When no electrons are exchanged (z = 0), the equilibrium between , , , and  only depends on  and is not affected by the electrode potential. In this case, the reaction is a classical acid-base reaction involving only  protonation/deprotonation of dissolved species. The boundary line will be a vertical line at a particular value of pH. The reaction equation may be written:
and the energy balance is written as , where  is the equilibrium constant: 
Thus:
or, in base-10 logarithms,
which may be solved for the particular value of pH.
For example consider the iron and water system, and the equilibrium line between the ferric ion Fe ion and hematite FeO. The reaction equation is:
which has . The pH of the vertical line on the Pourbaix diagram can then be calculated:
Because the activities (or the concentrations) of the solid phases and water are equal to unity:O] = [HO] = 1, the pH only depends on the concentration in dissolved :
At STP, for [Fe] = 10, this yields pH = 1.76.