Question

Engel and Reid's Physical Chemistry [1, p. 308] defines the electrochemical potential in terms of the charge in units of the electron charge (z), Faraday constant (F), and electrical potential (ϕ) as follows:

The electrochemical potential is a generalization of the chemical potential to include the effect of an electrical potential on a charged particle. It is the sum of the normal chemical potential μ and a term that results from the nonzero value of the electrical potential:
μ~ = μ + z F ϕ
Is the electrical potential ϕ due to electric field generated from charge separation between electrode and solution, or is it an externally applied electric field?
Isn't zFϕ electrical potential energy? How can we simply add it to chemical potential?

Answer 1

The electrochemical potential includes the chemical potential and an electrical potential energy term, combining both chemical and electrical forces affecting a charged particle. Electrical potential in the formula can arise from both internal and external electric fields and is crucial for understanding energy levels in redox reactions within electrochemical cells.

Step-by-step explanation:

The electrochemical potential represents the energy state of a charged particle in an electric field, and it takes into account both chemical and electrical forces.

The electrical potential (φ) in the formula μ~ = μ + z F φ can be due to an externally applied electric field or from the electric field generated by charge separation between the electrode and solution in an electrochemical cell.

The term zFφ represents the electrical potential energy per particle or ion of charge z. When this term is multiplied by the number of particles, it gives the electrical potential energy for the full amount of substance.

It is indeed correct that zFφ is electrical potential energy; however, the reason we can add it to the chemical potential is that both terms describe energy but in different contexts.

The chemical potential μ describes the energy associated with the concentration of particles, while zFφ describes the energy associated with their charge in the presence of an electrical potential.

By combining them, the electrochemical potential effectively describes the total energy level of ions in the system, which is key for understanding processes like redox reactions in electrochemistry.