Analytica Chimica Acta, 245 (1991) 271-282 Elsevier Science Publishers B.V., Amsterdam

271

Dissociation constants of Brarnsted acids in D,O and H,O: studies on polyaza and polyoxa-polyaza macrocycles

and a general correlation

Rita Delgado, J.J.R. Fratisto Da Silva *, M.T.S. Amorim, M.F. Cabral, Silvia Chaves and Judite Costa,

Centro de Quimica Estrutural, Complex0 I, Instituto Superior Tkcnico, 1096 Lisbon Codex (Portugal)

(Received 17th September 1990)

Abstract

Using data on a series of polyaza and polyoxa-polyaza macrocyclic compounds, a satisfactory linear correlation was established between the dissociation constants of their acid forms obtained in deuterium oxide (pK,) and in water

(pK,). The isotopic effect, ApK=pK, - pK,, increases with increasing pK, being larger for the weaker acids. The pK, vs. pK, correlation may be used to determine pK, or pK, values when one of the constants is known; the statistical errors of the estimates are not significatively higher than those of the experimental determinations. By including data available in the literature for a series of different acids (mineral and carboxylic acids, phenols,

protonated amines, amino acids, etc.; a total of 138 pairs of data for 70 different compounds), a good general pK, vs.

pK, correlation was also obtained (correlation coefficient 0.998), showing that the dependence of the isotopic effect on the nature of the acid is not as important as previous studies, based on limited and not always satisfactory ApK vs.

pK, correlations, suggested.

Keyworrls: Potentiometry; Brnnsted acids; Dissociation constants; Polyaza macrocycles; Polyoxa-polyaza macrocycles

It has long been known that water (H,O) has a larger self-dissociation constant than deuterium oxide (D,O) and that the dissociation constants of weak acids are larger in the former than in the latter. This property has been used to estimate values of the dissociation constants of very weak acids (pK, 2 12) that cannot be obtained in water.

Further, there is a general tendency for the difference ApK = pK, - pK, (K, and K, being the dissociation constants of the deutero-acid and the proto-acid, respectively) to increase with de- creasing strength of the acids. These observations were interpreted by several workers in terms of the zero-point energies of the dissociated deuterium and hydrogen ions relative to the covalently bonded deuterium and hydrogen atoms [l-4].

The deuterium ion, because of its greater mass, occupies a lower position than the proton in potential-energy curves and the difference will be larger the more tightly the two ions are bound in the acids. On account of this difference, the en- ergy required to remove the deuterium ion by ionization is larger than that necessary to remove the proton. A substantial difference in entropy also exists, but these contributions are impossible to calculate from first principles and their magni- tude must be determined by experiment [1,4].

Several workers stressed the importance of the interaction of the deuterium and hydrogen ions with the solvents D,O and H,O [5-71. The dissoci- ated proton exists in water as the hydronium ion (H,O+), which is strongly hydrogen bonded to

0003-2670/91/$03.50 0 1991 - Elsevier Science Publishers B.V.

272 R. DELGADO ET AL.

adjacent water molecules. The negatively charged conjugate base will also interact with water and will generally be more strongly solvated than the neutral molecule. These interactions are neces- sarily different for deutero-acids, as deuterium bonds are weaker than hydrogen bonds [5], and this must be reflected in the value of ApK, which is an overall measure of the isotopic effect in acid-base behaviour.

Subsequent to the first studies carried out in the 1930s and given the increasing availability of D,O as a by-product of nuclear energy research, experimental studies on the correlation of values of dissociation constants of deutero- and proto- acids (and of isotopic effects on kinetic constants) have proliferated and encompassed many different types of Bronsted acids (mineral, carboxylic, phe- nols, ammonium, imidazolium, etc.). The main objective in those studies was to derive the in- fluence of the functional type of the acid on the isotopic effect measured by ApK [8-lo].

In terms of zero-point energies, ApK ought to depend on the type of the acid and for a group of similar acids ApK ought to be a function of their acid strength measured by the value of pK, [8]. Indeed, Li et al. [9] have shown experimentally that ApK depends on the acid function involved for -COOH, -NH: and -ImH+ types of acid, and that for each type there is a different linear dependence of ApK on pK,.

Several other workers, e.g., Bell and Kuhn [lo] and McDougall and Long [7], obtained similar correlations and, although in a few studies con- stant ApK values were obtained [11,12], it is generally accepted that if results are grouped according to the structural type of the acid in- volved, ApK vs. pK, correlations give straight lines with slight differences in their slopes. Con- stant ApK values or a lack of correlation seem to be due to a short range of pK, values covered by the acids studied.

In these conditions, deviations from linear ApK vs. pK, correlations have been interpreted as the result of some particular “anomalous” effects, e.g., intramolecular hydrogen bonding in the acid or its conjugate base. If it occurs in the acid form, pK, will increase and ApK will decrease, causing negative deviations, as hydrogen bonds are

stronger than deuterium bonds; if it occurs in the conjugate base, the opposite will be observed, i.e., positive deviations relative to the normal linear correlation [6,7].

Such effects are frequently observed or pos- tulated in other families of compounds, e.g., poly- aminocarboxylic acids [13] and particularly poly- aza and polyoxa-polyaza macrocyclic compounds and their N-substituted derivatives, which may form differen+t types of intrfmolecular hydrogen

bonds, e.g., NH. a. N or -NH ..a -OOC-, and also exhibit changes of conformation on protona- tion [14,15] and other peculiarities that may possi- bly be reflected in deviations of ApK vs. pK, correlations.

Most of the work with these compounds was carried out in connection with ‘H NMR studies in D,O for which pK, values can be determined. This method is better for the determination of very small or very large pK values when the potentiometric techniques become less sensitive to pH (or pD) variations. Therefore, there is now available a considerable volume of data that can be used to’ test the ApK vs. pK, correlation and its applicability to detect “abnormal” effects. This was the main objective of the present work, but the opportunity arose to clarify the meaning of the different quantities measured or correlated from the measurements in D,O, which depend on the operational procedures and seem to cause some confusion.

EXPERIMENTAL

Materials The preparation of the macrocyclic compounds

has been described in previous papers [15-171. MeDOTA (see Table 1) was a gift from Guerbet (Aulnay-sous-Bois, France). D,O contained 99.8 atom-% deuterium (Merck, Darmstadt, Germany) and no correction to 100% deuterium was made to the results. CO,-free KOD and CsOD were pre- pared from the corresponding protonic com- pounds by repeated evaporations under vacuum of their solutions in D,O. CO,-free KOD and Me,NOH were prepared by previously described

DISSOCIATION CONSTANTS OF BR0NSTED ACIDS 213

techniques [18]. All the other chemicals were of analytical-reagent grade used as received.

Equipment For the potentiometric measurements a Crison

Digilab 517 instrument was used together with an Ingold U1330 glass electrode and a Radiometer K401 saturated calomel reference electrode, as

described previously [ 181. Fourier transform ‘H NMR spectra were re-

corded at 100 MHz and a probe temperature of 25” C with a JEOL JNM 100 PTF spectrometer

coupled to a JEOL 980A computer or with a Bruker CXP 300 spectrometer coupled to an

Aspect 2000 computer.

Measurements The potentiometric titrations were carried out

in a cell thermostated at 25.0 &- O.l”C and the ionic strength of the solutions was kept at 0.10 M with KNO, or Me,NNO, (when complex forma-

tion with K+ was expected), as described previ- ously [18]. A minimum of three titrations of solu- tions of the compounds were made at concentra-

tions varying between 8 x lop4 and 2 X lop3 M. For the NMR measurements, 0.05-0.1 M solu-

tions of the compounds were prepared in D,O and

the “apparent” pD values, denoted pD*, were adjusted by adding DC1 or CO,-free KOD or CsOD (when complexes with K+ were known to be formed but not complexes with Cs’). The

value of pD* corresponds to the reading of the pH meter previously calibrated with two standard

aqueous buffers at pH 4 and 7, using the same glass electrode and reference electrode (in this work a combined Ingold 405M3 microelectrode). Actual pD values (-log[D+] in D,O) were ob- tained from the equation pD = pD* + 0.40. {There is considerable evidence that the glass elec-

trode responds to D + in D,O as the theory pre- dicts for H+ in Hz0 [19-221. This would allow the direct determination of pK,, values from potentiometric titrations in D,O if convenient buffers for calibration in the pD range are availa- ble, but both these and the solvent itself are still

sufficiently expensive to preclude its general use. Glasoe and Long [19] found that when a pH meter with a glass and calomel combined electrode

calibrated with standard aqueous buffers is used to determine the concentration of accurately pre- pared solutions in pure D,O (therefore measuring

pD*), it was necessary to add a constant value of 0.40 f 0.02 to the readings to obtain the value of pD = - log[D+] corresponding to the correct con- centrations. This correction term arose solely from a change in potential of the glass electrode in D,O compared with that in H,O and it is the value that must be added to the observed pH meter readings

(pD*) for solutions in D,O when the pH meter and its electrodes are calibrated with standard

aqueous buffers to obtain values on the conven-

tional pD scale [21]. Numerous subsequent inves- tigators have confirmed the correctness of this value and demonstrated that it holds for different

electrolytes, different temperatures, over a wide range of pD* readings and for different commer- cial glass electrodes from different manufacturers.}

Solutions of the compounds were titrated to the totally deprotonated form in the NMR tube and

in all instances sodium trimethylsilyl-l-propane- sulphonate (DSS) was used as an internal refer- ence. The ionic strength (in KC1 or CsCl) could not be kept strictly constant as the concentration of the solutions was too high.

Calculations The dissociation constants in H,O (pK,) were

obtained from the potentiometric titrations using

the Superquad program [23]. The dissociation constants in D,O (pK,) were

calculated from the NMR titrations using a non-

linear least-squares curve-fitting procedure that minimizes the sum of the squares of the deviations between the observed and predicted (calculated) values of the chemical shifts [24-261. Provided that the exchange rate for the acid dissociation is

rapid compared with the nuclear relaxation T,-’ and T;‘, the predicted chemical shift (apred), for a given pD and for a particular resonance, is the sum of the chemical shifts for the various protona- tions states ai multiplied by the fractional popula-

tion of the i th species, I;I:

n+l

6 pred = c ‘ic’

214

The fractional populations are simply related through the acid dissociation constants (K;):

R. DELGADO ET AL.

pD, calculated by Eqn. 1 are compared with ob- served shifts to yield refined estimates of the Si and Ki values. The optimization criterion was the minimization of the sum of the squares of the differences between the observed and predicted (calculated) chemical shifts:

RESULTS AND DISCUSSION where n is the number of Ki values.

For a given resonance, the program requires initial estimates of the chemical shift in each of protonated and deprotonated forms (Si) and estimates of the pK, values.

The predicted chemical shifts (a,,,), at a given

TABLE 1

The compounds used in this work, the synthe- sis, acid-base behaviour and complexation prop- erties of which have been reported in previous papers [15-18,27,28], are representative of N-sub- stituted 9-, 12- and 1Cmembered polyaza and

General formulae of the compounds, systematic names and common abbreviations

No. Formula, name and abbreviation

1 2 3

4 5 6 7 8 9

10

11 12 13

R = H, 1-oxa-4,7-diazacyclononane ([9]aneN,O) R = CH,, 4,7-dimethyl-l-oxa-4,7-diazacyclononane (WMe,[9]aneN,O) R = CH,COOH, 1-oxa-4,7-diazacyclononane-4,7-diacetic acid (N-aq[9]aneN,O)

X=O,Z=N,R”‘=H R /NUX\,.

R,R’ = H, 1-oxa-4,7,10-triazacyclododecane ([lZ]aneN,O) R,R’ = CH,, 4,7,10-trimethyl-l-oxa-4,7,10-triazacyclododecane (N-Me,[lZ]aneN,O) R’ = H, R = CH,COOH, 1-oxa-4,7,10-triazacyclododecane-4,10-diacetic acid (N-acJlZ]aneNsO) R,R’ = CH,COOH, l-oxa-4,7,10-triazacyclododecane-4,7,lO-triacetic acid (N-acs[12]aneN,O) X,Z=O,R”’ = H, R = CH,COOH, 1,7-dioxa-4,10-diazacyclododecane-4,10-diacetic acid (N-acs[lZ]aneNsO,) X, Z = N, R”’ = H, R,R’,R” = CH,COOH, 1,4,7,10-tetraazacyclododecane-1,4,7,lO-tetraacetic acid (DOTA) X, Z = N, R”’ = CH,, R,R’,R” = CH,COOH, 2-methyl-1,4,7,10-tetraazacyclododecane-l,4,7,lO-tetraa~tic acid (MeDOTA)

R\Pv N

c” 1

;I_.._/”

R = H, l-oxa-4,8,12-triazacyclotetradecane ([14]aneNs0)R R = CH,, 4,8,12-trimethyl-l-oxa-4,8,12-triazacyclotetradecane (N-Me,[l4]aneN,O) Glycine

TA

BL

E

2

Dis

soci

atio

n

con

stan

ts a

det

erm

ined

by

pote

nti

omet

ric

(Pot

.)

(pK

,)

and

‘H

NM

R

(pK

,)

mea

sure

men

ts

AP

K

b P

K.,

AP

K

b P

K,,

AP

K

b P

K.~

h

L

igan

d N

o.

PK

,, A

pKb

ij

in

Pot

. N

MR

P

ot.

NM

R

Pot

. N

MR

P

ot.

NM

R

[9]a

neN

,O

1 5.

45 *

0.0

1=

6.13

e

0.68

9.

677

k 0.

006

’ 10

.63

=

0.95

N-M

e;?[

9]an

eN,O

2

4.82

+ 0

.08

’ 5.

26 e

0.

44

8.80

k

O.0

3 =

9.

60 =

0.

80

N-a

c,[9

]an

eN,O

3

1.8

f0.3

=

2.2

=

0.4

4.02

f

0.03

=

4.10

e

0.08

10

.578

f 0

.01’

11

.33

e 0.

76

[lZ

]an

eN,O

4

1.56

f 0.

04 ’

1.

87 =

0.

31

8.52

5 +

0.0

04 =

9.

59 e

1.

06

10.1

09+

0.00

3 c

11.1

5 e

1.04

N-M

e,[l

Z]a

neN

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S

1.67

kO

.O4=

e

- -

8.29

+

0.0

1’

9.25

0.

96

10.9

73 +

0.00

4 =

12

.21=

1.

24

N-a

c,[l

Z]a

neN

,O

6 1.

4 fO

.ld

- -

2.94

+

0.0

7 d

3.45

e

0.51

6.

02

+0.

04

d 6.

74 e

0.

72

11.2

4kO

.08

d 12

.35

=

1.11

N-a

c,[l

Z]a

neN

,O

7 2.

81+

0.01

d -

- 4.

05

+ 0

.07

d 4.

21 ’

0.16

7.

70

kO

.05

d 8.

63 ’

0.93

12

.61

kO

.03

d 11

.66

’ 1.

05

N-a

c,[1

2]an

eN,0

1 8

2.11

+0.

03

d 2.

22 e

0.

11

7.46

k

O.0

1 d

8.66

e

1.20

9.

532*

0.00

6 d

10.5

7 e

1.04

DO

TA

9

9.76

f 0

.05

d 10

.75

’ 0.

99

- 13

.84

’

MeD

OT

A

10

10.1

7+0.

01

d 11

.37

f 1.

20

f -

14.3

7

[14]

aneN

,O

11

4.5

8 + 0

.01’

5.

25 e

0.

67

8.67

3 +

0.0

07 ’

10.1

1 e

1.44

10

.097

~0.

006

’ 11

.86

=

1.76

N-M

e,[l

4]an

eN,O

12

5.

37 +

0.0

1 c

6.35

=

0.98

8.

121

f 0.

007

=

9.03

e

0.91

10

.098

+0.

003

=

11.2

4 e

1.14

Gly

cin

e 13

2.

33 +

0.0

3 ’

2.85

e

0.52

9.

64

kO

.01

c 10

.58

e 0.

94

’ D

isso

ciat

ion

s co

nst

ants

def

ined

as

step

wis

e pr

oton

di

ssoc

iati

on

con

stan

ts KHi = [

H+

][H

i_,L

]/[H

,L];

K,i = [

D+

][D

,_,L

]/[D

,L].

b

ApK

=

pK

, -p

K,;

pD

= p

D

* +

0.4.

=

T=

25

.0&

0.1°

C;

I =

0.1

M K

NO

,. d

T =

25.

0 o

C;

Z =

0.1

M M

e,N

NO

,. e

T =

25

o C

, ti

trat

ed w

ith

KO

D.

’ T

= 2

5 o

C,

titr

ated

wit

h C

sOD

.

216 R. DELGADO ET AL.

polyoxa-polyaza macrocycles. The general for- mulae of the compounds, their systematic names and common abbreviations are given in Table 1.

The dissociation constants, pK, and pK,, of the compounds, calculated from potentiometric and NMR titrations in H,O and D,O, respec- tively, together with values for other macrocyclic ligands reported in previous papers [E-17,27,28], are summarized in Table 2. ‘H NMR titration curves and the form of assignment of the reso- nances for the compounds used in this work are detailed elsewhere [14-171.

surements are less precise, the concentrations are higher, contamination of the bases (with CO,) is difficult to avoid and the ionic strength cannot be kept constant. An error of kO.3 in pK, values is probably an optimistic estimate.

The values of pK,, determined by potentiome- try in H,O, are lower than the corresponding pK, values, determined by ‘H NMR in D,O in all instances, and ApK = pK, - pK, increases with increasing pK,. A plot of ApK versus pK, gives an approximate straight line (Fig. 1) correspond- ing to the equation

As can be seen, the accuracy of the values of

PK, obtained from potentiometric titrations is fairly satisfactory, but it should be mentioned that the errors quoted were calculated by propagation rules from the standard deviations for the overall constants given by the Superquad program and refer to the quality of the data used for the calcu- lations. If other sources of error are taken into account, the best that can be achieved in work of outstanding quality is + 0.2 logarithmic units [29].

ApK = 0.11 + O.lOpK, (5)

Some of the points lie at considerable distance on either side of the line (the correlation coefficient is 0.80), as found by most of previous workers for different sets of compounds.

For the pK, values no standard deviations are quoted but naturally they are larger as the mea-

Most of the points for the 1Zmembered macro- cycles lie close to the straight line, although some anomalous points are found, but the 9-membered macrocycles show negative deviations and the 14- membered macrocycles show positive deviations;

1.4

1.2

APK 1.0

0.8

0.6

0.4

0.2

0

t -

0 2 4 6 8 10 12 14

PKH

Fig. 1. Plot of ApK= pK, - pK, as a function of pK, for the compounds listed in Table 1: (0) 12-membered macrocycles; (A)

9-membered macrocycles; (A) 1Cmembered macrocycles; (0) glycine; (*) compound 28 (see Table 3).

DISSOCIATION CONSTANTS OF BR0NSTED ACIDS 277

this suggests that separate correlations for each structural type might be more satisfactory.

changes on protonation and deuteration of the fully dissociated ligands.

However, in the authors’ opinion this kind of correlation is inadequate as the standard deviation of calculated y-intercept is comparable to the values of ApK. Indeed, as the values of ApK are obtained from the difference of two similar quan- tities, pKD and pKH, the propagated error turns out to be of the same order of magnitude as the ApK values themselves.

Under these conditions, it is considered prefer- able to use a pKD vs. pK, correlation that does not suffer from this inconvenience and is equiv- alent to the direct correlation of the free energy

Figure 2 shows the results obtained for the entire set of macrocyclic compounds used. The correlation is now fairly satisfactory; the equation of the straight line obtained is

pK, = 0.11 + 1 .lOpK, (6)

with a correlation coefficient of 0.997. The stan- dard deviation of the calculated y-intercept is 0.11 and that of the slope is 0.014. Hence, even in the most unfavourable instance the error in a pKD value estimated using Eqn. 6 falls within the nor- mal limits of the error when this constant is de- termined directly from NMR titration data.

14

12

10

8

pKD

8

I I I I

8 10 12 14

PKH

Fig. 2. Plot of pK, as a function of pK, for the compounds listed in Table 1. Symbols as in Fig. 1.

278 R. DELGADO ET AL,

TABLE 3

Dissociation constants in H,O (pK,) and in D,O (pK,)

Acid or base No. PKH PKD APK Ref.

Acetic acid

2-Acetylcyclohexanone

Alanme

N-(2-Aminoethyl)propane-

1,3-diamine

Ammonia

Aniline. HCI

Benzoic acid

Bromoacetic

Carbonic acid

Chloroacetic acid

4-Chloro-2,6-dinitrophenol

2Chforoethanol

Citric acid

Cyanoacetic acid

DACODA

2,CDinitrophenol

2,5-Dinitrophenol

2,6-Dinitrophenol

Ethylenediamine

Ethyl hydrogenfumarate

Ethyl hydrogenmaleate

Fluoroacetic acid

Formic acid

Fumaric acid

Glutamic acid

Glycine

Glycohc acid

Glycylgfycine

Glycylglycylglycine

14

15

16 PK,

PK,

17 PK,

PK,

pK3 18 19 20

21

22 PK,

PK,

23

24

25

26 PK,

PK,

PK, 27

zg PK,

PK,

PK, 29

30

31

32 PK,

PK, 33 34 35 36

37 PK,

PK, 38

13 PK,

PK,

39

40

41 PK,

PK,

4.73 5.25 0.52 19 4.64 5.13 0.49 9 9.47 9.98 0.51 7 2.24 2.73 0.49 11 9.79 10.46 0.67 12

6.28 6.96 0.68 12 9.24 10.02 0.78 12

10.24 10.75 0.51 12 9.26 9.75 0.49 7 4.55 5.13 0.58 19 4.22 4.71 0.49 2 4.21 4.71 0.50 7 2.92 3.46 0.54 10 6.35 6.78 0.43 I

10.33 10.96 0.63 19

10.25 10.89 0.64 I

2.76 3.20 0.44 2

2.851 3.339 0.488 7 2.96 3.45 0.49 10

14.31 15.01 0.70 7 2.95 3.44 0.49 9 4.38 5.02 0.64 9 5.80 6.55 0.75 9 2.50 2.94 0.44 10 1.84 1.98 0.14 30 4.70 5.32 0.62 30

12.27 12.99 0.72 30 4.07 4.59 0.52 10 4.12 4.82 0.70 7 5.20 5.73 0.53 10 3.73 4.22 0.49 10 3.92 4.42 0.50 I 7.41 7.95 0.54 12

10.19 10.76 0.57 12 3.396 3.847 0.451 6 3.077 3.532 0.455 6 2.72 3.13 0.41 10 3.75 4.20 0.45 19 3.75 4.15 0.40 I 3.095 3.557 0.462 6 4.602 5.025 0.423 6 1.96 2.59 0.63 11 2.47 2.86 0.39 9 2.24 2.78 0.54 11 9.65 10.28 0.63 9 9.90 10.43 0.53 I 3.83 4.26 0.43 10 3.74 4.27 0.53 9 3.90 4.37 0.47 7 8.18 8.76 0.58 9 3.28 3.15 0.47 9 8.00 8.58 0.58 9

DISSOCIATION CONSTANTS OF BR0NSTED ACIDS

TABLE 3 (continued)

Acid or base No. WH MD APK Ref.

279

Hi&line

Histidylhistidine

Hydrazoic acid (20 o C)

Hydroquinone

Imidazole

Iodic acid

Iodoacetic acid

o-Leucyk-tyrosine

Maleic acid

Malonic acid

Mercaptoacetate

Mercaptoethanol

Methylacetylacetone

Methyl rnercaptoacetate

m-Nitroaniline . HCl

m-Nitrobenzoic

o-Nitrophenol

p-Nitrophenol

4-Nitrothiophenol

Oxalic acid

Pentafluorothiophenol

Phenylacetic acid

Phenylalanine

Phosphoric acid

Pick acid

Proline

y-Resorcyclic acid

Salicylic acid

Sulphuric acid

Thioacetic acid

Thiophenol

Threonine

Tricarballylic acid

2,2,2-Trifluoroethanol

Trimethylacetic acid

Trimethylamine

42 PKI

PK,

PK, 43 PKI

PK,

PK, 44

45

46

41

48

49 PKI

PK,

PK,

50 PK,

PK,

51

52

53

54

55

56

57

58

59

60

61 PK,

PK, 62

63

64

65 PKI

PK, 66

67

68

69

70

71

72

73

74 PK,

PK,

PK, 75

76

11

Tris(hydroxymethyl)aminomethane 78

Water 79

Zn[2,2’-ethylenediiminobis

(ethylamine)](H20)2f 80

Zn[2,2’,2”-nitrilotris(ethylamine)]

W2Q2+ 81

Zn[2,2’-trimethylenediiminobis

(ethylamine)](H,O)*+ 82

1.81 2.14 0.33 9

6.11 6.65 0.54 9

9.20 9.83 0.63 9

5.54 6.04 0.51 9 6.80 7.30 0.50 9 1.82 8.39 0.57 9

4.68 5.01 0.33 7

10.58 11.20 0.62 277 7.09 7.65 0.56 9

0.848 1.151 0.303 7

3.19 3.61 0.42 10

2.87 3.28 0.41 9 8.36 8.96 0.60 9

10.28 11.07 0.79 9

1.98 2.53 0.55 19 1.910 2.535 0.625 6 6.28 6.61 0.33 19 6.332 6.711 0.379 6 2.86 3.30 0.44 9

10.25 10.65 0.40 34 9.61 9.96 0.35 34

9.35 9.75 0.40 7

7.91 8.26 0.35 34 2.48 2.96 0.48 19

3.62 4.12 0.50 7

7.19 7.94 0.75 I

1.26 1.14 0.48 7 4.50 4.81 0.31 34 1.270 1.666 0.396 7

4.30 4.19 0.49 7

2.68 2.98 0.30 34 4.33 4.79 0.46 10 2.02 2.56 0.54 11

2.11 2.31 0.20 19 2.128 2.362 0.234 I

7.19 1.75 0.56 2

0.38 0.82 0.44 I

10.58 11.23 0.65 34

1.87 2.33 0.46 I

2.94 3.69 0.75 7 1.90 2.20 0.30 7 3.20 3.50 0.30 34 6.43 6.76 0.34 34 2.10 2.59 0.49 11

3.50 4.03 0.53 9 4.60 5.28 0.68 9 5.15 6.55 0.80 9

12.31 13.02 0.65 7 5.03 5.52 0.49 10 9.90 10.49 0.59 I

8.19 8.75 0.56 34 15.72 16.56 0.84 7

9.07

10.57

10.30

9.14

11.21

10.91

0.67

0.62

0.61

12

12

12

280 R. DELGADO ET AL.

1E

14

1;

PK,

1c

6

I

4

2

2 4 6 a 10

PKH 12 14 16

Fig. 3. Plot of pK, as a function of pK, for compounds reported in the literature as listed in Table 3 (0) and for the compounds listed in Table l(o).

DISSOCIATION CONSTANTS OF BR0NSTED ACIDS 281

Figure 2 shows that the entire group of polyaza and polyoxa-polyaza macrocyclic compounds be- have similarly and the only cases for which some doubts arise ‘are those of compounds 11, which exhibits a positive deviation, 3 and 28, which exhibit negative deviations, relative to the straight line.

Compound 11 is 1-oxa-4,8,12-triazacyclo- tetradecane ([14]aneN,O), a 16membered macro- cycle, and 3 is 1-oxa-4,7-diazacyclononane-4,7-di-

acetic acid (N-ac,[9]aneN,O), a 9-membered mac- recycle for which no particular structural details

suggest any unusual behaviour. Compound 28 (see Table 3) is 1,5-d&a-

cyclooctane-1,5-diacetic acid (DACODA), which

may also be considered as a “ macrocyclic com-

pound”, although of a type different from those

studied in this work, and in this instance for pK,

a remarkable negative deviation from the straight line is observed. [28 was not included in the esti- mation of Eqn. 6 but it only causes minor alter- ations in the values of the intercept (+0.03) and the slope (- O.Ol)]. For this case the formation of

a strong intramolecular -NH . . . N hydrogen bond has been postulated on the basis of molecular mechanics calculations and thermodynamic data

[301. Alder et al. [31] have shown that a similar bond

occurs in the monoprotonated methylated amine 1,6-dimethyl-1,6-diazacyclodecane (N-Me,[lO]ane-

N,Hf II), the structure of which was determined by x-ray diffraction. Hence it seems likely that the

negative deviation of pK, for 28 is indeed due to intramolecular hydrogen bonding, but it appears to be the only case in which this occurs amongst the series of macrocyclic compounds listed.

It is interesting that Wieghardt et al. [32] have

also shown by an x-ray structural determination that in the compound N-Me,[9]aneN,H+ ClO,- the proton is bonded to one of the nitrogen atoms but interacts with the others. This does not seem to occur (or is not detected in the present pK, vs. pK, correlation) with the corresponding com- pound in which one of the nitrogen atoms is replaced with one oxygen, i.e., in N-Me,[9]aneN,O, or with N-Me,[l2]aneN,O, for which a negative deviation is barely detectable or very slight.

On the other hand, Barthelemy [33] could not

find any evidence for hydrogen bonding in the x-ray str+ucture of N-ac,[l4]aneN, (TETA), for

which -NH . . . -0OC bonds in the half and fully

protonated forms have been predicted [14]. From the results obtained, it seemed of interest

to use the data available to attempt a general

correlation of pK, and pK, constants. A search in the literature afforded over 100 pairs of values for 70 different Bronsted acids of various types (mineral and carboxylic acids, phenols, thiols, pro- tonated amines and imidazoles, amino acids, etc.; see Table 3). The correlation of these data, to- gether with the present data, also gives a satisfac- tory straight line with the equation

pK, = 0.32 + 1.044pKn (7) for 138 experimental pairs of results (see Fig. 3). The correlation coefficient is 0.998 and the stan- dard deviation of the y-intercept is 0.04 and that of the slcpe is 0.005. This means that the pK,

values can be estimated with errors that are not significatively higher (statistically) than those of the experimental determinations, although it is apparent in the graph that a few individual larger positive and negative deviations are observed.

As the pK, and pK, values listed in Table 3 were determined by a variety of methods (only

eight of them by NMR spectroscopy), under dif- ferent experimental conditions and with different levels of precision, detailed comments on the rea-

sons for the deviations are not possible. However, it is apparent that the present data on the macro- cyclic compounds usually display positive devia- tions relative to this graph which are larger the weaker is the acid considered, with the conspicu- ous exception of the already noted case of DACODA (28).

These are some of the reasons why the group of macrocyclic compounds might behave differently from the many other types of acids, as they are subject to various types of effects on protonation/ deprotonation, including changes of conforma- tion, and may even change the state of protona- tion/ deuteration of their basic centres depending

on the number of equivalents of H+/D+ added, as seen in the profile of many ‘H NMR titration

curves [14-171. Further, the trend is such that the isotopic effect becomes larger the stronger are the

282

basic centres of the molecules, which is the normal tendency, but this trend is more pronounced for the macrocyclic compounds.

Does this mean that the deuterium-containing molecules of these fairly large multibasic com- pounds are more stable than the hydrogen ana-

logues (i.e., occupy an even lower position in the potentials energy curve)? Is it the result of differ- ent calculation and experimental methods and conditions that give higher pKo values for the most basic centres (for pK, 2 8)? Or is it the result of too low pK, values for some of the acids reported in the literature, e.g., some thiols, which affect the slope of the straight line and lower its value?

At present it is not possible to answer these questions, but it is clear that a general pK, vs. pK, correlation does exist and that it does not

appear to be (much) influenced by the nature of the acids. This allows pK, or pKo values for Bronsted acids to be determined from each other using the present correlation, with a fair degree of accuracy, provided that no “anomalous” stabiliz- ing or destabilizing effects are to be expected. The analytical relevance of this result is well illustrated by the numerous efforts to obtain significant cor- relations in the cases of H,O and D,O, or non- aqueous solvents, a classical problem in analytical

chemistry [35].

The authors thank the Instituto National de Investiga@o Cientifica (INIC) and the Junta Na- cional de Investiga@o Cientifica e Tecnologica (JNICT), Portugal, for current financial assistance and a project grant, respectively.

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