Fractionation factors for the aqueous hydroxide ion and solvent isotope effects on the ionisation of 1,8-bis(dimethyamino)naphthalene (proton sponge)

摘要

1832 J.C.S. Perkin 11 Fractionation Factors for the Aqueous Hydroxide Ion and Solvent Isotope Effects on the lonisation of 1,8-Bis(dimethyamino)naphthalene (Proton Sponge) By Yvonne Chiang and A. Jerry Kresge,rsquo; Department of Chemistry, Scarborough Collage, University of Toronto, West Hill, Ontario M1 C 1A4, Canada Rory A. More Orsquo;Ferrall,rsquo; Department of Chemistry, University College, Belfield, Dublin 4, Ireland Isotopic fractionation factors and 46 for the hydroxy hydrogen and hydrogen-bonded water hydrogens of the solvated hydroxide ion are important in controlling solvent isotope effects upon reactions involving the hydroxide ion, and were required for a vibrational analysis of the solvated ion. The product 4Ab3= 0.434 is accurately available from e.m.f.measurements corrected for free energies of ion transfer between H20 and D,O, but separation of 4, and 4b,which requires measurements in H,O-D20 mixtures, is known to be subject to considerable un- certainty. Thus careful measurements with 1,8-bis(dimethyIamino)naphthalene gave K,,,,/K,,, = 0.420 f 0.006 for the ratio of basic ionisation constants in H20 and D20and $F = 0.901 f 0.01 4 for the fractionation factor of the protonated base, but measurements in 1 : 1 H,O-D,O gave an ionisation constant too small to be consistent with any reasonable fractionation factor model for the hydroxide ion, Alternative methods of dissecting 4u and q$, from measurements of isotope separation factors between hydroxide solutions and water vapour and auto- protolysis constants of H,O-D,O mixtures, are critically reviewed and optimum values are assessed.The results are shown to be sensitive to experimental error and to medium effects but not to departures from the Rule of the Geometric Mean. SOLVENTisotope effects offer a valuable tool for the a given value of $amp;b3, two solutions for dnand #amp; are investigation of acid- and base-catalysed rca~tions.l-~ However, their interpretation requires an understanding of the isotopic fractionation of the hydronium ion and hydroxide ion, and while for the hydronium ion this understanding has been largely achieved,7-l1 for the hydroxide ion in important respects it is still lacking. In 1967 Gold and Lowe made the useful suggestion that contributions to hydroxide isotope effects should be con- siclered as arising both from the hydrogen of hydroxide itself and from three hydrogens hydrogcn-bonded in its rsquo;b 7,OH Iba 3 ,#H H-o:--H -o H -lsquo;H lsquo;OH primary solvation shell (1).12 Writing fractionation factors for these hydrogens $a and $h, where $ denotes the D : H ratio at the hydrogen site relative to that of the bulk solvent in mixed isotopic solutions, the net con- tributions to kinetic and equilibrium isotope effects involving the hydroxide ion become +0+n3 in D20 and (1 -x + xda)(l-x + x+~)3 in a H,O-D20 mixture of atom fraction x.In principle +a and may be determined by com- bining suitable measureinents in pure and mixed iso- topic solvents ; for example, the autoprotolysis con-stants of H20, D,O, and H20-D20 mixtures corrected for isotopic fractionation of the hydronium ion.6912913 In practice separation of $a and #h is subject to certain difficulties which have been discussed by Gold and Grist l3 and by Taylor and Tomlinson.l4 On the one hand the separation is highly sensitive to errors; on the other, for The first difficulty is the subject of this paper.Exist-+fling data for evaluating and +b are analysed, and experimental measurements of the ionisation of 1,8-bis- (dimet1iylamino)naphthalene l6 equation (l) in H20, D,O, and 1 : 1 H20-D20 are described. The measure- ments were undertaken with the object of providing new values of +a and $6, although, as will be seen, they serve to underline the problems of effecting a separation. The second difficulty is examined in the accompanying paper,17 where an attempt is made to distinguish alternative solutions using calculations based upon vibrational analyses of a model for the solvated hydroxide ion. (2) EXPERIMENTAL lWateriaZs.-1,8-Bis(diniethylamino) naplithalenc (Aldrich Cheniical Co.) was purified by sublimation.Deionized water was purified further by distillation from alkalinc permanganate; D,O (Merck; 99.7 atom D) was used as received. Both H,O and D,O were made C0,-free just prior to use by boiling for a few minutes followed by cooling under protection by Ascarite. Sodium hydroxide stock solutions (GU.0.1~)were prepared from NaOH and either H,O, D,O, or 1 : 1 H,O-I),O; the latter was made by mixing equal volumes of H,O and D,O.Exact hydroxide ion concentrations of these stock solutions were determined by acitliiiietric titration. More dilute sodium hydroxide solutions were prepared by diluting stock solutions by weight. pK, Determinations.-These were carried out spectro-photometrically by making measurements at 335 nm where the free base, 1,8-bis(dimethylamino)naphtllalene,absorbs strongly and its conjugate acid does not absorb at all. A Cary niodel 11 spectrometer was used, and its cell block was thermostatted at 25.0 amp; 0.1" despite the fact that changes in temperature of as much as 1" were found to havc no perceptible effect on absorbance. Measurements were made in 1 cm cuvettes; the very limited solubility of 1,s- bis(dimethy1amino)naphthalene in water required use of the 0-0.1 spectrometer absorbance scale, but readings could nevertheless easily be made to 0.001 absorbance unit or better.In a typical experiment, 3 ml of sodiutn hydroxide solution of the appropriate concentration was pipettecl into the cell. After this had come to temperature equilibrum with the spectrometer cell compartment, the base line was adjusted and a fixed amount, usually 100 h, of stock 1,s- bis(dimethy1amino)naphthalene solution (H,O, D,O, or H,O-D,O) was added. The resulting mixture was shaken ancl an absorbance reading was taken. This procedure was repeated three times for each sodium hydroxide con- centration. The ratio of unprotonated to protonated 1,8-bis(dimethyl- amino)naphthalene was calculated using the relationship B/BH+ = (A -ABH+)/(AB-A); A, was measured in concentrated (1.3~)sodium hydroxide solution am1 A R~~ was taken to be zero.RESULTS The determinations were made at ionic strengths fixed by the sodium hydroxide concentrations, which were both appreciable and variable (sce Table 1). The data were therefore extrapolated to infinite dilution; this was done as follows. The thermodynamic or infinite dilution ionization con-stant for reaction (2) under investigation is given by B + L,O BL' + LO-equation (3) in which parentheses denote molar activities, square brackets denote molar concentrations, and yf and y-are the molar activity coefficients of the BH+ and LO-ions respectively.(The symbol L is used to signify either H or D.) The activity coefficient of the neutral base was taken to be unity, while those of the ions were assumed to depend on ionic strength, p, in the manner shown by equation (4)where 13, are specific ion interaction constants. -0.52/1logy* = -(4)1 + dI + Bd Combination of equations (3) ancl (4) gives an expression, which upon taking logarithms and making the substitutions pA', = -logRL'OL-/B and plc~,= -log ZCk, leads to equation (5). This expression shows tl~tpK,, may be obtained as the intercept of a linear plot of pKc$-2/Z/ (1 + dI) zreyszfis 41. Least-squares analysis of the data listctl in Table 1 gave TABLE1 Tonization constant measurements for 1,8-bis(dinxthyl- ~~miiio)iiaplitlialeilctin aqueous solution at 2P 103 NaOL "/M pK + 1'1 (1 t-vo H# 74.1 3.t143, 2.054 48.4 2.084, 2.055, 2.095 18.3 2.027, 2.033, 2.059 16.6 2.012, 2.002, 1 .992 13.2 1.997, 1.977, 2.007 11.8 1.987, 2.016, 1.978, 1.97s 10.2 1.993, 1.970, 1 .W3, 1 .HW 9.92 1.989, 1.979 9.65 1.981, 2.007 8.25 1.977, 1.977, 1.970 7.71 I .977, 1.994, 1.977 7.28 1.98, 1.99, 1.966 6.63 1.977, 1.984 6.09 1.976, 1.986, 1.976, 1.966 4.42 1 .!I77 4.27 1.988, 2.974 3.30 1.965, 1.983, 1,905, 1.974 2.52 1.989, 1.967 pl(c 4-t//(l + bsol;'I) -(I .973 -1: 0.oO:i) -1 (1 ,547 -b 0.142)NaOL O 14.8 2.382, 2.39s 10.4 3.405, 2.385, 2.886, .2111 9.8 2.410 7.81 2.411, 2.411 4 5.94 2.383, 2.392, 2.383, 2.302 3.94 2.406, 2.388, 2.379, 2.397 2.70 2.391 1.97 2.406, 2.396, 2.396 0.91 2.415, 2.378 PK + 1/1/(1 t bsol;/I) (2.395 -k0.005) -t (0.041 3.0.617)NaOL euro;ID0 13.36 2.200, 2.182 10.72 2.192, 2.17 7.96 2.192, 2.181, 2.192, 2.181 5.40 2.190, 2.165 4.61 2.181, 2.181, 2.168 2.63 2.194, 2.204, 2.183 1.65 2.173 PKc f 41/(1 + 41) (2.181 amp; 0.006) -+(0.667f 0.802)NaOL The symbol L is used to indicate either H or D. the following results, pKb 1.973 0.003 in H,O, 2.395 amp; 0.005 in D,O, and 2.181 i-0.006 in 1 : 1 H,O-D,O. These translate into the following thermodynamic basicity con-stants, KH*O(1.064 amp; 0.007) X KD~O(0.403 f0.005) x and KHDO(0.659 amp; 0.009) x niol l-l, and give the following isotope effects, KH~o/KD~~2.64 f0.04 and KH,o/KHDo1.61 amp; 0.03.The value ph'b 1.97 for H20 solution may be converted into pK, 12.03 by subtraction from pK, (=14.00). The result obtained is in good agreement with ph',' 12.1 amp; 0.1 measured at an ionic strength of 0.1~,1* and is consistent with ph', 12.34 reported for an unspecified ionic strength.I6 Fvactionntion Factor Determination.-The D :H fraction -ation factor for the acidic hydrogen of nionoprotonated 1,8- bis(dimethy1amino)naphthalene was determined by dis-solving the unprotonated substrate in an acidic (0.2~-hydrochloric acid) H,O-D20 solution of known deuterium content and then measuring the area of the n.m.r. signal froni the acidic proton located at 6 19.5. (Under these conclitions, exchange of this hydrogen with the solvent is slow on the 1i.m.r.time scale.) This signal area was translated into protium content by comparison with the area of the nearest other n.tn.r. signal of the protonated substrate, that from the six non-exchanging aromatic hydrogens located at about 6 8. Since these two signals were still more than 10 p.p.ni. apart, the comparison was clone stepwise using glacial acetic acid as an external reference, i.e. the area of the substrate acidic hydrogen signal was compared with that of the hydroxy-group signal from acetic acid and the area of the substrate aromatic hydrogens signal was compared with that from the methyl group of acetic acid; the presence of some water in the glacial acetic acid reference, which added to the hydroxy- group signal, was taken into account by determining the ratio of hydroxy to methyl group signal areas separately.The results, summarized in Table 2, give $p 0.901 f0.014. TABLE2 Measurements of the fractionation factor $p for the N-H+ hydrogen of protonated 1,8-bis(diniethylamino)naph-thalene D : H atom ratio substrate/^ Solvent Substrate 7 0.73 0.908 0.779 0.858 0.53 0.933 0.894 0.959 0.43 0.944 0.845 0.896 0.28 0.963 0.852 0.885 0.20 0.973 0.869 0.893 0.20 0.973 0.890 0.915 Average 0.901 f0.014 DISCUSSION Measurements in D20.-In evaluating fractionation factors for the hydroxide ion it is convenient to consider measurements in D20 and H20-D20 mixtures in turn.In pure isotopic solvents the ratios KD,~/K=,ofor equilibria involving hydroxide ion yield products of fractionation factors: in terms of model (l), $a$b3, or, more generally, rlq$. The general expression makes no i assumption about the number of fractionating hydrogens and includes a term for medium effects, denoted by Albery,6 representing fractionation effects too small to distinguish individually and commonly associated with ionic solvation; this term may also be considered as the activity coefficient counterpart of free energies of transfer between H,O and D20.15J9 In this paper the results are discussed in terms of model (1) with alterna- tive possibilities noted as appropriate. (a) Autoprotolysis and electrochemical measurements.Before considering the measurements for 1,8-bis(di-methy1amino)naphthalene it is pertinent to consider previous determinations of $a$$, and most importantly those from measurements of the ratio of autoprotolysis constants of H20 and D20, K@*/KWDa0.12v20-23 The ratio of autoprotolysis constants may be considered as an effective equilibrium constant for the isotope ex-change (6), and +amp;3 may be obtained from (Kbsol;vT)ao/ H,O+ + HO-(H20), + 5D20 D,O+ + DO-(D20), + 5H20 (ti) Klv~2o)/I3,where I is the fractionation factor for the hydronium ion, that is L-l/s where in turn L is the J.C.S. Perkin I1 equilibrium constant for the exchange reaction (7).Determination of $a$b3 thus requires a knowledge of L. 2D30++ 3H20 2H30+ + 3D,O (7) What is probably the best method of evaluating L has been summarised by Salomaa and Aalto.7 E.m.f.data for the electrochemical cells comprising hydrogen and silver-silver chloride electrodes in H20 and D20 are combined to give AGO for reaction (8). Further com- bination with measurements of the equilibrium constant of reaction (9) and the free energy of transfer of chloride (9) ions between H20 and D20 reaction (lo), yields I,. D20 + C1-(H20) @Cl-(D,O) + H20 (10) Of the data used by Salomaa and Aalto the e.m.f. values of Gary et al.24 are still applicable, but improved measurements for reactions (9) and (10) are now avail- able. For the isotope exchange between hydrogen gas and water (9), Rolston, et al. have made measurements at low atom fractions of deuterium25 to obtain 3.81 as equilibrium constant at 25" for the exchange (ll), which, when combined with K 3.26 for the dispro- portionation constant of HD (12)' calculated from Bron HD + H20(l)+H2 + HDO(l) (11) 2HD H2 + D, (12) et aL's convenient tabulation of isotopic partition function ratios and their temperature dependence,2s and 3.80 for the disproportionation constant of HDO (13), based on the average of gas phase measurements 27 2HD0 H20 + D20 (13) corrected to the liquid state,28 gives an equilibrium constant for (9) of 12.39.Taking Voice's measurement of 172 cal mol-l for sodium chloride as the molar transfer free energy of the chloride ion 29 gives L 9.85, which differs little from Salomaa and Aalto's original value of 9.0 and agrees well with Gold's n.m.r.determination of 9.7 and Heinzinger and Weston's 7~1~93~value of 9.6 from measurements of isotope separation factors between aqueous perchloric acid solutions and water vapour, although the last value is for 13.5"C and would be smaller (ca. 9.0) at 25". The data also allow calculation of the temperature depen- dence of L between 0 and 50" as equation (14), where Aeuro;' = -3 126 -14.08T + .02724T2 (14) AGO is the standard molar free energy change for reaction (7) in cal mol-1 and T is in degrees Kelvin. The value of L1I2 may now be combined with one of the recent measurements of KWHzO/KWD20,12~20-23 of which those of Gold and Lowe l2and Covington et aL20 are perhaps the most sati~factory.~~ From Gold and Lowe's value of 7.28 at 25" one obtains +,$b3 0.431.A similar combination using the value of Covington et al. however, leads to a cancellation of redundant terms because common e.ni.f. data are used for the calculations of KH1x20/Kbsol;VnJ)and L. Most directly $,+!? is obtained from e.m.f. measurerrielits for the cell H,,NaOH,NaCl- (H,O),AgCl;Ag 32 and its D,-D,O counterpart.20 E.m.f.s corresponding to the net reaction (15)have been w2 + NaOD(D20) $-NaCl(H,O) + H,O + +H2 + NaOH(H,O) + NaCl(D,O) + D20 (15) listed by Goldblatt and Jones,21 and combination with AGO for the D2-water exchange (8)and the transfer free energy of chloride ions (10) yields at 25" +.+b3 0.434, which compares satisfactorily with Goldblatt and Jones's own measurement at 25" giving 4c45b3 0.444.It should be noted that these values contain a, probably very small, contribution from the transfer free energy of sodium ions. Fronr the e.ni.f. measurements 21,23 the temperature dependence of +amp;,3 niay be calculated as equation (lo), AGO = -820 -0.466T +-0.000 56T' (16) where AGO = 2RT111 (+amp;3) or, more generally, 2RTh (TJ +d) is the standard molar free energy change for reaction (17) in which the hydroxide ion is written 2DO-+ H20 +2HO-+ I),O (17) formally without its solvation shell. At 25" the equilibrium constant for this reaction is 5.31. (b) Ionisation of 1,s bis(dimethy1amino)naphthalene. For 1,s-bis(dimethy1amino)naphthalene the ratio of basic ionisation constants in D,O and H20 may be written in terms of fractionation factors as equation (18), where +p refers to the ionising hydrogen of the protonated base cj.equation (l)and @S is the contribution of medium effects arising from transfer of free and pro- tonated base from H,O to D,0.6 Since ionisation occurs at concentrations of hydroxide ion (0.1-0.001~) determinable by titration or dilution no correction is required for the difference of pH from pD. The measured values of KH,O/KD,O and +p were 2.64 amp; 0.04 and 0.901 amp; 0.014, respectively Because Qs is unknown amp;4b3 cannot in this case be determined directly. However, with 0.434, we obtain $s 1.03, and it becomes possible to make transfer corrections and derive values of +,I and 4b from measure- ments in H,O-D,O mixtures.The nearness of QS to 1.0 suggests cancellation of transfer free energies between free and pronated base (plausibly because hydrogen bonding between the ionising species and solvent is weak), and this small correction for medium effects should be an advantage in evaluating +a and amp; iMeasurenzents iiz H,O -D20 Mixtures.-To obtain +u and +b separately the value of ~#4~~must be combined with suitable measurements in H,O-D,O mistures. Again, previous measurements may be reviewed before considering results for 1,s-bis (dimethylamirio) napht ha- he. 1835 (a) Liquid-vapour isotope sekaration factors. Weston and Heinzinger measured the fractionation of H and I isotopes between liquid water and aqueous hydroxide solutions and water vapour.33 Their measurements yield (1 -amp;,) + 3(1 -$*) or, in model independent terms, 2 (1 -$;), where again the +i may include a con-i tribution from a medium effect as.The relationship of fractioiiation factors to experimentally measured para- meters is expressed by equation (19) where ATis the mole fraction of NaOH or KOH, aB and aw are the liquid- vapour D -H separation factors for base solution and pure water respectively, and --In @s separates medium from specific fractionation effects.* The separation factors are defined by a = xV(1 -x~,)/xr,(l-xv) where x is the atom fraction of deuterium and the subscripts L and V denote liquid and vapour. Values of 2 (1 -+i) 1are shown in Table 3.TABLE3 2 (1 -+J for the liyclroxicle ion from Heinzinger and Weston's isotope separation measurements b (1 -bi) Base hT uB/aWe 'IJncorrected Corrected be NaOH 7.84 0.9638 0.442 0.442 0.021 NaOH 10.20 C.9567 0.480 0.480 0.010 NaOH 12.12 0.9472 0.486 0.486 0.014 IiOH 6.99 0.9626 0.573 0.519 0.011 KOH 10.30 0.9456 0.543 0.489 0.008 (I For model (I), 4-4, -34b. Ref. 33. Ratio of isotope separation factors between base solution and water vapour (ag)and liquid water and water vapour (uw). (2-N)(1-un/uw)/N. Average deviation. JThe measurements for KOH are corrected for the difference in free energies of transfer of Naf and K+ ions. Measurements were made for KOH and NaOH solutions, and their comparison requires a correction to be made for the difference in transfer free energies between potassium and sodium ions, Acto, which from Voice's measurements 29 amounts to 31 cal mol-1.Taking 1nQS = AC,O/RT and subtracting from 2 (1-di)i for KOH gives the corrected values shown in the right hand column of Table 3. Agreement between KOH and NaOH measurements is significantly improved. In a later discussion of the results, Gold and Grist 13 noted that a trend in Heinzinger and Weston's nieasure- ments with concentration of base could perhaps be discerned, and suggested extrapolation to zero base concentration. They made no correction, however, for the difference in free energies of transfer of Nat and K' ions and a linear extrapolation leads to a significantly higher value of (1 -+J + 3(1 -+b) without the correction (0.561) than with it (0.490 rf 0.064).Indeed Grist and Gold considered a higher value still (0.656) not inconsistent with the result. * In terms of fractionation, CDS = #", where n is large and 4 -+ 1.0. The contribution to b7 (1 -#) is thus n (1 -#) g --1.tln+ = --Inas. 7 J.C.S. Perkin I1 Further corrections may be made because the measure- ments were made at 13.5" rather than 25" and to take account of departures from the Rule of the Geometric Mean.6927 In practise these were found to be so small (2)as to be sensibly neglected. Values of +a and +b may be obtained by combining Heinzinger and Weston's measurements with = 0.434.The sensitivity of the values to the precision of the measurements is best shown by plotting (1 -+a) + 3(1 -+b) against a range of values of with $b = $'04/#: as in Figure I. A smooth curve is obtained O8 t h Q"m I Q" I z o.6 t P 0.5 1.0 1.5 1FIGURE Full curve, plot of 4 -4 -34b veysus with +a 4b3 0.434. Dashed curve, the same including a medium etiect 4 1.3. The patched area shows an experimental value and standard deviation based on the data of ref. 35. The upper line shows a value from the same data derived by Gold and Grist with a maximum at = +b, as shown by the full line in Figure 1. The ' observed ' value of (1 -+a) + 3(1 -+b) = 0.490, extrapolated to infinite dilution and corrected to 25"' is shown as the horizontal line, with the limits of the standard deviation of its mean indicated by cross hatching. Also shown, as an extreme comparison, is the value favoured by Gold and Grist,13 which lacks corrections for the difference in transfer free energies of Na+ and K+.Figure 1 illustrates the two solutions 13915 associated with measurements of (1 -+a) + 3(1 -$b), and Table 4 lists pairs of values of and +b. The vulnerability of +a and +b to errors is indicated by the difference between the values of of 0.39 or 1.54 obtained using the fully corrected results and of = 0.5 or 1.24 considered possible by Gold and Grist.12 While it is now clear that the latter values have a poorer experimental basis, their lesser divergence from 1.0 makes them more consistent with measurements of other OH fractionation factors.34 TABLE4 Fraction factors for the hydroxide ion * Medium Solution 1 Solution 2 Method effectb 1r---k-, c-n, @s d 4b 4a hVapour-liquidisotope separation 1.0 0.39 1.04 1.54 0.26 1.3 0.39 0.95 1.37 0.63 1.0 (0.50) (0.95) (1.24) (0.70)Autopro to1 ysis constant 1.0 0.55 0.92 1.15 0.72 1.3 0.58 0.83 1.00 0.69 Corrections for deviations from the Rule of the Mean are not included.Normally these amount to 3. When QS = 1.0, there is no medium effect. Values in parentheses are those suggested by Gold and Grist (see text) (b) A uio$rotoZysis measurements. The second source of results suitable for determining #a and f#V, are Gold and Lowe's measurements of the autoprotolysis constant of water in H,O-D,O mixtures.12 If Kwx is the auto-protolysis constant for a solvent of deuterium atom fraction x, K~z/K~H~*may be expressed in terms of fractionation factors as equation (20).Following Albery KLvr/Kbsol;bsol;.TEgo= (1 -x + q3(i-x + xC$b)3 (1-x + +a) (20) and Tavie~,3~ this expression may be rearranged to a functiony, isolating terms in +a and (21). Focusing = (1 -x + x+b)3(1-x + +a) (21) on -Y.~at x = 8 one obtains for yjt equation (22), or, if a specific model for the hydroxide ion is not used, yhtakes the general form of (23). Yn = n (1 + $42 (23) Solutions of +a and 4b are obtained as before by plotting y~ as a function of for +aC$b3 = 0.434 and reading off values of +a and $bb corresponding to the measured yn.In practice what is plotted in Figure 2 is not yk but the ' percentage curvature ' c, representing the deviation from linearity of a plot of KWr/KWH~Oagainst x at x = 0.5, defined by (24) where y1 is the value of y in pure D,O, i.e. +amp;b3 (=0.434). Expressed in this form the precision required of the measurements to define the fractionation factors is directly indicated. Although Gold and Lowe did not measure Kw at x = 0.5 directly, the value can be interpolated from their measurements at other values of x. The derived cur- vature is shown as the horizontal line aa' in Figure 2 and it is apparent that again two solutions exist. The values of and +b are also listed in Table 4, and it can be seen that compared with Heinzinger and Weston's measure- ments +a (0.55 or 1.15)is significantly closer to unity.It should be mentioned that these results have pre- viously been analysed by Alberyrsquo;s y method to give y 0.43 amp; 0.14.6 (c) 1,8-Bis(dimethyZamino)na~htl~alene.Ionisat ion of 1,8-bis(dirnetliylamino)naplithalenewas studied in the expectation that one or other of the previous measure- ments might be confirmed. The ratio of ionisation constants in 1 : 1 H,O-D20 and pure H20, K$/Ka,o may be written in terms of +a, 46, the fractionation factor of the exchangeable hydrogen of the protonated base, +p, and a correction (as)amp;for the small net medium effect upon transferring free and protonated base from 0.5 1.0 1.5 0, 2FIGURE Full curve, percentage deviation from linearity (c) of a plot of (1 -x + x +J(l -x + x +b)3 uersus x at x = 0.5 for various +.with 0.434.Dashed curves, the same in- cluding medium effects, I, 0.434 (upper curve) or 1.3 (lower curve). The lines represent experimental measurements from autoprotolysis constants (aarsquo;) and from the ionisation of proton sponge (bbrsquo;) pure H20 to the mixed isotopic solvents, as in equation (25). Rearrangement then gives the same expression for yb in terms of fractionation factors +u and $6 as from the autoprotolysis measurements, i.e. equation (26). It follows that if the curvature, :/oc, is calculated $a and $6 may be read from Figure 2, as before. For the observed values of KH~~/K;l.615, +p 0.90 and (1)s 1.03, the curvature for y1 0.434 is 7.7 amp; 1.6yo, * The value of hlberyrsquo;s y 2 -0.3 also indicates the poor fit to the hydroxide model; y = 0 corresponds to the wholc isotope effect being a medium effect. and this is included in Figure 2 as the line bbrsquo;.Thus, far from confirming previous values of $a and $6 the departure of Kz/Kn from a linear dependence upon the atom fraction of deuterium x at x 0.5 actually exceeds the maximum theoretical value of 6.1yoconsistent with our model (1) for the hydroxide ion! In view of the small range of allowed curvatures for 1,8-bi~(dimethylamino)naphthalenewe may ask whether the measurements are sensitive to small corrections hitherto neglected. It is shown in an Appendix that there is little influence from deviations from the Rule of the Mean, but the measured curvature can be reproduced if the fractionation model for the hydroxide ion is modified to include a sufficiently large medium effect.Thus if the effect of transferring a hydroxide ion from H20 to D20 is denoted @SOH we can write $,+b3@sOn 0.434 and equation (22) as (27). Maximum positive (1 + +/J3(1 + +a)(@sOH)) (27)Yt = 16 curvature results when the isotope effect is entirely a medium effect, and this is shown in the upper dashed curve of Figure 2, for which @SOH = 0.434. However, values consistent with the experimental measurement, represented by the line bbrsquo; are only just achieved and since the medium effect accounts only for fractionation effects beyond the four innermost hydrogens of thc solvated hydroxide ion it is unlikely to be as strong as would be required.* ConcZztsions.-Almost certainly the discrepancy for 1,8-bis(dimethylarnino)naphthalene,and indeed between Gold and Gristrsquo;s and Heinzinger and Westonrsquo;s measure- ments, reflects an intrinsic difficulty in separating sets of fractionation factors from measurements of the curvature of plots of K,/Ka against x when solutions occur in an insensitive range, even when, as here, the measurements are made with considerable care.This is particularly true when a plot of curvature as a function of has an extremum close to its solutions as in Figure 2. Thus despite the large difference in solutions of 4uand $6 implied, the values of y: on which the curvatures of the autoprotolysis measurements and ionisation of proton sponge are based differ by only 5.Probably the most reliable values of $a and $6 are those based on Heinzinger and Westonrsquo;s measurement^,^^ i.e. +a 0.39 and $6 1.04 or $a 1.54 and $6 0.66, but the more moderate values from Gold and Lowersquo;s autoprotoly- sis measurements l2 appear more reasonable.? Our own results may add weight to values of +u close to unity, but Taylor and Tomlinsonrsquo;s n.m.r. measurements of hydroxide solutions in H,O-D20 mixtures, while not yielding values of +a and $6 directly, suggest the con- trary.14 The combined measurements reflect the recog- nised uncertainty of the individual values of and #b. Nevertheless, lsquo; moderate rsquo; solutions for +u and 46 are implied by the calculations of the following paper, and it is worth examining further the sensitivity of the t The more limited autoprotolysis data in H,O-D,O mixtures of Pentz and Tliornton 22 give +a 0.44 or 1.45. measurements to medium effects.The dashed curve of Figure 1 and the lower dashed curve of Figure 2 incor-porate mild medium effects of (DsOH 1.3, and it can be seen from the Figures and from Table 4 that for the solution with 1.O, +* is significantly reduced: for the isotope separation measurements, from 1.54 to 1.37. A similar effect is produced by a minor fractionation contri- bution from the three outer hydrogens of the water mole- cules in the hydroxide solvation shell (l),i.e.with 93 1.3. With (DSoH 1.3 the medium effect on +, for the second solution of +u and +b is small. This solution is sensitive to additional fractionation but more so to a single fractionation site than to a medium effect which, in terms of a structural model, seems less likely. It is perhaps regrettable that a more precise dis- section of +u and +b and potential medium effects is not possible. How critical this is to the interpretation of kinetic measurements in H,O-D,O mixtures will be examined in a further paper. For the present the distinction between the two solutions for and $6 is sufficient to offer a basis for the calculations of the following paper. APPENDIX Deviations fvom the Rde of the Mean.-Values of y4 for proton sponge may be corrected for deviations from the Rule of the Mean as follows.It is assumed, and the results of the following paper confirm, that corrections for water molecules in the solvation shell of the hydroxide ion cancel with those of solvent water molecules. Corrections then arise only for the hydrogens of OH-itself and of the solvent water mole- cule that in the ionisation equilibrium (1) is the counterpart of the hydroxide ion and the fractionating hydrogen of proton sponge. Adapting Albery and Daviesrsquo; pr~cedure,~~ the simple expression for yg of equation (26) is modified by multiplying (1 + 9b)3(l+ $,)/l6 by the term l -0.25(36,b -26a1,0), in which the 6 values are correction factors representing interactions of fractionating hydrogens attached to a com-mon atom 11 which enter as differences of contributions between rcactants and product; amp;DO = 1 -K/4,where K is the equilibrium constant for disproportionation of HDO to H,O and D,O (13), corrects for interaction of the two hydrogens of a water molecule, and 36~6,defined in the following paper,17 corrects for interaction of the hydroxide hydrogen a with the three neighbouring hydrogens of its solvation shell.For reaction in an H,O-D,O mixture of atom fraction x the corrections enter as 6x(1 -x) and for 1 : 1 H,O-D,O, for which x = 0.5, as 0.256.36 The magnitudes of the corrections reffect the bending force constants between the bonds to the interacting atoms, ant1 calculations l7suggest that the value of 6amp; depends on which solution is adopted for 4, and 9b, since larger values of +u are associated with larger hydrogen bond bending force constants for the hydroxy group.For +u 1.2-1.5, ,amp;I, approaches 6H1)0/2 and the correction largely cancels with that for a water hydrogen, while for +u 0.6 Sob is sniall and the Iiytlrosy-group is sensibly treated as an isolated fractionating hydrogen (a,,, O), The latter case leads to the larger correction and with 6H1,0 0.05, y4 is now given by equation (28). However, the corrected value of J.C.S. Perkin TI the curvature is 8.9::, wliich differs little from the uncor- rected value of 7.7:(,. The magnitude of the correction is thus quite small, and its direction is such as to increase rather than decrease the discrepancy between observed and allowed values.Similar correction of the autoprotolysis measurements introduces an interaction term SH,DO for the hydronium ion, as shown in equation (29). From model calculations 37 ~~0 0.05,gives a value close to 8~ 2 @ano, which with 6~~0 the measured value of 6 0.03 for NH3.38 For the solution of the hydroxide fractionation factors with +u 1.O (amp;, = 0) the corrcctions cancel, while for 1.0 the curvature is reduced slightly, from 3.8 to R.2yo. Again the correction is very small. We arc grateful to the NATO Scientific Affairs Division and the National Science and Engineering Research Council of Canada for their financial support of this work. O/dl 1 Neceived, 5th February, 19801 REFERENCES A.J. Kresge, J. Pure Appl. Chem., 1964, 8, 243. V. Gold, Adv. Phys. Ovg. Chem., 1969, 7, 259. I. L. Schowen, Progr. Phys. Ovg. Chem., 1972, 9, 275. P. M. Laughton and I. E. Robertson in lsquo; Solute-Solvent Interactions rsquo;, eds. J. F. Coetzee and C. D. Ritchie, Marcel Dekker, New York, 1969. K. euro;3. J. Schowen in lsquo; Transition States of Biochemical Processes rsquo;, eds. R. D. Grandour and H. L. Schowen, Plenum, New York, 1978. 6 W. J. Albery in lsquo; Proton Transfer Reactions rsquo;, eds. E. F. Caldin and V. Gold, Chapman and Hall, London, 1975. P. Salomaa and V. Ralto, Acta Chem. Scand., 1966, 20, 2035. A. J. Kresge and A. L. Allred, J. Amer. Chem. Soc., 1963,85, 1541. V. Gold, Proc. Chem. SOC.,1963, 141, 10 K.Heinzinger and H.E. Weston, jun., J. Phys. Chem., 1964, 68, 744. l1 R.A. More Orsquo;Ferrall, G. W. Koeppl, and A. J. Kresge, J. 4mev. Chem. Soc., 1971, 93, 9. 1-V. Gold and B. ill. Lowe, Proc. Chem. Soc., 1963, 140; J. Chem. SOC.(A),1967, 936. l3 V.Gold and S. Grist, J.C.S. Perkin 11,1972, 89. lP C. E. Taylor and C. Tomlinson, J.C.S. Faraday I, 1974, 1132. E. A. Walters and I;.A. Long, J. Phys. Chem., 1972, 76, 362. 16 13, W. Alder, P. S. Bowman, W. R. S. Steele, and D. K. Winterman, Chem. Comnt., 1968, 723. 17 K.A. More Orsquo;Ferrall and A. J. Kresgc, following paper. 18 F. Hibbert, J.C.S. Pevkin 11, 1974, 1862. l9 V. Gold, Trans. Farada-y Sac., 1968, 64, 2143. 20 A. K. Covington, R. A. Robinson, and R. G. Bates, J. Phys.Chem., 196G, 70, 3820.21 M. Goldblatt and W. M. Jones, J. Chem. Phys., 1969, 51, 1881. 22 L. Pentz and E. euro;3. Thornton, J. Amer. Chem. Soc., 1967, 89, 6931. 23 P.Salornaa, L.L. Schaleger, and F. A. Long, J. Amer. Chem. Soc., 1964, 86, 1. 24 R. Gary, R. G. Bates, and R. A. Robinson, J. Phys. Chem., 1964, 68, 1186. 25 J. H. Rolston, J. den Hartog, and J. P. Butler, J. Phys. Chem., 1976, 80, 1064. 26 J. Bron, Chen Fce Chang, and M. Wolfsberg, 2. Natztr-fovsrh., 1973, 28a, 129. 1980 25 J. W. Pyper, R. J. Dupzyk, R. D. Friesen, S. L. Bernasek, C. A. May, A. W. Echeverria, and L. F. Tolman, Internat. J. Mass Spectrometry Ion Phys., 1977, 23,209 and references cited. 28 W. A. Van Hook, J.C.S. Chem. Comna., 1972, 479. 29 P. J. Voice, J.C.S. Faraday I, 1974, 498. 30 K. Heinzinger, 2.Naturforsch., 1965, 20a, 269. 31 P. Salomaa, Acta Chem. Scand., 1971, 25, 367. 32 H. S. Harned and G. E. Mannweiler, J. Amer. Cliem. Soc., 1935, 57, 1873. 33 K. Heinzinger and R. E. Weston, jun., .I. Phys. Chem.. 1964, 68, 2179. 34 R. L. Schowen in lsquo; Isotope Effects in Enzyme-catalysed reactions rsquo;, eds. W. W. Cleland, M. H. Orsquo;Leary, and D. Northrop, University Park Press, Baltimore, 1977. 35 W. J. Albery and M. H. Davies, J.C.S. Faraday I, 1972, 167. 36 W. J. Albery and M. H. Davies, Tvans. Faraday Soc., 1969, 65, 1059. 37 A. J. Kresge, 1rsquo;.Chiang, G. W. Ibeppl, and R. .4. More Orsquo;Ferrall, J. A mev. Chern. Soc., 1977, 99, 2245. 38 J. W. Pyper, K. S. Newbury, and G. W. Barton, jun., .I. Chem. Phys., 1967, 47, 1179.