Triprotic Acid Titration with Strong Base

Considered herein is the pH or titration curve that would be obtained when titrating a triprotic acid with a base. Three examples are given; phosphoric acid, and the two amino acids, aspartic acid and tyrosine. It is assumed that a strong base titrant, e.g., NaOH, is used.

The systematic approach to solving complex chemical equilibrium problems results in two main results that are useful here.

First is the relative fractions, a , for the various forms of the acids as a function of pH. For the triprotic acid, the a are

Second, the titration curves are calculated using a working equation for a triprotic acid being titrated with a strong base. The appropriate equation is

This equation is derived on a different page. Though the equation does not have simple roots, the roots, e.g., proton concentration, can be determined with a spreadsheet, or other computer program, using iteration methods.

Phosphoric Acid

Phosphoric acid is a good example of a titration where the first two equivalence points, corresponding to base reaction with the first and second protons, respectively, are clearly visible. By clearly visible, we mean that there is a large change in pH at the equivalence point.

The acid dissociation constants for phosphoric acid are quite different from each other with pKa's of 2.15, 7.2, and 12.15 Because the pKa are so different, the protons are reacted at different pH's. This is illustrated in the plot of the relative fraction as a function of pH shown below.

The pH at points where the relative fraction of two species are equal, e.g., where two relative concentration lines cross, have a simple relationship to the acid equilibration constants. For example, the first crossing occurs for [H3PO4] = [ H2PO4-]. The relationship to pH is most easily found by recognizing that all principle species are given in the first proton ionization equation

Taking the log of this equation results in the buffer equation

At equal acid and conjugate base concentrations, pH=pKa1. There are three such points for phosphoric acid. They are labeled on the plot. These points are important in the prediction of the titration curves. They correspond to points where half of an equivalent of proton has been consumed by addition of strong base. Thus, the point where pH=pKa1 is halfway to the first equivalence point. Where pH=pKa2 is halfway between the first and second equivalence points, etc. The solution has maximum buffer capacity at these points. In other words, there is maximum resistance to changes in pH.

The equivalence points can also be identified in the fraction plot. At the first equivalence point , [H3PO4] approaches zero. This occurs when [H2PO4-] is a maximum. One can see this point in the relative concentration plot. It occurs at a pH that is halfway between the two points with maximum buffer capacity. In fact, we can expect that the first equivalence point will occur at a pH of

Similarly, the second equivalence point, laying halfway between the points where pH=pKa2 and pH=pKa3 is

To summarize, without even performing the titration, or solving the fifth power polynomial equation that governs the proton concentration, we would predict the following pH at the halfway and equivalence points

The titration curve, found from iterative solutions to the governing equation, is illustrated below. The titration was for 0.1 F solutions of both acid and strong base. The solid line is the titration curve. The special points discussed above are given in pink. The equations for these points are also given. In fact, the halfway and equivalence point predictions work.

Notice, however, that only two of the three single-proton equivalence points exhibit large changes in pH. In fact, the third equivalence is obscured by competitive ionization of water. This is the same effect that occurs for monoprotic acid with pKa>10.

Tyrosine

Tyrosine is a triprotic, dibasic amino acid with pKa of 2.17, 9.19, and 10.47 The first proton is removed from the carboxylic acid, the second from the ammonium group. The third proton, with a pKa of 10.47, is the phenolic proton from the amino acid side chain. This case is of interest because the acid is dibasic. Moreover, the basic pKa are relatively similar, differing by only about 1 unit.

The relative fraction plot is shown here. The plot is labeled with the pH at the points where acid and conjugate base concentrations are equal (where the lines cross). It is different from that of phosphoric acid in that the relative concentration of one base species, the monoprotonated tyrosinate, HTyr, does not reach unity.

Of more importance to the prediction of the shape of the titration curve is the fact that there are several species in solution at the pH where the second equivalence point should be reached. The second equivalence point occurs when [HTyr] is a maximum.

The main effect of there being three species in solution at this point is to buffer the pH around the second equivalence point. Since the solution is effectively buffered by H2Tyr, HTyr, and Tyr at the second equivalence point, we might not expect to observe a sharp change. In fact, this prediction is borne out in titration curve shown below.

Only the first equivalence point shows a large change in pH with added titrant. Notice, however, that the major point pH's are those predicted for the halfway and equivalence points. Since there is only one clear change in pH with respect to titrant volume, Titrimetric tyrosine analysis should assume one equivalent (proton) per mole and use an indicator that changes at about pH 7.

Aspartic Acid

Aspartic acid is another triprotic amino acid. In this case the pKa are; 1.990, 3.900, and 10.002 The first two are carboxylic acid protons; the last is the ammonium proton. In this case we might expect that the first two equivalence point would be obscured by the fact that the two acidic pKa are relatively close. The relative fraction and titration curve plots are shown below. It is left up to the student to justify why the titration curve looks the way it does based on analysis of the relative fraction plot. Some questions to ask yourself are;

• What are the species in the relative fraction plot?

• What are the pH at the halfway and equivalence points?

• How will the fact that the 2nd species (olive colored) never attain a value of 1 affect the titration?

One thing to notice is that the first equivalence point is "lost" and a large change in pH only occurs at the second equivalence point. Some important questions to ask are;

• Why isn't the 3rd equivalence point observed in the titration curve?

• How would you design a Titrimetric analysis for aspartic acid?

• How many equivalents (protons) per mole are apparent?

• What indicator would you use?

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