Solutes polyprotic acids

Acids are described as monoprotic, diprotic, ortriprotic depending on whether they can donate one, two, or three protons per molecule, respectively, in aqueous solutions. Polyprotic acids include both diprotic and triprotic acids. 

A more challenging problem is to find the pH of a solution prepared from a polyprotic acid or one of its conjugate species. As an example, we will use the amino acid alanine whose structure and acid dissociation constants are shown in Figure 6.11. 

Ordinarily, successive values of for polyprotic acids decrease by a factor of at least 100 (Table 13.3). In that case, essentially all the H+ ions in the solution come from the first step. This makes it relatively easy to calculate the pH of a solution of a polyprotic acid. 

The theory of titrations between weak acids and strong bases is dealt with in Section 10.13, and is usually applicable to both monoprotic and polyprotic acids (Section 10.16). But for determinations carried out in aqueous solutions it is not normally possible to differentiate easily between the end points for the individual carboxylic acid groups in diprotic acids, such as succinic acid, as the dissociation constants are too close together. In these cases the end points for titrations with sodium hydroxide correspond to neutralisation of all the acidic groups. As some organic acids can be obtained in very high states of purity, sufficiently sharp end points can be obtained to justify their use as standards, e.g. benzoic acid and succinic acid (Section 10.28). The titration procedure described in this section can be used to determine the relative molecular mass (R.M.M.) of a pure carboxylic acid (if the number of acidic groups is known) or the purity of an acid of known R.M.M. 

The principal difference between a polyprotic acid and a monoprotic acid is that a polyprotic acid donates protons in a succession of deprotonation steps. For example, a carbonic acid molecule can lose one proton to form I ICO , and then that ion can donate the remaining proton to form CO, 2. We shall see how to take this succession of deprotonations into account when assessing the pH of the solution of a polyprotic acid or one of its salts. In addition, we shall see how the relative concentrations of the ions in solution, such as P043, HP042, and H,P04 depend on the pH of the solution. 

The parent acids of common polyprotic acids other than sulfuric are weak and the acidity constants of successive deprotonation steps are normally widely different. As a result, except for sulfuric acid, we can treat a polyprotic acid or the salt of any anion derived from it as the only significant species in solution. This approximation leads to a major simplification to calculate the pH of a polyprotic acid, we just use Kal and take only the first deprotonation into account that is, we treat the acid as a monoprotic weak acid (see Toolbox 10.1). Subsequent deprotonations do take place, but provided Kal is less than about fCal/1000, they do not affect the pH significantly and can be ignored. 

Suppose we need to estimate the pH of an aqueous solution of a fully deproto-nated polyprotic acid molecule. An example is a solution of sodium sulfide, in which sulfide ions, S2-, are present another example is a solution of potassium phosphate, which contains P04 ions. In such a solution, the anion acts as a base it accepts protons from water. For such a solution, we can use the techniques for calculating the pH of a basic anion illustrated in Example 10.11. The K, to use in the calculation is for the deprotonation that produces the ion being studied. For S2, we would use Ki2 for H2S and, for P043-, we would use Kai for H3P04. 

The pH of the aqueous solution of an amphiprotic salt is equal to the average of the pKlts of the salt and its conjugate acid. The pH of a solution of a salt of the final conjugate base of a polyprotic acid is found from the reaction of the anion with water. 

HOWTO CALCULATE THE CONCENTRATIONS OF ALL SPECIES IN A POLYPROTIC ACID SOLUTION... 

We assume that the polyprotic acid is the solute species present in largest amount. We also assume that only the first deprotonation contributes significantly to [H3Ot] and that the autoprotolysis of water does not contribute significantly to H30+] or [OH-]. 

EXAMPLE 10.13 Sample exercise Calculating the concentrations of all solute species in a polyprotic acid solution... 

The concentrations of all species in a solution of a polyprotic acid can be calculated by assuming that species present in smaller amounts do not affect the ------ —tions of species present in larger amounts. 

Sometimes we need to know how the concentrations of the ions present in a solution of a polyprotic acid vary with pH. This information is particularly important in the study of natural waters, such as rivers and lakes (Box 10.1). For example, if we were examining carbonic acid in rainwater, then, at low pH (when hydronium ions are abundant), we would expect the fully protonated species (H2C03) to be dominant at high pH (when hydroxide ions are abundant), we expect the fully deprotonated species (C032 ) to be dominant at intermediate pH, we expect the intermediate species (HC03, in this case) to be dominant (Fig. 10.20). We can verify these expectations quantitatively. 

For each of the following polyprotic acids, state which species (H2A, HA, or A2-) you expect to be the form present in highest concentration in aqueous solution at pH = 6.50 ... 

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. 

There are several acidic species present in any solution of a polyprotic acid. The solution of carbonic acid in Example contains the following concentrations of acidic species ... 

H2 CO3] =0.050 M [H3 0+]= 1.5 X IO M [HCO3] = 1.5 x lO" M What happens if we add a base to this solution The strongest acid donates protons preferentially, but the concentration of hydronium ions is so small that this ion is rapidly consumed. Then the next strongest acid, H2 CO3, reacts with added base. Generalizing, when a base is added to a solution that contains both a polyprotic acid and its anion, the base accepts protons preferentially from the neutral acid. Only after the neutral acid has been consumed completely does the anion participate significantly in proton transfer. Example provides molecular pictures of this feature. 

Because the K for HOC1 is more than 1000 times that of HOI, the pH in the solution is due only to the ionization of HOC1, following the same train of thought as for polyprotic acids. 

Polyprotic acids are fairly important and their potentiometric pH titrations are common. For 2-component systems of this kind, it is possible to turn around the computations and come up with explicit, non-iterative solutions. So far we have computed the species concentrations knowing the total component concentrations, which is an iterative process. This is the normal arrangement in titrations where volumes and total concentrations are known and the rest is computed, e.g. the [H+] and thus the pH. Turning around things in this context means that one calculates the titration volume required to reach a given (measured) pH. One knows the i/-value and computes the corresponding x-value. In this way there are explicit equations that can directly be implemented in Excel. 

Problem 33 What is the principle species in a solution of sulfiirous acid, H2SO3, a weak polyprotic acid List H2SO3, HSO3, SO3, and in order of decreasing concentration. 

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