Titrations of Polyprotic Acids

Boiling the solution removes the CO2, raising the pH to that of HCO3-. 

Bromcresol green can be used in a manner similar to methyl red. Its transition range is pH 3.8 to 5.4, with a color change from blue through pale green to yellow (see Experiment 7). Similarly, methyl purple can be used (see Experiment 19). 

During titration up to the first equivalence point, an HA /HaA buffer region is established. At the first equivalence point, a solution of HA exists, and [H ] /Ka Ka2- Beyond this point, an A /HA buffer exists and finally at the second equivalence point, the pH is determined from the hydrolysis of P. If the salt, A , is not too strong a base, then the approximate equation given can be used to calculate [OH ]. Otherwise the quadratic equation must be used to solve Equation 7.29 (see Example 7.19). 

Henderson-Hasselbalch equation cannot be used for thej rjt buffer region because the assumption in deriving that from the Kai expression was that the amount of [ or OH from dissociation or hydrolysis of H2A or HA was not appreciable compared to their concentrations. For a fairly strong acid, then, we can write 

The equilibrium concentration of H,A is decreased from the calculated analytical concentration by an amount equal to [H ] and increased by an amount equal to [OH-]  

The acid titrations we have considered so far have involved only monoprotic acids. When a polyprotic acid is titrated, the pH calculations are similar in many ways to those for a monoprotic acid, but enough differences exist to warrant special coverage. 

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 

This reaction occurs until the H3PO4 is consumed (to reach the first equivalence point). Therefore, at the first equivalence point the solution contains the major species Na+, H2P04 , and H 0. Then as more sodium hydroxide is added, the reaction 

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 

Solutions Containing Amphoteric Anions as the Only Acid-Base Major Species 

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Titration of Polyprotic Acids Sulfuric Acid and Phosphoric Acid... 

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. 

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. 

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.

Calculating acid-base titration curves Strong acids, strong bases (Table 8.1), p. 266 Spreadsheet calculations, p. 269 Weak acids, weak bases (Table 8.2), p. 272 Spreadsheet calculations, p. 277 Indicators (key equations 8.4, 8.5), p. 270 Titration of Na2C03, p. 280 Titration of polyprotic acids (Table 8.3), p. 281 Titration of amino acids, p. 286... 

Diphenylcarbazide as adsorption indicator, 358 as colorimetric reagent, 687 Diphenylthiocarbazone see Dithizone Direct reading emission spectrometer 775 Dispensers (liquid) 84 Displacement titrations 278 borate ion with a strong acid, 278 carbonate ion with a strong acid, 278 choice of indicators for, 279, 280 Dissociation (ionisation) constant 23, 31 calculations involving, 34 D. of for a complex ion, (v) 602 for an indicator, (s) 718 of polyprotic acids, 33 values for acids and bases in water, (T) 832 true or thermodynamic, 23 Distribution coefficient 162, 195 and per cent extraction, 165 Distribution ratio 162 Dithiol 693, 695, 697 Dithizone 171, 178... 

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 ) ... 

Conjugate base of polyprotic acid titrated with strong acid... 

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 titrating a polyprotic acid or base, two usable end points are obtained if the ratio of dissociation constants is greater than 10 and if the weaker acid or base has a dissociation constant greater than IQ-. ... 

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. 

Before describing precipitation titrations, we shall consider the effects of competing equilibria on the solubility of precipitates. Before you read any further, you might want to review the discussion of polyprotic acid equilibria and the calculation of a s, the fractions of each acid species in equdibrium at a given pH, in Chapter 7. 

How far apart must successive pK values be in order to have clearly distinguishable endpoints for titration curves of polyprotic acids Consider as examples H3PO4 and citric acid. What about equivalence points at very high or low pH How easy are they to locate ... 

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