Alpha Fractions and Diagrams

Because of the varied spacings of pK values, the polyprotic acid-bases do not have uniquely shaped a diagrams as do monoprotic 

The reciprocal form is used to give us simple ratios. These ratios are easily found in terms of H from the K expressions, set (5-1)  

Substituting these into the o expression above gives 

The remaining a s can be obtained in the same way, or more simply from the ao already found  

These rather complicated cubic H curves turn into symmetrical plots vs. pH. 

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