**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 pK_{a}'s of
2.15, 7.2, and 12.15 Because the pK_{a} 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 [*H*_{3}*PO*_{4}]
= [* H*_{2}*PO*_{4}^{-}]. 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, p*H*=p*K _{a}*1.
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 p

The equivalence points can also be identified in the fraction plot. At
the first equivalence point , [*H*_{3}*PO*_{4}] approaches zero.
This occurs when [*H*_{2}*PO*_{4}^{-}] is a maximum. One
can see this point in the relative concentration plot. It occurs at a p*H* 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 p*H* of

Similarly, the second equivalence point, laying halfway between the
points where p*H*=p*K _{a}*2 and p

To summarize, without even performing the titration, or solving the
fifth power polynomial equation that governs the proton concentration, we would predict
the following p*H* 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 p*H*. In fact, the third equivalence is obscured by
competitive ionization of water. This is the same effect that occurs for monoprotic acid
with p*K _{a}*>10.

*Tyrosine*

Tyrosine is a triprotic, dibasic amino acid with p*K _{a}*
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 p

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 p*H* around the second equivalence point. Since the
solution is effectively buffered by* H*_{2}*Tyr*, *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 p*H*
with added titrant. Notice, however, that the major point p*H*'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 p*Ka* 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 p*Ka* 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 p*H* 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?

This page was created by Professor Stephen Bialkowski, Utah State University

Last Updated Tuesday, August 03, 2004