DGÄ and TDSÄ charge relationships for the binding of carboxylicanions by open-chain polyammonium cations

Concetta De Stefano, Ottavia and Silvio Sammartano*¤Giu†reDipartimento di Chimica Inorganica, Chimica Analitica e Chimica Fisica dellÏUniversita,salita Sperone 31, I-98166 Messina (V ill. S. Agata), Italy

Enthalpies of formation have been determined by titration calorimetry for complexes formed by some polycarboxylic anions(citrate, 1,2,3-propanetricarboxylate, 1,2,3,4-butanetetracarboxylate) with open-chain polyammonium cations C2(n~1)Nn

H(6n~2)n`(n \ 2È6), at 25 ¡C. *H¡ values are generally positive and, therefore, these complexes are entropically stabilized. *G¡ and T *S¡follow a linear trend as a function of polyammonium cation and carboxylic anion charges. The linear dependence on charges of*G¡ is the same for di†erent systems, whilst that of T *S¡ is speciÐc for each system. *G¡ and T *S¡ charge relationships arereported.

The formation of polyammonium cation inorganic or organicpolyanion complexes in solution has been studied in severallaboratories in the last 25 years, mostly for cyclic polyamines.Thermodynamic parameters for the formation of polyazacy-cloalkane complexes with anions have been reviewed byBianchi et al.1 Thermodynamic and kinetic data for macro-cycle interactions with anions have been collected by Izatt etal.2 The binding of mono-, di- and tricarboxylic acids by somepolyazacycloalkanes has been studied by Kimura et al.,3 bypolarography in 0.2 mol dm~3 aqueous solution, andNaClO4by the research group of Lehn et al.,4h6 by potentiometry in0.1 mol dm~3 aqueous solution. These investigationsMe4NClwere performed at one temperature (25 ¡C) and at constantionic strength, i.e. without attempting to evaluate formationconstants at zero ionic strength, or to obtain *H¡ and T *S¡thermodynamic parameters. In other words, medium and tem-perature e†ects, have largely been ignored. Less attention hasbeen paid to the investigation of thermodynamic parametersfor the formation of organic anionÈopen-chain polyammon-ium cation complexes. In our laboratory, the formation ofthese anion coordination species has been studied7,8 at lowand variable ionic strength, in order to obtain stability con-stants at I\ 0 mol dm~3, and the e†ect of medium was takeninto account. A calorimetric investigation was carried out forATPÈpolyammonium complexes9 to obtain *H¡ and T *S¡ offormation. However, there is still no report of the determi-nation of these thermodynamic parameters for the binding ofcarboxylic anions by polyammonium cations. In this paper,we report a calorimetric investigation of the formation, inaqueous solution, of open-chain (n \ 2È6)C2(n~1)Nn

H(6n~2)n`amines with citrate, 1,2,3-propanetricarboxylate and 1,2,3,4-butanetetracarboxylate, at 25 ¡C.

ExperimentalMaterials

Amines [ethylenediamine (en), diethylenetriamine (dien),triethylenetetramine (trien), tetraethylenepentamine (tetren),pentaethylenehexamine (penten), Sigma products] were puri-Ðed by transformation into the corresponding hydrochlorides,and were used in this form. Solutions of Na2Hcit, Na2Htca

(cit\ citrate ; tca \ 1,2,3-Na3Hbtc, Na3cit, Na3tca, Na4btcpropanetricarboxylate, btc \ 1,2,3,4-butanetetracarboxylate)used in the calorimetric titrations, were prepared by adding

¤ E-mail : Sammartano=chem.unime.it

standard NaOH to their corresponding acids up to partial orcomplete neutralization. Solutions of NaOH and HCl wereprepared by diluting concentrated Fluka ampoules and werestandardized against potassium biphthalate or sodium car-bonate, respectively. Grade A glassware and twice distilledwater were used for preparation of all solutions.

Calorimetric measurements

Calorimetric measurements were performed by titrating 25 mlof the solution containing the hydrochloride amine understudy with cit or tca or btc sodium salts at 25.000 ^ 0.001 ¡Cusing a Tronac titration calorimeter model 450. Its accuracywas checked by titrating a TRIS [tris-(hydroxymethyl)amino-methane] bu†er with HCl (we found *H¡ \ [47.4^ 0.3kJ mol~1). *H¡ of protonation for amines and citrate havealready been reported.10,11 *H¡ of protonation of tca and btcwere determined by titrating their sodium salts with standardHCl. All the *H¡ of protonation are collected in Table 1.Concentrations used in the experiments were : CHnA \0.005È0.01 mol dm~3, mol dm~3 ;CL \ 0.15È0.30 CHnA \ 0.01mol dm~3, mol dm~3 (L\ anion of carboxylicCHL\ 0.15salt, HL \ monoprotonated carboxylic ligand, H

nA\ fully

protonated amine). The enthalpy of dilution was measuredbefore each experiment.

Table 1 *H¡ a of protonation of amines and carboxylic acids atI \ 0 mol dm~3 and T \ 25 ¡C

i enb dienb trienb tetrenb pentenb

1 [ 51.3 [ 49.2 [ 42.6 [ 42.2 [ 45.32 [ 96.3 [ 98.7 [ 88.9 [ 87.2 [ 90.23 [ 130.2 [ 131.2 [ 130.5 [ 131.44 [ 164.5 [ 161.8 [ 166.15 [ 188.0 [ 190.16 [ 218.8

j citc tcad btcd

1 1.6 3.4 6.62 [2.5 3.7 5.73 7.9 [0.9 4.44 0.4

a *H¡, overall protonation values, expressed in kJ mol~1 ; iH`(amines), and (carboxylic] A0\ H

iAi` jH`] Lz \H

jL(j~z)

ligands). b Ref. 10. c Ref. 11. d This work.

J. Chem. Soc., Faraday T rans., 1998, 94(16), 2395È2398 2395

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Calculations

Calorimetric titration data were analysed by the computerprogram ES5CM.12 The dependence on ionic strength of the*H¡ values was taken into account by using the methodalready proposed.12 A small heat contribution arises from theformation (or dissociation) of Na`-carboxylate or Cl~-aminecomplexes : this was taken into account in the calculations byconsidering the relative *H¡ values.10,11 Throughout thepaper, errors are given as P95% conÐdence intervals.

ResultsStability of amine–carboxylic ligand complexes

Formation constants for a large number of amineÈcarboxylicligand complexes have already been reported.7 The stability ofthese complexes depends mainly on the charges of the poly-ammonium cation and polycarboxylic ligand, according to thesimplest relationships

log Kij\ 0.56f (1)

[*G¡ \ 6.3 kJ mol~1 N~1 (2)

where indices for log refer to the reactionKij

HiAi` ] H

jL(z~j)~\ ALH

i`j(i`j~z) (I)

and N is the number of possible salt bridges,f\ zcat] o zan o ,obtained by the crude approximation N \ f/2. In Tables 2È4we report *G¡ values relative to the reaction

HnAn` ] H

jL(z~j)~\ ALH

n`j(n`j~z) (II)

(n \ maximum degree of protonation of amine). In Fig. 1 wereport *G¡ vs. n for the three systems studied here : a quite

Table 2 Thermodynamic parameters for the formationa of H`-amineÈcitrate complexes at T \ 25 ¡C and I\ 0 mol dm~3

n [*G¡ *H¡ T *S¡

j \ 0en 2 20.4 2.3b 23cdien 3 32.2 5.4b 38ctrien 4 46.0 7.7b 54ctetren 5 54.5 11.8b 66cpenten 6 60.2 19.4b 80c

j \ 1en 2 14.3 [ 3.3d 11edien 3 21.4 [ 3.6d 18etrien 4 31.8 [ 6.2d 26etetren 5 36.8 [ 4.7d 32epenten 6 39.6 [ 4.6d 35e

a In kJ mol~1, for reaction (II). b ^0.8. c ^1. d ^1.1. e ^1.5.

Table 3 Thermodynamic parameters for the formationa of H`-amineÈtricarballylate complexes at T \ 25 ¡C and I\ 0 mol dm~3

n [*G¡ *H¡ T *S¡

j \ 0en 2 19.0 10.1b 29cdien 3 32.1 18.5b 51ctrien 4 45.1 24.1b 69ctetren 5 50.8 31.0b 82cpenten 6 65.1 40.2b 105c

j \ 1en 2 13.7 7.5d 21edien 3 22.0 9.7d 32etrien 4 30.7 12.5d 43etetren 5 33.6 21.0d 55epenten 6 46.7 22.2d 69e

a In kJ mol~1, for reaction (II). b ^1.0. c ^1.5. d ^1.2. e ^1.5.

Table 4 Thermodynamic parameters for the formationa of H`-amineÈbutantetracarboxylate complexes at T \ 25 ¡C and I\ 0mol dm~3

n [*G¡ *H¡ T *S¡

j \ 0en 2 24.2 13.5b 38cdien 3 39.9 21.7b 62ctrien 4 55.1 30.3b 85ctetren 5 66.1 38.4b 105cpenten 6 79.8 50.9b 131c

j \ 1en 2 17.7 5.6d 23edien 3 30.3 6.8d 37etrien 4 41.8 9.9d 52etetren 5 48.9 15.5d 64epenten 6 59.7 18.5d 78e

a In kJ mol~1, for reaction (II). b ^0.7. c ^1. d ^0.9. e ^1.

good linearity is observed. By using the values of Tables 2È4one obtains (f\ o n( j [ z) o )

[*G¡nj

\ 3.50(^0.15)f (3)

and

[*G¡ \ 7.0(^0.3) kJ mol~1 N~1 (4)

Numerical values of eqn. (2) and (4) are comparable, but[*G¡ for eqn. (4) is signiÐcantly higher. This can beexplained by considering that cation charges are more e†ec-tive than anion ones in stabilizing these complexes,7 and foreqn. (3) and (4) we used equilibrium constants relative to reac-tion (II), i.e. the reaction with the fully protonated amine.

Fig. 1 *G¡ vs. n (maximum degree of protonation of amines) forreaction (II), for ligands : A, cit ; B, tca ; C, btc

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Table 5 *G¡/n and T *S¡/n,a at T \ 25 ¡C and I\ 0 mol dm~3

cit tca btc

[*G¡/n T *S¡/n [*G¡/n T *S¡/n [*G¡/n T *S¡/n

j \ 0en 10.2 11.5 9.5 14.5 12.1 19dien 10.7 13 10.7 17 13.3 21trien 11.5 13.5 11.3 17 13.8 21tetren 10.9 13 10.2 16 13.2 21penten 10.0 13 10.85 17.5 13.3 22

mean value 10.7 13.2 10.7 17.0 13.3 21.3

j \ 1en 7.15 5.5 6.85 10.5 8.85 11.5dien 7.1 6 7.3 11 10.1 12trien 7.95 6.5 7.7 11 10.45 13tetren 7.4 6 6.7 11 9.8 13penten 6.6 6 7.8 11.5 9.95 13

mean value 7.1 6.0 7.4 11.0 10.0 12.8

a In kJ mol~1.

Enthalpy and entropy changes

In Tables 2È4 we report the *H¡ and T *S¡ values relative toreaction (II) for j\ 0, 1. For the reaction of fully protonatedamines with unprotonated carboxylic ligands ( j\ 0), *H¡values are always positive and directly proportional to thecharge of the polyammonium cation. The same trend is fol-lowed for the reaction involving the monoprotonated carbox-ylic ligand but for citrate, where low negative values areobserved, T *S¡ values are always positive and are linearlydependent on n, as shown in Fig. 2. In Table 5, we report*G¡/n and T *S¡/n values : quite constant values are obtainedfor the same reaction of di†erent amines. As a Ðrst approx-

Fig. 2 T *S¡ vs. n (maximum degree of protonation of amines) forreaction (II), for ligands : A, cit ; B, tca ; C, btc

imation we have (T *S¡/kJ mol~1), for the formation ofamineÈcarboxylate systems altogether

T *S¡nj

\ 4.7(^0.8)f (3a)

and, therefore,

T *S¡ \ 9.4^ 1.6 kJ mol~1 N~1 (4a)

DiscussionCharge DGÄ and TDSÄ relationships

The simplest equations [eqn. (1)È(4a)] account for the generaltrend of thermodynamic parameters for the formation of themixed amineÈcarboxylate complexes considered in this work.Nevertheless, in order to have a better description of theseparameters, at a level comparable with the experimental preci-sion, we have now to consider the di†erent systems separately.Eqn. (4a) was obtained by forcing straight lines to a zero inter-cept. However, we have a better Ðt when using the equation

T *S¡ \ a ] bf (5)

the coefficients a and b of eqn. (5) are reported in Table 6, foreach carboxylic ligandÈamine system. A very good linearity isobserved, by considering the mean deviation in the Ðt (in mostcases less than the experimental error) and the linear corre-lation coefficient (generally [0.99). Values of a and b of eqn.(5) for the di†erent systems (and di†erent j values) are fairlysimilar, especially for tca and btc ; signiÐcant di†erences areobserved for cit, and this may be due to the involvement ofthe alcohol group in the coordination, as observed for severalmetal-hydroxyÈcarboxylic ligand complexes.

Comparison with other systems

*G¡Ècharge linear relationships have been found for severalopen-chain polyammoniumÈpolyanion systems studied in this

Table 6 Empirical coefficients of eqn. (5)

carboxylicligand j a b ea rb

cit 0 [ 4.6 4.73 0.7 0.99891 [ 0.4 3.10 1.2 0.9887

tca 0 [ 6.0 6.10 1.8 0.99651 [ 3.6 5.95 0.8 0.9986

btc 0 [ 7.4 7.63 1.0 0.99941 [ 4.0 6.85 0.5 0.9995

a 95% conÐdence interval in T *S¡ ; b r \ linear correlation coeffi-cient.

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Fig. 3 *G¡ and T *S¡ vs. f [eqn. (3) and (3a)] for di†erentpolyanionÈpolyamine systems (ocpa : open-chain polyamines ; paca :polyazacycloalkanes)

laboratory7,9,13h17 and for some cyclic polyammoniumÈpolyanion systems reported in the literature.3,4,6

In Fig. 3 we report *G¡ for the formation of di†erent ALHrcomplexes, considering both open-chain and cyclic amines(literature data were corrected to I\ 0 mol dm~3 using theequation reported in ref. 9) vs. f. Quite di†erent systemsbehave similarly and the linear dependence of *G¡ on f is thesame. We also found linear dependence on charge for T *S(this work and ref. 9, 15 and 17) but, in this case, the slopes ofthe function T *S¡ \ f (f) are generally signiÐcantly di†erent.

Table 7 *G¡/f and T *S¡/f mean valuesa for di†erent polyanionÈpolyamine systems, at I\ 0 mol dm~3 and T \ 25 ¡C

systemb [*G¡/f T *S¡/f ref.

ocpaÈcit3~ 3.55^ 0.25 4.3^ 0.3 this workocpaÈtca3~ 3.50^ 0.30 5.5^ 0.5 this workocpaÈbtc4~ 3.29^ 0.20 5.2^ 0.3 this workocpaÈATP4~ 3.66^ 0.32 3.5^ 1.2 9, 13ocpaÈFe(CN)64~ 3.09^ 0.5 3.1^ 1.7 14, 15ocpaÈP2O74~ 4.59^ 0.4 5.8^ 0.5 16, 17pacaÈmal2~ 3.1^ 0.4 È 3, 4, 5pacaÈcit3~ 3.0^ 0.5 È 3, 4, 6general mean values 3.5^ 0.5 4.6^ 1.2

a In kJ mol~1 ; b ocpa : open-chain polyamines ; paca : polyazacy-cloalkanes.

Table 8 Mean values per salt bridge of *G¡ and T *S¡ for di†erentpolyanionÈpolyamine systems, at I\ 0 mol dm~3 and T \ 25 ¡C

[*G¡ T *S¡system /kJ mol~1 N~1 /kJ mol~1 N~1 ref.

ATP4~ 6.7 5.9 9, 13P2O74~ 8.2 10.4 16, 17Fe(CN)64~ 7.2 6.7 14, 15carboxa 7.0 9.4 this work

a Carboxylic ligands studied in this work.

In Table 7 we report mean values of *G¡/f and T *S¡/f forsome quite di†erent systems : the general mean values are[*G¡/f\ 3.5^ 0.5 and T *S¡/f\ 4.6^ 1.2. In Table 8 arereported mean *G¡ and T *S¡ contributions per salt bridgefor ATP, pyrophosphate, hexacyanoferrate(II) andcarboxylateÈopen-chain polyamine complexes : the generalmean values are

[*G¡ \ 7.3^ 1.0 kJ mol~1 N~1 (6)

T *S¡ \ 8.1^ 3.4 kJ mol~1 N~1 (6a)

The values from Fig. 3 reported in Tables 7 and 8 and theconÐdence intervals for the mean values in eqn. (6) and (6a)demonstrate that the stability (*G¡) of di†erent amineÈanioncomplexes is the same as a function of charge, whilst T *S¡(and, therefore, *H¡) contributions are speciÐc for eachsystem.

Concluding remarksThe main conclusions are :(a) The thermodynamic parameters *G¡ and T *S¡ relative tothe formation of protonÈpolyamineÈcarboxylic ligand com-plexes depend mainly on the charges involved in the forma-tion reaction [Table 5, Fig. 1, 2, eqn. (2)È(6)].(b) The main contribution to the stability of these complexesarises from the entropic term [eqn. (4a) and (6a)], as expectedfor non-covalent interactions.(c) The linear dependence on charge of *G¡ is the same fordi†erent systems, including some polyazacycloalkaneÈpolyanion complexes [Tables 6 and 7, Fig. 3].(d) The linear dependence on charge of T *S¡ is speciÐc foreach system, i.e. quite di†erent slopes observed (Tables 6 and7, Fig. 3).

thank CNR (Consiglio Nazionale delle Ricerche, Roma)Weand Murst (Ministero della Ricerca ScientiÐca e Tecnologica,Roma) for Ðnancial support.

References

1 A. Bianchi, M. Micheloni and P. Paoletti, Coord. Chem. Rev.,1991, 110, 17.

2 R. M. Izatt, K. Pawlak, J. S. Bradshaw and R. L. Bruening,Chem. Rev., 1995, 95, 2529.

3 E. Kimura, A. Sakonaka, T. Yatsunami and M. Kodama, J. Am.Chem. Soc., 1981, 103, 3041.

4 B. Dietrich, M. W. Hosseini, J. M. Lehn and R. B. Sessions,J. Am. Chem. Soc., 1981, 103, 1282.

5 M. W. Hosseini and J. M. Lehn, J. Am. Chem. Soc., 1982, 104,3525.

6 M. W. Hosseini and J. M. Lehn, Helv. Chim. Acta, 1986, 69, 587.7 A. De Robertis, C. De Stefano, O. Giu†re and S. Sammartano,

J. Chem. Soc., Faraday T rans., 1996, 92, 4219.8 P. G. Daniele, A. De Robertis, C. De Stefano, C. Foti, O. Giu†re,

E. Prenesti and S. Sammartano, Ann. Chim. (Rome), 1997, 87, 415.9 C. De Stefano, O. Giu†re and S. Sammartano, J. Chem. Soc.,

Faraday T rans., 1998, 94, 1091.10 A. Casale, C. Foti, S. Sammartano and G. Signorino, Ann. Chim.

(Rome), 1998, 88, 55.11 P. G. Daniele, A. De Robertis, C. De Stefano, A. Gianguzza and

S. Sammartano, J. Chem. Res., 1990, (S) 300.12 A. De Robertis, C. De Stefano and C. Rigano, T hermochim. Acta,

1989, 138, 141 ; A. De Robertis, C. De Stefano, C. Rigano and S.Sammartano, J. Chem. Res., 1986, (S), 194.

13 C. De Stefano, C. Foti, A. Gianguzza, O. Giu†re and S. Sam-martano, J. Chem. Soc., Faraday T rans., 1996, 92, 1511.

14 C. De Stefano, C. Foti and O. Giu†re, J. Solution Chem., 1996,25, 155.

15 C. De Stefano, C. Foti, O. Giu†re and G. Signorino, J. SolutionChem., in press.

16 C. De Stefano, C. Foti, O. Giu†re and S. Sammartano, T alanta,1996, 43, 707.

17 C. De Stefano, C. Foti and O. Giu†re, J. Chem. Res., in press.

Paper 8/04169E; Received 3rd June, 1998

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