Proton Transfer to OlefinsBY V. GOLD AND M. A. KESSICKDept. of Chemistry, King’s College, Strand, London, W.C.2.Received 3rd March, 1965The experimental evidence relating to deuterium fractionation between hydrogen ions and wateris outlined. The conclusions which can be drawn from these measurements about the structureof the hydrogen ion are indicated. In the light of this information the rate and product isotopeeffects on the hydrogen-ion-catalyzed hydration of isobutene, the rate-limiting first step of whichinvolves a proton transfer to olefin, are discussed. The results are adequately described by thetheory of isotope effects on slow proton transfer from H30f to substrate. It is shown that morecomplicated mechanisms, in particular indirect pro ton transfer from H3O+ via a water molecule(or direct transfer from the outer protons of the H904f cluster), are likewise compatible with the results,but offer no advantages in the context of isotope effects.Recent discussions of proton transfer processes from the hydrogen ion in solutionhave been in terms of the formula H90,+ for that ion, whereas discussions of deuteriumsolvent isotope effects on protolytic reactions and equilibria have most frequentlybeen based on the formula H3O+.We here examine one aspect of the questionwhether the two approaches are mutually exclusive. The discussion is based inthe main on recent experimental work on olefin hydration, a reaction which lendsitself particularly well to the detailed study of kinetic solvent-isotope effects. Theinterpretation of reaction velocities and equilibrium constants of hydrion (i.e.,proton, deuteron or triton) transfer reactions in H20 + D20 mixtures involves theconsideration of isotope fractionation effects, especially between hydrogen ions andwater.This topic is reviewed as an essential preliminary to the main theme.1. ISOTOPE FRACTIONATION BETWEEN AQUEOUS HYDROGEN IONS ANDWATERA number of different methods of measurement point to the conclusion that,in a solution of a strong mineral acid in an H2O+D20 mixture, the deuteriumisotope is not randomly distributed between hydrogen ions and water moleculesbut shows a preference for the latter. The interpretation of the results of someof these measurements requires an assumption concerning the formulation of thehydrogen ion which makes the measurements particularly relevant to our maintopic.All these results for hydrogen ions are, to varying extents, complicated bythe unavoidable presence of the complementary anions.The main methods that have been used are :A. GALVANIC CELLS WITHOUT TRANSFERENCE.-The comparison of the e.m.f.of pairs of cells employing isotopically different media, such as 1Pt(D2) 1 DCl in D20 I AgCl, AgPt(H2) I HCl in H20 I AgCl, Ag8V. GOLD AND M. A . KESSICK 85in conjunction with the equilibrium constant for isotope exchange between hydrogenions and water, leads to a constant L', defined by(H + (H, 0),) ( DT)2X+ ' (C1 -)2(D +(D20)x)2(H20)2"''(C1-) 2'L' =where a bar over a formula denotes solution in heavy water and absence of a bara solution in light water.The numerical value of L' is independent of x, i.e., ofthe chemical formula assigned to the hydrogen ion in solution. However, L'measures not only the exchange constant but contains a contribution arising fromthe free energy of transfer of the ions between the two waters. The experimentalvalue of L' (at 25') is ca. 18. Swain and Bader 2 consider that the free energy oftransfer of hydrogen ions can be neglected and suggested a method for calculatingthat of the chloride ion. On this basis it is possible to correct L' for the transfereffect and to calculate a value of L = 8.25,3 where[ H + ( H2 O),l [ D 01 2x+ '[ D + (D, O)x] [ €3, O] 2x+L =(On the assumption that the transfer term for hydrogen ions is negligible it is nolonger necessary to distinguish between the different phases.)B.GALVANIC CELLS WITH TRANSFERENCE.-The e.m.f. Of the Cells 4Pt(D2) I DCl in D20 i KCl (sat.) in H2O I Hg2C12, HgPt(H2) I HCl in H20 i KC1 (sat.) in H20 I Hg2C12, Hg2D2 + Hg2C12 (solid)+2Df (in D20) +2C1- (in H20) f2Hg2H2 + Hg2C12 (solid) +2H+ (in H20) + 2C1- (in H20) + 2Hgare related to the electrode reactionsandbut, in addition, some changes will occur at the liquid junctions. On the assumptionthat the associated diffusion potentials cancel when the difference between the twoe.m.f. is taken, Purlee 5 has calculated L, and considers the value L = 11.0 to carryan uncertainty of only k0.2 arising from the neglect of the diffusion potential.As has been suspected before, 29 3 there appears to be a logical flaw in this procedure,and it can be shown that the true value of L must be less than 11.(A discussionof this problem and estimates of the size of the correction will be presented elsewhere.)C. PROTON MAGNETIC msoNANcE.-In a system in which there is rapid exchangeof protons between all non-equivalent positions, the chemical shift is the con-centration-weighted mean of individual shifts 6 attributable to these positions.We assume that the introduction of a strong monobasic mineral acid HX into watercreates j sets of different positions, each set containing vj members. These " posi-tions " include any which are created by the structure-forming or structure-breakingeffects of the ions.If we express the acid concentration a as the stoichiometric atom fraction ofhydrogen nuclei added in the form HX, i.e., a = [HX]stoich./([HX]stoich.+2[HzO]),irrespective of the isotopic nature of HX and H20, and measure the position of theresonance signal A relative to the resonance frequency in pure water, we can write -A = azvjSj = 6a. (1.3)iThe implied proportionality between a and A will hold provided that the nature andnumber of positions available to the protons inj-sites is not altered by the additio86 PROTON TRANSFER TO OLEFINSof acid. This will be true only for low values of a, i.e., as long as there is no inter-action between the “ spheres of influence ” of solute particles. Eqn. (1.3) is there-fore a limiting expression (aj-0).If the hydrogen nuclei in the system are not all protons but contain an atomfraction n of deuterium the development of the general equation requires someadditional assumptions.We expect the main effect to be due to the non-randomdistribution of isotopes between water and the j-positions and that the most im-portant fractionation will involve the positions most different from water, i.e.,the hydrogen nuclei that are actually part of the structural core of the hydrogen ion.The treatment assumes that the actual number of positions (vi andj) available to thehydrogen nuclei does not depend on isotopic composition, on the ground that struc-tural differences are more likely to arise beyond the more strongly held first one ortwo layers of water molecules around an ion, and at such distances the fractionationeffect relative to water is probably unimportant.It is also assumed that the ajvalues are independent of isotopic composition, which implies, for example, thatthere are no secondary isotope effects by neighbouring deuterons on proton shifts.This is not likely to be seriously wrong since the position of the proton resonancein water differs from that in deuterium oxide containing a small fraction of protium(and where nearly all protium would be present as HOD molecules) by only ca.0.01 p.p.m.6If A’ is the corresponding chemical shift in an isotopically mixed solvent charac-terized by n and at the same acid concentration a, it can be shown thatl-n+mjjwhere $j is the fractionation factor for thejth group of hydrogen nuclei relative towater, i.e.,The chemical shift of the water resonance caused by the addition of acids is muchgreater than that due to any other electrolyte.7 It is therefore natural to associatethis large effect with the proton or protons contained in the hydrogen ion and toascribe the smaller shifts observed with salts, as well as the differences betweenvarious strong mineral acids, to less definite “ solvation ” effects.In first ap-proximation the sums contained in eqn. (1.3) and (1.4) are therefore replaced by asingle term, so that 8A-= l-n+n$j.K *This expression is independent of v], the number of hydrogen nuclei-all consideredto be equivalent-in a hydrogen ion. With these simplifications, 4j represents aunique distribution coefficient of deuterium between hydrogen ions and water,which is in general given the symbol 1.The seriousness of these approximationscannot as yet be assessed exactly, but the following are relevant considerations.The value of t$j (or I ) determined by eqn. (1.6) for perchloric acid is 0-69+0-02and the corresponding value found for hydrochloric acid * is 0.70+0.02. Thevalues of for the two acids differ but in any reasonable division of 8 among* The previously quoted 8 value of 0-68 f0.02 involved a minor calculation errorV . GOLD AND M . A . KESSICK 87anion and cation effects,7 the molar shift due to the hydrogen ion is much greaterthan that due to the chloride or perchlorate ions. From a consideration of thesize of these effects we estimate that the true fractionation effect due to hydrogenions alone is within 0.03 of the experimental value of 1.This experimental result is again independent of any assumptions about thenumber of hydrogen nuclei in the hydrogen ion that are concerned in the fraction-ation equilibrium.However, the value L, determined by e.m .f. measurements, canbe reconciled with the n.m.r. result for 4j only if a specific structural assumptionabout the hydrogen ion is made.8 For reasons of simplicity we explicitly consideronly formulae with different numbers of equivalent nuclei, but we do not therebyimply that other formulae are necessarily to be excluded. The formula of such ahydrogen ion is written as Hzs+10;, although the number of oxygen atoms perhydrogen ion does not strictly matter.In the limiting case as n-1, the only isotopicforms of this ion to be considered will be D2z+10j; and HD2zOf,, with [D2z+~0Z]9[HD2,0:] and correspondingly [D20] 9 [HOD], so that9 (1.8) +L-- 1/2(2x+ 1)the rule of the geometric mean 9 being assumed to apply to the isotopic forms of thehydrogen ion. Values of 4j predicted in this manner from L on the assumption ofdifferent numbers x are given below. Since L is, according to the e.m.f. measure-ments, likely to be in the range 8-10, the calculations are reproduced for these twovalues of L. In comparing the calculated values with the experimental value of# a small correction for the different temperatures of the e.m.f. measurements(25") and the n.m.r.measurements (31") can be made : its effect would be unimportantin the present context. The assumption that x = 1 (v = 3) gives close agreementwith the experimental value of 4j, and gross experimental errors would have to beinvoked to make the data fit in with any other integral value of x.X 4j (calc.10 0.35 0.321 0-71 0.682 0.8 1 0.793 0.86 0.85L = 8 L - 10A somewhat different treatment of similar n.m.r. measurements 10 has led tothe same conclusion. In this work, chemical shifts were studied as a function ofboth perchloric acid concentration and n. Mutual consistency of results at differentvalues of n was obtained only if the hydrogen ions are all isotopic forms of H3O+,with I = 0-68+0-01.D. MEASUREMENTS OF COMPOSITION OF WATER VAPOUR, OVER AQUEOUS ACIDS.-111this method the isotopic composition of a sample of water vapour in equilibrium withan aqueous solution (containing more than one isotope) is analyzed.There issome fractionation in the absence of added solutes. The effect changes when saltsare added, most of the change being associated with the anion,ll but a larger changeoccurs with perchloric acid. These phenomena arise from the fact that the com-position of the vapour in the presence of solutes reflects that of the free liquid water,i.e., water not held in solvation shells. The isotopic composition of the free wateris naturally affected by the fractionation equilibrium between hydrogen ions an88 PROTON TRANSFER TO OLEFINSwater. The most informative study by this method would be to examine the frac-tionation effect for different values of It, both close to zero and close to unity.Theonly measurements available to date are confined to low concentrations of deuterium.In the detailed evaluation of the results some problems arise from the anion effectand also a minor one from the presence of some undissociated (perchloric) acidat high concentrations and the resulting isotope fractionation between undissociatedperchloric acid and water. The equilibrium constant evaluated from these measure-ments, for the limiting case n-+O at 13.5"C isThis constant is related to L, on the basis of the rule of the geometric meanaccording to(1.9) L- 1/2(2x+ 1) KL = -2x+1so that it is again possible to calculate KL from e.m.f.values for L or, by combinationof eqn. (1.8) and (1.9), from the n.m.r. result for $j. Heinzinger and Weston 3 per-form the latter calculation and show that the data are mutually consistent on the as-sumption that x = l(vi = 3). The calculation for KL from eqn. (1.9) is givenbelow for different values of x. In a more accurate comparison the temperaturedifference between the e.m.f. (25") and vapour measurements (135") can be takeninto account.XKL (calc.)L - a L- 100 5.66 6.321 0.94 0.982 0.49 0-503 0.33 0.34E. OTHER MEAsUREMENTS.-The statistical calculation of L has been describedby Swain and Bader.2 The value obtained (8.2 at 25") falls into the range of valuesgiven by the other methods, but the reliability of the spectroscopic data on whichit is based has been questioned.3The combination of fractionation measurements on the exchange betweenaqueous hydroxide ions and water 12 with values of the ionic products for ordinarywater and deuterium oxide should likewise lead to information about L, but therequired data are not as yet sufficiently well known to give values of L of comparableaccuracy to those obtained by other methods.The main experimental approaches to the problem all lead to values of L in therange 8-10.Results from the e.m.f. methods are independent of any assumptionabout the structure of the hydrogen ion in solution, but results from methods Cand D are compatible with each other 3 and with the e.m.f. result 8 only on thesupposition that each hydrogen ion contains three hydrogen atoms in equivalentpositions.These three hydrogen atoms are isotopically fractionated relative towater. The measurements do not exclude the presence of further hydrogen nucleiwithin the structure of the ion but they do imply that such further positions (e.g., inwater molecules hydrogen-bonded to the H30+ group) have essentially the sameisotopic composition as the bulk water.As will be evident from the comments on each method, the individual deter-minations all involve some assumptions which cannot be justified in detail. How-ever, these assumptions are different in each case and, taken together, the variouV . GOLD AND M. A . KESSICK 89methods provide strong evidence for the foregoing conclusions.These con-clusions were reached without any consideration of protolytic equilibria or reactionvelocities in H20 + D20 mixtures.5 These provide an independent approach tothis problem. The significance of one such study in relation tQ the investigationssummarized above will now be discussed.2. ISOTOPE EFFECTS IN THE HYDRATION OF ISOBUTENEA variety of detailed mechanisms have been advanced for the hydration ofolefins.13 They share the common feature, required by experimental evidence,that the first, rate-limiting step of the reaction involves proton transfer from thehydrogen ion to carbon. Our reaction models are specific versions of this commonmechanism only in the respect of specifying the nature of the hydrogen ion fromwhich proton transfer takes place.The proton in transit is considered not to havereached its terminal location in the transition state, but to have acquired a uniqueposition, whereas in the initial state it occupied one of a set of equivalent positionsfor hydrogen (e.g., three in H3O+).The hydration of isobutene is an acid-catalyzed reactionleading to a single product. The equilibrium constant is very large and the rateof reversal is not significant in the context of this study. Attempts to detect generalacid catalysis have been unsuccessful.14nFIG. 1 .-Rate isotope effect; curve calculated for kH/kD = 1.40 ; r = 4.The two isotope effects to which the present discussion can be restricted arethe rate isotope effect, defined as the effect of isotopic composition of the mediu90 PROTON TRANSFER TO OLEFINSon the rate of disappearance of isobutene from solution, and the deuterium productisotope effect, which is determined by the relative copcentration of isotopes in thesolvent and in the one newly-formed C-H bond of the product [eqn.(2.2)].*5The results discussed in this paper all relate to ca. 0.44 M aqueous perchloric acidat 25". The measurements performed 15 also include product isotope effects ontritium in competition with protiurn or deuterium or with mixtures of the two inthe solvent. The tritium effects quantitatively confirm the measurements withdeuterium, i.e., they are in accord with the relation,l6 ( k ~ / k ~ ) = (kH/kD)1*442.The rate of hydration, measured by spectrophotometric observation of thedisappearance of olefin, varies with the deuterium abundance n of the medium ina non-linear fashion (fig.1). The (slightly extrapolated) rate ratio for H20 andD20 iskH/kD = 1.45&0*1. (2.1)The product of the reaction contains deuterium in only one of its nine other-wise equivalent carbon-hydrogen bonds. In this one newly-formed bond theabundance of deuterium (atom fraction m) is less than that in the solvent (atomfraction n). This product isotope effect can be expressed in terms of the ratio r,n(1- m)m(1- n)r = = 3.9 0.2which is, within the limits of experimental error, independent ofposition of the medium (table 1).(2.2)the isotopic com-TABLE 1 .-DEUTERIUM PRODUCT ISOTOPE EFFECTS?I0-1590-2040.3190.4060.4980.6000-6900.8100.930m0-0500.0520.1 120-1450.2 120.2720-3780-5250-760r3.6 f0-63.9 k0.63.7 30.34.0 f0.33.7 *0.24-0 f0-23.7 f0-23.9 h0.24.2 &0-3(The stated limits of error are estimated maximum errors due to the limits of precision ofthe isotope analysis.)We now consider these results in terms of reaction models.A.DIRECT PROTON TRANSFER FROM H3O+ TO ISOBUTENEExpressions for the velocity of such a process in a medium containing bothH2O and D20 have previously been derived 17 and can be adapted to the treatmentof product composition. According to this theory the rates of proton and deuterontransfer from all isotopic H30 groups (H20, HzDO, HD20, D30), taken together,to a substrate, in fixed concentration, can be written asuH = ( kHclQ)( 1 - n)( 1 - n + n 1' - ") 2, (2.3)VD = ( ~ ~ c / Q ) T I Z ' ~ ~ " ( ~ - ~ + I I ~ ' - " ) ~ .(2.4)In these expressions k~ and k~ are the rate constants of hydrion transfer from the(light) H3O group and the D30 group respectively; these are also the rate co-efficients for reaction in ordinary water and deuterium oxide respectively, on thV . GOLD AND M. A . RESSICK 91assumption that (transfer) medium effects for the substrate, hydrogen ions andtransition states cancel or can otherwise be neglected. The acid concentration cmeasures the sum of the concentrations of all isotopic hydrogen ions; accordingto the rule of the geometric mean, Q is given by the expression (1 --n +nZ)3 ; a isthe exponent of the Bronsted catalysis law, and I is the fractionation parameterdefined in 5 1 .The total rate should then be given by the sum of eqn. (2-3) and (2.4),the relative rate coefficient in an isotopically mixed medium being given byThe isotopic composition of the product will be given by the ratioand the product isotope effect r [eqn. (231 byr = kH/kD11+2a.Combining the results of eqn. (2.1) and (2.2) with eqn. (2.7) and taking I = 0.69,we obtain a = 0.85+0.1. In this calculation r, I, and k ~ / k ~ are subject to someexperimental uncertainty, the slightly extrapolated rate ratio being the weakestlink. The value of a indicates that proton transfer is far advanced in the transitionstate but not complete. (In the related hydration of styrenes, a is small enoughfor general acid catalysis to be detectable from experiments with aqueous buffers.18)The general correctness of this analysis can be tested by substituting a possiblevalue of a in eqn.(2.5) and hence calculating reaction velocities in H20+D,Omixtures. A calculated curve obtained in this way is shown with the experimentalpoints in fig. 1.Eqn. (2.5) and (2.7) can also be cast entirely in terms of fractionation para-meters : 199 20k,,/k, = ( 1 - n + n l ) - 3 ( l - n + n ~ , ) ( l - n + n ~ 2 ) 2 , (2Wwhere 41(= l/r) expresses the isotope fractionation [as defined in eqn. (1.5)] ofthe hydrion in transit and 4 2 that of the newly forming H20 group. It also followsthatEqn. (2.5) and (2.8) are completely equivalent ; their comparison affords insightinto the physical significance of the parameter a.The agreement between prediction and results provides a more stringent testof the adequacy of this model of proton transfer reactions than rate measurementsby themselves do.The analysis also indicates an approach to the determinationof the Bronsted exponent a for reactions in which the value of this parameter rendersthe determination of catalytic coefficients for general acid catalysis difficult. Thisprocedure therefore permitted the evaluation of all parameters required in the theory,without use of any adjustable coefficients other than the minor adjustments withinthe limits of experimental error.kD/kH = 41&-3. (2.9)B. INDIRECT PROTON TRANSFER FROM H3Of TO ISOBUTENEThe question then arises whether the results would also be reconcilable witha mechanism in which the hydrogen nucleus transferred to the isobutene molecul92 PROTON TRANSFER TO OLEFINSis not the same as the hydrion lost by the H30 group, but in which a water molecule(or more than one such molecule) acts as intermediary.Such a process would beintelligible if proton transfer from a hydrogen ion H90: 21 involved the protonmovements 223H HIH-0I0-@+ s1 3I04H1/\H HIn an isotopically mixed solvent the isotopic composition of the outer water mole-cules is, according to the equilibrium measurements, close to that of the bulk water(5 1). Such a model of proton transfer would therefore be inadequate if one wereto assume that the transfer from an outer water molecule is uninfluenced by the iso-topic nature of the inner hydrogen nucleus to which that water molecule is joinedby hydrogen-bonding.However, the position is different if one assumes that allhydrogen nuclei numbered 1-4 in the above formula are concerned in the transfer.In an H20 + D20 mixture, that reaction velocity will then depend on the respectivefractionation parameters 41-44 and Z, but the isotopic composition of the newC-H bond will depend on 4 3 alone. We can thus writekJk, = (1 - n + nl)-3(l - n + n4,)(l- n + r~4~)(1- n + 124~)(l- n + n+4)2, (2.10)with 453 = l/r, and k ~ , l k ~ = $1&-434: Z-3. Eqn. (2.10) contains similar factors aseqn. (2.8), but also some additional ones. The relationship between the presenttreatment and that based solely on the H30 model becomes even closer if we assumethat the rate of the reaction is influenced by the acidity of the hydrogen nucleusnumbered 1 by a factor of the form of the Bronsted catalysis lawt = GK"(with appropriate statistical corrections). In this way the rate becomes dependenton the isotope fractionation and isotopic composition of the H3O group.When41-~$2+-1, the transition state will be described by similar parameters to thoseof the simpler model, and k,/kH curves similar to that in fig. 1 can be constructed.It follows that the model of indirect proton transfer from H30+ (or direct protontransfer from HgOt) can likewise account for the results of this work in a rationalway and undoubtedly so can other, even more complex models.In the contextof isotope effects at present available, the assumption of indirect proton transferoffers no advantages over the simpler H3O+ model, nor does it permit additionalverifiable predictions to be made. The description of isotope effects in terms ofdirect transfer of H+ from H30+ to isobutene is adequate and simpler and, solelyfor that reason, is accordingly preferredV. GOLD AND M. A . KESSICK 931 Noonan and LaMer, J. Physic. 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