Separation of Overlapping Protonation Constants for a Polyprotic Acid

SEPARATION OF OVERLAPPING PROTONATION CONSTANTS FOR A POLYPROTIC ACID 

In the case of a polyprotic acid for which the individual ionizations are well separated (ideally, by at least 3 log units), values for the individual constants can be calculated from data points in the appropriate regions of the titration curve. If the individual ionizations overlap, the Bjerrum fi (n-bar) method may be used. This mathematical approach was introduced by Bjerrum for the calculation of stability constants of metal-ligand complexes, but it can also be applied to the determination of proton-ligand equilibrium constants. 

The equilibrium constants to be determined in this example are protonation constants, introduced in Chapter 20. The protonation constant of a base L is the reciprocal of the acid dissociation constant Kg for the corresponding conjugate acid HL. For a polyprotic acid, the general expression for the protonation constant is given by equation 22-5. 

Protonation constants lend themselves much more readily to the systematic treatment of equilibria than do dissociation constants. Thus, for example, the 

If two equilibria overlap, the constants can be obtained from the slope and 

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