1. Introduction

For the dissociation of a diprotic acid H₂R we have the equilibria

(1a,b)

described by the equations

(2a,b)

where we are specifically neglecting charges for generality. The absorbance and the composition of any given solution of a diprotic acid having concentration C_R is given by [1-4]

(3)

(4)

where A₀, A₁, and A₂ are the limit absorbances of R, HR and H₂R, respectively, and f₂, f₁ and f₀ the molarity fractions (f_j=[H_jR]/CR and A_j=ε_jC_R).

From Eqn. (4), removing denominators and passing everything to the first member, we have

(5)

Multiplying Eqn. (5) by K_a2/[H], on rearrangement gives

(6)

and taking decadic logarithms we get

(7)

Plotting the left hand of Eqn. (7) against pH gives a straight line (y = a₀+ a₁ x) of minus unity slope and pK_a2 intercept, i.e. the intersection of the straight line with the x-axis gives the value of pK_a2

On the other hand on rearrangement Eqn. (6) we easily get

(8)

and taking decadic logarithms and rearranging

(9)

Plotting the left hand of Eqn. (9) against pH gives a straight lines (least squares method) of slope unity and minus pK_a1 intercept, i.e. intersection with the x-axis is equal to pK_a1 (=-a₀/a₁).

The value of A₁ is Eqns. (7) and (9) must be known. The evaluation of the limiting absorbances (A₁ and A₁^*) of the intermediate species HR from absorbance measurements at varying pH values, at two wavelengths λ and λ^*, known as Polster method [5-6], has been detailed in a previous paper [7] submitted to this journal. An orthogonal regression method is applied in the calculations because both variables A and A^* are assumed to contain analogous random error of measurements.

The application of Eqns. (7) and (9) require, however, the previous knowledge of pK_a1 and pK_a2, respectively. Different values of pK_a1, Eqn. (7) (or pK_a2, in the case of Eqn. (9)) may be assumed and the entire procedure then applied. The best value of pK_a2, Eqn. (7) (or pK_a1, Eqn. 9) may be taken as that minimizes the standard deviation of the corresponding regression line.

The error associated to the pK_a values are calculated by applying the random error propagation law [8]. The theory developed in this section has been applied to the p-amino benzoic acid diprotic system with good results.

2. Experimental Study of the p-Aminobenzoic Acid System

2.1. Reagents

- p-Aminobenzoic acid (C₇H₇NO₂) M=137.14 g/mol (99%, sigma aldrich); Hydrochloric acid (HCl) solution 1 M (Merck, analytical grade); Potassium hydroxide (KOH) solution 1 M (Merck, analytical grade); Water for ACS analysis (Panreac).

2.2. Apparatus

- Analytical balance (Metler AE200) (4 digits), Granatario (Metler PJ 400) (2 digits), pH-meter Crison GLP 21 (3 digits), with a combined Ag/AgCl glass electrode. The pH-meter is calibrated using pH buffers 4.01, 7.00 and 9.21, using a two-point calibration method. Ultraviolet-visible molecular absorption spectrophotometer (Shimadzu).

2.3. Solutions

- p-Aminobenzoic acid 7.39·10^-4 M: 0.1014 g of p-aminobenzoic acid are weighed into a beaker, and transferred into a 1 L volumetric flask completing to the mark with distilled water with the aid of an ultrasonic bath for the correct dissolution.

- Hydrochloric acid (HCl) solution 0.01 M: From a commercial stock solution 1 M, 0.5 mL is taken into a 50 mL volumetric flask completing to the mark with distilled water.

- Potassium hydroxide (KOH) solution 0.01 M: From a commercial stock solution 1 M, 0.5 mL is taken into a 50 mL volumetric flask completing to the mark with distilled water.

2.4. Experimental Procedure

2.5 mL of p-aminobenzoic acid solution (7.39·10^-4 M) is pipetted into a 25 mL volumetric flask. Then varying amounts of HCl and NaOH solutions are added in order to adjust the pH, completing to the mark with distilled water. The absorbance is measured in the range between 230 to 300 nm (quartz cuvettes, pathlength one-centimetre) versus a blank (see Figure 1). Finally the pH of the solution is also measured (passed into a 50 mL beaker).

Figure 1. Absorption spectra of p-amino benzoic acid as a function of wavelength at varying pH values

Table 1 shows the [A, pH] data at 250, 280, 290 y 300 nm in the acid region. The last two λ (Figure 2) are used in the pK_a evaluation, given the maximum differences obtained. Results are given with three decimal digits in order to show the precision of measurements achieved even if they are not significant.

Table 1. Absorbance versus pH data for p-aminobenzoic acid (A2=0 at 290 and 300 nm; A0=0.420 at 290 nm y A0=0.160 at 300 nm)

Figure 2. Absorbance versus pH curves at 290 and 300 nm for the p-aminobenzoic acid system. The anomalous point [4.493, 0.418] (290 nm); [4.493, 0.449] (300 nm), is not compiled in Table 1. The curves in the Figure are calculated with pKa1, pKa2 and A1 calculated in this paper

3. Results and Discussion

The p-aminobenzoic acid system shows, at pH values at which the neutral HR specie predominate (Figure 1), a maximum of absorption located towards 280 nm, suffering an hipso and hiperchromic displacement towards 265 nm as the pH values increase, the absorbance values being stabilized in alkaline medium. As the pH decreases, the absorption band located at about 280 nm gradually disappears, appearing at the same time another one located at λ < 230 nm. The largest differences between the limit absorbances occur at 290 and 300 nm (Figure 2), wavelengths that are selected for the evaluation of the pK_a values.

Figures 3 and 4 (top) show the application of Polster method in the calculation of A₁ by applying the orthogonal regression method, which led to values of A₁= 0.978 at 290 nm and 0.714 at 300 nm. The application of the bilogarithmic method based on the use of Eqns. 7 and 9 are shown in Figures 3 and 4 (middle and lower) and leads to the values of pK_a1 = 2.227 ± 0.027 and pK_a2 = 4.682 ± 0.009 at 290 nm, and pK_a1 = 2.210 ± 0.023 and pK_a2 = 4.660 ± 0.023 at 300 nm. The analysis of residuals is included in the representations pointing in all cases towards the absence of systematic errors, being randomly distributed. The results are in concordance with those obtained by Terada [9], pK_a1 = 2.31 and pK_a2 = 4.80, applying a distribution method, and Schmid et al. [10]: pK_a1=2.204±0.012 and pK_a2=4.680±0.014 using potentiometric data. Schmidt’s values derived from the standard potentiometric method agree better with those derived in this work than those from Terada [9].

Figure 3. Top: Polster’s method. Middle and bottom: bilogarithmic method of diprotic acid applied to the calculation of pKa1 and pKa2, respectively, at 290 nm

Figure 4. Top: Polster’s method. Middle and bottom: bilogarithmic method of diprotic acid applied to the calculation of pKa1 and pKa2, respectively, at 300 nm

ACKNOWLEDGEMENTS

Thanks are due to the University of Seville for the concession of a Grant destined to the publication of the Bachelor´s degree Final Projects of students.