Acid dissociation constants in selected dipolar non-hydrogen-bond-donor solvents (IUPAC Technical Report)

3.1 Conductometry

Conductometry utilizes the fact that when a neutral acid molecule dissociates into free ions, the conductivity of the solution increases. Measuring conductivity at different acid concentrations and relating the conductivity data to acid concentration data enables calculation of the pK _a value. The technique is by its nature “absolute”, i.e., it does not need to use a reference acid. Conductometry works best with medium to strong monoprotic acids, corresponding to a pK _a range of about 3–6. To limit the number of conducting species in solution, conductometric measurements are usually performed by changing only the acid concentration (e.g., by dilution).

Conductometry is unable to distinguish between neutral HA and ion pairs SH⁺A⁻. Thus, in principle, rather than pK _a as defined by equation (2), conductometry yields the overall dissociation constant pK _a ^d (equation (6)). In solvents of sufficiently high permittivity (here DMSO, MeCN, DMF, PC and usually acetone) ion pairing is negligible and pK _a values as defined by equation (2) can be measured by conductometry.

In non-HBD solvents, a key drawback of conductometry is that moisture in solvents makes acids seem stronger. This is because water molecules are efficient in selectively solvating the anions (and in some solvents also the hydrogen ions) thereby promoting ionization/dissociation. A second drawback is that if a relatively weak acid contains a strong acid as an impurity, then the conductivity can increase markedly because of the more extensive dissociation of the stronger acid. In extreme cases, essentially all the observed conductivity can be caused by impurities, leading to meaningless results. These drawbacks become more serious as the measured acid becomes weaker. The second drawback points to a more general limitation of the technique: conductometry provides no direct evidence of the origin of the conductance, be it the extent of the acid dissociation in the solution, or the presence of impurities, or some other source. In conductometry of acid solutions alone, homoconjugation is mostly not a problem because there are no acid/conjugate base (salt) mixtures. Upon partial dissociation, there are both HA and A⁻ in the solution and the degree of dissociation of HA increases upon dilution. However, dilution also suppresses homoconjugation.

3.2 Potentiometry

Potentiometry enables direct measurement of the solvated hydrogen ion activity a(H⁺) (subject to the usual Bates–Guggenheim convention ³⁹ ). It is mostly used in the potentiometric titration mode.

In a potentiometric titration, if the titrated acid is strong enough (or if correction for incomplete reaction is applied), then the concentrations/activities of HA and A⁻ in solution for use with equation (2) can be obtained from the amounts and concentrations of the solutions involved (the so-called Henderson–Hasselbalch equation ⁴⁰ ). However, potentiometric titration is unable to detect whether the formed A⁻ is free or ion-paired with SH⁺ or BH⁺. So, while in high permittivity solvents potentiometric titration gives the pK _a directly according to equation (2), in less polar solvents the presence of ion pairs of A⁻ with the conjugate acid BH⁺ of the basic titrant B (BH⁺A⁻) or other counter-cation may complicate direct calculation of the activity of HA.

One possibility is to group the ion pair with the neutral acid. In this case, the so-called overall dissociation constant (equation (6)) is obtained. For that, the formation constant of the salt ion pairs must be known (usually measured by conductometry) to calculate the overall dissociation constant (equation (6)). The other possibility is grouping the ion pair(s) with A⁻, which leads to the apparent constant K _aip (equation (7)).

Homoconjugation, if it occurs to a noticeable extent (which is favored by the relatively high concentrations used in potentiometric titrations), also has effects: it decreases pH before and increases pH after the half-neutralization point from that expected from the Henderson–Hasselbalch equation. To calculate the pK _a from the titration curve in such solvents, the homoconjugation constant must be measured first. An exception is the half-neutralization point of the titration where homoconjugation has no effect. According to the Henderson–Hasselbalch equation, the pH of the half-neutralization point of the titration corresponds to the pK _a value. Therefore, potentiometric half-neutralization points are often directly given as good estimates of pK _a, even neglecting the significant extent of homoconjugation. Of course, this approach is not applicable to low permittivity solvents where salts are not dissociated.

Potentiometric pH measurement can in principle be an absolute technique. However, usually it is used as a relative technique, especially in non-aqueous solutions. This means that the pH-sensitive electrode (typically a glass membrane electrode) is calibrated by buffer solutions composed of a reference acid with a well-known pK _a and its salt in the same solvent where the pK _a is measured. It is important that the pK _a of the reference acid(s) used for calibration is not too different from the expected pK _a value of the acid to be measured. Such calibration is often carried out as a potentiometric titration of the reference acid with a strong base. Such calibration, if correctly done, brings, besides the ability to obtain an estimate of a(H⁺), the advantage that the influence of some uncertainty sources that affect both the acid used for calibration and the acid for which pK _a is measured, most notably, the water content of the solvent, will decrease by partial cancellation.

Potentiometry has the same general limitation as conductometry: there is no way to directly monitor the process that occurs in solution during titration and whether it corresponds to the expected acid-base reaction. Only limited insights can be obtained from the shape of the titration curve. This limitation makes impurities quite dangerous, as for conductometry. It becomes especially noticeable with high and low pK _a values that are near the limits of the solvent under investigation. Another disadvantage of the technique is the relatively high concentrations that must be used, typically in the order of 10⁻³ to 10⁻² M. At this concentration level, homoconjugation and ion pairing become non-negligible in several solvents.

3.3 UV–VIS spectrophotometry

Direct UV–VIS spectrophotometry means that the relative amounts of the uncharged acid HA and its anion A⁻ in solution can be measured using their UV–VIS spectra. There are two important conditions: (1) the UV–VIS spectra of HA and A⁻ must differ measurably and (2) at least one of them must absorb at wavelengths where the solvent is sufficiently transparent. ⁶ The concentration/activity of the solvated hydrogen ion is found either (a) from the overall acid concentration and the [A⁻]/[HA] ratio; (b) from potentiometry or (c) from the dissociation ratio of a reference acid HA_ref, which is simultaneously present in the same solution. ¹⁰ In the first case, the technique is “absolute”, in the remaining two cases, it is “relative”. As in potentiometry, the relative way of measuring enables (at least partial but often substantial) canceling of some sources of uncertainty. If a measurement is carried out against a reference acid, then the difference of their pK _a values (ΔpK _a, equation (10)) is obtained and a rather complex data treatment is necessary because of the (almost inevitable) overlap of the UV–VIS spectra of the four species involved. ¹⁰ In the majority of cases, it can be assumed that activity coefficients of the species of the same charge type cancel so that equilibrium concentrations can be used in equation (10) instead of activities.

At the same time, in that case, since both acids are in the same solution and are influenced by the same factors, some uncertainty sources cancel either partially (e.g., water in the solvent) or fully (most importantly the uncertainty of measuring the activity of solvated hydrogen ion). Furthermore, depending on the exact procedure, concentration errors may also cancel. If this advantage is combined with measuring against different reference acids, then highly accurate results can be obtained.

In general, UV–VIS spectrophotometry cannot distinguish between free anions A⁻ and ion pairs BH⁺A⁻. Thus, in low permittivity solvents, UV–VIS spectrophotometry works according to equations (7) or (8). In fact, the large majority of ion-pair pK _a values have been measured this way (the rest have been measured mostly with NMR). However, the low concentration that can be used in spectrophotometry – typically 10⁻⁵ to 10⁻⁴ M – means that in most solvents of sufficiently high permittivity, (here: DMSO, MeCN, DMF, PC, acetone, and occasionally pyridine) ion pairing and homoconjugation are (usually) negligible and pK _a values corresponding to equation (2) are measured. The low concentration also enables use of ratios of equilibrium concentrations instead of ratios of activities in equation (10). ¹⁰ The possibility of working at low concentrations is a distinct advantage of direct UV–VIS spectrophotometry along with the possibility of directly monitoring the dissociation process. In most cases it is possible to detect side processes, such as decomposition, often also homoconjugation, from the spectra, by monitoring the shapes of the absorption bands and the sharpness of isosbestic points. Because of the possibility of directly observing the processes taking place in solution, UV–VIS spectrophotometry is more suitable than conductometry or potentiometry for determining pK _a values that are close to the solvent limits. Impurities that do not absorb in the used spectral range do not disturb direct UV–VIS measurements, even if they are acids or bases.

Important downsides of direct UV–VIS spectrophotometry are that (1) it is not applicable to all compounds; the compound needs to absorb radiation in a suitable range (typically at wavelengths longer than 230 nm) and the spectra of HA and A⁻ have to differ significantly and (2) it is not well suited to solvents with long-wavelength ultraviolet cutoffs (see Table A-4 in Reichardt and Welton ⁶ ).

Indirect UV–VIS spectrophotometry operates similarly to direct UV–VIS spectrophotometry when the acid HA and a reference acid HA_ref are titrated simultaneously in the same solution. However, it differs from the direct mode because the spectra of HA or A⁻ are not used. Instead, the [HA]/[A⁻] ratio is found using the amounts of HA_ref and A_ref ⁻ in solution (found from spectra), as well as the concentrations of the solutions and the amounts of titrant added. Indirect UV–VIS spectrophotometry has a broader applicability, both in terms of which HA can be measured (since its spectral properties are not important) and what solvents can be used (if HA_ref has changes in the UV–VIS spectrum at sufficiently long wavelengths). The obvious downside of indirect spectrophotometry is that the actual dissociation process of HA in the solution is not monitored, and information about side reactions is not obtained. The requirements with respect to the purity of the solvent and substrate are also much higher than with direct UV–VIS spectrophotometry.

3.4 NMR spectrometry

NMR spectrometry observes changes in the NMR spectrum of the acid HA upon its ionization. Usually ¹H–, ¹³C–, ³¹P–, or ¹⁹F-NMR are used. NMR is almost always used as a relative technique, similar to the relative mode of direct UV–VIS spectrophotometry. Under fast exchange conditions (which is the preferred way of working), the [A⁻]/[HA] ratio is found from the displacement of the chemical shift of a selected atom (reporter atom) in the molecule, where the chemical shift is influenced by ionization. In relative measurements, a reference acid HA_ref is added to the solution and the chemical shifts of its reporter atom are also recorded. As a result, the difference of the pK _a values of HA and HA_ref (ΔpK _a) is obtained. Because of the much higher resolution and discriminating power of NMR compared with UV–VIS spectrophotometry, it is almost always possible to find an HA_ref whose NMR signals do not overlap with those of HA. Even more, it is often possible to measure ΔpK _a simultaneously in the same solution against two different reference acids.

In general, NMR does not distinguish between free anions and BH⁺A⁻. ⁴¹ Thus, it works according to equation (7). However, when sufficiently low concentrations can be used, ion pairing, as well as homoconjugation can be negligible and pK _a values corresponding to equation (2) can be measured directly.

NMR is a more widely applicable technique than direct UV–VIS spectrophotometry, because almost all organic compounds have NMR spectra with at least one of the above-mentioned nuclei, and it is almost always possible to find a suitable reporter atom (which does not necessarily need to be in the immediate vicinity of the acid center ⁴² ).

NMR is similar to (but more informative than) UV–VIS spectrophotometry in that it “sees” processes occurring in solution. Chemical shifts can be measured with good accuracy, concentrations of compounds are not important (under fast exchange conditions) as long as signals can be measured, and in most cases, impurities do not hinder measurements. These things, put together, enable good accuracy and reasonable results are often obtained, even with impure compounds or when partial decomposition occurs, as long as the signals of the measured compounds are still present and distinguishable. For these reasons, NMR has become increasingly popular for pK _a determination, especially by research groups active in organic synthesis.

The main drawback of NMR is that in general it needs higher concentrations than UV–VIS spectrophotometry, which increases the probability of side reactions in low-polarity solvents. Depending on the used nucleus, the concentrations are usually in the range of 10⁻⁴ to 10⁻² M.

4.1 General

This compilation is available at the permanent address https://doi.org/10.5281/zenodo.12608876.

At the time of publication, it includes more than 9000 pK _a values for close to 5000 uncharged acids collected from around 800 original works published since the middle of the 20th century (the earliest included publication is from 1941).

Although the vast majority of acids included in this compilation are uncharged, ionic acids have been included in some special cases.

1. Second (in a few cases also third and fourth) ionization constants, i.e., pK _a2 values of acids, which are effectively the pK _a values of anionic acids, i.e., acids having a negative charge.

2. Compounds that are generally perceived as acids, although they actually have both acidic and basic properties. Typical examples are amino acids, for which all available data have been included, irrespective of the charge type (e.g., the pK _a value corresponding to ionization of the COOH group of most amino acids in DMSO refers actually to a cationic acid, i.e., an acid with a positive charge).

3. Acids that are cationic, but by their structures are best represented as “acids with charged substituents”. An example is (3-carboxyphenyl)trimethylammonium ion, which can be viewed as benzoic acid carrying the –N(CH₃)₃ ⁺ substituent in the position 3.

Most of the compiled pK _a values are experimental. As a rule, computational values have been omitted except where the following conditions were satisfied: (1) the tabulated pK _a value is a combination of several values obtained by different routes, e.g., from a number of high-level calculations (possibly combined with experimental evidence) and where the values obtained via different routes agree satisfactorily; (2) the acids are particularly important and (3) there is a reason to believe that for these acids, no reliable experimental value in the respective solvent can be obtained in the foreseeable future. The main reasons for the latter are too high acidity (e.g., the hydrogen halides in DMSO) or too low acidity (e.g., molecular hydrogen).

4.2 Order of data

The acids have been ordered according to the classification algorithm that is based on a structural identifier (see below) and is presented in the “Comments” tab of the data file (see Section 5). The two highest levels of ordering are presented here.

OH acids:

carboxylic acids; aromatic OH compounds; alcohols; NOH acids; SOH acids; POH acids; AsOH acids; other OH acids.

NH acids:

carboxamides, thiocarboxamides; amidines; sulfonamides; phosphonamides; aliphatic amines; aromatic amines; other amines; hydrazines/hydrazones; imines; aromatic heterocycles; other heterocycles; other NH acids.

CH acids:

monosubstituted methanes; disubstituted methanes; trisubstituted methanes; ethynes; carbocyclic CH acids; heterocyclic CH acids; other cyclic CH acids; other CH acids.

SH acids

PH acids

Metal hydrides

Other acids

The presentation follows chemical logic, starting off from the acid center (in compounds with several acid centers: the most acidic one) as the key feature and then splitting the body of data into further groups and subgroups based on their structure. There are 4 classification levels leading to altogether around 200 classes or subclasses. Within subclasses, the compounds are loosely ordered according to their structure.

There are some special situations. The two most important ones are: (1) compounds that markedly tautomerize and (2) compounds that have different acid centers of comparable strengths. Such compounds are located in the tables on the basis of the following considerations.

1. If there is experimental tautomeric equilibrium data available for a given compound in a given solvent, then the compound is positioned in the group of the most abundant tautomer and other tautomers are listed in the order of decreasing abundance. For example, the extensively enolized 1,3-diketones are typically positioned among alcohols (enols), not ketones. This information refers to solutions in a specific solvent, not to neat compounds.

2. All forms of amino acids are placed under OH acids, even though the acid center is often –NH₃ ⁺.

3. If there are experimental data in some other solvent or there is some other consideration (e.g., computational data or experimental data for similar compounds), the compound is placed in the group of the most abundant tautomer. However, this is not necessarily the most abundant tautomer in the specific solvent where the pK _a is determined. In such cases, the order of tautomers does not necessarily reflect their order of abundance.

4. In cases when there are no experimental data on tautomer abundance, the compound is positioned to the group where the original authors have deemed it to be. In such cases, the order of tautomers does not necessarily reflect their order of abundance.

5. Compounds that have different acid centers have typically been positioned according to the acid center indicated by the authors of the original work. Compounds for which there was no such indication were positioned according to the common chemical knowledge and experience of the present authors.

For most compounds, the Chemical Abstracts Service Registry Numbers (CAS RNs; serial numbers assigned to chemical substances), Simplified Molecular Input Line Entry System (SMILES; a text sequence that describes a molecule’s structure) and International Chemical Identifier (InChI; a unique text identifier for a chemical substance) are given and in the majority of cases, for all tautomers. Nevertheless, in some cases, compounds have been placed into groups where they are most commonly anticipated to belong, even if the actual acid center is different from the “canonical” one (e.g., amino acids, as indicated above). However, the names, acid types, CAS RNs, SMILES and InChI strings are given for both tautomers.

Importantly, in the case of compounds that can be present in the solution as mixtures of tautomers, the pK _a values correspond to the mixture, not to the individual tautomers, unless specifically indicated otherwise. All in all, in spite of the efforts to give as reliable as possible data on tautomer abundance, such data in this collection should be considered as approximate and mistakes are possible.

4.3 References

All listed pK _a values are from the original literature and are supplied with references to the respective original publications. The pK _a values initially found from compilations were verified with the original publications. As a special case, the large body of unpublished DMSO pK _a data from the F.G. Bordwell group (approximately 300 values, some of which are available at the website compiled by H.J. Reich ²² ) has been included in this compilation, although those pK _a values have not been published in peer-reviewed publications.

If the same pK _a value from same author(s) is given in several publications, then usually the earliest publication – where the experiments were actually performed – is cited in the compilation. If author(s) have corrected the earlier value without performing new experiments, e.g., due to the change of pK _a values of reference or calibration compounds, modification of data treatment model, taking into account association or counter-ion effects, then this new value is included as a separate entry.

References that contain only tautomer abundance data are given in parentheses.

4.4 Critical evaluation of data

The collected pK _a values have been critically evaluated. In some cases, corrections have been made (see below). In cases when the original publication presented insufficient detail but there is evidence that the presented pK _a values may be inaccurate, the values are marked as “doubtful”. If the evidence is very strong (i.e., the present authors are essentially convinced the reported value is inaccurate), then it is marked as “unreliable”. Unreliable values are typically thought to be in error by several pK _a units.

Although obviously inaccurate, we have retained the unreliable values in the table, mainly for two reasons. (1) Although these data are of low quality, they can still be of some help if one knows how to use them. For example, the relative order of strength of acids determined in the same work may still be correct, even if all the values are biased by several units. (2) Even more importantly, having the article cited and the reported values flagged as “unreliable” gives the potential user a clear warning and should minimize time-wasting “rediscovery”.

It is important to note that in spite of the critical approach and corrections, it is not always possible to reach a firm conclusion as to which of the published pK _a values of a compound is the most reliable.

Consistent with the present critical evaluation, approximate or less reliable data are flagged and pK _a values in a given solvent are mutually comparable (except in tetrahydrofuran, see below). We considered the following aspects during our critical evaluations.

1. Does the presented pK _a value have the claimed physico-chemical meaning? For example, if dissociation according to reaction 1 is claimed, is there evidence that ion pairs are not involved (or have been taken into account)? In cases when there is a reason to doubt this, the corresponding values are marked as “doubtful”. Specifically, if in low-permittivity solvents ion pairing was neglected, then the obtained values are typically marked as “doubtful”, unless there was evidence that neglect of ion pairing was justified.

2. How has the measurement system been calibrated in terms of a(H ⁺ )? Estimation (usually using the Bates–Guggenheim convention) of a(H⁺) in non-aqueous media is difficult and is one of the largest uncertainty sources of non-aqueous pK _a values. Therefore, usually reference compounds with known pK _a values are used for calibration. If none was mentioned or no information was given about calibration we almost always considered the values as “doubtful”. The selection of the reference compounds and their pK _a values served to determine the traceability – based on which “scale” values are presented. A good example is in DMSO where 9-phenyl-9H-fluorene (9PF) is frequently used as a standard by both the Bordwell ³⁶ and Petrov–Shatenshtein ⁴³ groups. However, the pK _a values that these groups use are different (17.9 and 18.5, respectively) due to different definitions. Such situations were typically handled by corrections, as explained below, separately for individual solvents. A special case is using reference compounds of different charge type, e.g., cationic acids for the calibration of pK _a measurements of uncharged acids or for direct comparison with pK _a values of uncharged acids. If the charge types do not match and activity coefficients are not explicitly used, we have typically marked such values as “approximate”. In some works, the potentiometric system was calibrated in water and thereafter measurements were carried out in non-aqueous solvents with the same electrode system. The pK _a values obtained in such works often differ from other authors by several units. Such values were marked as “doubtful” or “unreliable”.

3. Are the pK _a values of the reference compounds close to the measured values? A frequent problem that occurs with, e.g., potentiometric measurements is that the electrode system is calibrated in a narrow pa(H⁺) range, e.g., 1 to 5, and thereafter pK _a values are measured in a much wider range (up to, e.g., 20), requiring a lengthy extrapolation. Such a situation was usually considered a valid reason for marking the affected values as “doubtful”. Exceptions were occasionally made if the acids in question were measured more reliably in other work(s) and the results were either in good agreement with those from the work under question or could be used after correction.

4. Was the ionization ratio for the pK _a calculation measured directly (from UV–VIS spectra, NMR shifts, or similar approaches)? Direct monitoring of the ionization ratio, as opposed to obtaining it indirectly (as the ionization ratio of a reference compound via ΔpK _a measurements or pH measurements in solutions of very strong acids or bases in given solvent, or conductance), is generally more reliable. Indirectly obtained ionization ratios may be affected, to an unknown extent by the solvent impurities (e.g., acidic or basic impurities in the compound of interest or titrants), incorrect assumptions, etc. As an example, several sulfonic acids, HCl, and HBr have been measured in DMSO ⁴⁴ using conductance, without monitoring the actual ionization state of the molecules. pK _a values well above zero were obtained. At the same time, there is strong evidence that most of these compounds are strong acids in DMSO with pK _a values below zero. ⁴⁵

5. Was the concentration used sufficiently low (given the polarity of the solvent)? As discussed above, low concentrations are important for suppressing ion association and/or homoconjugation processes. ³³ The importance increases with decreasing solvent polarity. If such association processes have been considered appropriately when calculating the pK _a values from the measured data then that is of course fully acceptable.

6. Was the solvent appropriately purified and dried? Water strongly influences acid-base properties in non-HBD solvents, even if present in trace amounts. The two main effects of traces of water are (1) selective solvation/stabilization of H⁺ and (2) selective solvation/stabilization of the anion. The typical effects of using insufficiently dried solvents are (1) lowering the pK _a values (water supports acid dissociation) and (2) compression of the pK _a scale.

7. Is the pK _a value within the conveniently accessible range of the chosen solvent? The conveniently accessible pK _a ranges of the individual solvents (if available) are given below. Values of pK _a can be measured (or estimated) outside these ranges but are typically less reliable. This criterion was in some cases further supported by looking at the odd behavior of particular values in inter-solvent correlations. Examples of this are the reported pK _a values between 1 and 3 above zero. In several cases, the actual pK _a values of such acids are in fact around or less than zero.

8. Is difference between pK _a values of the same compound in different solvents consistent with available knowledge of the solvation energies of the species present in those solvents? In some cases, solvation energies of the species present in different solvents ^{46 , 47} or the transfer energies of the acid or anion of interest between solvents ²⁵ are available. Such data enable approximate estimates of differences in the pK _a values of a given compound between these solvents. The uncertainties of solvation energies are typically high compared to good-quality pK _a values, but solvation energies can still offer useful insights (e.g., see the MeCN, DMF, and PC sections below). For example, the pK _a values in MeCN are usually by 9 to 12 pK _a units higher than those in DMSO. Values outside that range can be found, but it is highly unlikely for any acid to have similar pK _a values in MeCN and DMSO.

9. Does the pK _a value follow common chemical intuition? If the compound under question is part of a family of compounds with similar structure (e.g., phenols, benzoic acids, sulfonamides, etc.,) and if pK _a values are available for some other members of the family, then inference can be made as to whether the pK _a value follows the general chemical logic. For instance, introducing electron-withdrawing substituents into acid molecules is unlikely to make pK _a higher. Obviously, care is needed with such inference because situations where the common chemical intuition does not hold (e.g., due to steric reasons) do exist.

If the experiments appear to have been made correctly but the pK _a values of reference compounds or calibrants used differed significantly from our “best estimates” (see below), then we give the corrected pK _a value but include the original pK _a with the comment (<original value>, corrected by < correction value>). For example, the (relative) pK _a of 9PF in DMSO, frequently used as a reference acid, is often taken to be 18.5. ⁴³ However, the “best estimate” is 17.9 (see below), so such values have been adjusted by −0.6 to make them comparable. In some cases, we have used correlation analysis within a series of substituted compounds to obtain a corrected pK _a value for an aberrant value. This is possible when a series of independent reliably-determined pK _a values exist. Reasons for choosing particular reference pK _a values are given below for specific solvents. It is important to note that in spite of our effort, this critical evaluation did not always lead to clarity as to which of the several published pK _a values for the same compound in the same solvent is closest to the true value.

The number of significant figures for pK _a values are typically those claimed by the original authors. Some special cases are explained below with individual solvents.

6.1 Dimethyl sulfoxide (DMSO)

Because of the relatively high permittivity and solvating ability of DMSO, acid dissociations in this solvent proceed according to equation (2), essentially without side processes. The Bordwell pK _a scale, termed as “absolute” in Matthews et al., ³⁶ serves as the primary reference for pK _a values in DMSO in this compilation. That scale has been built on the basis of a set of reference compounds (Table V in Matthews et al. ³⁶ ) assuming fixed pK _a values. In general, the pK _a values measured by the Bordwell group were considered the most reliable throughout this compilation. However, not all of Bordwell’s data have been denoted as preferred. If values from the Bordwell group were not available, then those of other groups related directly to the Bordwell scale were considered the most reliable. Values measured against references with explicitly different pK _a values (see below) were adjusted to be comparable with the Bordwell values.

The pK _a values of the Bordwell scale have been published as a rule with one decimal place. Thus, acids measured against (or corrected using those values) cannot have a better accuracy, especially as most reported measurements are less accurate than those made by the Bordwell group. Accordingly, such values are listed with just one decimal place.

The reliable range of pK _a values in DMSO is approximately between 2 and 30. As a solvent DMSO has a high basicity (electron-pair donor ability). This is evidenced by, among other factors, the highly negative transfer Gibbs energies of H⁺ from water to DMSO (−19 kJ mol⁻¹) or from MeCN to DMSO (−65 kJ mol⁻¹). ²⁵ DMSO is thus well suited for pK _a measurements of weak acids. Strong acids are fully ionized in DMSO. Nevertheless, several literature sources claim pK _a values around or above zero for acids such as HCl, HBr, and even trifluoromethanesulfonic acid (CF₃SO₃H). ²¹ In the light of a recent study on the acidities of strong acids in solution, ⁴⁵ it is possible to state that the pK _a values of all such acids in DMSO are negative. This is also supported by looking at the pK _a values of such acids in acetonitrile and the transfer Gibbs energies from acetonitrile to DMSO of H⁺ (see above) and of some anions (mostly up to few kJ mol^{−1 25} ).

Thus, similar to water, accurate measurement of near-zero pK _a values in non-aqueous solvents is difficult and any reported “near-zero” pK _a values of such acids, for which alternative evidence points to negative pK _a values, have been marked as doubtful or unreliable.

Specific comments on the works of some groups

As noted above, the “absolute” spectrophotometric pK _a scale from the Bordwell group is the primary reference for pK _a values in DMSO, both because of the very large number of pK _a values determined using the same approach and because of the high quality of their data. The potentiometric values of a number of groups (Pytela, Kulhanek, Koppel, etc.) are considered consistent with the Bordwell scale since they use Bordwell’s pK _a values to calibrate their potentiometric systems.

The pK _a values from the Kolthoff group have generally been obtained either conductometrically, potentiometrically (with glass electrodes) or (sometimes) spectrophotometrically. ^{51 , 52} In some cases, several techniques were used to increase the reliability. Some of the pK _a values from the Kolthoff group were corrected to align them with the Bordwell scale.

The Petrov–Shatenshtein group take the pK _a value of 9-phenyl-9H-fluorene (9PF) as 18.49, which is based on the H_– scale (measured in mixtures of DMSO and aqueous tetramethylammonium hydroxide), ⁵³ as their primary reference. The H_– concept was an attempt to expand the aqueous pK _a scale by successively adding more organic solvent to the aqueous solution of tetramethylammonium hydroxide acting as an OH⁻ source. By means of a series of indicator acids, apparent pH values were derived from the acid dissociation equilibria of appropriate indicators. Thereby, the estimates of aqueous pK _a values for weak indicator acids like 9PF (practically insoluble in pure water) could be obtained by extrapolation of aqueous solvent acid dissociation equilibria. The Petrov–Shatenshtein group used the extrapolated aqueous pK _a for 9PF 18.49 as the definition value for the “relative” pK _a values in all solvents. The rationale behind this is that this compound has good UV-spectral properties, and its anion has highly delocalized charge. For more detail on the H_– scale, see Stewart and O’Donnell ⁵⁴ and Shatenshtein and Shapiro. ⁵⁵ The absolute pK _a of 9PF in DMSO according to Bordwell is 17.9. The pK _a values obtained by the Petrov–Shatenshtein group are generally of high quality and were in this compilation typically adjusted by −0.6 or in some cases by the pK _a difference of some reference acid that is included in both the Bordwell and Petrov–Shatenshtein DMSO pK _a scales in order to align them with the Bordwell scale.

6.2 Acetonitrile (MeCN)

Because of the reasonably high polarity of acetonitrile, acid dissociation in this solvent proceeds according to equation (2) without significant interference from side processes, provided: (1) concentrations are below 10⁻² M ⁵⁶ and (2) the anion formed upon dissociation does not have a highly localized charge. As mentioned above, acetonitrile is significantly less basic (lower electron-pair donating ability) than DMSO. As noted above Δ_tr G°(H⁺ MeCN→DMSO) is −65 kJ mol⁻¹, ²⁵ which corresponds to roughly 11 orders of magnitude difference. This implies that the pK _a value for the same acid in acetonitrile should be, depending on anion solvation effects, greater by 9–12 than in DMSO. This is indeed what is mostly observed. As a result, acetonitrile is well suited for studies of relatively strong acids.

The primary standard substance for the pK _a values of acids in acetonitrile is 2,4,6-trinitrophenol (TNP, picric acid) with pK _a = 11.0 as determined using three independent approaches (conductometry, potentiometry, and spectrophotometry). ⁵⁷ As a result, the pK _a value of TNP can be considered reliable, which, together with good spectral properties, justifies its use as reference compound. Values either directly related to TNP or measured in reference to a pK _a scale set up using TNP, most recently revised in 2021, ⁵⁸ are considered the most reliable and not needing revision. The pK _a values of acids in ref. 58] range from 3 to 28. These values were regarded as reference values when evaluating data from other authors, which were revised if needed.

A pK _a range between 0 and 34 can be considered experimentally accessible in acetonitrile, with the range of 1–30 considered to be reasonably reliable. The upper limit of accessible pK _a values in acetonitrile is caused by the self-condensation (Thorpe reaction) of acetonitrile. ⁵⁹ This reaction leads to the formation of dimer 3-aminobutenenitrile, to trimer 2-amino-4,6-dimethylpyrimidine and to a tetramer ⁶⁰ which can act as buffer substances in the high pK _a range. It seems that these condensation reactions are dependent on the counterion. Soft cations like phosphazenium ions allow pK _a measurements of reasonable quality up to at least 33. ⁶¹

6.3 N,N-Dimethylformamide (DMF)

The Gibbs transfer energy of H⁺ from water to DMF is −14 kJ mol⁻¹, ²⁶ which is less negative than but still similar to the value from water to DMSO. Transfer energies of anions between water and these two solvents are also similar. DMF is thus well suited for acidity measurements of weak acids, and the pK _a values measured in DMF are not expected to be very different from DMSO and are usually somewhat higher.

One should be cautious when evaluating pK _a values of strong acids (hydrogen halides, 2,4,6-trinitrophenol, etc.) in DMF. In particular, 2,4,6-trinitrophenol (picric acid) is too strong an acid in DMF to be a reliable anchor compound or calibrant in potentiometry. Its published pK _a values in DMF range from 3.7 to complete dissociation (i.e., with pK _a ≲ 1). Nitro- and dinitro-phenols have pK _a values that are more convenient and these are preferred as calibrants (reference compounds) for potentiometry and for evaluating the need for corrections of the data from particular literature sources. Quite common calibrants in DMF are benzoic acid (pK _a ≈ 12.3) and 2-hydroxybenzoic (salicylic) acid (pK _a ≈ 8.2). Acetic acid (AcOH) pK _a ≈ 13.5 is close to the 13.2 obtained by combining its pK _a in water (4.8) with Δ_tr G°(H⁺ H₂O → DMF)(−18 kJ mol⁻¹) and Δ_tr G°(AcO⁻ H₂O → DMF)(66 kJ mol⁻¹). Using transfer Gibbs energies of ions for hydrohalic acids (aqueous hydrogen halides) yields pK _a estimates of −0.6 for HCl (published values 1.4 to 8), −5.6 for HBr (published values 1.8 to complete dissociation), and −9.1 for HI, all being much lower than the published experimental values. These estimates are approximate and rely on the assumption that the neutrals are solvated equally in water and DMF, but they should be treated as a warning sign with respect to the pK _a values of hydrohalic acids in DMF.

Data on weak acids from the groups of Kolthoff, Juillard, Demange-Guerin, Pytela, Ludwig, Bartnicka and Petrov are considered reliable and consistent by the present authors and do not need adjusting. The preferred values in DMF typically come from these groups. Values published by several authors from the former USSR (Butin, Aksenenko, etc.) and some others can be corrected in a reasonable way.

6.4 Pyridine

Pyridine is the most basic of the solvents being considered in this review and at the same time the second-least polar (Table 1). Because of its high basicity, pyridine favors the ionization of acids (HA). However, because of its low permittivity, some of the A⁻ produced, depending on concentration, can be in the form of ion pairs SH⁺A⁻ or BH⁺A⁻ instead of free ions. There are very few works that separately determined K _i and K _d. It has, nevertheless, been demonstrated by careful measurements using three independent techniques (potentiometry, differential vapor pressure, and UV–VIS spectrophotometry) ⁶² that TNP and dinitrophenols dissociate to free ions at sufficiently low concentrations (suitable for spectrophotometry). In part, this may be because the SH⁺ (pyridinium) ion is large and has a delocalized charge (compared with, e.g., conjugate acids of acetone or acetonitrile), which to some extent suppresses ion pairing. The pK _a value of TNP was determined by three independent methods as 3.0 and was demonstrated to be a free-ion pK _a (equation (2)). ⁶² This pK _a value of TNP can be regarded as the primary reference pK _a value in pyridine.

When looking at transfer Gibbs energies of ions from water to pyridine then it is useful to compare them with DMSO. Thus Δ_tr G°(H⁺, H₂O → pyridine) is by approximately 9 kJ mol⁻¹ more negative than in the case of H₂O → DMSO. At the same time, Δ_tr G°(A⁻, H₂O → pyridine) are sometimes lower and sometimes higher than from water to DMSO. Note however that transfer Gibbs energies are less reliable in low-permittivity solvents, such as pyridine, because low permittivity hinders dissociation of ion pairs to free ions. Nevertheless, assuming Δ_tr G° of neutrals are small compared with those of ions, and that at low concentrations ion pairs in pyridine dissociate, the pK _a values in pyridine and DMSO are expected to be not too different. This is what is mostly observed when looking at the data.

6.5 Acetone

The transfer Gibbs energy value Δ_tr G°(H⁺ H₂O → acetone) of the hydrogen ion and its Gibbs energy of solvation in acetone are not known but an estimate of Δ_tr G°(H⁺ H₂O → acetone) 29 kJ mol⁻¹ is presented in Table 1. This is by ca. 17 kJ mol⁻¹ less positive than in the case of acetonitrile. Basicity (electron-pair donor) parameters, such as β, ²⁴ also suggest that acetone is somewhat more basic than acetonitrile. At the same time, its relative permittivity (Table 1) and anion-solvating ability ²⁵ are lower. Thus, Δ_tr G°(X⁻ H₂O → acetone) are on an average 6 kJ mol⁻¹ more positive for the halide ions, compared to acetonitrile. Consequently, pK _a values in acetone are expected to be similar or somewhat lower than those in acetonitrile. This is indeed observed in most cases.

pK _a of 2,4,6-trinitrophenol (TNP) in acetone has been determined with great care ⁶³ using a similar approach to that adopted for acetonitrile, ⁵⁷ with two methods (UV–VIS spectrophotometry and potentiometry). The pK _a values obtained were 9.26 (UV–VIS spectrophotometry) and 9.2 (potentiometry). Most of the data from Czech authors (Ludwig, Pytela, etc.) are related to the average TNP pK _a value of 9.2 and this pK _a value of TNP can be considered as the primary reference pK _a value in acetone. Whenever possible, the data from other works were corrected, to be consistent with these Czech authors. The same authors have determined the pK _a of benzoic acid as 18.2. However, in a number of works, the pK _a of benzoic acid was found to be much lower. Such a systematic shift can be corrected by adjustments ranging from +5 to +8, these corrections are very large and we do not have information on the possible contraction of the obtained pK _a ranges. Accordingly, such values, even if corrected, were typically marked as doubtful or unreliable.

6.6 4-Methyl-1,3-dioxolan-2-one (propylene carbonate, PC)

PC and acetonitrile are rather similar solvents from the point of view of acid dissociation. Both have sufficiently high permittivities to support dissociation of ion pairs to free ions, although that of PC is markedly higher. Their basicities are similar. The transfer Gibbs energy Δ_tr G°(H⁺ MeCN → PC) is ca. 4 kJ mol⁻¹, ²⁵ indicating that MeCN is slightly more basic. Their β parameters are also very similar: MeCN 0.37 versus PC 0.40. The values of Δ_tr G°(X⁻ MeCN → PC) are just a few kJ mol⁻¹ negative ²⁵ for most anions. These things put together mean that unless there is a significant difference in solvation of some anions or neutral species, the pK _a values in acetonitrile and PC are expected to be similar.

In most reports, the primary reference for the pK _a measurements in PC has been the pK _a value of TNP 9.3. ⁶⁴ However, there is another serious work reporting the pK _a of TNP as 11.4. ⁶⁵ Given the pK _a of TNP in MeCN (11.0) and the similar properties of the two solvents, both of these values are realistic (a third value 6.9 published in Srivastava and Mukherjee ⁶⁶ is unrealistic). There are factors that support either value. In Talarmin et al. ⁶⁵ the solvent was drier {20 mg (H₂O) kg⁻¹ (PC) as opposed to 50 mg (H₂O) kg⁻¹ (PC) in Izutsu et al. ⁶⁴ }, and the pK _a value is higher (water content tends to lower pK _a values in non-protogenic solvents, especially in those having low basicity). If the basicities of these solvents are similar, then the pK _a values can also be expected to be similar. On the other hand, in Izutsu et al., ⁶⁴ the experiment is much more carefully described, while in Talarmin et al., ⁶⁵ the description of the measurement of pK _a(TNP) is essentially missing. The same group who published “Acid-Base Equilibria of Some Acids in Propylene Carbonate” ⁶⁴ has previously determined pK _a(TNP) = 11.0 in MeCN. The pK _a of 9.3 for TNP in PC is additionally verified by 3,5-dichloro-2,4,6-trinitrophenol (with pK _a measured using two independent methods). It is also unlikely for an increase in the water content from 20 to 50 mg (H₂O) kg⁻¹ (PC) to decrease of pK _a by 2 units.

Thus, both pK _a values 9.3 and 11.4 have some support and at this time, we are unable to prefer either. Accordingly, we did not make changes to the values of other authors who used the pK _a value of 9.3 as the reference value for their measurements.

6.7 Oxolane (tetrahydrofuran, THF)

Of the solvents included in this compilation, THF has the lowest permittivity (Table 1). As a result, the deviation of the physico-chemical meaning of the measured values from equation (2) is the largest in THF. Only a handful of reports took specific care to ensure and demonstrate that the published values corresponded to equation (2). Another set of values, reported mostly by the Barbosa group are the so-called “overall dissociation constants” K _a ^d, corresponding to equation (6).

The majority of the reported values in THF are relative ion-pair pK _a values (pK _aip values), measured relative to specified indicator acids, and belonging to certain “scales”. Such scales differ not only by their points of origin but also by the fundamental meaning of the values. They are anchored in different ways, sometimes to pK _a values from other solvents (e.g., DMSO). Not all authors discuss whether ion pairing is accounted for or not. If (1) the pK _a of the reference acid is a free-ion value, (2) the measured and reference acid are not too different and (3) the counterion is inert and has a delocalized charge, then the differences between free-ion pK _a values and pK _aip values are similar, because the ion pairing largely cancels out. The counterion does, however, have an influence on pK _aip values. The most frequently encountered counterions are Cs⁺, the [2.1.1] cryptate complex of Li⁺ (CAS RN 31250-06-3) and the 18-Crown-6 complex of K⁺ (CAS RN 17455-13-9).

The most important ion-pair pK _a (pK _aip) scales are:

1. Streitwieser’s Li^{+ 67} and Cs^{+ 68} scales. Most of the work has been done according to the revised scales ^{67 , 68} that are anchored to the pK _aip of 9H-fluorene, defined as 22.90 for both scales. ⁶⁹ In earlier works, different anchoring was used. In the present data table, where possible, the values have been corrected to align them with the revised scales. ^{67 , 68} Importantly, the Streitwieser group often reports the acidity values on “per hydrogen” basis and wherever this is the case, the values are labeled as “per hydrogen” in the present data table.

2. Antipin’s Li⁺ cryptate scale (see Antipin et al. ³¹ for a summary). Earlier values were anchored to the pK _a of 9PF in DMSO (18.5). More recent values are anchored to 9PF relative to DMSO (pK _a = 17.9 ²¹ ). The earlier values have been adjusted in this compilation to align them with the revised values. It has been established that ionized acids in THF exist almost exclusively as 1:1 ion pairs with the lithium cryptate ions. Monomeric 1:1 ion pairs are the main species under the experimental conditions. ³¹

3. Fraser’s Li⁺ scale is based on the pK _a values of 35.7 and 37.3 of diisopropylamine and 2,2,6,6-tetramethylpiperidine as acids. ⁷⁰ In principle, the scale could be aligned with the Streitwieser Li⁺ scale (by subtracting 1.5 from all values), but it was decided not to do that in this compilation as there is only one common compound (9H-fluorene) between the two scales.

4. The Morris group reports estimates of free-ion pK _a values (denoted in their works as pK _α). These values are derived from measured relative ion-pair values (using different counterions) and corrected for ion pairing using the Fuoss equation (with computationally estimated ionic radii). ⁷¹ The pK _α = 9.7 of tricyclohexylphosphanium tetraphenylborate {[HPCy₃]BPh₄} is used as anchor value. Such corrections are certainly approximate but facilitate development of a consistent set of values.

The values from Streitwieser (Li⁺, revised) and Antipin (Li⁺, revised) scales are similar and can be used interchangeably for practical applications not needing high accuracy. However, as a general rule, the shift between values from different scales is not constant and depends on the nature of the anions. Therefore, in this compilation, no translation was attempted between the scales in THF and the scale is indicated in the comments column of the pK _a table.