looking at an equilibrium involving hydrolysis of an aqua ion. Considering the dissociation equilibrium [M(H2O)n]z+ - H+ [M(H2O)n-1(OH)](z-1)+ the activity of the hydrolysis product, omitting the water molecules, is given by The alternative is to write the equilibrium as a complexation or substitution reaction [M(H2O)n]z+ +OH− :[M(H2O)n-1(OH)](z-1)+ + H2O In which case The concentration of hydrogen and hydroxide ions are related by the self-ionization of water, Kw = {H+} {OH−} so the two equilibrium constants are related as In practice the first definition is more useful because equilibrium constants are determined from measurements of hydrogen ion concentrations. In general, charges are omitted for the sake of generality and activities have been replaced by concentrations. are cumulative hydrolysis constants. Modeling the hydrolysis reactions that occur in solution is usually based on the determination of equilibrium constants from potentiometric (pH) titration data. The process is far from straightforward for a variety of reasons. Sometimes the species in solution can be precipitated as salts and their structure confirmed by X-ray crystallography. In other cases, precipitated salts bear no relation to what is postulated to be in solution, because a particular crystalline substances may have both low solubility and very low concentration in the solutions. First hydrolysis constant The logarithm of hydrolysis constant, K1,-1, for the removal of one proton from an aqua ion [M(H2O)n]z+ - H+ [M(H2O)n-1(OH)](z-1)+ [ [M(OH)]{(z-1)+ ] = K1,-1 [Mz+] [H+] −1 shows a linear relationship with the ratio of charge to M-O distance, z/d. Ions fall into four groups. The slope of the straight line is the same for all groups, but the intercept, A, is different. {| class="wikitable" |+log K1,-1 = A + 11.0 z/d !cation||A |- |Mg2+, Ca2+, Sr2+, Ba2+ Al3+, Y3+, La3+|| |- | Li+, Na+, K+Be2+, Mn2+, Fe2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+Sc3+, Ti3+, V3+, Cr3+, Fe3+, Rh3+, Ga3+, In3+ Ce4+, Th4+, Pa4+, U4+, Np4+, Pu4+, || |- | Ag+, Tl+ Pb2+ Ti3+, Bi3+, || |- | Sn2+, Hg2+, Sn2+, Pd2+ ||ca. 12 |} The cations most resistant to hydrolysis for their size and charge are hard pre-transition metal ions or lanthanide ions. The slightly less resistant group includes the transition metal ions. The third group contains mostly soft ions ion of post-transition metals. The ions which show the strongest tendency to hydrolyze for their charge and size are Pd2+, Sn2+ and Hg2+. The standard enthalpy change for the first hydrolysis step is generally not