J . Phys. Chem. 1990, 94, 6365-6367
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Figure 6. Calculated oscillations. Input concentrations: [IO3-l0 = 0.0136, [NH30H+],, = 0.05, [NaOH], = 0.04 M; ko = 1.51 X IO4 s-I. Rate constants as in Figure 4.
ratio that determines the redox potential.
Discussion The iodate-hvdroxvlamine oscillator has a numb r of fa :1nating features and rises several interesting questions. Its most striking feature, the very long period of oscillation, is to our knowledge rivaled only by the BZ reaction with methylmalonic acid as substrate” and by the Bray reaction.’* There are clearly many biological oscillators with periods of 24 h or even longer. Is the existence of so few long-period chemical oscillators simply a matter of the experimental inconvenience of looking for them? (17) Eptein, 1. R.;Kustin, K. Unpublished results. (18) Bray, W. C. J . Am. Chem. SOC.1921, 43, 1262.
6365
While it seems clear that periodate is rapidly reduced to iodate in the periodate-hydroxylamine system, the increase by over an order of magnitude in the oscillation period and the absence of detectable nitrite suggest that the oscillation in the iodate-hydroxylamine reaction may have a fundamentally different origin. It will be of interest to clarify the relationship between these two systems and to see if each may be capable of supporting two different modes of oscillation. The essential role of iodine evaporation is another special feature of this system. The removal of one species from the CSTR, not only by the common output flow but also selectively in another way, may be a useful approach to generating new oscillators. Evaporation of bromine plays a key role in several modified BZ-type oscillator^^^^^ in a closed system. One may also envision systems in which the selective removal occurs not to the gas phase but to an immiscible liquid phase or by precipitation, as may occur with MnO, in the family of permanganate oscil1ators.l Perhaps the most important instances of this phenomenon may occur in biological oscillators where different products can be excreted through membranes at very different rates. While our model built from component processes succeeds in reproducing the observed dynamics with only a handful of free parameters, it is by no means a complete mechanism for this complex system. The quest for mechanistic details should be aided considerably by the fact that, like the iodate-sulfite-ferrocyanide system,I4 the hydroxylamine-iodate system is one of the few oscillating reactions in which more than one or two periodic properties may be simultaneously monitored. Further detailed study of elementary steps in both the iodate and periodate oxidations of hydroxylamine and their connection to other iodatebased oscillators is an ongoing project in our laboratory.
Acknowledgment. We thank IstvZin Lengyel for assistance with the calculations and Kenneth Kustin for a critical reading of the manuscript. This work was supported by the National Science Foundation (CHE-8800169) and by a US.-Hungarian cooperative grant from the NSF and the Hungarian Academy of Sciences. Registry No. NH30H, 7803-49-8; IO3,15454-3 1-6. (19) Beck, M. T.; Bazsa, G.; Hauck, K. Ber. Bunsenges. 1980,84, 408. (20) Noszticzius, 2.;Bodiss, J. J . Am. Chem. SOC.1979, 101, 3177.
Isotope Effect on Weak Acid Dissociation R. Krishnan, J. Lee, and G. W. Robinson* Subpicosecond and Quantum Radiation Laboratory, P.O. Box 4260, Texas Tech University, Lubbock, Texas 79409 (Received: February 27, 1990; In Final Form: April 2, 1990)
Weak acid dissociation of the deuterium-substituted I-naphthol-2-sulfonate potassium salt (1 -ROD-2-S) was examined as a function of pD and temperature. The kinetics of kdisand of the recombination rate k,, in agreement with our findings for 1-ROH-2-S, is dictated by the orientational motions of surrounding water molecules, specifically the Debye relaxation time TD. The dissociation rate kdirdeclines by approximately 1/3 upon deuteration, while the activation barrier AE* associated with kdisremains essentially constant. As in our other studies, this isotope effect is attributed to a larger hydration entropy difference A S for the hydration of D+ compared with H+.
Introduction Proton dissociation is one of the most fundamental processes in chemistry.l Steady-state measurements, such as those obtained by using the pH indicator, X-ray diffraction, and IR spectroscopy, provide information on equilibrium constants and averaged solution structure. However, the dynamic evolution from the initial-state
neutral molecule to the final-state dissociated species cannot be investigated without a measuring technique having ultrafast time resolution. Using picosecond laser spectroscopic methods and an acid that can be photon initiated on ultrafast time scales, molecular aspects of the Proton dissociation Process have been The
( I ) Bell, R. P. The Proton in Chemisrry, 2nd ed.; Chapman and Hall: London, 1973.
(2) Robinson, G . W.;Thistlethwaite, P. J.; Lee, J. J . Phys. Chem. 1986, 90, 4224.
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0 1990 American Chemical Society
6366 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990
Krishnan et al. 1200
model has suggested that kdis and k,, of a weak acid can be quantitatively correlated with the thermodynamic quantities ASi" and AHi" of the probe molecule and the Debye or transverse rotational relaxation time rD of the pure water solvent, where Mi0 and AHi" are thermodynamic ionization entropy and enthalpy. For I-naphthol-2-sulfonate potassium salt (1-ROH-23, 1-ROD2-S), I-naphthol (I-ROH, I-ROD), and 2-naphthol (2-ROH, 2-ROD), the activation enthalpy AH+&@equals AH:, and AG#, equals 0 (case 11, page 4230, ref 2). Thus, the desired rates are kdis (S-I) = 7 6 ' 0 eXp(ASio/R - AHi"/RT) (I)
k,, (M-' S-I) = TD-IR (2) where reactants are at 1 M and 0 is a steric/mobility factor introduced by Eigen and K ~ s t i n . The ~ model has been successfully applied to I-ROH, 1-ROD,42-ROH, 2-ROD,5 and I-ROH-2-9 in a water solvent. However, no systematic set of experimental data is available for the latter molecule in deuterated water as a function of pD and temperature. This paper addresses the isotope effects on eqs 1 and 2 using I-ROD-2-S and then compares these results with those from 1- and 2-naphthol.
960
240
Results and Discussion The excited-state I-ROH*-2-S gives two emission bands in HzO, one at 360 nm from the neutral molecule (l-ROH*-2-S) and the other at 460 nm from the anion (I-RO-*-2-S). Upon deuteration, the emission quantum yield of the neutral species increases, but no spectral shift is observable. Consistent with the behavior of the protonated system, the I-ROD*-2-S emission band remains constant in intensity, while the I-RO-*-2-S band decreases in intensity with a decrease in pD. In addition, both bands become weaker with increasing temperature. To analyze these data, we (3) Eigen, M.; Kustin, K. J . Am. Chem. SOC.1960, 82, 5952. (4) Webb, S. P.;Philips, L. A.: Yeh, S. W.: Tolbert, L. M.; Clark, J. H.
J . fhys. Chem. 1986, 90, 5154. ( 5 ) Lee. J.; Robinson, G. W.; Bassez, M.-P. J . Am. Chem. Soc. 1986,108, 7477. Lee, J.; Robinson, G. W.; Webb, S. P.;Philips, L. A.; Clark, J. H. J . Am. Chem. SOC.1906. 108. 6538. ( 6 ) Krishnan, R.:~Fillingim, T. G.: Lee, J.; Robinson, G. W. J . Am. Chem. SOC.1990, 112, 1353. (7) Weller. A. f r o g . Reacf. Kiner. 1961, I , 187.
(8) Lee, J.: Griffin. R. D.: Robinson, G. W. J . Chem. Phys. 1985, 82, 4920.
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Time (ns) Figure 1. The rise (1.8 ns) and decay (6.7 ns) of I-RO-*-2-S in pD 4 solution at 40 "C. The symbols (0)represent the experimental data. The solid line represents the fitted curve with a x 2 of 1.3. The dashed line represents the instrumental response function. Intensity is in arbitrary units.
Experimental Section
I-ROH-2-S was purchased from Eastman Kodak Co., and DCI (99.9%) and D 2 0 (99.98%) were from Aldrich. The chemicals were used without further purification. A set of pD values between 0 and 7 was investigated. These pD values were calculated from the DCI concentrations and corrected by the Bransted kinetic activity coefficient.' Concentrations of I-ROH-2-S, whose labile H+ readily exchanges with D+, were kept below M and their absorbances were less than 0.1. System temperatures between 0 and 60 "C were controlled by a Borg-Warner LHP-150 heat pump and a TC-IO8 temperature monitor. Absorption and fluorescence spectra were recorded on Shimadzu UV-265 and Perkin-Elmer MPF-44 fluorescence spectrophotometers, respectively. System lifetimes were determined by a time-correlated single photon counting apparatus using a mode-locked argon ion laser (Coherent, 18W INNOVA) which operates at 72 MHz repetition rate and pumps a dye laser (Coherent, 599). The output of the dye laser was cavity dumped (Coherent, 7210) at 7.2 MHz. The output pulse (fwhm = 15 ps) was frequency doubled to 305 nm. The emission from 1 -ROD-2-S was then selected by an ISA double monochromator and collected by a fast-response microchannel plate photomultiplier (ITT, F4129f). Signals were processed by using a discriminator (TENNELEC, TC454) and a multichannel analyser (ORTEC, 7010). The digitized data were then transferred to a VAX 11/730 computer for future analysis. The instrumental response of about 150 ps is limited by the present detection system. However, this time resolution is fully adequate for the studies reported here. A more detailed account of the experimental apparatus and data analysis techniques have been discussed elsewhere.s
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Figure 2. 1 / T I 1/ r 2 as a function of pD; symbols represent observed values and solid lines represent the theoretical values from eqs 3 and 4. Values on t h e y axis are to be multiplied by 10' s-'. 0 O C (O),20 OC (*), 40 "C, ( 0 ) , 60 O C (+).
employ a scheme like that used in the 1-ROH-2-S work.6 Since the proton (deuteron) rapidly dissociates only upon photoexcitation, the following excited-state rate scheme is used d[ROD*] dt [ROD*]o - (ko + kdis + k,[D+]][ROD*] + k,,[D+][RO-*] (3) d [RO-*] -- -{kd dr
+ (k,,, + k,')[D+])[RO-*] + kdi,[ROD*] (4)
where ko ( k d ) and k , (kq')are the intramolecular rate constant and proton-induced quenching rate constant for l-ROD*-2-S (1-RO-*-2-S). The parameter [ROD*],, is the initial ROD* concentration. The solution of these two equations gives two time constants, 71 and T ~ for , I-ROD*-2-S and 1-RO-*-2-S, respectively.& Figure 1 shows the instrument profile along with a typical lifetime spectrum of the anionic species l-RO-*-2-S in pD 4 solution at 40 "C. Here, the rise time ( T ~ of ) 1-RO-*-2-S corresponds to the decay time of l-ROD*-2-S, indicating that the excited anionic species is indeed formed from the excited neutral species. The T' and 7 2 obtained from lifetime measurements of 1-RO-*-2-S can then be correlated with kdis and k,,
+ I / T Z = ko + kd + kdjs + ( k , + k,' + k,,)[D+] ( 5 ) Semilog plots of I / T ' + 1/szvs [D+] at four temperatures are
1/ T I
shown in Figure 2. The corresponding linear plots for eq 5 (not shown) lack clarity because of the wide range of [D+] (6 orders of magnitude). However, the values of kdis and k , can be extracted analytically from the slopes and intercepts of these lines if k,, k"'. k,, and k,' are known. Since k , and k{ are intramo-
I
The Journal of Physical Chemistry, Vol. 94, No. 16. 1990 6367
Isotope Effect on Weak Acid Dissociation 120.0
1
I
-I
A
I
I
/ / /
TABLE I: Self-Consistent Parameters for H+and D+ Dissociation in H,O and D,O at 298 K I-ROH-2-S I-ROH' 2-ROHb H C D d H D H D ko, ns-' kgl, ns-l k,, ns-I M-l kgl, ns-' M-' k,,, ns-l k,,, ns-I M-I
0.0
I
250
kpl: ns-I I
,
A
270
I
1
290
I
,
310
I
I
I
330
I
350
I
370
Temperature ( K ) Figure 3. kdia( X ) and k,, (A)as a function of temperature. The solid line and dashed line correspond respectively to kdil and k, calculated from eqs 1 and 2. kdis values are to be multiplied by 10's-I and k, values by I O9 s-I.
lecular rate constants, they are assumed to be isotope and solvent insensitive and are therefore approximated to the values obtained from the protonated system. Separation of k,, k,, and k,' is made by the best fit of lifetime and quantum yield measurements of neutral and anionic species. For pD values greater than 2, the determined rate constants are in good agreement with the proposed rate scheme using eqs 1 and 2. However, for pD values lower than 2, impurity interference from the DCI causes the measured lifetimes to deviate from the proposed rate scheme. Figure 3 compares the observed kdis and k,,, using eq 5, and calculated kdis and k,,,, using eqs 1 and 2, for five temperatures. Table I summarizes the kinetic rate constants for 1 -ROD-2-S together with its protonated partner I-ROH-2-S at 25 'C. The 1- and 2-ROH(D) results, where available, are also included in Table I for comparison. For the deuterated species, the fitting accuracy for k,, k,, and k,' is about 13%, which is poor in comparison with the 4% for the protonated system6 The increased degree of fitting inaccuracy is very likely caused by impurity interference from the DCI we used. A new batch of 99.96% DCI and 99.996% D 2 0 purchased from Aldrich was found to be little better with respect to this presumed impurity emission. Furthermore, severe spectral overlap between neutral and anionic species and the extremely weak neutral emission intensity create difficulties in obtaining 0 and 0' or k, and k;. As a result, it is meaningless to attempt a correlation of k, and k,' between H and D or among I-, 2-ROH, and 1-ROH-2-S. It is interesting to point out that the fitted steric factor $2, which depends on the size and structure of the probe molecule, remains constant upon deuteration. This is to be expected. For I-ROH2 4 , where the intramolecular hydrogen bond may interfere with the kdhand k , processes, il is smaller than it is for 1- or 2-ROH!q5 This is also the expected result. The reasonable agreement between calculated and observed kdis and k , in Figure 3 further supports the idea that the dynamical aspects of the dissociation process of H or D weak acids are controlled by the orientation motions of D 2 0 or HzO. Furthermore, the 2.8 ratio of kdi,(H) to kdis(D)for I-ROH-24, as for the cases of I-ROH and 2-ROH, is attributed to the entropy
AE/kcal/mol AS, cal/(mol K)
a
PK, *
0.143 0.125 12.97 11.79 0.882 33.5 29.48 2.08 -0.25 0.24 1.58 1.49
0.143 0.125 26 46 0.315 33 10.51 1.96 -2.28 0.30 2.02 1.49
6.8 0.125 6 33 25 68 25 0 -1.9 0.49 0.4 2.0
6.8 0.125 0 9.1 7.9 48 7.9 0 -3.69 0.44 0.81 2.0
0.115 0.115 0.100 0.100 22 0.103 58 8.89 2.64 -3.8 0.46 2.72 2.5
0.039 50.6 2.2 2.4 -6.24 0.46 3.12 2.5
PK,*(FC)~ From refs 2 and 4. From refs 2 and 5. From ref 6. dThis work. e kpf = q,-'Q exp(AS:/R). /These values are from the best Arrhenius fits of equations such as eq 5 . However, the AE differences between H and D systems are too small to be considered experimentally significant. ZFrom refs 9 and IO. a
difference for hydrating a H+ ion compared with a D+ ion. The entropy change is always more negative for the D+ ion. This difference arises from the lower librational frequencies in liquid DzO compared with H 2 0 and the severe stiffening of these vibrations in the hydrated D904+and H904+complexes. Table I also compares pK,* obtained from the rate scheme with pKa*(FC) estimated from the Forster cycle.9 Although pK,*(FC) agrees with pKa* in the case of 1-ROH-23, 2-ROH, and their deuterated analogues, both having nonzero AHzdis,it does not predict a correct value for 1-ROH (AH+&= 0) nor does it reveal any difference between the protonated and deuterated 1-ROH systems. The disagreement emphasizes the importance of entropy in the theoretical evaluation of pKa* values.
Conclusions A number of important conclusions can be drawn from this work. The dynamical theory that we have previously proposedZ for weak acid dissociation/recombination in aqueous solvent systems seems to hold up well for a range of acids, protonated as well as deuterated. The ideas are really nothing more than an extension of Eigen's concepts3 to a dynamical framework. The work confirms, for example, that the H / D isotope effect, not only on the dynamics but also on the equilibrium properties of weak acid dissociation, has mainly to do with the entropy decrease as free liquid water molecules become strongly bound to the ion (H+ vs D+). Acknowledgment. Financial support at the SPQR Laboratory has been shared by the Robert A. Welch Foundation (D-0005, 64% and D-1094, 5%), the National Science Foundation (CHE8611381, 17%) and the State of Texas Advanced Research Program (1 306, 14%). (9) Forster, T.Natunvissenschaften 1949, 36, 186. (IO) Martynov, I. Y.; Demyashkevich, A. B.; Uzhinov, B. M.; Kuz'min, M. B. Usp. Khim. 1977, 46, 3-31 (Russ. Chem. Rev., Engl. Trans/.).
