Polyprotic acid calculation

The common amino acids are simply weak polyprotic acids. Calculations of pH, buffer preparation, and capacity, and so on, are done exacdy as shown in the preceding sections. Neutral amino acids (e.g., glycine, alanine, threonine) are treated as diprotic acids (Table l-l). Acidic amino acids (e.g., aspanic. acid, glutamic acid) and basic amino acids (e.g., lysine, histidine, arginine) are treated as triprotic acids, exactly as shown earlier for phosphoric acid. 

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. 

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... 

The values for K, listed here have been calculated from pK, values with more significant figures than shown so as to minimize rounding errors. Values for polyprotic acids—those capable of donating more than one proton—refer to the first deprotonation. 

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. 

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

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. 

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. 

Each successive proton transfer reaction of a polyprotic acid has its own value for, and each successive value is approximately 10 times smaller than its predecessor. We explain the reasons for this trend in Section 17-1 and show how to treat calculations involving polyprotic acids in Section 17-1. 

Special Case Explicit Calculation 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. 

The concentrations of the differently protonated species, as a function of pH, are calculated with the explicit function we developed in Special Case Explicit Calculation for Polyprotic Acids, (p.64). A data matrix Y is constructed as before. Data eqAH2a. m generates the data, it is called by Main eqAH2a. m. 

Problems that involve polyprotic acids can be divided into as many sub-problems as there are hydrogen atoms that dissociate. The ion concentrations that are calculated for the first dissociation are substituted as initial ion concentrations for the second dissociation, and so on. You can see this in the following Sample Problem. 

All polyprotic acids, except sulfuric acid, are weak. Their second dissociation is much weaker than their first dissociation. For this reason, when calculating [HsO" ] and pH of a polyprotic acid, only the first dissociation needs to be considered. The calculation is then the same as the calculation for any weak monoprotic acid. In the Sample Problem, [HP04 ] was found to be the same as the second dissociation constant, Ka. The concentration of the anions formed in the second dissociation of a polyprotic acid is equal to... 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base (see Toolbox 11.1). First, we have to consider the reaction stoichiometry to recognize what stage we have reached in the titration. Next we have to identify the principal solute species at that point and the proton transfer equilibrium that determines the pH. We then carry out the calculation appropriate for the solution, referring to the previous worked examples if necessary. In this section, we see how to describe the solution at various stages of the titration our conclusions are summarized in Tables 11.3 and 11.4. 

Polyprotic acid solutions contain a mixture of acids—H2A, HA-, and H20 in the case of a diprotic acid. Because H2A is by far the stronger acid, the principal reaction is dissociation of H2A, and essentially all the H30+ in the solution comes from the first dissociation step. Worked Example 15.11 shows how calculations are done. 

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 ... 

In the case of polyprotic acids, K is often so much greater than K2 that only the equilibrium need be considered to calculate [H+] in a solution of the acid. Examples where this assumption may and may not be made will be given in specific Solved Problems with the reasoning included. 

Another problem of interest is the calculation of the concentration of the divalent ion (2 ) in a solution of a weak polyprotic acid, when the total [H+] is essentially due to a stronger acid present in the solution or to a buffer. In such a case, the concentration of the divalent ion can best be calculated by multiplying the expressions for and K2. Again, illustrating with H2S, we find the following ... 

The extent of the second dissociation is so small that it does not either lower [HS-] or raise [H+] as calculated from the first dissociation significantly. Notice that in a solution of a polyprotic acid the concentration of the conjugate base resulting from the second dissociation is equal to K2. This result is general whenever the extent of the second dissociation is less than 5% (an application of the five percent rule). 

Citric acid is a polyprotic acid with pK, pK2, and pKj equal to 3.15, 4.77, and 6.39, respectively. Calculate the concentrations of H+, the singly charged anion, the doubly charged anion, and the triply charged anion in 0.0100 M citric acid. 

When dealing with polyprotic acids, the exact solution for pFl calculations quickly becomes very daunting. Flowever, Le Chatelier s principle can come to our rescue. The first ionization is much more complete than the second, because the first K3 is larger than the second. The hydrogen ion produced by the first ionization is also a product of the second ionization. Thus, the increase in hydrogen ion concentration pushes the second equilibrium back to the left, suppressing the acid ionization of H,P()4. Therefore, with polyprotic acids, we can usually just consider the first acid ionization and ignore the subsequent acid ionizations. 

D. W. King and D. R. Kester, A General Approach for Calculating Polyprotic Acid Specification and Buffer Capacity, J. Chem. Ed., 67, 932 (1990). 

Before taking up polyprotic acids, let us review. Suppose we rework Example 19.17, but we will add HCl instead of sodium acetate and we will calculate the acetate ion concentration. The same principles apply. 

Although we might expect the pH calculations for solutions of polyprotic acids to be complicated, the most common cases are surprisingly straightforward. To illustrate, we will consider a typical case, phosphoric acid, and a unique case, sulfuric acid. 

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