Polyprotic acids and bases

The treatment of diprotic acids and bases can be extended to polyprotic systems. By way of review, let s write the pertinent equilibria for a triprotic system. 

Solution 0.10M H,His2+ Treating H His24 as a monoprotic acid, we write 

We have reduced acid-base problems to just three types. When you encounter an acid or base, decide whether you are dealing with an acidic, basic, or intermediate form. Then do the appropriate arithmetic to answer the question at hand. 

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Polyprotic acids and bases are compounds that can donate or accept more than one proton. For example, oxalic acid is diprotic and phosphate is tribasic ... 

For polyprotic acids and bases, several Ka values are given. Pyridoxal phosphate is given in its fully protonated form as follows 3... 

The principles developed for titrations of monoprotic acids and bases are readily extended to titrations of polyprotic acids and bases. We will examine two cases. 

For the single, monoprotic acids and bases in the above example, the distribution and logarithmic concentration diagrams are rather simple, yet they clearly show the relative and absolute concentrations respectively of the various species present. Such diagrams become all the more useful when we consider more complicated systems, such as polyprotic acids and bases, where it otherwise becomes increasingly difficult to envision what happens as a function of pH. We will do so in exercises 4.5 and 4.6. 

The approaches we have discussed so far to determine the precise location of the equivalence point use more than just one point, and are therefore in principle less prone to experimental error. The Schwartz and Gran plots rely on a linearization of the titration curve unfortunately, for samples that contain more than one monoprotic acid or base, linearization is no longer possible, nor is it (in general) for polyprotic acids and bases. And as for the alternative, we have seen that taking the derivative is easily overwhelmed by experimental noise. Is there no more robust yet general way to determine the equivalence volume with better precision ... 

Fortunately, there is such a method, which is both simple and generally applicable, even to mixtures of polyprotic acids and bases. It is based on the fact that we have available a closed-form mathematical expression for the progress of the titration. We can simply compare the experimental data with an appropriate theoretical curve in which the unknown parameters (the sample concentration, and perhaps also the dissociation constant) are treated as variables. By trial and error we can then find values for those variables that will minimize the sum of the squares of the differences between the theoretical and the experimental curve. In other words, we use a least-squares criterion to fit a theoretical curve to the experimental data, using the entire data set. Here we will demonstrate this method for the same system that we have used so far the titration of a single monoprotic acid with a single, strong monoprotic base. 

So far we have only considered monoprotic acids and bases. Fortunately, the corresponding relations for diprotic and polyprotic acids and bases are quite similar. The relations for diprotic acids and bases will be given here, while those for their polyprotic counterparts (with three or more dissociable protons) can be found in section 4.9. 

In order to extend the discussion to polyprotic acids and bases, we first consider a triprotic acid such as orthophosphoric acid,... 

This principle applies equally well to polyprotic acids and bases. In these cases, the concentration terms in the PBE are multiplied by the number of protons consumed or released in the formation of the species in question from the starting material. 

Table 9-2 lists pA a for common buffers. Some buffers have more than one acidic proton, so more than one pA is listed. We consider polyprotic acids and bases in Chapter 11. 

Borkovec, M., and G. J. M. Koper. 1994b. Ising models of polyprotic acids and bases. The Journal of Physical Chemistry 98, no. 23 6038-6045. doi 10.1021/jl00074a034. 

A Write stepwise equations for protonation or deprotonation of each of these polyprotic acids and bases in water, (a) C03 (b) H3ASO4 (c) NH2CH2C00 (glycinate ion, a diprotic base). 

Calculations involving the ionization of polyprotic acids and bases present no great difficulties, provided that one makes a simplifying assumption, Because the second ionization constant is usually much less than the first, we can assume that the concentration of A , which is produced in the second ionization, is much less than the concentration of HA , which is produced in the first ionization. Another way of looking at it is that the first ionization accounts for most of the H+, only a little more being added by the second ionization. Calculations involving the first ionization can then be performed as if the acid were monoprotic, and the results of this calculation can then be used to find [A ]. Corresponding remarks apply to ionization of polyprotic bases. 

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