General Analytical Procedure for Determination of Acidity Parameters of Weak Acids and Bases

The paper presents a new convenient, inexpensive, and reagent-saving general methodology for the determination of pK a values for components of the mixture of diverse chemical classes weak organic acids and bases in water solution, without the need to separate individual analytes. The data obtained from simple pH-metric microtitrations are numerically processed into reliable pK a values for each component of the mixture. Excellent agreement has been obtained between the determined pK a values and the reference literature data for compounds studied.


Introduction
Prediction or determination of p a value is of great importance in chemistry, in particular in life and material sciences, pharmaceutical industry, and other R&D oriented enterprises. Important drug properties, such as lipophilicity, solubility, and transmembrane transfer, are all pH dependent. Also, rational drug formulation requires the knowledge of p a . The proportion of drugs with an ionizable group has been estimated at 95% [1], but only 62.9% of drugs under analysis were ionizable at pH 2-12 [2]. According to Wells data 75% of drugs are weak bases and 20% weak acids and the remaining contain nonionics, ampholytes, and alcohols [1].
Recently, some theoretical approaches were employed to predict the p a value, for example, ab initio quantum mechanical calculations [3,4] or QSPR (quantitative structure-property relationship) modeling [5,6] as well as QSPR models which employ partial atomic charges as descriptors [7,8]. The theoretical models take into account electronic effects (induction, resonance), solvation of compounds of type HA, BH and their ionic forms, that is, A − and BH + , hydrogen bonding, and various stereochemical effects.
This report presents an application of pH-metric microtitration to determine standard p a parameters of components of mixtures of various weak acids and bases by employing a technologically advanced potentiometer device and a software based on an algorithm straightforwardly accounting for complex acid-base equilibria (see below). A composition of the mixtures under study can be expressed as follows: where H 3 A 1 + H 2 A 2 + HA 3 represents 3-H, 2-H, and 1-H protic carboxylic acids, B 1 + B 2 represents organic bases, (R 1 R 2 )CH 2 represents the so-called C-H acids, R 1 R 2 N-H-represents the N-H acids, and ArOH denotes phenolic/enolic moiety (O-H acids). The C-H, N-H, and O-H acids are often reported as tautomeric forms of heterocyclic compounds with pharmacological activity and are identified within different groups of natural compounds (flavonoids, quinines, etc.).
Numerical Modelling. Numerical procedures are based on an original algorithm elaborated by Kostrowicki and Liwo [9] as well as the CVEQUID program, which was adopted in the Cerko Lab software within the Cerko Lab System microtitrator unit (Cerko, Gdynia, Poland). All details concerning Kostrowicki and Liwo algorithm were described previously [10]. The CVEQUID program is based on a least-square method for the determination of all parameters and takes into account all the sources of experimental errors considered in potentiometry, that is, (a) electrode calibration parameters ( 0 , the standard potential (cell constant) and , the standard Nernstian slope parameter); (b) composition of titrand D, its concentration 0 (mol/L), and volume 0 (mL); (c) composition of titrant T, its concentration (mol/L), and added volume (mL); (d) measured EMF (the electromotive force) in mV.
Within the Cerko Lab System software, the equilibrium is denoted as model. The model consists of a set of equations. Each equation is related to a particular p value and to p w . The model includes also information about the composition of titrant T and titrand D. The stoichiometric matrix, required for the numerical procedures, is generated from the model automatically. The representative models and the corresponding stoichiometric matrix for H 2 A (model 1) as well as H 3 A + H 2 A 1 + HA 2 (model 2) systems are given below.

Model 1.
Reagents include titrand D = H 2 A and titrant T = OH. Individual equilibria that contribute to the overall equilibrium of the system are as follows: The stoichiometric matrix for the above model is presented in Table 1.
the Lauda E100 circulation thermostat. The electrode was calibrated with the use of buffer solutions: potassium hydrogen phthalate (pH 4.00), citric acid/Na 2 HPO 4 (pH 7.00), and boric acid/KCl/NaOH (pH 10.00). Titrant T (0.1 mol/L NaOH) was standardized according to the general analytical procedure and protected from carbon dioxide. Double distilled water of conductivity approximately 0.18 S/cm was used throughout for the preparation of aqueous solutions of organic acids and bases under study. It was freshly produced in order to avoid carbon dioxide absorption. Other reagents together with their abbreviations used in the text are listed in Abbreviations section.   Tables 3 and 4.

Mixtures of Amino acids with Organic Acids and Bases.
The presented general procedure was applied for studying the system consisting of amino acids, organic acids, and bases. The p a values of this type of mixtures were calculated based on a single titration curve. Experimental results confirm the general application of the proposed procedure for the determination of p a value for mixtures of any degree of complexity composed of weak acids and bases. The p a values of weak acids (H A), bases (B), and amino acids (AB ± ) in the mixture of these types of components were determined. Composition of the tested mixtures (titrand D) and p a values are listed in Table 7.

Phenol and Enol OH-Acids as Components of Titrand D.
The acidity of the phenol group (OH-acid) depends on the substituent of the aromatic ring and its p a ranges from 4 to 11 [8]. We have performed the titration and relevant calculations for several mixtures of phenolic compounds, exemplified by 4-NO 2 phenol and a drug N-(4-hydroxyphenyl)acetamide (paracetamol) with different type of organic acids and bases as titrands D. The results are summarised in Table 8.

Heterocyclic N-H-Acids as Components of Titrand D.
The barbituric acid (BA) and a new class of 2(1H)-pyrazylidene acetonitrile derivatives (2(1H)PyAN), with marked pharmaceutical importance [13,14], were tested at the presence of phthalic acid. Barbituric acid was also tested at the presence of different drugs (Table 9).

Determination of p a Values for Different Drugs as a Components of Titrand D.
For all tested compounds with pharmaceutical importance we confirmed that the elaborated method could be recommended as a general approach to the determination of p a values for weak acids and bases in mixtures of any degree of complexity. The composition of titrand D and the p a values determined for drugs under study are listed in Table 10.

Conclusions
A new approach for studying equilibrium constants for the dissociation of different types of weak electrolytes present in a mixture of any degree of complexity has been proposed. Potentiometric titration technique and numerical procedure based on an original algorithm elaborated by Kostrowicki and Liwo and adopted in the Cerko Lab software have successfully been applied to obtain the p a values of a variety of classes of compounds comprising of common organic acids and bases, amino acids, phenols and enols OHacids, and heterocyclic N-H-acids as well as compounds of pharmaceutical importance. It was shown that the p a values of the compound present in the mixture can be determined directly without the need to separate individual analytes. The obtained p a values of the electrolytes under study are in a good agreement with those reported in the literature (Table 11, Figure 3). Thus, the presented methodology can be considered as a fast, simple, inexpensive, and reagents-saving way for studying equilibria in the mixture of electrolytes. Moreover, it does not require a highly trained personnel. The methodology described in this paper can be routinely used in a regular analytical practice.