Polybasic acid titration curve

Define monoprotic acid, polyprotic acid, monobasic base, polybasic base, titration curve, and inflection point. 

The relative precision is inversely related to the slope of the titration curve at the end point, and important conclusions from this relation are for a strong acid-strong base titration the relative precision is approximately VKJC , for a weak acid-strong base titration the relative precision is approximately JkJKjC, and for an intermediate end point in a polybasic acid titration the relative precision is approximately... 

Thus the pK value is equal to the pH when the ratio of free acid to salt is unity, Lethe titration is half completed. The pK value for acetic acid in the titration represented in Fig. 2 is shown by the point x on the curve (b) and corresponds to a value of about pK =4.6 whereas the limiting thermodynamic value, pK, is 4.75. The estimate of PK may obviously be made at other points in the titration curve by computing the appropriate values of the ratios [A-]/[HA]. Or this, process may be reversed, and the curve (b) obtained from the observed value of pK and these ratios. The same procedure may also be extended to polybasic acids. A titration curve of malonic acid from the work of Gane and Ingold 5 is shown in Curve I of Fig. 3. Here... 

Dibasic acids, polybasic acids, and proteins, with two or more ionizable groups, give more complex titration curves than the sinqile monobasic adds (Schulz, 1994). Consider the titration curve of a simple amino acid which has no charge in its side chain. In aqueous solution, a monoamino, monocarboxylic add is distributed between three species, namely the fully protonated acid, the zwitterion, and the fully dissociated base ... 

Let us now consider titration curves of polybasic acids which can donate more than one proton and can consequently possess more than one pK corresponding to the successive dissociation of each of the protons. A good example is afforded by phosphoric acid, H PO, for which three ionization steps and there corresponding pK are... 

Exact Equations of the Titration Curves of Mixtures of Acids, Bases, Polyacids, Polybases, etc. 

The exact equations of the titration curves of mixtures of acids, bases, polyacids, polybases, and so on are easily established by starting from the relationships expressing the equilibria, the charge, and the mass balances in solution. The equations giving the corresponding titration errors are found in the same way as earlier. They are set up from the corresponding exact titration curves expressed in fractions titrated. One titration error exists, of course, for each equivalence point. 

A titration such as that of a monobasic weak acid with a strong base or of the last step of a polybasic weak acid usually shows two inflection points, one where the slope of the curve is at a minimum and the other where it is at a maximum. The first inflection point is usually near the 50% neutralization point, but follows it for very weak acids, precedes it for moderately strong acids, and disappears for the strongest acids. The second inflection point precedes the equivalence point the difference amounts to as much as 1 ppt only for very weak adds (K < 10 for 0.1 Af solutions) or highly dilute solutions. The second inflection point disappears for highly dilute or exceedingly weak acids. Automated techniques for end-point detection normally rely on the inflection point signiflcant error therefore may be incurred under certain circumstances. 

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