The Titration of a Polyprotic Acid

A FIGURE 16.8 Titiation Curve Weak Base with Strong Acid 

A FIGURE 16.9 Titration Curve Diprotic Add with Strong Base This curve represents the titration of 25.0 mL of 0.100 M H2SO3 with 0.100 M NaOH. 

The first equivalence point in the titration curve represents the titration of the first proton while the second equivalence point represents the titration of the second proton. Notice that the volume required to reach the first equivalence point is identical to the volume required to the reach the second one because the number of moles of H2SO3 in the first step determines the number of moles of HS03 in the second step. 

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Because many biological systems use polyprotic acids and their anions to control pH, we need to be familiar with pH curves for polyprotic titrations and to be able to calculate the pH during such a titration. The titration of a polyprotic acid proceeds in the same way as that of a monoprotic acid, but there are as many stoichiometric points in the titration as there are acidic hydrogen atoms. We therefore have to keep track of the major species in solution at each stage, as described in Sections 10.16 and 10.17 and summarized in Figs. 10.20 and 10.21. 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base by using the reaction stoichiometry to recognize what stage we have reached in the titration. We then identify the principal solute species at that point and the principal proton transfer equilibrium that determines the pH. 

The titration of a polyprotic acid has a stoichiometric point corresponding to the removal of each acidic hydrogen atom. The pH of a solution of a polyprotic acid undergoing a titration is estimated by considering the primary species in solution and the proton transfer equilibrium that determines the pH. 

In the titration of a polyprotic acid, the added base reacts first with the more acidic hydrogen atoms of the neutral acid. For example, the titration of maleic acid takes place in two steps. For removal of one acidic hydrogen atom of maleic acid, p = 1.82 (. al = 1-5 X 10 ) ... 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base (see Toolbox 11.1). First, we have to consider the reaction stoichiometry to recognize what stage we have reached in the titration. Next we have to identify the principal solute species at that point and the proton transfer equilibrium that determines the pH. We then carry out the calculation appropriate for the solution, referring to the previous worked examples if necessary. In this section, we see how to describe the solution at various stages of the titration our conclusions are summarized in Tables 11.3 and 11.4. 

TOOLBOX 11.1 How to predict the pH during the titration of a polyprotic acid... 

Determine the pH at any point in the titration of a polyprotic acid with a strong base, Toolbox... 

As mentioned above, the calculations involved in obtaining the pH curve for the titration of a polyprotic acid are closely related to those for a monoprotic acid. The same principles apply, but we must be very careful in identifying which of the various equilibria is appropriate to use in a given case. The secret to success here is, as always, identifying the major species in solutio... 

FIGURE 15.17 A titration curve for the titration of a polyprotic acid (phosphoric acid) by a strong base. The curve shown is for 100.0 mL of 0.1000 M H3PO4 titrated with 0.1000 M NaOH. No clear third equivalence point is seen at 300 mL because for HP04 is not much greater than for H2O in aqueous solution. 

The titration of a polyprotic acid with sufficiently different pK s displays two equivalence points. Why ... 

Compare the alkalimetric titration of a polyprotic acid (e.g., polyaspartic acid) with that of an Al203 dispersion show in either case the effect of the presence of a metal ion (e.g., Cu2+) on the titration curve. 

From an acid-base titration curve, we can deduce the quantities and pK.d values of acidic and basic substances in a mixture. In medicinal chemistry, the pATa and lipophilicity of a candidate drug predict how easily it will cross cell membranes. We saw in Chapter 10 that from pKa and pH, we can compute the charge of a polyprotic acid. Usually, the more highly charged a drug, the harder it is to cross a cell membrane. In this chapter, we learn how to predict the shapes of titration curves and how to find end points with electrodes or indicators. 

The pH of the solution of a polyprotic acid at any point in a titration can be predicted by considering the species present at each stage. 

A titration curve is a plot of a solution s pH charted against the volume of an added acid or base. Titration curves are obtained if a pH meter is used to monitor the titration instead of an indicator. At the equivalence point, the titration curve is nearly vertical. This is the point where a rapid change in pH occurs. In addition to determining the equivalence point, the shape of titration curves may be interpreted to determine acid/base strength and the presence of a polyprotic acid. 

Titration of a polyprotic acid results in multiple equivalence points and a curve with more "bumps" as shown below for sulfurous acid and the carbonate ion. 

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 titration of amino acids with the dissociable R groups conforms to the same principles but requires three equivalents of bases. The general shape of the titration curve resembles that for the titration of a polyprotic weak acid with strong base (Figure 2.4). The pi of any amino acid can be calculated according to the following formulae ... 

This is a titration of a polyprotic weak acid with a strong base, and the titration curve for this problem should look very similar to Figure 17-12. In the titration of a weak acid by a strong base we know that at the point of half-neutralization, pH = pfCa and therefore pK should be the pH at 8.12 mL. For pK, we will use expression (17.10) since at this point in the titration we will have an aqueous solution of HOC6H4COONa, which is a salt of a polyprotic acid. The pH of the first equivalence point is given and to find the pH of the second equivalence point we must perform an ICE calculation similar to the one in Example 16-14. 

The titration curve of a polyprotic acid can be obtained by using the same approach as for monoprotic weak acids or weak bases. The mass and charge balance equations... 

In the titration of a typical polyprotic acid, the various acidic protons are titrated in succession. For example, as sodium hydroxide is used to titrate phosphoric acid, the first reaction that takes place can be represented as... 

Titrat.xls is an example of the calculation of the pKa values of a polyprotic acid from titration data, using the Solver. 

If all acidic functional groups in a molecule are absolutely identical and are physically so far apart that there are no electrostatic effects on pKa values, the titration curve of a polyprotic acid can be represented by the titration curve of a suitable monoprotic acid whose Ka value is the statistically corrected intrinsic K for the polyprotic acid. For instance, in the previous example, if there were no electrostatic effects to be considered and A and B were identical, then Ka would equal Kc - The thermodynamic con-... 

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. 

If the acid or base is polyprotic, there will be a jump in pH for each proton that is titrated. Fig. 2 shows (on the right) the titration of a solution of sodium carbonate with HCl. Both solutions have identical concentrations. The COg ion is a base, so the pH of the solution starts out quite high. As protons are added they convert COg into HCOJ and eventually to carbonic acid, H2CO3. 

When enough base has been added to react completely with the hydrogens of a monoprotic acid, the equivalence point has been reached. If a strong acid and strong base are titrated, the pH of the solution will be 7.0 at the equivalence point. However, if the acid is a weak one, the pH will be greater than 7 the neutralized solution will not be neutral in terms of pH. For a polyprotic acid, there will be an equivalence point for each titratable hydrogen in the acid these typically occur at pH values that are 4-5 units apart. 

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