pKa values in organic chemistry – Making maximum use of the available data

Acids and bases are ubiquitous. Sometimes, it is essential to know the accurate strength (pK_a values) of the acids/bases to work with, but sometimes just acidity/basicity order is enough. We often receive requests to measure pK_a values of different substances in different solvents for answering questions like “what acids can be used to protonate this substance” or “what base is able to deprotonate that compound?” Such questions can, in fact, often be answered using published pK_a data in different solvents. This digest/tutorial will give an overview of how to make efficient use of the existing pK_a data.     

Isotachophoretic determination of mobility and pKa by means of computer simulation : V. Evaluation of mo and pKa of twenty-eight dipeptides and assessment of separability

Isotachophoretic qualitative indices, R_E, for twenty-eight dipeptides were measured in the range pH 7.4–9.6. The absolute mobility, m_o, and pK_a values were evaluated by the use of the least-squares method, utilizing a simulation of the isotachophoretic steady state. The m_o values were newly evaluated and the pK_a values were in good agreement with literature values. By comparison of the evaluated m_o and pK_a values of the dipeptides with those of the constituent amino acids, simple relationships were found which may be used to estimate the m_o and pK_a values of other dipeptides. The separability of the dipeptides was also evaluated by considering the differences between their simulated effective mobilities. It is concluded that isotachophoresis is very convenient for the separation of dipeptides and their constituent amino acids.     

Potentiometric and spectrophotometric pKa determination of water-insoluble compounds: validation study in a new cosolvent system

In this paper the validation of pK_a determination in MDM-water mixtures is presented. The MDM-water mixture is a new multicomponent cosolvent mixture (consisting of equal volumes of methanol, dioxane and acetonitrile, as organic solvents) that dissolves a wide range of poorly water-soluble compounds. The cosolvent dissociation constants (p_sK_a) of 50 chemically diverse compounds (acids, bases and ampholytes) were measured in 15-56 wt% MDM-water mixtures by potentiometric or spectrophotometric titration and the aqueous pK_a values obtained by extrapolation. Three different extrapolation procedures were compared in order to choose the best extrapolation in MDM-water mixture using a sub-set of 30 water-soluble compounds. The extrapolated results are in good agreement with pK_a values measured in aqueous medium. No significant difference was found among these extrapolation procedures thus the widely used Yasuda-Shedlovsky plot was proposed for MDM cosolvent also. Further we also present that the single point estimation based on measurement in 20%/v MDM-mixture using a general calibration equation may be suitable for rapid pK_a determination in the early phase of drug research.     

Evaluation of potentiometric acid-base titrations by partial-least-squares calibration

Partial-least-squares calibration is used for the evaluation of acid-base titration curves. The method is advantageous because no physical model is assumed and only information from the titration curves is used. In the procedure, a model is developed from samples of known composition (calibration set) and is then used to predict unknowns (test set). The only assumption is that the two sets are similar. The method was evaluated first by titrating mixtures of two monoprotic acids with a small difference in pK_a values and then by titrating samples containing four or five diprotic acids. The results show that it is possible to determine monoprotic acids having a difference in pK_a of only 0.1, or up to five diprotic acids having pK_a values in the range 1.8–7.2, simultaneously.     

Calculations of pKa values of carboxylic acids in aqueous solution using density functional theory

With the specific aim of calculating the acidity equilibrium constant (K_a) of carboxylic acids in aqueous solution we investigated the solute-solvent interactions of these acids and their corresponding anions. The pK_a (−lg K_a) values have been calculated using density functional theory (DFT). The polarized continuum model (PCM) is used to describe the solvent. Using these methods, we successfully predicted the pK_as of 66 carboxylic acids in aqueous with the average error of 0.5 in pK_a units. Two different thermodynamic cycles have been studied. The theoretical values are in better agreement with the experimental results for those acids with moderate strength of acidity with the pK_a value higher than 3.     

Dependence of site-site interactions on pore diameter on amine-modified stationary phases

m-Cresol purple stationary phases were prepared on a series of amine-silica substrates and studied by visible photoacoustic spectroscopy. Site-site interactions between residual, unreacted amines were shown to lower the pK_a of m-cresol groups and the magnitude of this effect was found to depend on the average pore diameter of the silica substrate. Two effects appeared to be operative: (1) solvent exclusion from small pores and (2) charge repulsion involving neighboring groups which effectively lowers the apparent pK_a. Surface “buffering” by unreacted amines may also occur in such systems.     

Acid-base strengths in 1,2-dichloroethane

The pK_a value of hydriodic acid in 1,2-dichloroethane was determined from conductivity measurements. A glass electrode was calibrated for dichloroethane in the potentiometric titration of hydriodic acid with tetramethylguanidine. From potentiometric titrations, the pK_a values in dichloroethane of hydrobromic acid, hydrochloric acid, picric acid and some sulfonphthaleins as well as some protonated nitrogen bases were determined. In the curves of the titrations of the carboxylic acids and the hydrogen halides with TMG, evidence was found for the formation of the complex B(HX)₂.     

Influence of Water Content on Basicities in Acetonitrile

The influence of water content at impurity level (5–10,000 ppm) in acetonitrile, on the changes in relative basicity differences (ΔpK _a values) of 13 pairs of bases, was studied both experimentally and computationally (COSMO-RS). The ΔpK _a values involving smaller bases with localized charge in the cationic form were found to be more affected. A computational parameter, weighted average negative sigma (WANS), was proposed to quantify the charge delocalization in cations and succeeded in describing the observed changes of ΔpK _a. The results validate the previously published basicity scale in acetonitrile with respect to solvent dryness and give guidelines for better experimental planning.     

Determination of pKa values of some hydroxylated benzoic acids in methanol-water binary mixtures by LC methodology and potentiometry

An accurate estimation of pK_a values in methanol-water binary mixtures is very important for several separation techniques such as liquid chromatography and capillary electrophoresis that use these solvent mixtures. In this study, the pK_a values of 11 polyphenolic acids have been determined in methanol-water binary mixtures (10%, 20% and 30% (v/v)) by potentiometry, liquid chromatography (LC) and LC-DAD methodology.The results show a similar trend for the pK_a values of all the studied compounds, as they increase with increasing concentration of organic modifier, which allows a linear relationship between pK_a values and mole fraction of methanol to be obtained. The pK_a values obtained in aqueous medium have been compared with those given in the literature, and also with the values predicted by the SPARC on-line pK_a calculator. The data obtained have been used to test the feasibility of an estimation of dissociation constants in a methanol-water medium from the relationship between pK_a values and the organic cosolvent fraction in the mixtures.     

Single-point titrations: Part-I. The determination of bases

Equations are derived for the calculation of acid mixtures, which upon titration with base show a linear relation between pH and the amount of base. Three to five weak acids were used and a linearity of better than ±0.02 pH units was obtained. The use of such mixtures for analysis of the base content of samples by means of a single pH measurement is described. A procedure for obtaining conditional pK_a values of the components of the acid mixture is also described. The single-point titration method is advocated for use when better accuracy than that of direct potentiometry is desired but less than that of an ordinary titration can be accepted. It is not necessary to know the pK_b or the number of weak bases.     

Acidity of several polyprotic acids, amiodarone and quetiapine hemifumarate in pure methanol

Methanol is the organic solvent closest to water and able to dissolve a huge amount of organic compounds. Therefore, it is a good candidate for pK_a determination of drugs sparingly soluble in water or a basic drug presented as a salt which pK_a is close to that of its counter-acid. In this work, the acidic dissociation constants in pure methanol of the most common acids used in pharmaceutical preparations (lactic, tartaric, fumaric, maleic and citric) were determined. In addition, the pK_a values of the antipsychotic quetiapine presented as hemifumarate (Seroquel) and the very insoluble antiarrhythmic amiodarone were also determined by potentiometry. From these values, the aqueous pK_a of these drugs were estimated by means of previously established equations. Estimated values are consistent with those from literature and show the interest of methanol for drug discovery pK_a measurements.     

Uncertainty estimation in measurement of pKa values in nonaqueous media: A case study on basicity scale in acetonitrile medium

The difficulties in estimating uncertainty of pK_a values determined in nonaqueous media are reviewed and two different uncertainty estimation approaches are presented and applied to the pK_a values of the compounds on a previously established self-consistent spectrophotometric basicity scale in acetonitrile. One approach is based on the ISO GUM methodology (the “ISO GUM” approach) and involves careful analysis of the uncertainty sources and quantifying the respective uncertainty components. The second approach is based on the standard-deviation-like statistical parameter that has been used for characterization of the consistency of the scale (the “statistical” approach). It is demonstrated that the ISO GUM approach somewhat overestimates the uncertainty. The statistical approach is based on long-term within-laboratory statistical data and it is demonstrated that it underestimates the uncertainty. In particular it neglects the laboratory bias effects that are taken into account at least to some extent by the ISO GUM approach. Thus, together these two approaches allow to “bracket” the uncertainties of the pK_a values on the scale. The uncertainties of the pK_a values are defined in two different ways. Definition (a) includes the uncertainty of the pK_a of the reference base (anchor base of the scale) pyridine. Definition (b) excludes it. It is demonstrated that both definitions have their virtues. Definition (a) leads to the uncertainty ranges of 0.12-0.22 and 0.12-0.14 pK_a units at standard uncertainty level for different bases using the ISO GUM and statistical approach, respectively. Definition (b) leads to the uncertainty ranges of 0.04-0.19 and 0.02-0.08 pK_a units, respectively. The uncertainty of the pK_a of a given base is dependent on the quality of the measurements involved and on the distance from the reference base on the scale. The importance of the correlation between the pK_a values of bases belonging to the same scale is stressed.     

Determination of dissociation constants of sparingly soluble phenothiazine derivatives by second-derivative spectrophotometry

The dissociation constants (pK_a) for sparingly soluble phenothiazines (promazine, chlorpromazine, trifluoropromazine) in water were measured by second-derivative spectrophotometry. The intense background signals in the absorption spectra due to the turbidity caused by the precipitation of insoluble free base of the phenothiazine derivatives were eliminated in the second-derivative spectra, and the solubilities of the phenothiazine derivatives could be easily determined from the peak-to-trough lengths (D values) of the second-derivative signals. The pK_a values were calculated from the pH dependence of the D values. The pK_a values obtained agreed well with reported values and the standard deviations for 6–10 determinations were ? 0.02. The solubilities of the free bases of the phenothiazines were also determined.     

A universal approach for continuum solvent pK a calculations: are we there yet?

This paper reviews several pK _a calculation strategies that are commonly used in aqueous acidity predictions. Among those investigated were the direct or absolute method, the proton exchange scheme, and the hybrid cluster–continuum (Pliego and Riveros) and implicit–explicit (Kelly, Cramer and Truhlar) models. Additionally, these protocols are applied in the pK _a calculation of 55 neutral organic and inorganic acids in conjunction with various solvent models, including the CPCM-UAKS/UAHF, IPCM, SM6 and COSMO-RS, with a view to identifying a universal approach for accurate pK _a predictions. The results indicate that the direct method is unsuitable for general pK _a calculations, although moderately accurate results (MAD <3 units) are possible for certain classes of acids, depending on the choice of solvent model. The proton exchange scheme generally delivers good results (MAD <2 units), with CPCM-UAKS giving the best performance. Furthermore, the sensitivity of this approach to the choice of reference acid can be substantially lessened if the solvation energies for ionic species are calculated via the IPCM cluster–continuum approach. Reference-independent hybrid approaches that include explicit water molecules can potentially give reasonably accurate values (MAD generally ~2 units) depending on the solvent model and the number of explicit water molecules added.     

Potentiometric acid-base properties of the chloroazoxine S dyes

The pK_a of the sulfonic group in the Azoxine S dye o-, m-, and p-chloro derivatives and the parent 7-phenylazo-8-hydroxyquinoline-5-sulfonic acid was determined potentiometrically. The indicators were prepared, obtained in the acid form by percolation through a cation exchange resin, and titrated with NaOH. The pK_a amounts to 3.69, 4.25, 3.65, and 3.71, respectively. Interpretation of the pK_a values is given.     

Theoretical Study of Firefly Luciferin pKa Values—Relative Absorption Intensity in Aqueous Solutions

Ground‐state vibrational analyses of firefly luciferin and its conjugate acids and bases are performed. The Gibbs free energies obtained from these analyses are used to estimate pK_a values for phenolic hydroxy and carboxy groups and the N–H⁺ bond in the N‐protonated thiazoline or benzothiazole ring of firefly luciferin. The theoretical pK_a values are corrected using the experimental values. The concentrations of these chemical species in solutions with different pH values are estimated from their corrected pK_a values, and the pH dependence of their relative absorption intensities is elucidated. With the results obtained we assign the experimental spectra unequivocally. Especially, the small peak near 400 nm at pH 1–2 in experimental absorption spectra is clarified to be due to the excitation of carboxylate anion with N‐protonated thiazoline ring of firefly luciferin. Our results show that the pK_a values of chemical species, which are contained in the aqueous solutions, are effective to assign experimental absorption spectra.     

Evaluation of Acid Dissociation Constants in DMSO and DMF by Quantum-Chemical Methods

We have calculated total electronic energies (E) and Gibbs energies (G) of a large number of acids and their anions in water, dimethylsulfoxide, and dimethylformamide using the hybrid B3LYP functional DFT method in the 6-31++G(d,p) basis set, taking into account the solvent effect by the conductor-like polarizable continuum model method. A linear correlation has been found between the experimental values of acid dissociation constants (pK_a) of different nature and the difference between anion and acid E values, and between pK_a and the difference between anion and acid G values. The obtained correlations allowed us to evaluate the pK_a values of both inorganic and organic acids. Such an evaluation is of special importance for nonaqueous solvents as it is quite problematic to determine these dissociation constants.     

A reliable and efficient first principles‐based method for predicting pKa values. 4. organic bases

The ionization (dissociation) constant (pK_a) is one of the most important properties of a drug molecule. It is reported that almost 68% of ionized drugs are weak bases. To be able to predict accurately the pK_a value(s) for a drug candidate is very important, especially in the early stages of drug discovery, as calculations are much cheaper than determining pK_a values experimentally. In this study, we derive two linear fitting equations (pK_a = a × ΔE + b; where a and b are constants and ΔE is the energy difference between the cationic and neutral forms, i.e., ΔE = E_neutral?E_cationic) for predicting pK_as for organic bases in aqueous solution based on a training/test set of almost 500 compounds using our previously developed protocol (OLYP/6‐311+G**//3‐21G(d) with the the conductor‐like screening model solvation model, water as solvent; see Zhang, Baker, Pulay, J. Phys. Chem. A 2010 , 114, 432). One equation is for saturated bases such as aliphatic and cyclic amines, anilines, guanidines, imines, and amidines; the other is for unsaturated bases such as heterocyclic aromatic bases and their derivatives. The mean absolute deviations for saturated and unsaturated bases were 0.45 and 0.52 pK_a units, respectively. Over 60% and 86% of the computed pK_a values lie within ±0.5 and ±1.0 pK_a units, respectively, of the corresponding experimental values. The results further demonstrate that our protocol is reliable and can accurately predict pK_a values for organic bases. © 2012 Wiley Periodicals, Inc.     

What are the pKa values of organophosphorus compounds?

A first-principle theoretical protocol was developed, which could successfully predict the pK_a values of a number of amines and thiols in DMSO with a precision of about 1.1 pK_a unit. Using this protocol we calculated the pK_a values of diverse types of organophosphorus compounds in DMSO. The accuracy of these predicted values was estimated to be about 1.1 pK_a because phosphorus is in the same group as nitrogen and in the same period as sulfur. The theoretical predictions were also consistent with all the available experimental data. Thus, a scale of reliable pK_a values was constructed for the first time for organophosphorus. These pK_a values would be helpful to synthetic chemists who need to design the experimental conditions for handling deprotonated organophosphorus. On the basis of these pK_a values we also studied, for the first time, some interesting topics such as the substituent effects on the pK_a values of various types of organophosphorus, and the differences between the pK_a values of organophosphorus and organic amines.     

Accurate pKa Calculation of the Conjugate Acids of Alkanolamines,Alkaloids and Nucleotide Bases by Quantum Chemical Methods

The pK_a of the conjugate acids of alkanolamines, neurotransmitters, alkaloid drugs and nucleotide bases are calculated with density functional methods (B3LYP, M08‐HX and M11‐L) and ab initio methods (SCS‐MP2, G3). Implicit solvent effects are included with a conductor‐like polarizable continuum model (CPCM) and universal solvation models (SMD, SM8). G3, SCS‐MP2 and M11‐L methods coupled with SMD and SM8 solvation models perform well for alkanolamines with mean unsigned errors below 0.20 pK_a units, in all cases. Extending this method to the pK_a calculation of 35 nitrogen‐containing compounds spanning 12 pK_a units showed an excellent correlation between experimental and computational pK_a values of these 35 amines with the computationally low‐cost SM8/M11‐L density functional approach.