J. Phys. Chem. 1996, 100, 18415-18421
18415
Kinetic and Thermodynamic Study of the Proton Transfer Equilibria in the 3,5-Dinitro-2-hydroxybenzoic Acid/Ammonia System Antonio Sa´ nchez and Manuel Gala´ n* Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, UniVersidad de SeVilla, C/Prof. Garcı´a Gonza´ lez s/n, E-41012 SeVilla, Spain ReceiVed: June 24, 1996; In Final Form: August 15, 1996X
A kinetic and thermodynamic study of the proton transfer equilibria in the 3,5-dinitro-2-hydroxybenzoic acid (DNSA)/ammonia system with different added electrolytes has been undertaken. A common mechanism has been proposed for the proton transfer relaxation pathways involving DNSA as a proton donor/acceptor and water or ammonia as the other donor/acceptor couple. The rate constants are highly dependent on the nature of the anion of the added electrolyte. The results with the organic anions oxalate, propionate, and acetate are particularly noticeable, since no chemical relaxation is observed but just the expected increase in the absorbance of the solution due to the temperature jump. A reasonable explanation for this effect is given on the basis of the intermolecular hydrogen bond between these organic anions and DNSA. The salt effects observed in this work could be of interest in relation to molecular electronics, since in electronic circuits the different elements are subjected to electric and magnetic fields.
Introduction Proton transfer reactions are usually very fast chemical processes. They are diffusion-controlled. However, if intramolecular hydrogen bonds are involved, the rate constants become slower by several orders of magnitude and well suited for study by temperature jump (T-jump) relaxation methods.1 From a theoretical point of view, a system undergoing a proton transfer can be described as a two-level system (see Figure 1) with proton transfer occurring through tunneling mechanism.2 The tunnel doublet, |1〉 and |2〉, is the basis for the description of the proton transfer process. They can be combined to give a left, |L〉, and right, |R〉, localized state characterizing the system before and after the proton transfer reaction occurs. These combinations are
|L〉 ) |R〉 )
1 (|1〉 + |2〉) x2 1 (|1〉 - |2〉) x2
Figure 1. Potential energy surfaces and first tunnel doublet for proton transfer reactions.
(1)
The transition probability from the left localized state to the right localized state is the fundamental quantity in order to predict the rate constant of the proton transfer reaction. Particularly interesting is the proton transfer reaction in the presence of an external field, since it has been predicted that an external electric field may well drop the transition probability to zero3 and thus completely impedes the process. This fact opens the possibility of an external control of the proton transfer and, thus, its application as an electronic component of molecular dimensions.4 As a first approximation to this question, a kinetic and thermodynamic T-jump study on the different proton transfer reactions involved in the 3,5-dinitrosalicylic acid (DNSA)/ ammonia system has been done as a function of an added * To whom all correspondence should be addressed. E-mail: galan@ cica.es. X Abstract published in AdVance ACS Abstracts, October 15, 1996.
S0022-3654(96)01876-X CCC: $12.00
electrolyte. The electrolyte provides the external field. This field is on a macroscopic scale zero in average but very different from zero on a microscopic scale.5 The selected system seems to be very appropriate, since the completely deprotonated anion of DNSA absorbs strongly in the visible region (440 ) 6900 mol-1 dm3 cm-1) while the partially or totally protonated species do not absorb significantly at this wavelength. Thus, the system is well suited for study with T-jump relaxation techniques and spectrophotometric detection, since a displacement in the acid-base equilibria is always accompanied by a measurable absorbance change. In the Scheme 1, the different equilibria involved in the system studied in this work are shown where L stands for deprotonated 3,5-dinitro-2-hydroxibenzoic acid and B for the deprotonated buffer species, NH3, and the charges have been omitted for simplicity. The kij are the rate constants of the different relaxation pathways. This scheme is completely general and applies to any system where relaxation occurs through proton transfer equilibria.1 All possible proton transfer relaxation pathways are included in this scheme. © 1996 American Chemical Society
18416 J. Phys. Chem., Vol. 100, No. 47, 1996
Sa´nchez and Gala´n species has been examined carefully in order to show if the complete eq 4 or the simplified expression applies. Furthermore, the different rate constants have been determined in the presence of different supporting electrolytes. The results have been compared with the predictions of simple models of rate processes in solution to test the predictive power of these models. Such a test is of interest in order to predict the response of a system based on proton transfer equilibria in an electronic circuit of molecular components.
SCHEME 1
Experimental Section
As can be seen, the description of the relaxation after a small displacement in the equilibrium concentrations through a temperature jump is rather complicated, since three independent relaxation times are expected.1,6 However, usually the three relaxation times cannot be observed experimentally, since depending on the experimental conditions usually one of the three relaxation times describes the process. In this paper, since the pH ranged from 7 to 8 throughout our study, the proton and hydroxide concentrations are small (∼10-7 mol dm-3). The changes in the concentration of these two species are even smaller, and, thus, the steady state hypothesis can be applied to the H+ and OH- concentrations. Under these conditions, only one relaxation time is expected.1,6 This relaxation time contains mainly the contribution from the direct proton exchange between DNSA and ammonia1,6 and is given by the following equation,
[
]
k24k43 × k42[HB] + k43[HL] k31k12 + ([HL] + [B]) + k32 + k12[L] + k13[B] k34k42 ([L] + [HB]) (2) k42[HB] + k43[HL]
1/τ ) k23 +
k21k13
k12[L] + k13[B]
+
[
]
where all concentrations are equilibrium concentrations after the temperature jump of the different species. By use of the acid dissociation constants for the two proton donor/acceptor couples, this expression can be simplified:
1/τ ) kfF
[
kf ) k23 +
k21k13 k12[L] + k13[B]
+
Reactants. 3,5-Dinitro-2-hydroxybenzoic acid (3,5-dinitrosalicylic acid, DNSA) was purchased from Fluka and used as received. The sodium perchlorate, sodium nitrate, sodium sulfate, sodium acetate, and sodium propionate were from Merck (quality P. A.) and used also without further purification. Sodium trichloroacetate was prepared by neutralization of the acid with a standarized sodium hydroxide solution. The trichloroacetic acid employed was also from Merck (quality P. A.) and used as received. Deionized water was employed throughout the study. NH4+/ NH3 was used as a buffer to stabilize the pH and to act as donor/ acceptor in the proton transfer equilibria. The desired concentration was prepared with a diluted standardized ammonium hydroxide solution, which was neutralized with the acid of the same anion as the supporting electrolyte to avoid adding different anions to the solution. The pH values of the solutions were always in the range 7.8-8.2. According to the conditions employed by other authors,8 the concentrations of DNSA and ammonia were varied in the ranges (1-5) × 10-4 and (2.5-30) × 10-3, respectively. pH Measurements. The pH was measured with a Crison 2000 pH meter previously calibrated with Merck buffer solutions in the range 4-10. T-Jump Experiments. For the T-jump experiments a HiTech TJ-64 apparatus was employed. The cell was thermostatized at 20 °C with a Techne C-400 thermostate and a TECAM 1000 heat exchanger. The T-jump unit achieved, according to the technical specification, a 5 °C temperature jump with a heating time constant smaller than 5 µs by discharging two 0.02 µF capacitors loaded with 11 kV. Thus, relaxation times of about 30 µs are the shortest ones that can be measured with our equipment. The heating time is directly related to the resistance of the solution and capacitance through
(3) k24k43
τh ) (RC)/2
]
k42[HB] + k43[HL]
F ) [B] + [HL] + (KHB/KHL)([HB] + [L])
(4)
Thus, by use of different concentrations of L, HL, B, and HB, the different rate constants can be determined independently. If the direct proton exchange (eqs 2 and 3) is a fast process,1,6,7 contributions from the relaxation pathways through states 1 and 4 are not expected, and the expression for kf simplifies to kf ) k23. In this case, Scheme 1 simplifies, and only states 2 and 3 need to be considered. However, the expected dependence of the relaxation time on the concentrations of HL, L, HB, and B is quite difference than predicted by the full expression (eqs 3 and 4). In the system investigated here, since the direct exchange reactions are not fast because of the intramolecular hydrogen bond present in the protonated DNSA molecule, the dependence on the concentrations of these four
(5)
Thus, a supporting electrolyte is required to lower the resistance of the solution. To achieve the heating time mentioned above, an ionic strength of about 0.3 mol dm-3 is always needed. Measurements with a lower ionic strength were not intended because of this limitation. Since the absorbance change in relaxation experiments is not large, the measurements for a given concentration were repeated and averaged over 20 repetitions to improve the signal-to-noise ratio. In this way the uncertainty in the relaxation times determined is lower than 5%. Results and Discussion Kinetic Results. For a given salt more than 25 different experiments with different DNSA and/or ammonia concentrations were made to study the concentration dependence according to eqs 3 and 4, since the relaxation times are expected to be a function of four concentrations. First, a plot of 1/τ vs F was
Proton Transfer Equilibria
J. Phys. Chem., Vol. 100, No. 47, 1996 18417 TABLE 1: Proton Transfer Rate Constants at 298.15 Ka k12 × 10-10 mol-1 dm3 s-1 k21 × 10-3 s-1 k13 × 10-10 mol-1 dm3 s-1 k31 s-1 k23 × 10-6 mol-1 dm3 s-1 k32 × 10-4 mol-1 dm3 s-1 a
NaCl3C2O2
NaClO4
NaNO3
Na2SO4
3.6
5.6
7.1
8.9
3.5
5.4
6.8
8.5
4.7
3.8
5.0
7.8
23.6
19.0
25.0
38.8
6.0
3.3
3.2
1.9
3.1
2.5
1.7
1.0
Ionic strength ) 0.3 mol dm-3 in all cases.
Figure 2. Experimental relaxation curve with NaClO4 as supporting electrolyte: [DNSA] ) 5 × 10-4 mol dm-3, [NH3] ) 2.5 × 10-3 mol dm-3, T ) 298.15 K.
tried, and if the simplified version of eqs 3 and 4 applied, a straight line should be obtained. Such a linear dependence was not observed, and therefore, a fit with eqs 3 and 4 was tried. The values of KHB and KHL, the acid dissociation constants of the two donor/acceptor pairs involved, were found in the literature: pKHB ) 9.3 and pKHL ) 7.02 (at an ionic strength of 0.3 mol dm-3).8 The best fit was always obtained by considering a three-state system without contribution of the hydrolytic path. This means that the term containing k42, k24, and k43 does not contribute to kf.8 In conclusion, from the completely general Scheme 1, state 4 can be ignored, but the experimental results can only be explained if state 1 is considered. Thus, in what follows the hydrolytic path will not be considered. Accordingly, eq 4 is further simplified to
[
kf ) k23 +
k21k13
]
k12[L] + k13[B]
F ) [B] + [HL] + (KHB/KHL)([HB] + [L])
(6)
A typical relaxation curve is shown in Figure 2. A fast increase in the absorbance is always observed due to the change of the molar extinction coefficient with temperature.9 Although electronic spectra are generally almost independent of temperature, DNSA is a well-known exception to this rule. For this reason, DNSA has been proposed as a useful molecular temperature display.9 This first part of the relaxation curve is affected by the heating process (as a matter of fact, it is a visual display of the heating process, as mentioned above). The long time scale relaxation curve is the chemical relaxation in Scheme 1. Other relaxation processes could occur in the solutions, for example Diebler et al.10 have investigated the complexation of DNSA with Ni2+ and shown that this is a long time process in comparison with the proton transfer reactions. Thus, if some complexation equilibria (for example, between DNSA and Na+) occurred under our conditions, we would reasonably expect some deviation from the monoexponential decay curve in the final part of the curve. Under all the experimental conditions intended here no deviations were found, and a monoexponential function fitted the experimental data quite well, since the χ2-
Figure 3. Fit of relaxation times to eq 6 for NaClO4 as supporting electrolyte.
test was satisfied.11 Therefore, we have not considered other possible chemical relaxation processes in the discussion. These relaxation times have been fitted to eq 3 with F and kf given by eq 6 using a nonlinear multiparameter regression analysis (the Sigmaplot program was used) to yield values of k12, k13, and k23 and, through the equilibrium constants, also k21, k31, and k32. The results of these fittings are shown in Table 1. In Figure 3 the fit is shown for one of the salts employed. As mentioned above, in the presence of sodium acetate, oxalate, and propionate with the same experimental conditions as explained above, no relaxation curves were observed. Only the absorbance increase due to the change in the acid equilibrium of DNSA with temperature was observed. This suggests that the relaxation time is strongly shortened in the presence of these salts. To analyze this effect further, we have measured the relaxation times with small concentrations of these salts and also, for comparison, with sodium trichloroacetate. The ionic strength was adjusted with NaNO3, and the pH value was held constant with a NH4NO3/NH3 buffer. The results with different concentrations of salt and also the pKa values of the corresponding organic acids are shown in Table 2. These salts have a large effect on the relaxation time, which is probably due to the different and larger pKa values compared to those of trichloroacetic acid. We believe that in the other cases the organic anions act as proton donor/acceptor, thus providing an additional relaxation pathway to those presented in Scheme 1. In the case of trichloroacetate this relaxation pathway through
18418 J. Phys. Chem., Vol. 100, No. 47, 1996
Sa´nchez and Gala´n
TABLE 2: Relaxation Times (τ/µs) for Different Organic Salt Concentrations at 298.15 Ka
TABLE 3: Calculated Radii and Diffusion-Controlled Rate Constantsa,b
[salt] mol dm-3
oxalate
acetate
propionate
trichloroacetate
0.0 0.001 0.01 0.05 0.1 0.275
91.0 93.0 61.7 29.5 c c
91.0 76.9 32.0 c c c
91.0 76.9 32.0 c c c
91.0 93.5 95.2 101.0 101.0 101.5
pKab
4.29
4.76
4.86
k2 k3 k13
0.66
Ionic strength adjusted to 0.3 mol with NaNO3. [DNSA] ) 5.0 × 10-4 mol dm-3. [NH3] ) 2.5 × 10-2 mol dm-3. b Taken from Perrin, D. D.; Dempsey, B. Buffers for pH and Metal Ion Control; Chapman and Hall: London, 1974. c Relaxation times were too fast to be measured. dm-3
a
the donor/acceptor characteristics of this anion is certainly absent at the pH value selected in this study, since the pKa is close to zero. So the critical pKa value to activate the additional relaxation path should be at first in the range 5-0. Moreover, the measurements with Na2SO4 allows for a further reduction of this critical range, since the second pKa of sulfuric acid is 1.96, and no catalytic effect is observed in this case. Furthermore, taking into account that k23, the smallest rate constant in Scheme 1 that appears in the expression of the relaxation time, contains a contribution from the breaking of an intramolecular hydrogen bond (see eq 7 below), we can conclude that the catalytic effect of the organic salts is due to the breaking of this hydrogen bond with participation of the organic anions. They build an intermolecular hydrogen bond with HL. The concentration of this hydrogen-bonded species relaxes to equilibrium faster than the intramolecular hydrogen bond.12 Apparently, trichloroacetate, perchlorate, nitrate, and sulfate cannot break the intramolecular hydrogen bond . In what follows, we will try to rationalize the observed rate constants. k12, k21, k23, and k32 correspond to similar processes: proton transfer from protonated DNSA to water or ammonia (k21 and k23, respectively) and the inverse protonation reactions of DNSA. In principle one would expect a similar mechanism for both processes. Moreover, it can be thought to occur according to the following two-step mechanism: k1
(1) LH y\ z LH′ k -1
k2
z L + H3O+ (2) LH′ + H2O y\ k -2
k3
(3) LH′ + NH3 y\ z L + NH4+ k -3
(7)
where steps 1 and 2 correspond to the proton transfer equilibrium of DNSA with H2O and steps 1 and 3 to the proton transfer equilibrium of DNSA with ammonia. Step 1 is thus common for both proton transfer equilibria. The difference between LH and LH′ is that the intramolecular hydrogen bond has been broken in the second species. By application of the hypothesis of the stationary state to the concentration of LH′, k12, k21, k23, and k32 can be identified as
k12 ) k32 )
k1k2 k-1k-2 ; k21 ) k-1 + k2 k-1 + k2
k-1k-3
; k23 )
k-1 + k3[NH3]
k1k3 k-1 + k3[NH3]
L LH+ NH4+ NH3
(8)
a/Å
b/Å
c/Å
Rav/Å
5.06 5.09 1.93 1.96
5.12 5.11 1.93 1.96
1.86 1.87 1.93 1.66
3.64 3.65 1.93 1.85
2.0 × 1010 s-1 7.4 × 109 mol-1 dm3 s-1 7.4 × 109 mol-1 dm3 s-1
a The radii were estimated as explained in the text, starting with the AM1 optimized geometries. The rate constants were calculated with the Smoluchowsky equations. b For H3O+ a value of 1.3 Å was taken for the calculation (Marcus, Y. Ion SolVation; Wiley: Chichester, 1985).
As an estimation of k-1, the value for salicylaldehyde13 of 2.2 × 107 s-1, where the second step of the proposed mechanism is absent, has been suggested,8 due to the strong similiraty between both species. k2 and k3 are expected to be diffusion controlled, and they can be estimated with the Smoluchowski equations1 for diffusion-controlled reactions. For these calculations the radii of the molecules were calculated. Their geometries were fully optimized in vacuum with the AM1 semiempirical Hamiltonian.14 These geometries were then used for the calculation of an optimized ellipsoidal or spherical cavity,15 and the semiaxes obtained allow for the calculation of an averaged radius: R ) (abc)1/3. The values of the semiaxes, the averaged radii for the different species, and the calculated values of k2 and k3 are given in Table 3. Under our working conditions, the following condition is fulfilled: k-1 . k3[NH3]. Thus, k23 ) K1k3 and k32 ) k-3, where K1 is the equilibrium constant for the opening of the intramolecular hydrogen bond. With the experimental values of k23 and k3, a value of K1 ) 4.4 × 10-4 is obtained, and the free energy for this equilibrium should be ∆G ≈ 19 kJ mol-1. This is the free energy difference corresponding to the breaking of the hydrogen bond. Since ∆H is usually about 25-30 kJ mol-1,12 the entropic contribution is about ∆S ≈ 30 J mol-1 K-1. These results are of interest for discussing the thermodynamic results, and we will refer to them later. The estimated value of k1 is then 104 s-1. To verify if the suggested mechanism is consistent with all the experimental evidence, the values of k1 and k-1 should be substituted in the expressions for k12 and k21. With k2 from Table 3 the calculated value of k21 is ∼10 000 s-1. This value is in good agreement with the experimental results. Finally, we obtained k-2 ≈ 1013 mol-1 dm3 s-1. This value is higher than the diffusioncontrolled limit but in agreement with other reported results in water.1 As a matter of fact, the special mechanism of proton displacement in water16,17 justifies a larger value of the rate constant. Besides, this estimated rate constant, k-2, is rather sensitive to the value taken for k-1, and as stated above the value accepted in our discussion corresponds to a related but not the same system as considered here. This may also be the reason for the large value obtained in our calculation. So we can conclude that a consistent explanation of the different rate constants can be achieved with the proposed mechanism. Finally, the values of k13 and k31 will be analyzed. k13 is diffusion controlled, and its estimated value also appears in Table 3. It corresponds to the proton transfer from a water molecule to an ammonia molecule. Through the pKa of ammonia (9.3), the value of k31 in Table 1 has been obtained. It is activation controlled. The values are in good agreement with the published values.18 Kresge et al.19 suggested on the basis of medium effects upon the deprotonation reaction of different ammines and upon their acid dissociation constants
Proton Transfer Equilibria
J. Phys. Chem., Vol. 100, No. 47, 1996 18419 TABLE 4: Individual Activity Coefficients γa anion L LH+ NH4+ H+ TS12 TS13 TS23
Cl3C2O2-
ClO4-
NO3-
SO42-
0.2480 0.7201 0.7470 0.7424 1.0 1.0 1.0
0.2067 0.6793 0.7039 0.6779 0.5045 1.0651 1.7154
0.1897 0.6667 0.6902 0.6862 0.3581 0.8034 1.7362
0.2090 0.6911 0.7210 0.7159 0.3288 0.5613 3.031
a The individual activity coefficients, γ, were calculated with the Robinson-Stokes model, while the activity coefficients for the transition states, TSij, are relative values to the values with sodium trichloroacetate as the supporting electrolyte. They were obtained from γTS ) kij°γiγj/kij, where kij° is the rate constant at infinite dilution.
Figure 5. Schematic representation of the transition state for the process 2 and 3. Note that the repulsive Coulombic interaction between the negative charge of DNSA and the anion is larger, and thus unstabilizes the transition state, than the stabilizing interaction between the transferring proton and the anion. Figure 4. Plot of experimental rate constants vs charge to radius relation of the different anions.
that the reason for these slow rate constants is a small escaping rate of the products from the solvent cage after the activationless proton transfer reaction has occurred. In a highly structured media such as water these could be a reasonable explanation. However, Gao21 has shown, for the parent proton self-exchange reaction in [NH3-H-NH3]+, that it is highly solvent dependent. As a matter of fact, the activation barrier increases from approximately 3 to 10 kcal mol-1 on passing from the gas phase to the solution. Assuming a similar behavior for the reaction in [NH3-H-H2O]+, the proton being transferred from nitrogen to the water molecule would justify the small value of k31. Note that in this case, since ∆G° > 0 for the proton transfer reaction from NH4+ to H2O, if the potential energy surfaces for proton transfer within the species [NH3-H-NH3]+ and [NH3-HH2O]+ are similar, then the expected activation barrier would be larger, and for the reverse process the activation barrier would be lower, in qualitative agreement with the experimental results. The specific salt effects observed have not been addressed so far. They are clearly related to the charge to radius ratio of the different anions as shown in Figure 4 for k12, k13, and k23. This correlation shows, according to the theoretical predictions, the large effects of electric fields on proton transfer reactions.2,3,5 However, the change of the slope’s sign from k12 and k13 to k23 requires more detailed consideration of the different equilibria implied in Scheme 1. For this purpose, a transition state-initial state analysis has been tried. This analysis is resumed in Table 4, where the expected values of the activity coefficients, γi, for the reactants and transition state are presented. The activity coefficients of the transition state are given relative to its value in sodium trichloroacetate solutions, since the values of kij°, which are the rate constants for the processes i-j at infinite dilution, are not known. According to this analysis, the reason for the increase in the values of k12 and k13 with increasing charge to radius ratio is the decrease in the activity coefficient of the transition state on increasing the charge to radius relation of the anions. The opposite trend in the activity coefficients of the transition state
for k12 and k23 can be understood, since in the first case a charge is neutralized while in the second case the charges of the products in absolute value are higher (although of different sign to hold electroneutrality). That means that the transition state is in the first case depolarized compared with the initial state, while in the second case the transition state is more polar than the initial state.5 If the proton is transferred to a water or ammonia molecule, which solvates an anion of the added salt as shown in Figure 5, then the trends in the activity coefficients of the transition states can be readily understood. Infrared spectroscopy confirms the existence of water solvating the anions of added electrolytes, which gives stretching vibrations of O-H22 that are different from those of bulk water. In the case of the more polarized transition state, compared to the initial state, k23, the anion with a larger charge to radius ratio (larger microscopic electric field) causes a larger Coulombic repulsive interaction with the negatively charged DNSA molecule, whose charge is being increased in absolute value through proton transfer, and thus increases the energy of the transition state (see Figure 5). This would justify the negative salt effect observed for these rate constants. The same arguments would justify the increase in the rate constants k12, since in this case the transition state is less polar then the initial state. As a matter of fact, salt effects on electron transfer reactions have been successfully explained on the basis of the specific ion-pairing effects considered here.22 In the protonation reaction of ammonia, since no change in the charges on going from reactants to products occurs, the explanation of the observed salt effects is not straigthforward, since neither charge neutralization nor charge creation occurs. It is a charge shift reaction. The stabilization of the transition state on increasing the charge to radius ratio of the anions should be understood on the basis of a larger stabilization of the proton bounded to ammonia compared to the stabilization of the proton on the side of the water molecule. Thermodynamic Results. As is well-known,7 the relaxation technique allows the determination of the kinetic parameters
18420 J. Phys. Chem., Vol. 100, No. 47, 1996
Sa´nchez and Gala´n
and, through the amplitude of the equilibrium change, the enthalpies of the different “normal reaction coordinates”6 to be obtained. Each ‘normal reaction coordinate’ is described by a single exponential:
Yk(t) ) Yk° e-(t/τk)
(9)
where Yk(t) is the concentration change at time t, τk is the relaxation time of the normal reaction coordinate k, and Yk° is the corresponding amplitude. It also has concentration dimensions. Furthermore, this amplitude is related to the reaction enthalpy through
( ) ∆HkδT
Yk° ) Γk
RT2
(10)
where Γk is an “amplitude factor” related directly to the equilibrium being considered and the stoichiometric coefficients in this equilibrium. For the system considered here the normal coordinate analysis has been done previously.6,23 Thus, according to Citi et al.,23 the normal reaction coordinate in the system DNSA/ammonia is
(1 - V)L + VB + H+ h (1 - V)HL + VHB
TABLE 5: Reaction Enthalpies and Entropies at 298.15 Ka
(11)
where V is defined by
V)
[H+] + [L] + [B] + KHL KHL - KHB
(12)
Note that the stoichiometric coefficients are complex quantities. They appear in the diagonalization procedure of the relaxation equations.24 The amplitude factor is generally defined as6
Γ)
(∑ ) Vi2
i
-1
ci
(13)
where ci are equilibrium concentrations. If the reaction is followed spectrophotometrically, then
δA° ) ∆lYk°
(14)
where the concentration change Yk° is converted into an absorbance change through the extinction coefficients, ∆ ) (1 - V) (HL - L), and the path length, l. Finally, we can write
∆Hk )
δA° RT2 ∆lΓk δT
(15)
Since eq 11 is a linear combination of steps 1 and 2 plus V times eqs 2 and 3, we can also write
∆Hk ) ∆H12 + V∆H23
Figure 6. Plot of reaction enthalpies for the “normal reaction coordinate” (see eq 11 in the text) vs V (see eq 12 in the text for definition).
(16)
We have used eqs 13-16 in order to calculate the values of ∆H23 and ∆H12 from a plot of ∆Hk, calculated with eq 15 vs V. In Figure 6 such a plot is shown for one of the salts employed in this study. In Table 5 the results for the four salts are given. The values of ∆H12 could be obtained from the intercept of such plots. However, the values obtained in this way are affected by a large error as previously stated by Citi et al.23 For this reason we have not included the values of ∆H12 obtained in this way in Table 5.
salt
∆H23
∆H13b
∆H12
T∆S23c
NaClO4 NaNO3 Na2SO4 NaCl3C2O2 Born modelf MSA modelg
-32.2 ( 2 -31.3 ( 3 -31.4 ( 1 -33.9 ( 2
-53.2 -53.3
-21 -22
-20 -19 -19 -21 -11 -12.4
T∆S13d
T∆S12e
-0.4 -0.5
+19 +18
+4
+14
+3
+14
a ∆H and T∆S in kJ mol-1. b Taken from ref 25. c ∆G ij ij 23 ) 2303RT(pKHL - pKHB). d ∆G12 ) -2303RT pKHL. e ∆G13 ) -2303RTpKHB. f Calculated with Born model for ionic solvation. g Calculated with MSA model for ionic solvation.
The values of ∆H23 determined in all cases are very similar, showing no remarkable salt effect. Our value of ∆H23 in NaClO4 is in close agreement with the value for this salt previously determined by Citi et al.23 Furthermore, we have taken data from the literature25 for ∆H13 to estimate ∆H12 according to the thermodynamic cycle contained in Scheme 1:
∆H23 ) ∆H13 - ∆H12
(17)
These results also appear in Table 5 for the salts for which experimental data were found. To complete the thermodynamic analysis, the entropic contributions have been calculated with aid of the pKa values found in the literature. Model calculations, on the basis of the Born model for ionic solvation16 and the mean spherical approximation (MSA),26 have been undertaken, and the results also appear in Table 5. For this the previous estimation of the entropy of breaking a hydrogen bond has been considered when necessary. As can be seen, both models reproduce qualitatively the experimental trends. As a matter of fact, a semiquantitative agreement is obtained. To improve this agreement, other contributions as multipoles and dispersion contributions should be taken into account.27,28 Concluding Remarks The development of molecular electronics requires knowledge of the behavior of chemical systems under the influence of
Proton Transfer Equilibria electric and magnetic fields.29 With this idea in mind the specific anion effects on the kinetic and thermodynamic magnitudes characterizing the different proton transfer equilibria in the DNSA/ammonia system have been studied to investigate the external field effects on these processes. These seem particularly meaningful, since precise predictions have been made about the behavior of proton transfer reactions in the presence of external fields.2,3,5 In this work, the anion’s nature causes a large variation of the observed rate constants. Moreover, addition of organic anions such as oxalate, acetate, or propionate results in an extremely fast relaxation time to the new equilibria after the temperature jump. In terms of molecular electronics this means that the response time of such a component can be decreased by several orders of magnitude by addition of small concentrations of salt. In contrast with this, the enthalpy is salt independent for NaClO4, NaNO3, Na2SO4, and NaCl3C2O2. The entropy is also salt independent. The calculation of the entropy with the Born and MSA models results in a semiquantitative agreement. Multipoles corrections would be needed to achieve a quantitative agreement between experimental and calculated quantities. Acknowledgment. Financial support by the Consejerı´a de Educacio´n y Ciencia de la Junta de Andalucı´a and Ministerio de Educacio´n y Ciencia is gratefully acknowledged. We thank HI-Tech Lt. for technical advice on the T-Jump apparatus at all stages of this research, Professor Emilio Rolda´n for implementing an electronic trigger for the T-Jump apparatus, as well as for helpful discussions, and Professor W. R. Fawcett for helpful discussions on the MSA theory. References and Notes (1) Eigen, M. Angew. Chem., Int. Ed. Eng. 1964, 3, 1. (2) Cukier, R. I.; Morillo, M. External Field Control in DissipatiVe Two-state System; Jortner, J., Ratner, M., Eds.; IUPAC, A Series on Chemistry for 21st Century Monograph: Molecular Electronics; IUPAC.
J. Phys. Chem., Vol. 100, No. 47, 1996 18421 (3) Morillo, M.; Cukier, R. I. J. Chem. Phys. 1993, 8, 4548. (4) Introduction to Molecular Electronics; McPetty, M. C., Bryce, M. R., Bloor, D., Eds.; Oxford University Press: New York, 1995. (5) Scheiner, S.; Redfers, P.; Szczesniak, M. M. J. Phys. Chem. 1985, 89, 262. (6) Castellan, G. W. Ber. Bunsen-Ges. Phys. Chem. 1963, 67, 898908. (7) Eigen, M; De Maeyer, L. In InVestigation of Rates and Mechanisms of Reactions; Hammes, G. G., Eds; Wiley Interscience: New York, 1974. (8) Diebler, H.; Secco, F.; Venturini, M. J. Phys. Chem. 1984, 88, 4229. (9) Oliver, R. W. A.; Stott, A. J. Phys. E: Sci. Instrum. 1974, 275. (10) Diebler, H.; Secco, F.; Venturini, M. J. Phys. Chem. 1987, 91, 5106. (11) Bevington, P. R.; Robinson, D. K. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1992. (12) March, J. AdVanced Organic Chemistry, 4th ed.;; J. Wiley and Sons: New York, 1992. (13) Yaninaga, T.; Tatsumaoto, N.; Inoue, H.; Miura, M. J. Phys. Chem. 1969, 73, 477. (14) MOPAC 6.0 was used to perform these calculations. (15) Ford, G. P.; Wang, B. J. Comput. Chem. 1992, 13, 229. We acknowledge Dr. B. Wang for kindly providing us with a copy of the program for the optimum ellipsoid calculation. (16) Bockris, J. O’M. Modern Electrochemistry; Plenum Press: New York, 1970; p 482. (17) Kresge, A. J. Chem. Soc. 1973, 475. (18) Connors, K. A. Chemical Kinetics; VCH Publishers: New York, 1990. (19) Kresge, A. J.; Capen, G. L. J. Am. Chem. Soc. 1975, 97, 1795. (20) Gao, J. Int. J. Quantum Chem. Symp. 1993, 27, 491. (21) Zundel, G.; Fritsch, J. The Chemical Physics of SolVation; Elsevier: Amsterdam, 1986; Part B, Chapter 2. (22) Piotrowiak, P. Inorg. Chim. Acta 1994, 225, 269-74. (23) Citi, M.; Secco, F.; Venturini, M. J. Phys. Chem. 1988, 92, 6399. (24) de Groot, S. R.; Mazur, P. Non-Equilibrium Thermodynamics; Dover Publications: New York, 1984. (25) Maeda, M. J. Phys. Chem. 1986, 90, 1134. (26) Blum, L.; Fawcett, W. R. J. Phys. Chem. 1992, 96, 408-414. (27) Sa´nchez-Marcos, E.; Capita´n, M. J.; Gala´n, M.; Pappalardo, R. R. J. Mol. Struct.: THEOCHEM 1990, 210, 441. (28) Fawcett, W. R. Private communication. (29) Aviram, A. Int. J. Quantum Chem. 1992, 42, 1615-24.
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