NMR determination of the microscopic constants of diprotonated diamines in aqueous solution

Jalanra. Vol

20. pp 973-97X

Per@mon

Press. 1973 Prmted I” Great Bntam

NMR DETERMINATION OF THE MICROSCOPIC CONSTANTS OF DIPROTONATED DIAMINES IN AQUEOUS SOLUTION H. S. CREW, L. C. VAN POUCKEand Z. EECKHAIJT Department of General and Inorganic Chemistry, University of Ghent, Ghenf Belgium (Receiwd

21 February

1973. Accepted 9 April 1973)

Summary-The microscopic acidity constants of the diprotonakd asymmetric N-methylsubstituted ethylenediamines and N-methylpiperazine were determined by using the change of the chemical shift of the methyl protons with varying acidity. The determination was carried out at 25” m aqueous solution and in an ionic medium of 1M KNOs. The basicity of the amino-functions follows the expected sequence: secondary > primary % tertiary. The influence of the substituent on the basicity of the end-group is primary > secondary $ tertiary.

The dissociation of asymmetric diprotic acids can be described in terms of microscopic constants. In this study the microscopic constants of N-methyl-substituted ethylenediamines and N-methylpiperazine were investigated. According to King,’ the dissociation scheme can be represented as follows: A-Bil

k \ ;

AA-B

A-B ’

where A-B is the unprotonated molecule, A stands for the basic site that is the less substituted, and B for the basic site that is the more substituted by the methyl group. Many methods such as ultraviolet and infrared spectrophotometry,2-5 potentiometry,6 calorimetry’.* and NMR3,‘*r0 have been used to determine microscopic constants. The last named method seems to be very appropriate. In this investigation proton resonance may be expected from the methylene and methyl groups. These protons attached to nitrogen are labile and their resonance is combined with that of water, which is used as a solvent. In some studies,” methylene proton chemical shifts were used for determining microscopic constants. A preliminary investigation revealed that resonance of the methylene protons turned out to be second order at higher pH values. Since low concentrations were used here, it was difficult to distinguish some of the response signals from the noise. This second-order phenomenon has been confirmed by using higher concentrations, as illustrated in Fig. 1. The resonance signal from the methyl group is one sharp peak over the whole pH range, indicating a fast equilibrium between the different species. Moreover the resonance is influenced only by changes in the protonation of the nitrogen atom adjacent to the 973

H. S. CREYF,L. C.

974

VAN

POUCKEand 2. EECKHAUT

IO CPS

Fig. 1. Proton

magnetic resonance of methylene groups in unprotonated concentration (l*SM), showing second-order spectrum.

a-dimen at high

methyl grdup. Therefore in this investigation microscopic constants were determined from the chemical shift of the methyl group(s) as a function of pH. EXPERIMENTAL NMR spectra were recorded on a HFX-5 Bruker Physik spectrometer at a proton frequency of 90 MHz. Tetrarnethylsilane was used as an external standard Sample tubes were rotated at a speed of about 4500 rpm. The sample temperature was 25 + 1”. Shifts were recorded in Hz units. The reproducibility was estimated to be better than 0.2 Hz. The diprotic acids were prepared from the corresponding amines and nitric acid as described previously.” The following abbreviations are used: en (ethylenediamine), men (N-methylethylenediamine), s-dimen (symmetric dimethylethylenediamine or NJ’-dimethylethyknediamine), a-d&en (asymmetric dimethylethylenediamine or N.N-dimethylethylenediamine). trimen (N,N,N’-trimethylethylenediamine), tetramen (N,N,N’,N-tetramethylethylenediamine), pip (piperazine), mpip (N-methylpiperazine) and dimpip (N,N’dimethylpiperazine). For each asymmetric diprotic acid and for s-dimen lo-15 solutions were prepared, with total concentration of OG5&f for the protonated diamines, 1M potassium nitrate as an indifkrent electrolyte, and a varying amount of potassium hydroxide. To the first solution no potassium hydroxide was added. The last solution of each series contained an excess of base to ensure the fuil deprotonation of the acid For the symmetric acids only two solutions were prepared: one without potassium hydroxide, and a second with an excess of base. The concentration of the diprotic acid should be low in comparison with the concentration of the indifFerent electrolyte, so that the macroscopic acidity constants determined in IM potassium nitrate can be used in the calculations. Otherwise large errors can be made as mentioned by Martin. ’ 2 Calculations were performed with a Siemens computer model 4004/150 and appropriate programmes were written in Fortran IV. Method The dissociation of the diprotic acid can be described by H2L2+

e

HL+

=

H+ + HL+ H+ + L

(1) (4

Microscopic

975

constants

The acidity constants are defined as K

(IH[HLI

_

‘_[H,Ll

charges being omitted for simplicity. The values of these “mtxed” acidity constants have been reported elsewhere.” acidity constants and the microscopic constants can be expressed by K, =k,+

k,

1 _=‘+’ Kz k,

k,

The relation between the (3) (4)

The method for determining the microscopic constants is based upon two assumptions: (i) the shielding of the basic site adjacent to the methyl group is linearly related to the fraction of time it is protonated; (ii) the other basic site has no influence on the shielding. Assumption (i) was proved by Grunwald et al.;” (ii) seems to be a fairly good assumption since the methyl protons are five atoms away from the non-adjacent basic site. Thus protonated s-dimen will act as a monoprotic acid with concentration twice the concentration of the original acid. In this case:

d_Wl+

WWIM

+b

2CL

(5)

Ib

in which S is the chemical shift of the methyl protons, A& is the difference of the chemical shift between the fully protonated and deprotonated acid and db is the chemical shift of the fully deprotonated acid In or&r to check equation (5), au was calculated from the relation cBaH3 + (CBK, - K, - CLKl)aH2 + (CBK,K2 - KwK, - 2K,K,CL)aH

- KwK,Kz

= 0

(‘3)

where Kw = au[OH] and was obtained experimentally for this medium, as reported earlier.” By use of the known macroscopic acidity constants” [Ll, [HL] and [HaLI were calculated. The value of d as a function of ([HL] + 2[H,L]) gives a straight line with correlation coefficient O-991; M, calculated from the slope was 46.8 Hr and from the intercept and the S value for total protonation it was 46.4 Hz, so assumptions (i) and (ii) can be considered as sufficiently valid, and formulae can be established in order to calculate the microscopic constants of the asymmetric diprotic acids. If there is only one substituted nitrogen atom the difierence of the chemical shift from hb, AS, is given by M _ W-B1

+ F2Ll

M

t

(7)

Then, from this equation, and considering the dissociation scheme: k

=

&

%

-

[H,Ll

(8) (9)

The values of kb and kd can be calculated from k., k, and equations (3) and (4). In the case of trimen where both basic sites are substituted, kb and kd can be calculated from equations similar to relations (8) and (9).

RESULTS

AND

DISCUSSION

Table 1 summarizes the chemical shift values of the symmetric and asymmetric diprotic acids: n = 0 and n = 2 mean fully unprotonated and fully protonated acid respectively. It is remarkable that foi tertiary amines the chemical shift is about 10 Hz units lower for n = 0 than for the secondary amines, and about 15 Hz units higher for n = 2. As

976

H. S. CREW. L. C.

VAN

POUCKEand Z.

EECKHAUT

Table 1. Chemical shift values of fully unprotonated (n =0), and protonated (n = 2,) acids, in Hz us. TMS Acid men s-dimen trimen

-NHCH,

--NW&

a-dimen tetramen mpfp dimpip

n=O

n=2

249.2 249.5 249.9 239.0 238.7 239.1 238.7 240.5

2946 294.4 29.52 309.7 308.6 309.2 311.5 313.5

a result, in the case of trimen, with decreasing pH, the value of the resonance peak due to the methyl groups belonging to the tertiary amino function will shift to the other side of the resonance peak due to the methyl group of the secondary amino function. The results of the calculations of microscopic constants from equations (8) and (9) are shown in Table 2. The a-values given in the last column are defined as k

[A-BH] a = [A-BH] + [HA-B] = & Table 2. Microconstants Acid men trimen a-din-ten mpip

pk. 7.677 f 7.500 i 7.342 + 5.721 f

with standard deviations and a-values, for asymmetric acids pkb

0.008 0.019 0.025 0.015

= ck, + kd

7.899 f 6.972 f 7.135 f 5354 f

0013 0.008 0,015 0007

Pk. 10.076 f 9.306 + 9.417 + 8.794 f

pkd 0.008 0.019 0.024 0.016

9.854 k 9.834 + 9623 + 9.162 +

0.013 0,008 0.014 0.007

a* 0.38(0.42) 0.77(0.79) @62(@62) 0.70(0.68)

* Values in brackets are those obtained by ca1orimetry.t’

These values agree quite well with those reported earlier” and obtained by a calorimetric method described by Paoletti et a1.l4 The hypothesis, made by Paoletti, that the enthalpy change involved in the dissociation of a proton is dependent on the dissociating group, therefore seems valid, and thus for primary amino-functions the values from en may be used, and similarly those from sdimen for the secondary amino-function and from tetramen for the tertiary. This means that the influence of the substituent seems to be an entropy effect. This is confirmed by the fact that the second method mentioned by Paoletti et al.l4 for calculating microscopic constants from macroscopic constant values, gives results which deviate to a large degree from the results obtained here and earlier.” This could be explained by the fact that the values of the macroscopic constants are more influenced by the substituents than the values of the enthalpy changes. For securing more insight, the results of Table 2 are rearranged in Table 3 as a function of the acidic group and of the substituent on the second site. They are completed with the microscopic constants of the symmetric diprotic acids. The latter have been obtained from the macroscopic constants” by taking into account the contribution of the symmetry effect

Microscopic

977

constants

For symmetric diamines both acidic groups are equivalent, k, = kd. Then it follows from equations (3) and (4) that

thus

k, = kb

and

pk, = pk,, = pK1 + log 2 pk, = pk,, = pK2 - log 2 Thus, microscopic constants of symmetric acids can be obtained directly from the macroscopic constants. ii In Table 3 the microscopic constants for symmetric and asymmetric diamines are given as a function of the acidic group and the substituent on the second site. In that table the acidity constants are given for all possible dissociations of the N-methyl-substituted ethylenediamines and piperazines. Table 3 can be interpreted in the following way: e.g., for CH,NH:CH,CH,NHl there is the possibility of considering two dissociations; if NH: is the dissociating group then CH,NHi is the substituent and the pK values is 7.68; if CH,NH: is the dissociating group then NH; is the substitutent and the pK value is 7.90. For a protonated form, e.g., NH,CH,CH,NH:CH, there is only one possibility: CH,NH: is the dissociating group and NH2 the substituent. Table 3. Microconstants

of acids as a function substituent

Ethylenediamine

of acidic group and

and derivatives

-N;I,CH,

-NlG,

-N;I(CH,),

-N;I,

790

7.84

7.14

-N&H,

7.83

7.68

6.97

-NI$CH,),

7.50

7.34

6.66

-NH, -NHCH, -N(CH&

1@08 9.96 9.83

9.93 9.85 9.62

9.42 9.31 9.15

Piperazine and derivatives /‘NH;

>NHCH,

~NH;

6.34

5.35

;NI~H,

5.72

4.93

/‘NH

9.70

8.79

9.16

8.24

INCH,

J

978

H. S. CREYF,L. C.

VAN

POUCKEand Z. EECKHALT

Several trends can be noted in the values of the microscopic constants in Table 3. In each case, the secondary amino-function is a stronger bas4 than the primary, which itself is a much stronger base than the tertiary amino-function. This is demonstrated by the horizontal lines of Table 3. The vertical lines of Table 3 show the.influence of the substituent. It is noteworthy that here the sequence between primary and secondary amino-functions has changed. Indeed, the primary amino-function as a substituent strengthens in each case the basicity of the end-group more than the secondary amino-function does. This is true for both the series of protonated and unprotonated substituents, and could be an explanation for the roughly equal values for the macroscopic constants of en and sdimen. Acknowledgement-The authors wish to thank Dr. E. Van Den Berghe and Mr. L. Delmulle for helpful discussions and Mr. F. Persijn for experimental assistance. REFERENCES 1. E. J. King, Acid-Base Equilibria, Pergamon, Oxford, 1965. 2. D. C. Olson and D. W. Margerum, J. Am. Chem. SOL, 1960,82, 5602. 3. D. Chapman, D. R. Lloyd and R. H. Prince, J. Chem Sot., 1963, 3645. 4. N. Nakamoto, Y. Morimoto and A. E. Martell, J. Am. Chem. Sot., 1963.85, 309. 5. D. T. Sawyer and J. E. Tacket, ibid., 1963, 85, 314. 6. G. Schwarxenbach and H. Ackermann, Helv. Chim Acta, 1947,X$ 1798. 7. D. P. Wrathall, R. M. Ixatt and J. J. Christensen, J. Am. Chem Sot., 1964,86, 4779. 8. M. Ciampolini and P. Paoletti, J. Phys. Chem., 1961, 65, 1224. 9. R. J. Kula. D. T. Sawver. S. I. Chan and C. M. Finlev. J. Am Chem Sot., 1963, 85, 2930. 10. J. L. Sudmeier and C.‘N: Reilky, Anal. Chem, 1964, j6, 1698. 11. H. S. Creyfand L. C. van Poucke, Thermochim Acta, 1972 4, 485. 12. R. B. Martin, J. Phys. Chem, 1961,6S, 2853. 13. E. Grunwald, A. Loewenstein and S. Meiboom, J. Chem Phys., 1957, 27, 641. 14. P. Paoletti, R. Barbucci, A. Vacca and A. Dei, J. Chem Sot., (A), 1971, 310.

Zusammenfaasuag-Die mikroskopischen Aciditiitskonstanten der zweifach protonierten asymmetrisch N-methylsubstituierten Athylendiamine und von N-Methylpiperaxin wurden bestimmt durch Messung der Anderung der chemischen Verschiebung der Methylprotonen mit der Anderung der Aciditiit. Die Bestimmung wurde in wti8riger Liisung bei 25” und in einem Ionenmedium von 1 M KNOs ausgeWhrt. Die Basizitiit der Aminofunktionen zeigt den erwarteten Gang: sekundiir > primiir & tertiti. Der Einflu5 des Substituenten auf die Basizitlt der Endgruppe ist primiir > sekundPr 3 tertiiir. Resume-On a determine Ies constantes d’acidite microscopiques des Cthylinediamines N-methyl substitubs diprotonies asymetriques et de la N-methylpiperazine en utilisant Ie changement du deplacement chimique des protons du methyle avec l’acidite variable. Le dosage a Ctt men6 a 25” en solution aqueuse et dans un milieu ionique de KNO, 1M. La basicite des fonctions amine suit la sequence attendue: secondaire > primaire * tertiaire. L’influence du substituant sur la basicitt du groupe terminal est primaire > secondaire 4 tertiaire.