Polyprotic acid, titration curve

Figure 2.4 Titration curve for a polyprotic acid titrated with NaOH.

Figure 15-4 shows titration curves for three other polyprotic acids. These curves illustrate that a well-defined end point corresponding to the first equivalence point is observed only when the degree of dissociation of the two acids is sufficiently different. The ratio of to K. 2 for oxalic acid (curve B) is approximately 1000. The curve for this titration shows an inflection comesponding to the first equivalence point. The magnitude of the pH change is too small to permit precise location of equivalence with an indicator however, the second end point provides a means for the accurate determination of oxalic acid. 

This approach can be used to sketch titration curves for other acid-base titrations including those involving polyprotic weak acids and bases or mixtures of weak acids and bases (Figure 9.8). Figure 9.8a, for example, shows the titration curve when titrating a diprotic weak acid, H2A, with a strong base. Since the analyte is... 

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. 

Titrations curves for polyprotic acids have an inflection point for each hydrogen in the formula if the dissociation constant (Ka) for each hydrogen is very different from the others and if any dissociation constant is not too small. The titration curves of the polyprotic acids H2S04 and H3P04 are shown in Figures 5.6 and 5.7. Sulfuric acid has essentially one inflection point (like hydrochloric acid—compare with Figure 5.1(a)), while phosphoric acid has two apparent inflection points. Both hydrogens on the... 

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

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. 

We can calculate pH titration curves using the principles of aqueous solution equilibria. To understand why titration curves have certain characteristic shapes, let s calculate these curves for four important types of titration (1) strong acid-strong base, (2) weak acid-strong base, (3) weak base-strong acid, and (4) polyprotic acid-strong base. For convenience, we ll express amounts of solute in millimoles (mmol) and solution volumes in milliliters (mL). Molar concentration can thus be expressed in mmol/mL, a unit that is equivalent to mol/L ... 

Titration curves for polyprotic acids show multiple buffering regions and equivalence points, which indicate the stepwise manner in which polyprotic acids are deprotonated. 

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. 

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... 

Be able to interpret titration curves of weak mono- and polyprotic acids. 

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... 

There are two ways to represent the titration curve for a protein or other polyprotic weak acid. The usual thermodynamic way used in Chapter 2 is to represent the average number of hydrogen ions bound with... 

In this chapter you ll learn how to calculate species distributions of polyprotic weak acid species, how to apply Gran s method for the estimation of end-points in titrations and a general method for the calculation of titration curves. 

Equation 20-8 permits the calculation of all points on a titration curve by means of a single equation. As written, it handles strong acids, weak acids or mixtures, and it is readily expanded to handle mixtures of polyprotic acids. 

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. 

There are a number of computer programs available for the determination of stability constants from pH titration data. The most general of these perform a least-squares fit of the data to a calculated titration curve. The programs are able to handle protonated complexes, polynuclear systems, etc. In this example least-squares curve fitting is applied to a somewhat simpler case, a polyprotic acid in which the equilibria overlap extensively. The method is that used in the... 

Compormds with two or more acidic or basic functional groups will yield multiple endpoints in a titration, provided the acidic or basic groups differ sufficiently in strength. Computational techniques permit the derivation of reasonably accurate theoretical titration curves for polyprotic acids or bases, provided the ratio K1IK2 is above 103. Ki and K2 are dissociation constants. The titration curve of a dibasic weak acid with NaOH resembles that shown in Fig. 6. 

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. 

Titrations of polyprotic acids will have more than one equivalence point and more than one half equivalence point. For the MCAT, assume that the first proton completely dissociates before the second proton begins to dissociate. (This assumption is only acceptable if the second proton is a much weaker add than the first, which is usually the case.) Thus we have a titration curve like the one shown below. 

Use your Weh browser to connect to http //chemistry.brookscole.com/skoogfac/. From the Chapter Resources menu, choose Web Works. Locate the Chapter 13 section, and click on the link to the Virtual Titrator. Click on the indicated frame to invoke the Virtual Titrator Java applet and display two windows the Menu Panel and the Virtual Titrator main window. To begin, click on Acids on the main window menu bar, and select the diprotic acid o-phthalic acid. Examine the titration curve that results. Then click on Graphs/Alpha Plot vs. pH and observe the result. Click on Graphs/Alpha Plot vs. mL base. Repeat the process for several monoprotic and polyprotic acids, and note the results. 

Compounds with two or more acid functional groups yield multiple end points in a titration provided that the functional groups differ sufficiently in strength as acids. The computational techniques described in Chapter 14 permit construction of reasonably accurate theoretical titration curves for polyprotic acids if the ratio is somewhat greater than 10-. If this ratio is smaller, the error becomes excessive, particularly in the region of the first equivalence point, and a more rigorous treatment of the equilibrium relationships is required. 

Figure 1 5-4 Curves for the titration of polyprotic acids. A 0.1000 M NaOH solution is used to titrate 25.00 mL of 0.1000 M H3PO4 (curve A), 0.1000 M oxalic acid (curve B), and 0.1000 M H2SO4 (curve Q.

Experimental neutralization curves closely approximate the theoretical curves described in Chapters 14 and 15. Usually, the experimental curves are somewhat displaced from the theoretical curves along the pH axis because concentrations rather than activities are used in their derivation. This displacement has little effect on determining end points, and so potentiometric neutralization titrations are quite useful for analyzing mixtures of acids or polyprotic acids. The same is true of bases. 

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-... 

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. 

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