Kinetics of Proton Transfer to Weak Aromatic Bases*BY B. C. CHALLIS AND F. A. LONGDept. of Chemistry, Cornell University, Ithaca, N.Y., U.S.A.Received 1 1 th January, 1965The rates of proton transfer to and from the weakly basic aromatic species azulene are sufficientlyslow that the rate of approach to a displaced equilibrium can be measured in a fast-flow apparatus.Independent measurements of the equilibrium protonation then permits calculations of the separaterate coefficients ky and kr for protonation and deprotonation respectively. For the ionization ofthe azulenium ion as an acid, AGO = -2-4 kcal ; ASo = - 11 cal/mole deg., and AH' = -5.8 kcal.At 7.3", over the acidity range 1.5-4-0 M HC104, kf = 1-52 hk26 and kr = llOh;P.68 where ho isthe Hammett acidity function.The Arrhenius parameters for the protonation reaction are similarto those for the acid catalyzed-tritium exchange of azulene-1-t in aqueous media and the aciditydependence of protonation is similar to the acidity dependence of the tritium exchange for sub-stituted azulenes, suggesting related mechanisms. Quantitative evidence that the exchange reactiondoes go via a conjugate acid intermediate, is provided by the fact that, after some necessary medium,isotope effect and statistical corrections are made, the specific rate for protonation of azulene isfound to agree within limits of error with a protonation rate derived from the tritium exchangedata assuming the 2-step A - sE2 mechanism for the latter.The exchange of hydrogens attached to an aromatic nucleus with the hydrogensof an aqueous solvent has been studied in recent years by a number of groups.1-*The reaction is catalyzed by acids but not by bases and exhibits general acid catalysis.This and a number of the other details, including the kinetic isotope effects and themagnitude of the Arrhenius parameters, strongly suggests that the reaction involvesan electrophilic attack of the solvated proton on a carbon atom of the aromaticsystem. This offers a particularly simple example of electrophilic acid substitution.There has been considerable discussion of the mechanism for the reaction. Thebulk of the evidence clearly supports a two-step A - S E ~ mechanism.H L H LIt is clear that the kinetic data themselves do not require that the reaction gothrough the comparatively stable conjugate acid as an intermediate. On the otherhand, such a mechanism, leading to a " two hump " diagram for the free energyof activation as function of reaction co-ordinate (fig.3), is very plausible and isentirely consistent with the similar mechanism proposal made earlier by Melanderfor more obvious electrophilic substitutions on aromatic ring systems.6One way to obtain evidence on the validity of this mechanism, and the subjectof this paper is to study directly the rate of proton transfer from acidic media to andfrom an aromatic ring system. That this direct proton transfer reaction shouldoccur, and at a measurably slow rate, is indicated by the free energy of activationdiagram of fig.3 which is approximately to scale, if one assumes that the reactiondoes go via the conjugate acid.* work supported by a grant from the Atomic Energy Commission.668 PROTON TRANSFER TO AROMATIC BASESThe rate of tritium exchange of azulene occurs at an easily measurable rate forcatalyst concentrations of around 0.001 M hydrogen ion; kex the specific rate co-efficient for the reaction between azulene-1-1 and H3O+, is 0.183 1. mole-1 sec-1at 25O.3 However, to measure the proton transfer directly one must go to sufficientlyacidic solutions so that the equilibrium is measurably displaced. The base strengthof azulene is such that it is half-protonated at about 2-2 M perchloric acid. Hencea displacement of equilibrium of a magnitude which permits easy spectroscopicanalysis involves working at acidities of around 2 M strong acid, at which pointthe reaction rates bewme large.The solution to this has been to use a fast flowapparatus of the Partridge-Roughton type, with a mixer and observation systemthat permits analysis within less than 10 msec after mixing.Symbolizing the neutral azulene molecule by AzH, the reaction concerned isfkrAZH + H + +AZH,+,where kf and k, are the first-order rate coefficients for protonation and deprotonationrespectively. The observed reaction is the first-order approach of a displacedsystem to a new equilibrium. The first-order rate coefficient kut for this processis linked to those above bywhere the subscript e denotes equilibrium concentrations. Hence a measurementof kist and of the indicator ratio I = [AzHg],/[AzH], permits determination of kfand kr.For later use, one can further define a second-order rate coefficient forprotonation, kbi = kf/[H+].EXPERIMENTALThe fast-flow apparatus was specifically fabricated to permit use of concentrated aqueousmedia. A 4-jet circular tangential mixer was employed; this permitted mixing to within1 msec. In a typical experiment one syringe contained nearly saturated azulene (about10-5 M) in 1 M perchloric acid. Another syringe of equal cross-section contained 5 Mperchloric acid. These solutions were mixed in equal volumes by a plunger moving at apredetermined rate. After mixing the solution flowed along a quartz observation tube ofknown diameter. Extent of reaction at a given point along the tube was determined bymeasuring the change in light absorption at 350A, a wavelength where azulenium ionabsorbs strongly and azulene almost negligibly2 Final acid concentration was determinedby titration of the mixed solution. Temperature was measured for the flowing solutionwith a thermocouple; temperature control was always to within f0.4".A few experi-ments were performed in which equilibrium was approached from the more acid side;the results agreed with those from studies of the above type.A typical signal record for a kinetic experiment is shown in fig. 1. The lines A and Brefer to the intensities of the initial perchloric acid and unreacted azulene solutions respec-tively ; line C refers to the combined solutions under flow and line D to the hal equilibrium.The calculation of the rate coefficient involves2.303 [AzH,C], - [AzH'] 2.303 D -(A + B)/2log10 D-C 9o = -loglo [AzH2f],- [AzHl], t klst = - twhere D, A, B and C are heights of the above lines from the base line and where t wascalculated from the flow rate and geometry.The normal procedure was to plot valuesof log10 D-(A+B)'2 D-c against i for a series of measurements at constant acidity but varyinB . C . CHALLIS AND F. A . LONG 69reaction times. The slope of the line gives 2.303/klSt. Reactions were accurately first-order up to at least 85 % reaction.The equilibrium ratio [AzHz],/[AzH], was determined in a Cary model 14 spectrometerwhich permitted temperature control to 0.1".Spectra were recorded at several wavelengthsbetween 2200 and 3600A and the indicator ratio was calculated from the results in theusual way. At each temperature data were recorded at a number of acidities. Therrno-dynamic dissociation constants KA& were determined by plotting values of log ([AzHz]/[AzH][Hf]) against perchloric acid concentration and extrapolating to zero acid con-centration .9Itime-,FIG. 1.-Diagram of the recorded signal for a single kinetic point.RESULTSTable 1 records the acidity constants KAH; as a function of temperature. Thesedata lead. for the ionization reaction, to AGO = -2.4 kcal; ASo = -11 cal/moledeg. ; AHo = - 5.8 kcal. As the small value of AGO indicates, the azulenium ionis of comparable stability to azulene itself.TABLE 1 .-THERMODYNAMIC DISSOCIATION CONSTANTS KA~HZAS FUNCTION OF TEMPERATUREtemp.O C KA& mole 1-15.7 106 f 615.5 69 f 625.0 56 f 638.6 36 f 6The results for an extended list of kinetic studies at 7.3" are given in table 2where the data are analyzed into values of kf and kr. Fig. 2 gives plots of log kfand log kr against the acidity function Ho. For the protonation reaction the datalead to log kf = 0.18 + 1.26 (-Ho). The deprotonation reaction, whose stoichio-metry does not require acid, also varies strongly with acidity, i.e., kr~Ch,0-68, in-dicating a very pronounced medium effect on the reaction70 PROTON TRANSFER TO AROMATIC BASBSTABLE 2.-vARIATION OF kist, kf AND k, WITH ACIDITY AT 7.3f0.4"CIHCI041M1.461 -481 -491.161-711.781 -922-052-092-502-572-582-692.852.993-003.283-313-653.91- HO0.5100.5270-5320.5920.6440.6800.7500,8050.8251.011 -401.w~1 -091-161 *221 a231.341.351.541.67[AzHiI *1-10.1390.1480.1500.1950.2450,2840.3850.5040-5431-281 *461 -491-862.603-513.576.2 16.4313.221.6kist sm-151.351.448-348-348.852-052.447.852.250.053.951.159.868.974.673.783-998.3139174kf sec-16.36.66.38.79-611.514.616.018.628.132-030-638-949.858.157.672.385.6129166* from equilibrium studies at 57°C.TABLE 3.-vARIATION OF kist, kf AND k, AS FUNCTION OFTEMPERATURE FOR HC104 = 1.93 Mkist sec-1 kf sec-1 temp.O C7.3 f0.4 0.398 52-4 14.912.7 f0.4 0.427 79.0 23.616.7 f0-2 0.450 108 33.519.9 f 0.2 0.470 138 44.1[AzH;l1-1kr sec-144.944.642-039-639.240.534.832.034221.921.920-518.919.115.516.111.612.49.87.7k, sec-137.555.474.593.9Table 3 gives the temperature dependence of the rate coefficients for reactionin the single medium 1-93 M perchloric acid. These data lead to the followingprotonation (sec-1) deprotonation (sec-1)AG', kcal 16.0 15.6AH*, kcal 15.1 12.4AS*, cal/mole deg. - 3.2 -11.0Arrhenius parameters. These data imply that the thermodynamic parameters forequilibrium in this solvent differ appreciably from the values for an infinitely diluteaqueous medium.Specifically for equiIibrium in 1-93 M perchloric acid, AG =-0.4 kcal; AH = -2-8 kcal; A S = -8.1 cal/mole deg.DISCUSSIONIf the acid-catalyzed tritium exchange of azulene-1-t goes by a two-step A - S E ~mechanism (see fig. 3), via the conjugate acid as an intermediate, then the first stepof the reaction should proceed at essentially the same rate as the direct protonationof azulene. Qualitatively, there is marked indication of similar behaviour. Forthe exchange reaction, with rate coefficients, in 1. mole-1 sec-1, the Arrhenius para-meters for reaction in dilute aqueous solution 3 are : AGTx = 19 kcal ; AS; B . C . CHALLIS AND F . A . LONG 71- 10.1 cal/mole deg. ; AH: = 16 kcal. These values are similar to those forprotonation in 1.93 M perchloric acid. A further point is that for azulenes withexchange rates slow enough to be measurable in concentrated acid solutions, first-order rate coefficients for exchange vary with acidity much like the protonationreaction does.Thus, for I-CN-azulene-3-t,3 kexcchk2. It is therefore of interestto see if there is quantitative agreement between the rates for the protonation re-action and for the presumed first step of the exchange reaction.If mechanism (I) is correct for the exchange reaction, then with tritium used attracer level so that k-2 can be ignored,kzx = kT/(l+ k'! JkT),where the superscript T means only that the rate coefficient is for mechanism I.The comparison which is desired is between kbi for protonation and k? in the samemedium for the hypothetical exchange of hydrogen atoms.Comparison for thesame medium is important because of the strong medium effects indicated by fig. 2.5 0-5 1.0 1.5(-H0)?5'FIG. 2.-Plot of loglo k, and loglo kf against ( -Ho), 7.3".For the exchange reaction we shall first assume that kT = ky, i.e., that thesecondary isotope effects on the rate of protonation are negligible.11, 12 The problemthen is to calculate kl from available information on the exchange rates. For-tunately this can be done if data on both kinetic and deuterium solvent isotope effectsare available. This is true for the azulene exchange reaction.2, 3 Using the availabledata and the procedure of Kresge 1 we obtain 72 PROTON TRANSFER TO AROMATIC BASESThe latter ratio then leads to a predicted kinetic tritium isotope effect on k2 of kF/kT= 12 which in turn means a predicted A(AG*) between the two humps of fig.3of 1500 cal mole-1 at 25". Since by fig. 3 it is evident that kT, /kT is, except forsecondary isotope effects, the same as ky/kT, we may write,kY kYkT, = 1 +(ky/kT) = 1 + exp (+ 1500IRT)'The Schulze and Long tritium exchange data 3 interpolated to 7.3" give k', =0.032 1. mole-1 sec-1 for reaction in an aqueous solution containing 0.1 M electro-lyte. Application of the above equation then gives k? = 0-5 1. mole-1 sec-1 asthe rate coefficient for protonation at (a single) 1-position of azulene at thistemperature.reaction co-ordinateFIG. 3.-Free energy profile for two-stage A-S& mechanism, 25".Two corrections need be made on the data for kbi before comparing it with k?.The simpler is a statistical correction of 2 to take account of the fact that the pro-tonation reaction has two equivalent base sites to attack (the 1- and 3-positions),lowhereas k y is for attack at only one of these.The more difficult correction is formedium effects. The most reasonable procedure is to extrapolate the data forkbj and k,. to give the limiting rate coefficients k& and k," for infinitely dilute aqueoussolutions. The appropriate type of extrapolation is indicated by the following.The coefficient k& is defined by the equations-d[AzH]/dt = kf[AzH] = kbj[AzH][H+] = k,",[AzH][H+]f,,~f,+/f*,where f k ~ f , f ~ f and f* are activity coefficients of azulene, hydrogen ion andtransition state respectively.If, as usual, the activity coefficients are referred to a value of unity at infinite dilution,Rearrangement and taking logs leads tolog k& = log kf-log [H+]-log (j&JH+/f*).log k; = lim [log kf-log [H']].[H+]+OThe form of the activity coefficient ratio involved here is similar to that enteringin the similar extrapolation for ionization equilibrium data.Since a linear extra-polation has been found to be valid in the equilibrium case,9 it should be valid foB. C . CHALLIS AND F. A . LONG 73the kinetic case also. A similar development for the deprotonation reaction leadsto the relationshiplog k," = lim [log k,.][H+]-OThe appropriate plots for the kinetic data are shown in fig. 4 ; both are linearwithin limits of experimental accuracy.Least-squares treatment leads to kii =1-17 1. mole-1 sec-1 and k," = 135 sec-1 at 7.3" and infinite dilution. A good testof the extrapolation is to compare the calculated equilibrium constant k,"/k,"i = 115with the previously determined value of K ~ H ; = 100 at the same temperature.The agreement is as good as can be expected.FIG. 4.-Linear extrapolation for protonation and deprotonation reactions at 7.3".The plot of fig. 4 can also be used to give a value of kbi at the electrolyte con-centration of 0.1 M which is the one of interest for comparison with kf: from theexchange data. From fig. 4, the value of kbi at this concentration is 1-28 1. mole-1sec-1. Hence the desired comparison between protonation data and ky fromexchange data is between kbi/2 = 0.64 1. mole-1 sec-1 and k y = 0.5 1. mole-1 sec-1.These agree to well within the experimental error of the assumptions and extrapola-tions involved. We conclude that results on the protonation reaction provide semi-quantitative evidence for the validity of the proposed 2-step A - S E ~ mechanismfor the exchange.1 Kresge and Chiang, (a) J. Amer. Chem. SOC., 1959, 81, 5509 ; (b) Proc. Chem. SOC., 1961,81;2 Colapietro and Long, Chem. and Ind., 1960, 1056.3 Schulze and Long, J. Amer. Chem. SOC., 1964, 86,322,327,331.4 Gold and Satchell, J. Chem. Soc., 1956,2743 ; 1960,2461 ; see also ref. (5).(c) J. Amer. Chem. SOC., 1961, 83, 2877; (d) J. Amer. Chem. SOC., 1962, 84, 397674 PROTON TRANSFER TO AROMATIC BASES5 Gold, Friedel Crafts and Related Reactions (ed. Olah) (Interscience, New York, 1964), vol. 11,p. 1253.6 (a) Melander, Isotope Eflects on Reaction Rafes (Ronald Press, New York, 1959) ; (6) Melanderand Olsson, Acta Chem. Scand., 1956, 10, 879.7 Eaborn and Taylor, J. Chem. Soc., 1960,3301.8 Thomas and Long, J. Amer. Chem. Soc., (a) 1964, 66, 4770 ; (b) J . Physic. Chem., 1964, 29,9 Paul and Long, Chem. Rev., 1957,57, I .10 Heilbronner and Simonetta, Helv. chim. Actu, 1952, 35, 1049.11 Streitweiser, Jagow, Fahey and Suzuki, J. dmer. Chem. SOC., 1955, 80, 2326.12 Olsson, Arkiv. Kerni, 1960, 16,487.341 1