 '23 at 12:49
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@MariusLadegårdMeyer I can understand this on my own since this is the defintion of the derivative. I cannot understand however why we defined the potential in that way – Kani Pen Feb 20 '23 at 13:58
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The term chemical "potential" is traditional, but I assume the concept is different from the electrostatic "potential" in electromagnetism. My anecdotal understanding is that $\mu$ is a coefficient, but not a potential. – HEMMI Feb 21 '23 at 01:35
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Gibbs free energy is a thermodynamic state function, whose differential can be written as $$ dG = -SdT + VdP + \mu dN, $$ hence, by definition, $\mu$ is a partial derivative of $G$ in respect to the particle number: $$ \mu=\left(\frac{\partial G}{\partial N}\right)_{T, P}. $$
See this answer regarding differentials and derivatives.
Roger V.
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