The key step in the derivation of this statement is to realize that the forward and reverse partial current densities are equal in the relevant case and, therefore, that the term proportional to the logarithm of their ratio vanishes.  
The key step in the derivation of this statement is to realize that the forward and reverse partial current densities are equal in the relevant case and, therefore, that the term proportional to the logarithm of their ratio vanishes.  Its formulation leads to the idea of a concentration cell, since it indicates one can create both sides of a battery from the same materials, provided different concentrations are used in each side.  Probably most useful in determining unknown concentrations from a measured voltage, it states that the standard reference potential of an electrochemical cell is equal to the kinetic temperature divided by the total charge times the logarithm of the reaction quotient.  FTP, name this equation of electrochemistry, which is named for a German scientist who won the Nobel Prize for Chemistry in 1920.
The key step in the derivation of this statement is to realize that the forward and reverse partial current densities are equal in the relevant case and, therefore, that the term proportional to the logarithm of their ratio vanishes.  
Nernst equation