For compounds that have multiple ionizable groups, like phosphoric the distribution of species is initially guessed (by say the H-H equation). These various concentration values are then used to calculate the equilibrium constants. These values are then compared to the true equilibrium constants and the concentrations are adjusted slightly to give less error in the calculated equilibrium constants. This cycle of adjustment and calculation is repeated until the calculated Ka's are very close to the known values. This is the, so-called, "numerical method" or "successive approximation" approach often used in computing. Another way is a solution method based on the solution of simultaneous equations. For our purposes, however, when we use the H-H equation we will assume that only one pKa is important (the one nearest the pH in question).

Slide 19 tells us that the width of a pH profile that has a "bell" shape is related to the two pKa's that determine that shape. If the shape has a width at a point half way up the curve that is less than a few pH units, then the difference between the two pKa's will be quiet a bit less that this width. So, for example, if the width of the pH profile were 2.0, the difference in the pKa's would only be about 1.25. So if the peak of the curve were 6.7, the two pKa's that determine the shape of the curve would be 6.075 (6.7-1.25/2) and 7.325 (6.7+1.25/2) respectively.