Equilibrium Acidities of Superacids
Agnes Kütt,1* Toomas Rodima,1 Jaan Saame,1 Vahur Mäemets,1 Ivari Kaljurand,1 Ilmar
A. Koppel,1* Romute Yu. Garlyauskayte,2 Yurii L. Yagupolskii,2 Lev M. Yagupolskii,2
Helge Willner,3 Ivo Leito.1*
1
Institute of Chemistry, University of Tartu, Ravila 14a, Tartu 50411, Estonia
Institute of Organic Chemistry, National Academy of Sciences of Ukraine, 02094,
Murmanskaya 5, Kiev, Ukraine
3
Anorganische Chemie, Bergische Universität Wuppertal, Gaussstrasse 20, D-42097
Wuppertal, Germany
2
* To whom correspondence should be addressed. Email: agnes.kutt@ut.ee,
ilmar.koppel@ut.ee, ivo.leito@ut.ee
ABSTRACT
For the first time, the equilibrium solution acidities of a wide selection of superacids have
been measured in a medium of constant composition – 1,2-dichloroethane (DCE). DCE
has very weak basic properties and is an appropriate solvent for measuring acidities of
very strong acids of different chemical structure. DCE pKa values of well-known
superacids (CF3SO2OH, (CF3SO2)2NH, cyanocarbon acids, etc.) as well as common
mineral acids (H2SO4, HI, HBr, etc.) are reported in this work. In order to get reliable
results, many other strong acids have been used to compile a self-consistent acidity scale.
Acidities of altogether 62 acids have been determined from 176 interlinked relative
acidity measurements. From the weakest acid (picric acid) to the strongest acid
(1,1,2,3,3-pentacyanopropene) the scale is spanning for more than 15 orders of
magnitude.
TEXT
Acids of very high strength – superacids1 – and their anions (usually weakly coordinating
anions – WCAs) have found wide area of applications.2,3,4 WCAs are of key importance
as counterions in catalysis and stabilizing of highly reactive species, as well as charge
carriers in electrochemical power sources.5,6,7,8
Cyanocarbon acids,9,10,11 sulfonic acids,3 sulfonimides12 and other types of strong acids
have been known and used for a long time, but solution acidity data of most of them
range from scarce to non-consistent,13 and are often indirect.14 Although (besides their
gas-phase acidities15,16) the pKa values of some of them have been published in acetic
acid,17 most of the acidity data have been obtained in solvent mixtures of changing
composition, such as aqueous H2SO4 at different concentrations,2 acetonitrile acidified to
different extent,13 i.e. not in constant-composition liquid media. Accurate self-consistent
scale of superacids in a solvent of constant composition would be desirable, as this would
enable rigorous analysis of structure and solvent effects on acidity.
The choice of the medium for measurement of acid strength of strong acids is not
straightforward. A large part of the available solvents (e.g. heptane,18 SO2) are either not
very convenient for acid-base measurements (low polarity, poor solvating ability of ions
1
and polar solutes) or are too basic (e.g., DMSO19) for studying strong acids. A large body
of data has been obtained using the H0 approach,2 whereby different acid strengths
actually refer to different compositions of the medium. The Reed group has reported an
infrared spectroscopic scale of ion-pairing ability of superacid anions with
trioctylammonium counterion – NH scale.14 Although being useful in characterizing
anions of superacids and providing implications for the acidities of the parent acids, the
scale is not an equilibrium acidity scale and characterizes the hydrogen-bond acceptor
strength of anions rather than the Brønsted acidity of their parent acids.
In the present work, the acidities of many of previously reported superacids have been
measured using equilibrium acidity measurements in 1,2-dichloroethane (DCE). DCE is
an appropriate solvent for studying superacids because it combines negligible basic
properties and inertness with the ability to dissolve many polar and ionic compounds.
Although its dielectric constant ( = 10.60) is among the highest known for chloroalkanes
it is still too low to efficiently support dissociation of ions.20 For this reason and because
of DCE's low ion solvating ability relative ion-pair acidities (pKip) can be directly
measured. Due to the relative inertness of DCE, several problems in acidity
measurements may arise: side-processes like ion-pair formation and homoconjugation are
much more extensive in DCE than in e.g. AN, also, measurements in DCE are more
influenced by traces of water and other polar or ionic impurities.
pKa value is the most commonly used value to describe the equilibrium acidity of an
acid HA in a solvent S:
Ka

HA + S  A– + SH+
pK a   log
a(SH  )  a(A  )
a(HA )
(1)
(2)
Using the previously published method21,22 based on relative acidity measurements of
acids HA1 and HA2 we can eliminate the need to determine the activity of solvated
proton a(HS+) and taking into account formation of ion-pairs of acid anion and
protonated base during the relative direct acidity measurements:
Kip
+
–
HA1 + [HB A2 ] 
 HA2 + [HB A1 ]
+
–
pK ip  log
a([HB  A1 ])  a(HA 2 )
a([HB  A 2 ])  a(HA 1 )
(3)
(4)
Assuming that the ratio of activity coefficients of ion-paired and neutral species of both
acids are similar at each titration point: f([HB+A1–])/f(HA1) = f([HB+A2–])/f(HA2),
concentrations can be used instead of activities. Also, because of the large size and
2
inertness of the counterion HB+ (protonated phosphazene base t-BuP1(pyrr) or Alk4N+)
used in this work we can assume that both anions A1– and A2– will be influenced by ionpairing to the same extent and thus pKa  pKip. Thus
pK a (HA 2 ) - pK a (HA 1 )  pK a  pK ip  log
[HB  A1 ]  [HA 2 ]
[HB  A 2 ]  [HA 1 ]
(5)
The results are presented in Table 1. pKa values of 62 acids are interconnected with 176
relative acidity measurements to obtain a self-consistent acidity scale ranging from picric
acid 1 (pKa = 18.7) to 1,1,2,3,3-pentacyanopropene 62 (pKa = 3.4), i.e. altogether 15 pKip
units. The exact positions of the individual acids on the scale were found similarly to the
previous works21,22 by minimizing the sum of squares of differences between the directly
measured pKip values and differences of the assigned pKa values. Our measurement
method allows to measure relative acidities expressed as pKa values. In order to obtain
absolute pKa values, the scale has to be anchored to an acid with known pKa value. There
are currently no reliable absolute experimental pKa values available. We thus keep the
scale relative at this time, until a sound anchor point is found. That is, we arbitrarily
anchor it to the pKa value of Picric acid 1 (equal to 0.0 units). At present, we use only
relative values in discussion of the data.
X
NC
CN
CN
H
CN
X-TCNP
O
O
S CF3
S
O
O
Tf
N
CH3
N P N
N
Tos
t-BuP1(pyrr)
Scheme 1. Abbreviations for compounds and groups used.
3
b
b
Table 1. Equilibrium acidity scale in 1,2-dichloroethane.
b
No
Acid
b
1
Picric acid
b
2
HCl
3
2,3,4,6-(CF3)5-C6H-CH(CN)2
-0.4
-0.7
c
4
4-NO2-C6H4SO2NHTos
5
HNO3
-1.7
6
4-NO2-C6H4SO2NHSO2C6H4-4-Cl
-2.4
7
H2SO4
-2.5
8
C6(CF3)5CH(CN)2
-2.6
9
(4-NO2-C6H4-SO2)2NH
-3.7
10
3-NO2-4-Cl-C6H3SO2NHSO2C6H4-4-NO2
-4.1
11
(3-NO2-4-Cl-C6H3SO2)2NH
-4.5
12
HBr
-4.9
13
4-NO2-C6H4SO2CH(CN)2
14
2,4,6-(SO2F)3-Phenol
15
2,4,6-Tf3-Phenol d
16
CH(CN)3
17
4-Cl-C6H4SO(=NTf)NHTos
18
NH2-TCNP
-1.5
11.0
b
b
b
b
b
b
b
-6.8
2,3,5-tricyanocyclopentadiene
Pentacyanophenol
21
4-Cl-C6H4SO(=NTf)NHSO2C6H4-4-Cl
-7.6
22
HI
-7.7
23
4-NO2-C6H4SO2NHTf
b
-7.6
-7.8
Me-TCNP
25
3,4-(MeO)2-C6H3-TCNP
26
4-MeO-C6H4-TCNP
27
C(CN)2=C(CN)OH
28
4-Cl-C6H4SO(=NTf)NHSO2C6H4-NO
b 2
-8.9
29
2,4-(NO2)2-C6H3SO2OH
-8.9
30
C6F5CH(Tf)2
31
HB(CN)(CF3)3
b
32
Ph-TCNP
b
b
b
0.28
2.08
1.78
1.00
9.6
9.4
1.01
1.13
0.88
0.08
0.24
0.12
1.26
1.02
1.02
1.48
0.47
8.8
8.7
8.6
1.05
7.7
0.80
7.3
1.35
0.93
0.62
7.0
0.36
0.39
6.6
6.4
5.7
5.2
0.94
0.42
1.14
0.33
0.65
5.1
1.12
0.51
0.24
4.9
0.20
4.7
-8.6
-8.7
0.67
0.84
4.2
1.77
4.1
1.56
1.64
1.00
0.98
1.10
1.01
0.96
0.09
0.13
-0.02
-8.7
0.22
b
33
HBF4
34
FSO2OH
35
3-CF3-C6H4-TCNP
36
H-TCNP
-10.7
37
[C6H5SO(=NTf)]2NH
-11.1
38
[(C2F5)2PO]2NH
-11.3
39
2,4,6-(NO2)3-C6H2SO2OH
-11.3
40
[C(CN)2=C(CN)]2CH2
-11.4
41
TfOH
-11.4
-10.3
-10.5
0.90
3.3
1.42
3.2
3.2
0.24
3.1
3.0
0.74
0.06
0.67
3.0
0.59
0.60
-9.0
-9.4
4.0
0.81
0.12
0.12
0.46
0.28
1.61
0.59
b
-9.3
4.1
1.13
0.93
1.04
-8.8
b
4.9
0.05
-7.0
24
b
10.3
0.74
0.64
20
b
b
0.77
-6.4
-6.8
10.6
1.09
-5.9
19
b
0.73
0.71
1.48
0.36
0.19
1.03
0.80
1.33
-5.1
-6.5
e
pK a(AN) b
0.0
b
b
Directly measured pK ip values in DCE a
pK a(DCE)
2.9
0.52
0.44
0.47
1.33
1.56
0.83
1.57
2.7
0.13
1.62
2.5
1.23
1.06
0.26
0.01
0.21
0.60
-10.5
1.8
1.34
0.58
0.73
0.78
1.5
1.5
0.22
1.4
0.46
1.0
0.84
0.84
0.89
0.9
0.91
0.29
0.93
0.8
0.28
0.44
0.10
0.12
0.04
0.40
0.36
0.07
0.47
0.32
0.20
0.8
0.21
0.7
0.47
0.09
0.49
0.25
b
0.10
0.67
0.73
0.06
0.75
0.63
0.19
0.21
0.45
0.19
0.30
0.31
0.42
0.15
0.01
0.46
0.36
0.43
0.10
0.40
0.21
0.13
0.29
0.19
0.69
0.27
0.10
1.29
0.93
1.06
0.02
1.05
1.06
0.72
1.04
0.47
0.44
0.96
4
b
0.21
0.60
0.58
0.73
0.78
b
0.22
0.46
0.84
0.84
b
0.89
b
0.91
0.29
0.93
0.28
41
TfOH
42
C6H5SO(=NTf)NHTf
43
TfCH(CN)2
0.44
0.10
0.12
-11.4
b
-11.5
0.04
0.40
0.21
0.07
0.47
0.32
0.7
0.47
0.09
0.49
0.7
0.6
-11.6
0.36
44
Br-TCNP
b
45
[C(CN)2=C(CN)]2NH
b
46
3,5-(CF3)5-C6H3-TCNP
-11.8
47
Tf2NH
-11.9
48
4-Cl-C6H4SO(=NTf)NHTf
0.20
0.25
0.4
-11.8
0.10
-11.8
0.67
0.73
0.06
0.75
0.4
0.63
0.19
0.21
0.19
0.30
0.4
0.45
0.3
0.31
b
0.42
-12.1
b
0.15
0.01
0.2
0.46
0.36
49
Cl-TCNP
50
(C3F7SO2)2NH
51
(C4F9SO2)2NH
52
CN-CH2-TCNP
53
(C2F5SO2)2NH
-12.3
54
CF3-TCNP
-12.7
55
HClO4
-13.0
56
CF2(CF2SO2)2NH
-13.1
57
4-NO2-C6H4SO(=NTf)NHTf
-13.1
58
HB(CN)4
-13.3
59
(FSO2)3CH
-13.6
60
Tf2CH(CN)
-14.9
61
2,3,4,5-tetracyanocyclopentadiene
-15.1
62
CN-TCNP
-15.3
-2.7
-16.4
-3.7
-12.1
0.43
0.10
63
64
Tf3CH
-12.2
b
-12.2
0.40
0.21
0.13
0.2
0.1
0.29
b
0.19
0.27
0.10
0.69
0.0
1.29
-12.3
0.93
1.06
0.02
1.05
1.06
0.72
0.0
1.04
0.47
-0.1
0.44
0.96
0.77
-0.4
0.80
0.80
0.40
0.11
0.89
-0.7
1.04
-0.7
0.56
0.86
0.07
-0.8
0.19
-1.0
0.44
1.76
f
CF3SO(=NTf)NHTf
b
b
f
-18
1.92
2.16
1.46
1.73
0.40
0.21
-1.2
-2.4
0.22
-2.5
0.23
-5
a
Directly measured relative acidity values in DCE. b Predicted pKa values of AN (see SI
for details). c Tos represents 4-Me-C6H4SO2– group. d Tf represents CF3SO2– group. e XTCNP represents 2-X-1,1,3,3-tetracyanopropene. f Estimated DCE pKa values, see text.
Acidity of the acids on the scale. The set of 64 acids measured includes all common
strong mineral acids and a number of acids from different families. The critical factor for
the acidity of a superacid is the stability of its anion and lack of well-defined protonation
centers in the anion.6 It is fair to say that designing of a superacid for the most part
consists in designing of its anion.24
From Table 1 two rather different design concepts (@need conceptid võiks skeemil olla
ühtsetes värvides) of superacid anions emerge as the most potent:25 cyanocarbon anions
and anions of poly-SO2X-imides and methanes, especially those where in some sulfonyl
groups the =O fragment is replaced by =N-Tf. Both of these anion groups obtain their
stability from excellent charge delocalization but with different mechanism. Cyanocarbon
anions are an excellent example of delocalization of negative charge by efficient polar
resonance in a planar C3 (45, 49, 52, 54, 62, etc) or C5 (19, 61) moiety. In the sulfoanions the efficient combination of polarizable sulfur atom and the high electron-acceptor
power of the =O atoms (or the even much higher electron-acceptor power of =N-Tf26) is
put to work. Both of these concepts lead to the formation of anions that have a number of
protonation centers with similar (and very low) basicity.
5
Both of these families of superacids stretch across the whole scale and neither of the two
have been taken to their limits in this scale. For example, obviously HC5(CN)5 is a
significantly stronger acid than 61 and both 63 and 64 can still be strengthened by
additional =O → =N-Tf modifications.
Out of the acids not belonging to either of these groups the strongest is HB(CN)4 (58).
Although composed according to a different principle, its anion displays charge
delocalization similar to anions of the cyanocarbon acids by forming 4 equally weakly
basic protonation centers. Ion B(CN)(CF3)3– is a good example of loosing this symmetry:
the CF3 groups with their weaker electron-acceptor power leave the single –CN
significantly more basic than in B(CN)4– and as a result 31 is by 4 orders of magnitude
weaker acid than 58. HB(CN)4 is also significantly stronger than HBF4: the small size of
the BF4– anion creates relatively high partial charges on the –F substituents so that the
very low intrinsic basicity of the –F center increases considerably.
Except HClO4, all classical strong mineral acids are in the upper half of the scale. Their
relative weakness compared to the acids discussed above is especially noticeable in the
case hydrogen halides: HCl (pKa ca -8 in water19) is just slightly stronger than picric acid
(pKa = 0.3 in water21), HI (pKa ca -10 in water27) is by more than 5 orders of magnitude
weaker than HClO4 (pKa ca -10 in water27). The reason for this is obvious: most of the
classical mineral acids have small anions and a large part of their strength in water comes
from the efficient solvation of the anions.
CF3SO(=NTf)NHTf 64: The acidic titrant used in this work to protonate the anions of the
strongest acids is a very strong neutral acid 64. It is highly interesting to know the acidity
of this compound. The Yagupolskii substitution,26 i.e. replacement of =O by =NTf group
in aromatic or aliphatic sulphone imides leads to an acidity increase of 6.4 (6 and 28) to
5.3 (23 and 57) units. Introducing Yagupolskii substitution to the Tf2NH 47, compound
64 is obtained. Taking account the average acidity increase (5.9 units), pKa value of 64
can be estimated, giving the pKa value of -18 units.
The spectrophotometric titration method used in this work is mostly the same as
described earlier.21,22 The method is based on UV-Vis spectrophotometric titration of a
DCE solution of two acids with the DCE solution of a non-absorbing base t-BuP1(pyrr)28
to obtain neutral and anionic forms of the solution of mixture. Both acids were also
titrated separately to obtain spectra of neutral and ionized forms. From the titration data,
the relative acidity of the two compounds – the difference of their pKa values (pKa) – is
obtained. The reversibility of protonation-deprotonation process was tested for all
compounds. Compounds that did not behave reversibly (HPF6, HAl[OCH(CF3)2]4) were
not included to the scale. Titration of Bu4N+ BF4– with acid 64 and afterwards base
t-BuP1(pyrr) was stable and reversible based on UV-Vis spectra and molar ratios. The
formed complex HF∙∙∙BF3 seems to be stable in solution because of its very low
concentration and the extremely low Lewis basicity of DCE. During this experiment, it is
impossible, that the acidity of HF was measured. HF is so weak acid (considerably
weaker than HCl), that it could not be included to the present scale.
6
Usually sharp isosbestic points were obtained during titrations (see spectra of all UV-vis
spectra having compounds in supporting material), indicating that the measured
compounds did not contain significant amounts of impurities.
1. Here and below the term „superacid“ refers to a superacidic molecule not to a
superacidic medium. Superacidic molecule can be defined as a molecule having in
a particular medium higher acidity than H2SO4.
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Wiley-Interscience, New York, 2009.
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Green Chem. 9, 30 (2007).
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3175 (2006).
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Yagupolskii, L. M. Yagupolskii, Org. Biomol. Chem. 3, 2239 (2005). b) A. G.
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Zhang, M. Mishima, L. M. Yagupolskii, R. Yu. Garlyauskayte, and A. A. Filatov.
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19. F. G. Bordwell, Acc. Chem. Res. 21, 456 (1988).
20. C. Reichardt, Solvents and Solvent Effects in Organic Chemistry, Wiley-VCH,
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Koppel, J. Org. Chem. 71, 2829 (2006).
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7
24. (a) L. Lipping, I. Leito, I. Koppel, I. A. Koppel. J. Phys. Chem. A 2009 (DOI:
10.1021/jp905449k). (b) I. A. Koppel, P. Burk, I. Koppel, I. Leito, T. Sonoda, M.
Mishima, J. Am. Chem. Soc. 122, 5114 (2000).
25. It is expected that the carborane-based superacids are still stronger.7,14 Our
attempts to measure the equilibrium acidity of the unsubstituted CB11H12H failed.
See the SI.
26. I. A. Koppel, P. Burk, I. Koppel, I. Leito, J. Am. Chem. Soc.124, 5594, (2002).
27. S. Brownstein, A. E. Stillman, J. Phys. Chem. 63, 2061, (1959).
28. I. Kaljurand, A. Kütt, L. Sooväli, T. Rodima, V. Mäemets, I. Leito, I. A. Koppel,
J. Org. Chem. 70, 1019, (2005).
29. This work was supported by the Grants No. 7374 and 6701 from the Estonian
Science Foundation and by the target financing projects SF0180061s08 and
SF0180089s08 from the Ministry of Education and Science of Estonia. We are
indebted to Prof. Takaaki Sonoda and JEMCO Inc., for compounds 47, 50, 51, 53,
56. We are indebted to Prof. O. W. Webster for compounds 19 and 61 and to Elin
Raamat for the synthesis of compounds 10 and 11.
Supporting Online Material
www.sciencemag.org/
Choosing an anchor compound of the acidity scale;
Comparison of DCE pKa values with NH frequencies, gas-phase acidities and AN pKa
values;
Homoconjugation;
Estimates of pKa values for the compounds not reached by this scale;
Attempts to include some other compounds to the scale;
Description of pKa measurements;
Revision of pKa values of AN;
AN pKa values of hydrogen halides;
Origin, synthesis and characterization of used compounds;
NMR spectra of newly synthesized compounds;
UV-Vis spectra of all UV-vis active compounds.
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