Hello Franklin,

The chemical potential is defined by the ratio between differential Gibbs energy per differential mole unit (µ = ∂G/∂n), and is defined by µ = µo + RT ln a. And the electrochemical potential is similar: µ = µo + zFø. The first equation is deduced for a chemical reaction, whereas the second equation can be applied in a electrochemical reaction.

As you can see in chemical potential, the Gibbs energy will drive the chemical (or electrochemical) reaction, once those reactions share the same thermodynamics. But you cannot compare directly both equations because the nature of reactions are different, so µ will be changed in activity (or fugacity) terms for chemical reactions, and electrochemical potential will be changed when the electrical potential changes.

If you still have issues on how chemical and electrochemical potentials work, you can take a look at Castellan's Physical Chemistry textbook (third edition), chapter 11 (for chemical potential) and chapter 17 (for electrochemical potential).

Hope it helps!

Chemical potential does not include the term of ZFE which appears only because of charge on Species.

Elecrochemical potential =chemical + ZFE

Dear Othon !:

Thak you for your answer to this discussion.

I understand that in a Thermodynamic system in equilibrium, we can define the Chemical Potential not just as: (µ = ∂G/∂n), T, P, = cte. but also as a function of the Internal Energy, Entalphy and the Helmholtz free energy, depending on what the conditions of your system are (whether you have S, V, T, or P as a constants). i.e.

- if Entropy and Volume are constant: (µ = ∂U/∂n)

- if Temperature and Pressure are constant: (µ = ∂G/∂n)

- if Entropy and Pressure are constant: (µ = ∂H/∂n)

- if Temperature and Volume are constant: (µ = ∂A/∂n) where A is the Helmholtz free Energy.

Thank you for the linear expressions for µ . btw, What does µo represent in these equations ? The standard Chemical Potential ? I notice you did n't make a difference in the notation between:

µ = µo + RT ln a and

µ = µo + zFø

I suppose a is the "activity" of the species involved in the reaction.

I like to see the definition of µ in a Thermodynamic System as you stated : " by the ratio between differential Gibbs energy per differential mole unit" . I believe this is the most popular definition it can be found in any recommendable Chemistry or Chemical Thermodynamics book.

Although I would like to address the question into another direction:

I would like to know more about Chemical Potential, but not in the context of the macroscopic view of Thermodynamical systems or chemical and/or electrochemical reactions, but in the context, from a small systems of many individual particles to individual particles, i.e. free electrons in a solid, charged particles, phonons, etc.

Best wishes :)

Uriel ,