Systematic Treatment of the Electrochemical Potential

Recall how the the internal degrees of freedom were extended to include work terms associated with the transfer of charged particles from one electrostatic potential to another:

$$\input{equations/27-4A}$$ (34-8)

(Note: $dn_i$ represents the change in the number of moles of species $i$ if $\mu_i$ is the chemical potential of a mole of species $i$. This is done so that the Faraday constant ${\ensuremath{\cal F}}$ appears in the equation from the start-the Faraday constant is the charge on a mole of electrons.)

Equation 34-8 can be rewritten as

$$\input{equations/27-4B}$$ (34-9)

where

$$\input{equations/27-5A}$$ (34-10)

$\eta_i$ is called the ``electrochemical potential''.

The conditions for equilibrium are analogous to all other reactions:

$$\input{equations/27-5B}$$ (34-11)

and when, in addition, the system is closed ( $\sum dN_i = 0$)

$$\input{equations/27-5C}$$ (34-12)