J. Phys. Chem. 1987, 91, 5106-51 11
5106
that can be drawn from thermodynamics concerns the sign of these coefficients. 4. Restrictions Imposed on the Signs of the Constitutive Coefficients It is directly checked that the rate of entropy production d is still given by the classical relation (1.10). Elimination of E between (1.10) and (3.17) yields
d = p T I A w [ l - exp(-A/RT)] 2 0
(4.1)
From the positiveness of 8,it follows that
w(T,p,E) > 0 for
%0
(4.2)
In equilibrium, d assumes its minimum zero value; this property entails the inequality ($)e
=& --2 Pe
>0
(4.3)
The inequalities (4.2) and (4.3) express the positivity of w whatever the value taken by E. This generalizes the result 1 > 0 obtained in classical thermodynamics. We now explore the consequences resulting from the stability of equilibrium. Accordingly, G must be minimal in equilibrium, at constant values of temperature and pressure; it follows that
( a Z G / ~ E 2 )> e 0 or equivalently
(dA/a$)'
0
(4.5)
By combining (4.3) and (4.5) and using the definition (3.18) of out that
w, it turns
(4.6)
p > 0
indicating that, at equilibrium, the coefficients positive.
w,
M , and $ are
5. Conclusions The purpose of this work was to show that nonequilibrium thermodynamics provides a natural way for establishing the nonlinear kinetic mass action law. This is achieved by working in close parallelism with extended irreversible thermodynamics. Like in EIT, one enlarges the space of the conserved variables T and p by addition of a nonconserved quantity, namely, the extent of the reaction E. Still in analogy with EIT, it is assumed that the behavior of this extra variable in the course of time is governed by a first-order time-differential relaxation equation. It must, however, be stressed that in earlier formulations of EIT only dissipative fluxes with the property to vanish in equilibrium were selected as supplementary variables. Although 5 meets the requirement to vanish at equilibrium, obviously, it does not have the structure of a flux. This is the reason that motivated Garcia-Colin et al. to choose E as the extra variable. In the present article, it is shown that the kinetic mass action law in the form of (3.17) does not require an extension of the set of the classical variables formed by T, p , and E. The present paper is intended to focus on chemical reactions, and therefore heat and diffusion effects have been disregarded. Moreover, one single chemical reaction is supposed to occur between the species. The extension of the present formalism to more complicated systems wherein several coupled chemical reactions take place with nonnegligible heat and transport processes does not raise fundamental difficulties. This problem should be solved by including into the subset of extra variables the heat flux and the diffusion fluxes. Acknowledgment. We thank Prof. J. Casas-Vasquez (University of Barcelona, Barcelona, Spain) and Prof. L. Garcia-Colin (UNAM, Mexico) for their interest in this work. One of us (G.L.) wishes also to thank the members of the Dipartimento di Matematica dell' Universita di Catania and in particular Prof. A. M. Anile for their kind hospitality during his stay in Catania. A grant from the Consiglio Nazionale delle Ricerche (CNR Italy) is also gratefully acknowledged. This work is partially supported by NATO Research Grant 0355/83.
Influence of Intramolecular Hydrogen Bonding on Chemical Reactivity. A Temperature-Jump Study of Complex Formation between Nickel(II ) and Substituted Salicylic Acids H. Diebler,* Max-Planck-Institut fur Biophysikalische Chemie, 3400 Gottingen-Nikolausberg, West Germany
F. Secco, and M. Venturini Department of Chemistry, University of Pisa. Pisa, Italy (Received: March 3, 1986)
The equilibria and kinetics of complex formation of Ni2+with 2-mercaptobenzoic acid (TSA), 2,6-dihydroxobenzoic acid (DHBA), and 3,5-dinitrosalicylic acid (DNSA) have been investigated at 25 OC and ionic strength Z = 0.3 M (NaCIOJ. The stability constants of the complexes with the dinegative salicylate ligands increase with the basicity of the phenolic -0(or -S-) atom and are KML= 6 X lo3 M-I (Ni-DNSA), 3.4 X lo4 (Ni-TSA), and 2.0 X lo' (Ni-DHBA). Kinetic studies, carried out by stopped-flow and temperature-jump relaxation techniques, revealed that in the pH range 5-7 the reaction of Ni2+with the monoprotonated ligand species (HL-) represents an important (or almost the only) path for complex formation. In the case of DHBA and DNSA (but not TSA) the rate constants of this pathway are much smaller (65 and 380 M-' s-', respectively) than those of many other simple ligands reacting with Ni2+. The same has been reported for SA (unsubstituted salicylic acid). The decrease in rate is attributed to the strong intramolecular H bonding which has been found for these three ligands (but not for TSAH-), and some mechanistic details are discussed.
Introduction Intramolecular hydrogen bonding in ligand molecules can strongly affect their rates of reaction. This was first recognized and discussed by Eigen and co-worker~l-~ in several studies on
deprotonation processes. Likewise, complex formation reactions between metal ions and (1) Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, I .
0022-3654/87/2091-5106$01.50/00 1987 American Chemical Society
Influence of H Bonding on Chemical Reactivity chelating ligands may be slowed down considerably if the ligand’s donor groups are bridged by internal hydrogen bonds. This has been observed first for the complexation of La3+ with pyridylazoresorcino14and subsequently for the complexation of Mg2+with alizarine yellow GSand of Ni2+with tropaeolin.6 More recently, systematic studies on the kinetics of complex formation of Ni(I1) and Co(I1) with substituted salicylic acids have been carried These metal ions behave “normally” toward ligands with completely deprotonated binding sites, whereas the rate constants for their complexation with monoprotonated salicylates are lower by about 2 orders of magnitude than expeCted for a dissociative interchange mechanism. The rate constants have been found to be independent of the strength of the phenolic 0-H bond (pKA2). This has been taken as evidence that the ring-closure step (assumed to involve loss of the phenolic proton) cannot be rate determining, and the results have been interpreted in terms of the mechanism discussed earlier.* In the present study we report upon the kinetics of complex formation of NiZ+ with 2,6-dihydroxobenzoic acid (DHBA), 3,5-dinitrosalicylic acid (DNSA), and 2-mercaptobenzoic acid (thiosalicylic acid, TSA). Previous investigations have demonstrated that the internal hydrogen bonds in DNSA,9 DHBA, and S A (see below) are much stronger than that in TSA. It is of interest to see whether this difference is reflected in the rates of the complex formation reactions.
The Journal of Physical Chemistry, Vol. 91, No. 19, 1987 5107
15
a
8 N
0 10
5
0.1
0.2
0.3 [OH-] ( M I
Figure 1. Spectrophotometrictitration of 2 X lo4 M DHBA with 1 M NaOH (25 OC, initial ionic strength 0.3 M, X = 270 nm). The line represents the best fit (see text).
Experimental Section
Materials. All chemicals were of analytical grade (Fluka or Merck). 2,6-Dihydroxobenzoic acid and 3,5-dinitrosalicylic acid were recrystallized from water. 2-Mercaptobenzoic acid, nickel perchlorate, sodium perchlorate, and cacodylic acid were used without further purification. The concentrations of stock solutions of nickel perchlorate were determined by titration with EDTA, using murexide as indicator.I0 Stock solutions of the salicylic acids were prepared by weight and standardized by potentiometric titrations with NaOH. Triply distilled water was used to prepare all solutions. Methods. All measurements were carried out at 25 (fO.l) “ C and at an ionic strength I = 0.3 M, adjusted with sodium perchlorate. The protolytic dissociation constants of the phenolic groups of DHBA were determined by spectrophotometric titrations with NaOH, using a micrometer syringe. The stability constants of the Ni2+-salicylate complexes were evaluated from spectrophotometric and potentiometric titrations. The spectrophotometric studies were carried out by titrating the ligand solution in the spectrophotometer cell with 0.1 M Ni2+, again using a micrometer syringe. Values of pH were measured and converted to H+ concentrations as described previo~sly.~ In the spectrophotometric titrations of the ligands with NiZ+as well as in the kinetic investigations, the pH of the reactant solutions was buffered by adding 3 X IO-3 M cacodylic acid. At this concentration the buffer components do not interact noticeably with Ni2+.” Test measurements confirmed that varying the buffer concentration (1 X 10-j-4 X 1O-j M) does not affect the kinetics. The kinetic studies with DHBA and DNSA were carried out by means of the temperature-jump relaxation technique with spectrophotometric detection.’* The temperature of the reactant solutions was raised by 3.0 “C with a time constant of 2 ps by (2) Eigen, M.; Kruse, W.; Maass, G.; de Maeyer, L. Prog. React. Kinet. 1964, 2, 286.
(3) Eigen, M.; Kruse, W. Z . Naturforsch., B 1963, 18, 857. (4) Onodera, T.; Fujimoto, M. Bull. Chem. SOC.Jpn. 1971, 44, 2003. (5) Perlmutter-Hayman, B.; Shinar, R. Inorg. Chem. 1977, 16, 385. (6) Perlmutter-Hayman. B.; Shinar, R. Inorg. Chem. 1976, 15, 2932. (7) Mentasti, E.; Pelizzetti, E.; Secco,F.; Venturini, M. Inorg. Chem. 1979, 18, 2007. (8) Mentasti, E.; Secco, F.; Venturini, M. Inorg. Chem. 1980, 19, 3528. (9) Diebler, H.; Secco, F.; Venturini, M. J . Phys. Chem. 1984,88, 4229. ( I O ) Schwarzenbach, G.; Flaschka, H. Die komplexometrische Titration; Enke: Stuttgart, 1965; p 197. ( 1 1 ) Taylor, R. S.; Diebler, H. Bioinorg. Chem. 1976, 6, 247. (12) Eigen, M.; de Maeyer, L. In Techniques in Organic Chemistry, 2nd ed.; Weissberger, A., Ed.; Wiley: New York, 1963; Vol. VIII, Part 11, p 895.
TABLE I: pK Values of Acid Dissociation Constants (25.0 OC, Z = 0.3 M) PKAl
DHBA DNSA TSA cacodylic acid
1.08“
0.28 3.45 6.19
PKA2
13.2 ( l O . l ) b
PKA3
13.1 ( l O . l ) b
7.02 (10.02)
8.09 (10.02)
“ I = 0.1; ref 13, Vol. 3, p 209. bDuring the titration the ionic strength increased from 0.3 to 0.58 M.
discharging a 0.05-bF capacitor loaded to 30 kV. The chemical relaxation process was monitored in the UV range, at a wavelength where the complexation produces relatively large spectral changes. The time constant and amplitude of the relaxation process were evaluated with the help of an electronic simulator as described earlier.9 At least four individual measurements were made with each solution and the results averaged. In preliminary experiments with Ni2+-TSA, a gradual change in the absorption and a slight decrease of the relaxation amplitude in repeated jumps indicated that some decomposition of the reactant solution occurs in the T-jump cell, probably with catalysis by the metal electrodes (Au or Pt). In addition, appreciable amounts of 1:2 complexes, Ni(TSA),Z-, are formed under the concentration conditions required for the T-jump experiments. In order to avoid these complications, the kinetics of the Ni2+-TSA system were studied by the stopped-flow method, using an instrument built at our institute (dead time 1.3 ms). The exponential reaction curves obtained with a large excess of Ni2+ ions over ligand were evaluated as described above. Results
Protolytic Equilibria. A potentiometric titration curve of DHBA does not show any inflection between pH 7 and 12, indicating that the two phenolic protons dissociate only at pH > 12 (where potentiometry is not suitable). This is consistent with the large changes in the UV spectrum of DHBA (in particular near 270 and 310 nm) which appear with increasing pH above pH 12. (Practically no variation is observed in the range pH 5-12.) Therefore, a spectrophotometric titration of 2 X M DHBA with 1 M NaOH (applying a micrometer syring) was carried out at 270 nm (25.0 “C, initial ionic strength I = 0.3 M). The experimental data have been evaluated by a computer program in which the two protolytic equilibrium constants and the extinction coefficients of the unprotonated and monoprotonated species were variable parameters. A best fit to the experimental data was
5108 The Journal of Physical Chemistry, Vol. 91, No. 19, 1987
L
lo
i
CL
z-
Diebler et al.
pH 5.00 151
8-
2
L
6
8 10-6(1/tH'1)
IO (M-')
Figure 3. Dependence of the apparent stability constant of NiDHBA on l/[H+]: circles, spectrophotometricdata (A = 334 nm); triangles, kinetic values ( k , / k , ) (25 O C , I = 0.3 M). 1
200
1000
600 l/CM
lL00
(M-'1
Figure 2. Spectrophotometric titration of 1
X M DNSA with 0.1 M Ni2+at various pH values. Plots are according to eq 2 (25 OC, I = 0.3 M, X = 380 nm).
obtained when the two proton dissociation constants were about equal. With the ionic product of water, K, = 1.7 X M2,I3 M (pK = 13.1) their values are calculated to be KA3= 7.2 X M (pK = 13.2); see Figure I . The proton and KA2 = 5.7 X dissociation constants of the other compounds used in the present study have been determined r e ~ e n t l y . A ~ summary of the pK values is given in Table I. Complex Formation Equilibria. In order to avoid the formation of complexes of composition other than 1:1, the spectrophotometric measurements were carried out under the condition CM>> CL( CM = total metal = (1-50) X M; CL = total ligand = (1-10) X M). At constant pH, an apparent equilibrium constant Kappcan be evaluated Kapp = [ML11/[M2+l [LI,
(1)
where [ML], is the sum of all 1:l complexes and [LIf is the sum of all free ligand species. With CM>> CL,the apparent stability constant is related to the spectral data by CL AA
-=
I KappA~CM
-1+ A€
where AA = A - eLCL- c M C M and Ae = eML - eL - eM. A is the total absorbancy, and EML and eL are the apparent extinction coefficients of the complex and ligand species at a given pH. Plots of C L / M vs. 1/cM according to eq 2 yield straight lines, as demonstrated in Figure 2 for Ni2+-DNSA at various pH values (AA at X = 380 nm). The intercepts and slopes provide values of Ae and Kapp. Because of the protolytic equilibria of the complex and ligand species, the values of Kappvary with pH. Under our conditions the following equilibria (scheme 3, charges omitted) may be of kl
M + L - M L
7
If M t HL
\Jr M t H2L
k2
& k3 k-2 A
\k-3
JI MHL
(3)
.lr MH2L
( 1 3 ) Smith, R. M.; Martell, A. E. Critical Stability Constants; Plenum: New York, 1976; Vol. 4, p 1.
relevance. In scheme 3 and in the further considerations the species L always represents a dinegative salicylate anion. (For DHBA, this means that one of the two phenolic O H groups is still protonated; the concentration of completely deprotonated DHBA is negligibly small.) The fully protonated salicylic acid groups are not expected to bind metal ions to a significant degree; Le., MHzL will only exist as a steady-state concentration (if at all). The relationship between Kappand the individual binding constants is then given by Kapp(
1
+KA2 + E )= [H']
KAI KA2 [H+l KMHL+ KML+ KMH~L- (4) [H+l KA1
where KMH,L = [MH,L]/[M][H,L] ( n = 0-2). A plot of the left-hand side of eq 4 vs. l / [ H + ] is shown in Figure 3 for Ni*+-DHBA. A similar plot was obtained for NiZ+-DNSA. In both systems the expression on the left-hand side of eq 4 is close to Kappunder our conditions (KA2
