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 Fe3+ ion and hematite Fe2O3. The reaction equation is: 2 Fe^{3+}(aq) + 3 H_2 O (l) <=> Fe_2 O_3 (s) + 6 H^+ (aq) 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: [Fe2O3] = [H2O] = 1, the pH only depends on the concentration in dissolved : At STP, for [Fe3+] = 10−6, this yields pH = 1.76. Horizontal boundary line When H+ and OH− ions are not involved in the reaction, the boundary line is horizontal and independent of pH. The reaction equation is thus written: As, the standard Gibbs free energy : Using the definition of the electrode potential ∆G = -zFE, where F is the Faraday constant, this may be rewritten as a Nernst equation: or, using base-10 logarithms: For the equilibrium /, taken as example here, considering the boundary line between Fe2+ and Fe3+, the half-reaction equation is: Fe^3+ (aq) + e^- <=> Fe^2+ (aq) Since H+ ions are not involved in this redox reaction, it is independent of pH. Eo = 0.771 V with only one electron involved in the redox reaction. The potential Eh is a function of temperature via the thermal voltage and directly depends on the ratio of the concentrations of the and ions: For both ionic species at the same concentration (e.g., ) at STP, log 1 = 0, so, , and the boundary will be a horizontal line at Eh = 0.771 volts. The potential will vary with temperature. Sloped boundary line In this case, both electrons and H+ ions are involved and the electrode potential is a function of pH. The reaction equation may be written: Using the expressions