6688
plication by (k-l/k2)EtoH= 1.710 gives [k-lD/k2D]EtoH = 1.895, which is indistinguishable from 1.885 found in ethanol-0-d. We conclude that there is a nil solvent isotope effect on benzhydryl benzoate ion-pair partitioning in ethanol. Swain and Pegues found a solvent isotope effect (kMeoH/kMeo= D 1.07) on the methanolysis of trityl chloride in benzene.Iz They established that the product-forming step is much slower than ion-pair return. A difference between benzene and more polar, hydroxylic solvents is not unreasonable. The absence of a solvent isotope effect in the DDM-HOBz reaction in ethanol suggests either that there is little external ion-pair return or that there is no solvent isotope effect on partitioning of I11 or both. Both the absence of a solvent isotope effect and the absence of an a-PIE on I11 are consistent with Ingold's theory of cation capture in hydroxylic solvents.* The dependence of isotope effect on ion-pair return suggests that isotope effects o n solvolytic processes may prove useful in assessing return. Acknowledgment. Acknowledgment is made to the National Science Foundation for support of this work. (12) C. G. Swain and E. E. Pegues, J. Amer. Chem. Soc., 80, 812 ( 1958).
*
Address correspondence t o this author.
isotopic ion pairs 111 that solvolyze. The observed solvolysis isotope effect (ktH/ktT = 1.217, see footnote 6, Table I) was combined with previously measured quantitiesl~~ (eq 2a and 2b) to calculate klH/klT from eq 2. For benzhydryl benzoate in ethanol FHII1/
1.' The PIETlH and the solvolytic isotope effect were measured at 25 and loo", respectively. The PIET/Hat 100" was calculated from eq 3,j which assumes FTII1 =
A(AAE,)
=
RT In (P1ETIH)
(3) no appreciable isotope effect on the preexponential factor. Product data at 100" and (PIET/H)looo gave (FH/FT)lnoo.Equation 2 gave (klH/klT)loo"" and eq 4 gave (k1HjklT)250.The Swain-Schaad relation
AAE,
=
RT In ( k l H / k l T )
(4) [ ( k H / k D= ) ( k H / k T ) 1 i 1 . 4afforded 4] k l H J k l Dand (k-lD/ k_iH)/(kzD/kzH).' The isotope effect on I8O equilibration is shown in eq 5 where RHjRT is the ratio of fractions of ionizations
B. L. Murr,* M. F. Donnelly Department of Chemistry, The Johns Hopkins Uniuersity Baltimore, Maryland 21218 Receiced M a y 29, 1970
that give return. Equation 6 gives the isotope effect H
keq keqT
Dissection of a-Isotope Effects on the Solvolysis of Benzhydryl Benzoate Sir : Knowledge of the ion-pair partitioning isotope effect' allows dissection of the solvolytic isotope effect into an ionization isotope effect k l H / k l Tand a fractionation isotope effect FHIFT, the isotope effect on the fraction of ionizations that results in solvolysis (eq 1).
We report the separation of the solvolytic isotope effect for benzhydryl benzoate in ethanol and an estimate of the isotope effect on IaO equilibration. The analysis is based on the minimum elaboration of Winstein's solvolysis scheme2 consistent with Goering's studies of p-chlorobenzhydryl p-nitrobenzoate (Scheme I). Steady-state treatment affords eq 2 for ktH/ktT, Scheme I
RX
ki e R+Xk1
I
IS
k2
k-
k3
R+JIX- --+ ROS HOS
1
111
where FHII1and FTII1 are the fractions of the respective ktH k tT H
ki _ _ kiT
+ [(k-iT/k-iH)/(kzT/kzH)]jpj
(kzH F I1/k-iH) ~l
+
(k2HFH111/k-1H) 1
(2)
(1) B. L. Murr and M. F. Donnelly, J . Amer. Chem. Soc., 92, 6686 ( 19 70). (2) A. F. Diaz, I . Lazdins, and S. Winstein, ibid., 90, 1904 (1968). (3) H. L . Goering and J. F. Levy, ibid., 86, 120 (1964).
Journal of the American Chemical Society
+
on 0lgequilibration if kl were keq k , (cf. eq 2.)4$7 The discrepancy is apparently not great for benzhydryl b e n ~ o a t e . ~Expressions for kracH/kracT(mechanism dependent) have also been derived. Suffice it to say that kracH/kracT is greater than klH/klTin the absence of tunneling or nucleophilic catalysis in the racemizing process. The a-tritium and deuterium effects subject to the errors inherent in eq 3 and 4 are summarized in Table I. The solvolytic isotope effect k t H / k t Dis substantially greater than the lgO-equilibration isotope effect. The ionization isotope effect is much smaller than (ktH,' ktD),,, (calculated from eq 2 assuming kzHik-lH = 0), the latter being between Shiner's proposed maximum isotope effect ( 1.22)8 and Stewart's experimental equilibrium isotope effect (1 .29).9 In discussing isotope effects and mechanism it is useful to have a name for each solvolytic pathway. Winstein's ion pair symbols (11, 111, and IV) have been used to specify mechanism according to product precursor for the three possible SNI type mechanisms (Scheme 11). The molecularity of the rate-determining (4) A. F. Diaz and S. Winstein, ibid., 88, 1318 (1966). (5) S . Seltzer, ibid., 83, 2625 (1961); see footnote a, Table IV.
(6) C. G. Swain, E. C. Stivers, J. F. Reuwer, and L. Schaad, ibid., 80, 5885 (1958). (7) H. L. Goering and R. W. Thies, ibid., 90, 2968 (1968). (8) V. J. Shiner, Jr., and W. Dowd, ibid., 91, 6528 (1969). (9) M. M. Mocek and R . Stewart, Can. J. Chem., 41, 1641 (1963).
1 92:22 November 4, 1970
6689 Table 11. Estimates of Ionization and Partitioning Isotope Effects for Nonrearranging Systems
Table I. Dissection of Solv~lysisIsotope Effects for Benzhydryl Benzoate in Ethanol 25 '
100O Tritium, Isotope Effects (k-iT/k-iH)l(kzT/kzH> FH/FT kiH/klT ktH/ktT ( k t H / ktT)max keqHlkeqT RH/RT Deuterium Isotope Effects (k-lD/k-iH):(kzD/kzH) FH/FD kiH/kiD ktH/ktD (ktH/ktD)max keqH/keqD RH/RD
1.12 1.062 1.147 1.217 5 O.OIOb 1.28 1.09 0.952
1.165 1.093 1.180 1.30 1.37 1.12 0.95
1.08 1.04 1.10 1.145 1.187 1.065 0.97
1.11 1.06 1.12 1.19 1.24 1.08 0.965
Substrate i-PrOBs i-PrC1 i-PrBr i-PrI sec-OcOBs PhCHzOBs PhCHzCl PhCHCHKl PhzCHOBz PhzCHCl PhzCHCl i-PrOBs
Measurement described in ref 1. Measured by Method I, V. Raaen, G. Ropp, and H. Ropp, "Carbon 14," McGraw-Hill, New York, N. Y . , 1965, p 53. Average of three independent determinations. Samples were chromatographed and crystallized to constant specific activity.
step is not used in classifying mechanism. Intramolecular ion-pair l80 equilibration is designated SNi" or s ~ i ' ~ I . 7 Scheme I1 ks e R+X- e R+IJX-e R+ + XkiiI;i;l
RX
122
1
I HosJ:,
ROS sN2
3
2
I1
HosJw ROS sN1"
I11
HOsJI;,IIr
ROS sN1"'
IV Hos k
.1
p
i-PrC1 i-PrBr i-PrI
Solvent
(kP/ktD),ina (ktH/ktD)bPIED"c
cr-Isotope Effects per D, 25' HOAc 1.14d 1.22' 50-80zTFE 1.120 1.22' HzO 1.13* l.22e H20 1.09' 1.15' HzO 1.079 1.12* Hz0 1.056 1.Oga MeOH 1.11h 1.22" HOAC 1.14d 1.22e 50% EtOH 1.086l 1.151 50% EtOH 1.098m 1.16' EtOH 1.12" 1.24" 80% acetone 1.10" 1.15* MeNOz 1.05p 1.12, P-Isotope Effects per CD8, 25" HzO 1.2459 1.4Y HzO 1.20Y 1.45e HzO 1.17q HzO 1,1539 Hz0 1.1459
1.07' 1.091 1.081 1.055' 1.04' 1.03' 1.10f 1.071
1.062 1.06i 1.11" 1.067 1.06i 1.1651 1.2051
a Estimate of klH/klD. Estimate of (klH/klD)(k-lD/k-lH)/kzD/kZH), eq 7. Estimate of (k-1n/k-1H)/(k2D/k2H). K. Mislow, S . BorEi6, and V. Prelog, Hela Chim. Acta, 40, 2477 (1957). e References 8 and 11. f Calculated, see text. Reference 17. Reference 14. * Estimated from Br and 1 ' 4 as suggested in ref 20. 1 Assumed, see V. J. Shiner, et a/., J. text. Reference 16. Reference 10. Amer. Chem. Soc., 90, 418 (1968). "This work. calculated from eq 2 and k,/kt = 2.5 ( S . Winstein, et ai., Tetrahedron Lett., No. 22, 12 (1960)) assuming k , = kl. PA. F. Diaz and S. Winstein, J. Amer. Chem. Soc., 86, 5010 (1964). g Reference 15. rPinnacolyl brosylate; V. J. Shiner, et al., J . Amer. Chem. SOC., 91, 7748 (1969). Maximum value from ref 20 and private communication from Professor V. J. Shiner, Jr.
ROS SN 1IV
Benzhydryl benzoates, which solvolyze by an SNI"' process, would exhibit a minimum isotope effect (ktH/ktD)mi, = k l H / k l Dwhen kz >> k-l and k;I1 >> kdz (Scheme 11). The same isotope effect is possible for an SNI'I reaction if ksl' >> k-1 and ksI1 >> kz. Thus, the mechanism is not uniquely defined by the isotope effect as noted by Shiner.l0 The maximum solvolytic isotope effect (ktH/ktD)=, (eq 7) for the SN1'" process would be observed if
(7)
k-1 >> kz. The ratio (ktH/ktD),,, :(ktH/ktD)minprovides the PIE if k l H / k l Dis solvent insensitive. The solvolytic isotope effect can vary smoothly between (ktH/ktD),i, and (ktH/ktD),,, as kzH/k-lHvaries from 0 to 10. In Table I1 are summarized estimates of the magnitudes of a- and (3-PIE'S for several nonrearranging systems. Some of these estimates are necessarily inexact and they are presented only to show that PIE'S can be substantial. Values of (ktH/ktD)min are for the most part experimentally observed isotope effects. In most of the cases, experimentally observed (ktH/ktD)max values were combined with (ktH/ktD),i, values to calculate PIEDIH. In the other cases, PIEDIH was estimated and (ktH/ktD),,, or (ktH/ktD)minwas calculated. Shiner8 has shown that trifluoroacetolysis of isopropyl brosylate is an sN1"' reaction with k-l >> kz (IO) V. J. Shiner, Jr., M. W. Rapp, and H. R. Pinnick, Jr., J. Amer. Chem. Soc., 92, 232 (1970).
(Scheme 11).l 1 Hence, the trifluoroacetolysis a- and @-isotope effects12 provide estimates of (ktH/ktD),,,. Kinetics and stereochemistry (complete inversion) of hydrolysis,13" a l c o h ~ l y s i s , ~ ~and " ~ ~ acetolysis13b of sec-octyl sulfonates place these solvolyses in the SN1" category. The corresponding isotope effects provide estimates of k l H / k l D . The isotope effects on hydrolysisl47l5 and a l c o h o l y ~ i sare ~ ~lower ~ ~ ~ limits to k l H / k l D because of a possible s N 2 component. The acetolysis isotope effects provide upper limits to k l H / k l Dbecause of a PIE on I1 of unknown magnitude. Actually, the latter PIE cannot be very large judging by the isotope effects on solvolyses of isopropyl brosylate. Lower limits to internal return have been established for secondary brosylate, but Shiner's experiment showed that l80equilibration grossly underestimates return.8 The ratio k,"/k-l probably varies greatly for hydrolysis, methanolysis, and acetolysis but the isotope effect shows only minor variation. Consequently, the hydrolysis isotope effect for all isopropyl derivatives appears to provide a good estimate of klHlklD. (11) J. A. Bone and M. C. Whiting, Chem. Commun., 115 (1970). (12) A. Streitwieser and G. A. Dafforn, Tetrahedron Lett., 1263 (1969). (13) (a) H. Weiner and R. A. Sneen, J. Amer. Chem. Soc., 87, 287, 292 (1965); (b) A. Streitwieser, Jr., T. D . Walsh, and J. R. Wolfe, Jr., ibid., 87, 3682, 3686 (1965). (14) K. T. Leffek, J. A. Llewellyn, and R. E. Robertson, Can. J. Chem., 38, 1505 (1960). (15) K. T. Leffek, J. A. Llewellyn, and R. E. Robertson, ibid., 38,2171 (1960). (16) E. S. Lewis and R. R. Johnson, Proc. Chem. SOC.,52 (1958). (17) V. J. Shiner, Jr., N. Dowd, R. D. Fisher, S . R. Hartshorn, M. A. Kessick, L. Milakofsky, and M. W. Rapp, J . Amer. Chem. Soc., 91, 4838 (1969).
Communications to the Editor
6690 The largest isotope effect reported for tert-butyl-& chloride is 2.624 at 45" (2.79 at 2 5 " ) for elimination in acetonitrile-pyridine. l8 The rate is pyridine independent. Ion-pair dissociation is a likely rate-limiting step for this elimination (El'"). l9 If so, then the isotope effect represents (ktH/ktD),,,. The value (2.79)'/3 = 1.41, an upper limit for the isotope effect per CD3for the sN1"' reaction, is close to that for trifloroacetolysis of isopropyl brosylate. The evidence is not compelling, however. Shiner's interpretation of the increased isotope effect in trifluorethanolysis17 remains a possibility. A direct observation of a &PIE is not available. The theoretical finding that transition-state force constants for a-C-H bonds in TS2 (see ref 1, Figure 1) depends much less strongly on the particular leaving group than do force constants in reactants suggests?O that a-PIE'S may be approximately proportional to (ktH/ktD),,,. This conclusion is supported by PIE estimates for isopropyl derivatives in Table 11. The PIE for isopropyl chloride was assumed from other chlorides in Table 11. To summarize, the isotope effect on ionization reflects the ZPE change between the initial state and the transition state for ionization (see ref 1, Figure 1, TSl). The maximum isotope effect reflects the ZPE change between the initial state and the transition for intimate ion-pair separation (see ref 1, Figure 1, TS2). The solvolytic isotope effect for an SNlI" reaction varies between these limits as intimate ion-pair partitioning varies. An evaluation of the PIE on internal return us. solvent capture of ion pair I1 is necessary to delineate isotope effects for an SN1" reaction. Acknowledgment. Acknowledgment is made to the National Science Foundation for partial support of this work. (18) D. N. Kevill and J. E. Dorsey, Chem. Ind. (London), 2174 (1967). (19) Y.Pocker, I
