J. Phys. Chem. 1992,96, 1729-1733 systems can now be understood in terms of the mechanism.
Discussion
1729
ferroin could be oxidized by the different bromine-containing species in two-electron processes, resulting in an iron(1V) complex
as an intermediate. However, it is important to point out that A model for the ferroin-bromate-bromide oscillatory system the experimentally determined rate laws could equally be derived in a CSTR has been constructed by extending the NFT mechaon the basis of either one- or two-electron elementary step nism with direct reactions between ferroin (ferriin) and different mechanisms. bromine species. In the calculations, the proposed composite In the proposed scheme, we neglected the dissociation of ferroin, reactions have been taken into account by overall rate equations which is a slow Consequently, the oxidation of that were determined experimentally or constructed by analogy. dissociated ferroin with different bromine ~ p e c i e s ~was ~ J ~not* ~ ~ The calculated high-amplitude oscillations and the kinetic phase considered. Since ferroin is always resupplied by the inflow, the diagram are in good accordance with the experiments. We have exclusion of these reactions is justifiable for the flow-through demonstrated that by completion of the scheme with just one more system. However, they might be of importance for a quantitative step, accounting for the precipitation and dissolution of a ferdescription of the batch experiments. roin-tribromide salt, the peculiar batch oscillations can also be In order to learn the important species and composite reactions simulated. in determination of the characteristic behavior of the ferroinOscillations cannot be calculated if the oxidation of ferroin with bromate system, the sensitivity analysis of the model is in progress. BrOz’ radical is neglected. It shows that the NFT-type core of We conclude that the difference in behavior of the ferroin- and the model is essential for the appearance of periodic solutions. cerium-bromate systems is, in fact, related to the reactivity of The small-amplitude oscillations generated by the NFT mechanism ferroin (and ferriin) toward bromine species other than the BrO,’ in a CSTR, however, are amplified by the additional reactions, radical, while such reactivity of the cerium(III)/(IV) ions is not and high-amplitude oscillations emerge. known. What was predicted by thermodynamic argumentaEstablishing an elementary step mechanism for the ferroin tionsI2J4is supported by the results of kinetic investigations resystem requires further experiments. A deeper understanding of ported here. the mechanism of the composite processes, especially the ferAcknowledgment. This work has been supported by a joint roin-hypobromous acid and the ferriin-bromide reactions, is grant of the Hungarian Academy of Sciences and the Ministry essential. of Education (Grants A-MM-268 and OTKA 156/86) and also Melichercik and Treind132have recently shown that it would by a joint research project funded by the National Science be easier to quantitatively describe even the acidic oxidation of Foundation (Grant INT-8822786) and the Hungarian Academy ferroin with cerium( IV), if disproportionation of ferriin were of Sciences. We thank G. Bazsa and I. Lengyel for kindly sharing allowed. It would result in the simultaneous formation of iron(1V) their unpublished results and the staff of the Analytical Laboand iron(I1) complexes. Existence of the iron(1V) ion as an ratory, Department of Organic Chemistry, Kossuth L. University, intermediate was postulated by Bray and G ~ r i as n ~early ~ as 1932. Debrecen, Hungary for their helpful service. V.G. is in the debt Conoochioli et alaMrepeated this proposal in the 1960s. Formation of iron(1V) complexes in solution has been reported r e c e n t l ~ . ~ ~ . ~of~ N. Ganapthi, Y.Sasaki, K. Showalter, and A. M. Zhabotinsky for the enlightening discussions both in person and by correThere is experimental evidence of the existence of iron(1V) in the solid states3’ It was also suggested in several r e p ~ r t s ~ ~ Jthat ~ J ~ - * ~spondence. Registry No. Br03-, 15541-45-4; ferroin, 14708-99-7. (32) Melichercik, M.; Treindl, L. J. Phys. Chem. 1989, 93, 7652. (33) Bray, W. C.; Gorin, M. H. J. Am. Chem. Soc. 1932, 54, 2124. (37) Warren, I. F.; Benneth, M. A. J. Am. Chem. SOC.1974, 96, 3340. (34) Conocchioli, T. J.; Hamilton, E. J.; Sutin, N. J.Am. Chem. Soc. 1965, 87, 926. (38) Burgess, J.; Prince, R. M. J. Chem. SOC.1963, 5752. (39) Beck, M. T.; Vgradi, Z . Chem. Commun. 1973, 30. (35) Groves, J. T.; Watanabe, Y . J. Am. Chem. SOC.1986, 108, 507. (36) Balasubramanian, P. N.; Bruice, T. C. J. Am. Chem. Soc. 1986,108, 5495.
(40) Gillard, R. D. Coord. Chem. Rev. 1975,16, 67. (41) Tubino, M.;Vichi, J. S. E.; Lauff, I. K. Chem. Scr. 1989, 29, 201.
Hydrogen Bond Donor Acidity Parameters for Kinetics Studies in Nonaqueous Solvents Orland W . Kolling Chemistry Department, Southwestern College, Winfield, Kansas 671 56 (Received: May 24, 1991;
In Final Form: October 21, 1991) Several multiterm linear solvation energy models which incorporate directly or indirectly hydrogen bond donor-acceptor parameters were compared experimentally. These included the Kamlet-Taft a K T scale, the Abraham a: scale, and the acceptor (AN*) parameter of Riddle and Fowkes. An enlarged data base for a range of hydrogen bonding, hydrogen bondingstrongly associated, and weakly hydrogen bonding aprotic solvents was developed for this analysis. Although the aKT and at parameters are fundamentally parallel in their origins, the latter is less responsive to the differentiation of structural characteristics of the donor species. The AN* quantity is shown to be a coupled mixture of solvent properties in which hydrogen bond donor acidity appears to dominate for the strongly self-associated solvents.
Some of the most troublesome aspects in the problem of modeling kinetic influences of solvents for very rapid reactions arise with media which are hydrogen bonded (HBD). Because such solvents cover the structural range from the simplest monomolecular species within weak HBD liquids (Le. CHCl,) to complex molecular equilibria among several polymeric species in
the self-associated liquids (i.e. carboxylic and other protonic acids), the quantitative scaling and meaning of “hydrogen bond donor acidity” as a single universal variable appears to be fundamentally ambiguous. Two different approaches have been used in the development of predictive models for the description of effects of the medium
0022-365419212096-1729%03.00/0 0 1992 American Chemical Society
1730 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
upon electron-transfer (e-t) kinetics in solution. One assumes a uniform solvent environment depicted as a dielectric continuum for which the corresponding solvent descriptors are the dielectric constant (e) and the square of the index of refraction (n2or the optical dielectric constant). The Marcus theory and its variations are the most representative of the first approach's2 in which the effect of the solvent upon the activation AG* may be tracked either through the AGO' (standard free energy change in a particular solvent) or through X (a solvent reorganizational energy term).2 A second avenue for modeling influences of the medium upon e-t processes is to resolve the composite solvent effect into contributions from known molecular characteristics, i.e. dipolarity, Lewis basicity, Hildebrand solubility, hydrogen bond acidity, and other specific solvent effects. Models of the second type incorporating the linear solvation energy concepts of Kamlet and Taft2s3have been used with some success in accounting for the variable solvent influences observed in the kinetics for the forward electron transfer in porphyrin-amidoquinone, the back electron transfer by tram-stilbene-fumaronitrile, as well as the cleavage of bromobridged Pt(I1) complexes in aprotic The early four-parameter enthalpy equation of Drago7 interpreted all Lewis acid (A)-base (B) reactions, including hydrogen bond donor-acceptor processes, by a general set of parameters, E and C, assigned to electrostatic and covalent contributions, respectively, for the donor-acceptor bonded pair. Phenols were used as the reference HBD species in haloalkane solutions. Kamlet et al. observed significant dipole/dipole influences along with the anticipated hydrogen bonding effects upon formation constants for such phenol HBD-acceptor reactions in haloalkane media.s The parallel two-parameter system of Gutmann is also an enthalpy scale for donor (DN) and acceptor (AN) characteristics in solution without differentiation between electron pair donoracceptor processes and HBD donor-acceptor i n t e r a c t i o n ~ . ~ J ~ Again the critical analysis by the Taft group" demonstrated that the DN values exhibit an important family dependence upon the electron pair donor species and that there is a variable mix of hydrogen bonding and dipolarity contributions in the measured AN values. More recently, Riddle and FowkesIz have modified the AN scale to compensate for van der Waals contributions to the donor-acceptor interaction and have denoted their revised values as AN*. A critique of the AN* scale based upon a resolution into likely component factors is included herein. There are two specific empirical HBD scales which are currently used to measure hydrogen bond donor acidity through a single isolated parameter. The first is the Kamlet-Taft aKT parameter derived from the linear solvation energy relationship in eq 1 as a free energy f~nction.~ This summation of the variables includes
XYZ = xyzo + S ( T *
+ d6) + (IOLKT + b & ~+ h6H + et
(1)
the dipolarity and polarizability parameters (r* and a), the hydrogen bond acceptor basicity (&T), the Hildebrand solubility parameter (6,) and the family-dependent factor (t)if applicable. It should be noted that the parameters in eq 1 refer to the pure solvent as the reaction medium; however, as the most fundamental characteristic of the solvent molecule, the solution dipolarity (r*) appears to adequately correlate with the dipolarity and dipole ( 1 ) Marcus, R. A . J . Phys. Chem. 1963, 67, 853-857. (2) Lay, P. J . Phys. Chem. 1986, 90, 878-885. (3) Kamlet, M.; Abboud, J.; Abraham, M.; Taft, R. J . Org. Chem. 1983, 48, 2877-2887. (4) Kolling, 0. W. J. Phys. Chem. 1991, 95, 192-193. (5) Kolling, 0. W. J . Phys. Chem. 1986, 90, 4664-4665. (6) Kolling, 0. W. J . Phys. Chem. 1987, 91, 4388-4390. (7) Drago, R.; Vogel, G.; Needham, T. J . Am. Chem. SOC.1971, 93, 60 14-6026. (8) Kamlet, M.; Dickinson, C.; Gramstad, T.; Taft, R. J . Org. Chem. 1982, 47, 4971-4975. (9) Gutmann, V. The Donor-Acceptor Approach to Molecular Interactions; Plenum: New York, 1978. (10) Gutmann, V. CHEMTECH 1977, 255-260. (1 1) Taft, R.; Pienta, N.; Kamlet, M.; Arnett, E. J . Org. Chem. 1981, 46, 66 1-661. (12) Riddle, F.; Fowkes, F. J . Am. Chem. SOC.1990, 112, 3259-3264.
Kolling moment of the isolated gas-phase molecule as well.13 Theoretical models underpinning the empirically based ?r* scale have been reviewed14 and extended by Brady and Carr.15 Because the degree of self-association by the alkanols and phenols is extensive when either in pure form or at the higher concentrations required for the E/C and AN-DN measurements, numerical hydrogen bond donor-acceptor values in neat solvents most likely represent weighted means for the mix of monomeric and oligomeric species. Thus, a second scale for HBD acidity as a? has been derived by Abraham et a1.16 from the equilibrium of eq 2 for dilute solutions of a donor HD. Here, B is the acceptor HD(S)
+ :B(S)
DH-.:B(S)
+S
(2)
base and S the chosen common solvent (i.e. CC14or cyclohexane). The acidity and basicity parameters are related to K, through eqs 3 and 4 when pyridine N-oxide is used as the simple reference
K, + 1.1)/4.6363
(3)
log K , = 7.354~$# - 1.094
(4)
a? = (log
base (:B). The qualitative trends in both aKT and a? data often show parallel structural patterns for the simple alkanols and hal~alkanols.~~ For the interpretation of empirical effects of the solvent upon reaction kinetics, hydrogen bond donoracceptor parameters based upon free energy models are obviously preferable for the usual cases where the concommitant entropy factors are unhown. Thus, the present investigation has three objectives: (a) to examine both the a K T and a? HBD acidity scales with respect to their ranges, using an expanded data base including a greater number of the common strongly hydrogen bonded solvents; (b) to assess the respective scales in terms of their ability to differentiate the subtler shifts in HBD behavior between homologues and between very weak donor acids; and (c) to compare the three parameters a K T , a?, and AN* for their potential suitability for applications to electron-transfer kinetics in solutions where clear distinctions between Lewis basicity and hydrogen bonding effects must be made. The ChastrettePurcell'* generalized solvent classification scheme was used to identify specific hydrogen bonding solvents to be considered herein. Twenty one solvents drawn from the hydrogen bondmgstrongly associated (HBSA), hydrogen bonding (HB), and weak hydrogen bonding members among the aprotic dipolar (AD) classes were included in this study. Experimental Section Materials. For the alcohols, all starting materials were spectral grade reagents. These solvents were further purified by refluxing over calcium oxide followed by fractional distillation,z0 and the purities of the retained distillates were verified by comparison to literature boiling points and indices of refraction and by gas chromatography. Reagent grade carboxylic acids were treated with their corresponding anhydrides and refluxed for 24 h. Then P205was added, and the mixture was purified by fractional distillation. All aprotic dipolar solvents were dried with molecular sieves and redistilled. The water contents of the purified products were monitored by Karl Fischer titration.20 Procedures. The Kamlet-Taft a values for the carboxylic acids and alcohols were determined from the solvent shift the the I5N (13) Abboud, J.; Guiheneuf, G.; Essfar, M.; Taft, R.; Kamlet, M. J. Phys. Chem. 1984, 88, 4414-4420. (14) Brady, J.; Carr, P. J. Phys. Chem. 1984, 88, 5796-5799. (15) Brady, J.; Carr, P. J . Phys. Chem. 1985, 89, 5759-5766. (16) Abraham, M.; Duce, P.; Grellier, P.; Prior, D.; Morris, J.; Taylor, P. Tetrahedron Lett. 1988, 29, 1587-1590. (17) Abboud. J.; Sraidi, K.; Abraham, M.;Taft, R. J . Org. Chem. 1990, 55, 2230-2232. (18) Chastrette, M.; Rajzmann, M.;Chanon, M.;Purcell, K. J . Am. Chem. SOC.1985, 107, 1-11. (19) Barton, A. Chem. Reu. 1975, 75, 731-753. (20) Riddick, J.; Bunger, W. Organic Soluents, 3rd ed.; Wiley-Interscience: New York, 1970; pp 636-638, 770-775, 798-804.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1731
Hydrogen Bond Donor Acidity Parameters TABLE I: Hydrogen Bond Donor Acidity Values (at 296-298 I() and Related Quantities
Kdexptl),
donor species
dm3/mol
ay(expt1)
aKTa
Class: HB and HBSA
16.6 18.9b 15.5
1-butanol ethanol 1-hexanol methanol
18.0b 15.8
0.30 0.33b 0.29 0.37 0.32 0.29
18.8 18.7b
0.31 0.32
19.4
0.42 0.52
25.3b
2-methyl-2-propanol 1-pentanol 1-propanol 2-propanol 2-chloroethanol 2,2,2-trichloroethanol 2-fluoroethanol 2,2-difluoroethanol 2,2,2-trifluoroethanol acetic acid butanoic acid formic acid
330b 58.9 219 78gb 107
66.1 1552
propanoic acid
75.9
0.40 0.51 0.57b
0.45 0.41 0.67 0.42
0.69 0.83 0.6Y 0.93 0.68 0.67e 0.78
0.76 1.04 1.36' 0.97 1.40 1.50
1.12 1.04' 1.83
1.06'
Class: A D (Weak HB) 1.29 0.09 0.08 acetone acetonitrile 2.57 0.14 0.19 chloroform 4.73b 0.20b 0.44 methylene chloride 2.41b 0.13b 0.30 a Kamlet-Taft H B D acidity values from summary tab1es.j bLiterature data from equilibria with respect to pyridine N-oxide as the reference base in cy~lohexane.~~ New experimental Kamlet-Taft HBD acidity values. NMR spectrum of benzonitrile as reported earliera2l Results for the alkanols were also re-determined with phenol blue as the solvatochromic indicator.22 For these stronger hydrogen bond donor solvents, the uncertainties in the mean values listed in Table I range from f0.02 for the simple alkanols to f0.04 for the carboxylic acids. Experimental procedures of Frange et aL2j were used without alteration to determine a? values from the hydrogen bond donor-acceptor equilibrium constants with respect to pyridine Noxide with cyclohexane as the s01vent.I~
Discussion In general if only a single dominant solvent characteristic must be specified in order to represent the influence of the medium upon the electron-transfer kinetics, then it is most likely that either the continuum descriptors (e and n2) or a comparable dipolarity parameter (**) will be sufficient to quantify the solvent variable in free energy functions. Thus,the Marcus statement in eq 5 gives Xo = Ne2(1/2al
+ 1/2a2 - l/rl2)(1/n2 - l/e)
(5)
the solvent reorganizational energy contribution (&) in terms of the usual bulk properties' where a1 and a2 are reactant radii, rI2 is the electron-transfer distance for charge e, and N is Avogrado's number. Then, the solvent reorganizational energy is related to the activation free energy (AG*) by eq 6. It is uncommon for
AG* = (AGO + X O ) ~ / ~ X O
(6)
a solvent characteristic other than dipolarity-polarizability to be the sole determinant of the reaction rate; however, the electronic coupling ( E ) between a x-acceptor metal and a x-donor ligand in the Ru(III)-cyanamide bond24 illustrates such exceptional behavior in aprotic media, and the data can be fitted to eq 7. E = 5.04 (f0.07)/9KT
+ 12.54 (f0.02)
(7)
(21) Kolling, 0. W. Anal. Chem. 1984, 56, 430-432. (22) Kolling, 0. W. And. Chem. 1981, 53, 54-56. (23) Frange, B.; Abboud, J.; Benamou, C.; Bellon, L. J . Org. Chem. 1982, 47, 4553-4551. (24) Saleh, A.; Crutchley, R. Inorg. Chem. 1990, 29, 2132-2135.
It appears that the more probable situation in electron-transfer reactions in solution involves the coupling of at least two distinct characteristics of the solvent, dipolarity with hydrogen bonding acidity or dipolarity with basicity effects. This observation has been documented by Abbott and Ruslingz5as well as in the earlier work on electron transfer by porphyrinquinone systemsV4As has been noted by Abbott and R u ~ l i n git, ~is~the solvent reorganizations both about the transition state and about the product species which are governed in part by changes in the polarity, HBD acidity, and for basicity of the solvent. HBD Acidity Parameters. Numerical values for the two specific hydrogen bond donor acidity scales, Q~KTand a?, are listed in Table I for twenty one donors. For the weak-to-strong HBD species included here, the uncertainties in the K, values are of the order of f9.1% SD, and the influence of this variable upon the differential response of the a? scale will be discussed separately. The critical initial test for the data in Table I is to compare the effect of conditions of the shift from pure solvent (YKT to a? acidities in cyclohexane solution. Although the anticipated pattern of a? < CYKToccurs, it will be noted that the qualitative order of decreasing HBD strength from formic acid to acetone is largely the same on both scales. The linear regression in eq 8 applies to a! = 0.338 (fo.O02)(uKT 0.06 (f0.01) (n = 21; r = 0.99; calcd f0.015SD) (8)
+
the full data set without statistically outlying points. Likewise, the HBD acidity for the monomeric donor among the HBSA members is less in the cyclohexane solution than in the neat solvents themselves. Consistent with these results are the findings on the self-association of the alkanols obtained by Frange et aL2jwho observed a systematic solvent dependence for K, (eq 2) as well as for other equilibrium constants for dimeric OH species with changes in the aprotic solvent (i.e. cyclohexane to CClJ. Also, for a limited data set, the equilibrium constant for the dimeric species for the alkanol is linearly related to ( r K p 2 j However, other published results demonstrated that it is the hydrogen bond basicity values which exhibit the greater dependence upon the monomer-dimer equilibria for the alkanols in cyclohexane and which also reflect the greater steric effects upon the respective equilibria.26 A second essential test imposed on the single parameter HBD acidity variables is to compare the trends in the two a scales to those in the more general acceptor number-type series, and representative of the latter is the recent AN* system of Riddle and Fowkes.12 The empirical basis for the AN* numbers is the downfield shift (A6) in the jlP NMR spectrum of triethylphosphine oxide which is then resolved into two solvent-dependent contributions, i.e. a van der Waals A@ and an acid-base Asab, in eq 9. The ydis the van der Waals contribution to the surface tension
+
A6 = Aad Asab; Aad = 0 . 3 1 2 ~ ~ (9) of the pure solvent. Then, the acceptor number (AN*) is obtained from eq 10 as a difference between the Gutmann (AN) and the AN* = 0.288(AN - ANd); A N - ANd = 2.348(A6 - Alid) (10) van der Waals contribution to that number.12 Because the AN* scale is a composite acid-base system, the role of hydrogen bonding contributions to the numerical values is not easily discerned. However, it does appear to share some characteristics with the anion-solvating variable (A,) of Swain et al.,27since the approximate correlation in eq 11 applies to 15 weak-to-strong hydrogen AN* = 17.2 (f0.2)[AS - 0.10 (fO.l)]; (AN* calcd f0.7; r = 0.93) (11) bond donors. It should be noted as well that AN* values for (25) Abbott, A.; Rusling, J. J . Phys. Chem. 1990, 94, 8910-8912. (26) Abboud, J.; Sraidi, K.; Guiheneuf, G.; Negro, A,; Kamlet, K.; Taft, R. J . Org. Chem. 1985, 50, 2810-2873. (27) Swain, C.; Swain, M.; Powell, A.; Alumni, S. J . Am. Chem. SOC. 1983, 105, 502-513.
1732 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 TABLE II: Acceptor Numbers, Solubility and Dispersion Force Variables for Pure Solvents at 298 K solvent class" member 8~~ Asdc APbc ANSc
AD and AHD
benzonitrile 1,2-dithloroethane dimethylacetamide dimethylformamide dimethylsulfoxide ethyl acetate methyl acetate ARA and ARP benzene carbon tetrachloride EPD 1,Cdioxane diethyl ether n-hexane tetrahydrofuran HB, HBSA, and acetone weak HBDs acetic acid acetonitrile n-butyl alcohol terf-butyl alcohol chloroform ethanol formamide methanol methylene chloride nitromethane isopropyl alcohol trifluoroethanol water
13.35 12.21 0.09 10.2 10.07 2.73 10.8 9.05 2.44 11.76 9.70 2.81 12.0 9.30 4.61 8.90 7.41 2.24 9.50 7.83 2.42 9.15 8.93 0.25 8.58 8.36 0.97 10.1 10.35 -0.06 7.20 5.28 2.05 7.27 5.68 -0.01 9.30 8.27 0.81 9.66 7.32 3.70 7.22 20.98 11.74 6.79 6.95 10.7 7.86 13.50 9.1 6.31 10.92 9.34 8.40 7.98 12.9 6.54 15.29 17.9 8.93 13.71 14.45 5.61 17.75 9.88 8.61 5.75 12.61 8.12 6.30 11.5 6.59 13.43 4.46 23.93 23.4 6.73 22.31
0.06 1.8 1.6 1.9 3.1 1.5 1.6 0.17 0.7 0.0 1.4 0.0 OS 2.5 14.2 4.7 9.1 7.6 5.4 10.3 9.3 12.0 3.9 4.3 9.1 16.2 15.1
a Chastrette-Purcelll* solvent classes: aprotic dipolar and aprotic highly dipolar (AD, AHD); aromatics (ARA, ARP); electron pair donor (EPD); hydrogen bonding, hydrogen bondingstrongly associated (HB, HBSA). bHildebrand solubility parameters from the summary tables of Barton.19 'Acceptor numbers calculated by Riddle and Fowkes'*; dispersive forces and acid-base parameters from the same source.
aprotic dipolar and aprotic highly dipolar solvents are confined to a very narrow range from 0 to 1.9 while the HBD solvents cover a wide interval from 2.5 to 32 units.12 For the aprotic solvents, there is no correspondence between AN* and the Kamlet-Taft (r*)dipolarity parameter nor between their respective dipole moments. On the other hand, there is in general a parallel qualitative trend between the AN* and LYKT values for the hydrogen bonding solvents in Table 11. Although the latter trend is quantitatively inexact, the approximate regression in eq 12 can be deduced from the data. The intercept AN* = 9.8aKT+ 2.0; (r = 0.91)
(12)
is a residual contribution associated with aprotic properties of the solvents. It should be noted that the original A N values of the Gutmann scale have been shown to contain multiple interacting solvent characteristics, including a substantial hydrogen bond acidity ~omponent.~ The initial clue to the origin of the AN* dependence upon (YKT (eq 12) is to be found in the Asabcontribution to the NMR spectral shift in eq 9. The APb values from Table I1 conform to the typical pattern that was normally encountered in the linear solvation energy investigations of Kamlet, Abboud, Abraham, and Taft.) As was true with the AN* data, the A6abvalues for the aprotic species fall in a narrow range (Le. from -0.06 to 2.5) while the weak to strong HBD solvents as a group have much larger values. The specific linear solvation energy function derived from the A6ab data for only the hydrogen bonding solvents is given by eq 13. Adab= 3.0 (fO.l).rr* + 15.5 (fl.O)aKT; ( n = 14; r = 0.95; Adabcalcd & 1.OSD) (13) A second but less obvious source of HBD acidity effects upon AN* values is found within the van der Waals term (Add)in eqs 9 and 10, as well. This is apparent from comparisons between the A6d data and the Hildebrand solubility parameters for HBD solvents listed in Table 11. As a measure of the internal cohesive energy of the liquid, the latter has been interpreted to be an
Kolling TABLE III: Structural Distinctions from Hydrogen Bond Donor Acidity Parameters HBD dissimilarity index (ApJ functional structural group difference (Am.) ACYP A~KT 0.04 0.10 alkanols CIJC,
0.01 0.01
0.06 0.02 0.22 0.03 0.01 0.07
0.05 0.09 0.02 0.02 0.43 0.10 0.07 0.71 0.06 0.02 0.14
h0.03-0.04a
*O.OZ(w-HBDs)
0.01
haloalkanols
0.00 CS/C, F,-ethanol/F2-ethanoI 0.11
F,-ethanol/F3-ethano1
F-ethanol/Cl-ethanol alkanoic acids
haloalkanes uncertainties (exptl)
CIF2 Cdc3 Cdc4
CH2CI2/CHCI3
f0.03-0.07
(st-HBDs)* "Composite range based on both the data of Abboud et a1.I' and the experimental results from the current study. *Uncertainties as high as 10.08 have been reported by Kamlet et aL3 for the strongest HBD acids.
estimate of the magnitude of solvent/solvent interactive forces disrupted by a solute when forming a cavity space within the solvent ~tructure.~ (A solubility parameter treatment by Karger, Snyder, and Eonz8 illustrates the successful application of this approach to the classification theory in chromatographic separations.) Thus, the regression in eq 14 applies only to the hyAdd = O.84dH - 21.6(aKT- 0.62); ( n = 13; r = 0.92)
(14)
droxylic solvents, including water, as members of the HBSA class in the Chastrette-hrcell scheme for which the effect of hydrogen bonding on Abd is most pronounced. The scattering among the data for aprotic solvents obscures the HBD acidity effect upon the very weak donors, Le. acetone, acetonitrile, etc. Therefore, it is clear that even though the AN* scale is a composite one with variable mixing from dipolar and HBD acidity components, the coefficient ratio (a:s) equal to 5.2:l from eqs 1 and 13 suggests that HBD acidity is the dominant characteristic being represented by the AN* values. HBD Acidity Scale Discriminators. For electron-transfer reactions, the accurate description of the effect of the solvent upon the kinetics requires that the solvent parameters by capable of differentiating between the subtler shifts associated with structural and/or steric factors within a series of solvents having a functional group in common. A superficial examination of published A N and AN* values12 for only the aprotic solvents indicates that the structural distinctions are often unresolved in such composite scales. In order to make quantitative comparisons among the single parameter scales, one may define a generalized dissimilarity index by eq 15 where pa is a specific solvent parameter a, b, or
c (i.e. T * , CYKT,a?, etc.) and j , the structural variable (mass units
m, in the simplest case). Then, for a series of homologues like the normal alcohols, the index would be AaKT/Am,or Aay/Am, where Amsis the -CH2increment. Although scaling factors can artificially magnify the empirical Adi indices, the most critical comparison to be made is that between the experimental precision for pa and the Adivalues. Obviously, Adi must exceed the standard deviation in Apa. Enough data are now available for the stronger hydrogen bond donors to compute dissimilarity index values for several series, and these results, which are listed in Table 111, may be summarized as follows. (1) Among the C , to C6 alkanols, the (XKT scale does appear to distinguish shifts in donor acidities; however, because of the (28) Karger, 9.; Snyder, L.; Eon, C. Anal. Chem. 1978, 50, 2126-2136.
J. Phys. Chem. 1992,96, 1733-1737 overlapping precisions in the L Y values, ~ structural distinctions from the latter are often unclear. (2) Both scales demonstrate the influence of increasing halogen substitution on HBD acidity for the haloalkanols and haloalkanes. (3) The overall trends in the dissimilarity indices for the two HBD acidity scales are parallel among the members of all four functional classes, including the full range from weak-to-strong hydrogen bond donors. On the other hand, the AaKT values are consistently the superior discriminators with respect to the identification of smaller structural influences upon solvent donor acidity. (4) For the scaling intervals used in the three HBD acidity parameters, there are significant numerical differences as well. These may be demonstrated by comparing the parameter ratios for the strongest (st-HBD) and weakest (w-HBD) members in Tables I and 11, i.e. trifluoroethanol and acetone. As measures of the scale ranges, it is clear that the AN* and a? parameters are similar in spread with ratios (st-HBD:w-HBD) of 6.5:l and 6.3:1, respectively; however, the corresponding ratio for the LYKT scale is nearly 3 times larger (18.8:l) than the other two acidity scales and leads to the LYKT parameter being a more sensitive factor in linear free energy descriptions of kinetic solvent effects. The search for universal HBD acidity parameters for applications to electron-transfer kinetics in solution seems justified because of the evolving structural models for self-associated solvents. Even those strongly associated solvents having very diverse polar functionalities appear to have solvent characteristics
1733
in common. Rossky has concluded that packing effects are a major structural determinant and that for even the lower alkanols the unit structure can be depicted as a simple heteronuclear diatomic species with the alkyl and hydroxyl groups defining the dipolar sites in that molecule.29 Likewise, among such dissimilar HBSA liquids as alkylamides and alkanols, there appear to be common polar liquid structures (Le. “winding chains”) in which the monomeric unit is hydrogen bonded to two nearest neighbors. Computer models of solute solvation by such liquids indicate that there are only slightly stronger nearest-neighbor HBD interactions in solution rather than major population shifts favoring more linear hydrogen bonded combinations within the solvent structure.29 Registry No. Benzonitrile, 100-47-0; pyridine N-oxide, 694-59-7; 1-butanol, 71-36-3; ethanol, 64-17-5; 1-hexanol, 11 1-27-3; methanol, 67-56- 1; 2-methyl-2-propano1, 75-65-0; I-pentanol, 7 1-41-0; 1-propanol, 7 1-23-8; 2-propanol, 67-63-0; 2-chloroethanol, 107-07-3; 2,2,2-trichloroethanol, 115-20-8; 2-fluoroethanol, 37 1-62-0; 2,2-difluoroethanol, 359-13-7; 2,2,2-trifluoroethanol,75-89-8; acetic acid, 64-19-7;butanoic acid, 107-92-6;formic acid, 64-18-6; propanoic acid, 79-09-4; acetone, 67-64-1; acetonitrile, 75-05-8; chloroform, 67-66-3; methylene chloride, 75-09-2; 1,2-dichIoroethane, 107-06-2; dimethylacetamide, 127-19-5; dimethylformamide,68- 12-2; dimethyl sulfoxide, 67-68-5; ethyl acetate, 141-78-6; methyl acetate, 79-20-9; benzene, 71-43-2; carbon tetrachloride, 56-23-5; l,Cdioxane, 123-91-1;diethyl ether, 60-29-7;n-hexane, 110-54-3; tetrahydrofuran, 109-99-9;formamide, 75-12-7;nitromethane, 75-52-5. (29) Rossky, P. J. Annu. Reo. Phys. Chem. 1985, 36, 321-346.
Arrhenius Parameters for Ionic Fragmentations Cornelius E.Mots Chemical Physics Section, Health and Safety Research Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -61 25 (Received: June 1 1 , 1991; In Final Form: October 15, 1991)
Rate constants as a function of energy for the dissociation of more than 25 molecular ions, drawn from the literature, are analyzed in order to extract their attendant Arrhenius parameters. Subtleties of the extraction process are discussed, and uses to which the parameters might be put are indicated.
Introduction The rate constant for a unimolecular reaction is typically a strong function of pressure and temperature. The pressure dependence can be thought of as arising from an imperfect contact between the reacting species and its heat bath. The limiting, high-pressure rate constant is the parameter of greatest intrinsic interest. It may be obtained from an extrapolation of measurements obtained at finite pressures, guided by theory and with due attention to artifacts arising from such matters as the cage effect.’ Finally, the temperature dependence of this limiting rate constant may be studied. Using a standard Arrhenius plot one may extract an activation energy, M a , and then cast the rate constants in the form k ( T ) = A exP(-L\E,/k,T)
(1)
This representation contains two parameters, the activation energy and the frequency factor, A . Each is of interest. Nevertheless, the traditional experimental method just outlined for obtaining them is both problematical and tedious. An alternative method for obtaining the same information has been describedS2 It makes use of measurements of k ( E ) , rate (1) Troe, J. J . Phys. Chem. 1986, 90, 357.
0022-365419212096-1733$03.00/0
constants for the reaction under consideration as a function of the energy. The measurements are made on isolated molecules, Le., under conditions which are the antithesis of the high-pressure heat bath. Nevertheless, generalized Arrhenius plots can be constructed, and the parameters Ma,, and A can be extracted. In effect, data garnered in the energy domain can be transferred to the temperature domain. Such transformations require that one know the properties of the parent molecule, in order to calculate canonical energies and heat capacities. One does not need to know anything about transition states, or what the products of the reaction are, or even whether or not it involves chemistry. In that sense the transformation is model-free. In addition to the opportunity for data-smoothing which generalized Arrhenius plots offer, two uses of such a transformation will be evident: it provides a convenient two-parameter condensation of the data and it permits a direct comparison with data garnered in the temperature domain by conventional means. Because of the facility with which charged particles can be manipulated, most of the existing measurements of rate constants as a function of energy involve the fragmentation of ions.3 We (2) Klots, C . E.J . Chem. Phys. 1980, 90, 4470; 1990, 93, 2513. (3) Baer, T. Adu. Chem. Phys. 1986, 64, 111.
0 1992 American Chemical Society
