R . L. HEPPOLETTE AND R. E. ROBERTSON
1831
1'01. 83
lies much closer to the straight line than indicated ery of a phenanthroline group, but instead i t i n Fig. 2. Since the unsubstituted, the 5-substi- may be necessary for the ferrous ion to penetrate tutetl, the 5,B-dimethyl- and the 3 , ~ , ~ , S - t e t r a t i i e t h q the l space between the phenanthroline groups. plienanthroline complexes a11 lie on the straight This conclusion is supported by the fact that the lines, there appears t o be 110 specific steric effect entropy of activation of the reaction between present in the reactions of the 1 ,IO-phenanthroline ferrous ions and the tris-( 1,10-phenanthroline)complexes of iron(II1) with ferrous ions. I t thus iron(II1) ion is considerably more negative than seenis reasonable to suppose that the eleciron-irans- that of other iron(I1)-iron(II1) reactions. fer between the iron(II1) complex and the ferrous Acknowledgment.-\Ye wish to thank Dr. R. ]I7. ion does not take place in an activated complex Dodson for his interest in this work and for helpful in which the ferrous ion is located on the periph- discussions.
[COSTRIRUTIOS FROM
TIIE
DIVISIONO F
PURE
CHEMISTRY, r\-ATIONAL RESEARCHCOUNCIL
OF
CANADA,
OTTATVA,
CASADA 1
The Temperature Dependence of the Solvent Isotope Effect] BY R. L. HEPPOLETTE? AND R. E. ROBERTSON RECEIVEDSEPTEMBER 28, 1960 Rate data for the hydrolysis of isopropyl bromide in deuterium oxide have been determined over a temperature of 35 to 80". By comparison with earlier data for hydrolysis in water, it was shown t h a t the solvent isotope effect ( ~ D ~ o / ~ H decreased with increasing temperature more rapidly than the solvent isotope effect for relaxation processes in bulk solvent. Ii'hile this conclusion may be general for the hydrolysis of halides, it will not hold for the sulfonates where very much smaller values of d(kn,o/k=zo)/dr are found. The sources of the solvent isotope effect for hydrolysis are examined. The results are shown t o be consistent with the hypothesis that the major contribution t o the observed characteristic differences resides in the relative structural stability of the initial state solvation shells.
I n a recent paper3 evidence was given to show how the "solvent isotope effect" obtained from the ratio of the rates of hydrolysis in light and heavy water ( k D 2 0 / k H 2 0 j might appreciably alter with temperature over the available experimental range. This conclusion was at variance with our earlier claim4 that the temperature dependence of this ratio was small or zero and that of Swain and Baders who concluded that the change in the solvent isotope effect with temperature was rapid at lower temperatures (say below 1 8') but became small or zero above this temperature. Our earlier inference was based on limited data for the hydrolysis of the benzenesulfonates and methanesulfonates and is still essentially correct for those molecules which interact only weakly with water in the initial state. However, some doubts were raised as to the generality of this conclusion when the similarity was noted between the trend in the values of the k D 2 0 / k H 1 0 ratio for a series of halides reacting over a wide range of temperature and the corresponding variation in the values for the relative fluidity6 ($Dz0/$H20) and time of dielectric relaxation' (TD~O/TH,O) for bulk H20 and D20 over the same range. But, while it may be quite reasonable to relate the temperature dependence ~O TD~O/TH,O observed in the ratios ~ D ~ O / @ H and to corresponding relative changes in structural stability of the bulk solvent (see below), a similar postulate for the temperature dependence of kD?o:/ (1) Issued a s N.R.C. No. 6209.
( 2 ) National Research Council of Canada Postdoctoral Fellow. (3) P. M. Laughton and R . E. Robertson, Can. J . Chem., 37, 1491 (19.59). ( b ) R. E . Robertson a n d P. A4. Laughton, ibid., 36, 1319 (1957). %'. Bader, Tetrahedron, 10, 183 (1960). (3) C. G. Swain and R . F. 1 (The authors are grateful for receiving a preprint of this paper.) (a) R . C. H a r d a y and R . L. Cottington, J . Resear:h S a t l . Birr. Slatzdavds, 4 2 , 373 (1949). (7) C. H . Collie, F. B. Hasted and D. h f . Ritson, Proc. Phys. Soc., 6 0 , 145 (1948).
from data for a series of halides was less obvious. Thus, because of the possibility of specific differences in both the initials and transition states,Y our conclusions concerning the temperature dependence of k D z o / k H z O was less convincing in our recent paper3 than if i t had been based on data for a single compound obtained over a range of temperature. This has now been done and we report here the results of such a study for the hydrolysis of isopropyl bromide. Isopropyl bromide was chosen as a suitable test compound, not only because other evidence suggested that in hydrolysis nucleophilic interaction was reduced compared to the primary halides but also because of convenient rates of hydrolysis in the accessible temperature range. Rate data for the hydrolysis of isopropyl bromide in H20 over the necessary range of temperature were already known1° and could be expressed within experimental error by the equation ( T i n O K . j log k = -9306.912/T - 27.375G9 log T 93.53701 (1) Corresponding data for hydrolysis in heavy water were obtained by the same conductometric techniques which have been described prev i o ~ s l y . ~ ~ -Temperature '~ control and measurement as well as methods of calculation were uniform with the earlier work. The isopropyl bromide used was a fractionated sample of Eastman White Label (b.p. 59-60' and T Z ~ O D 1.4251) and was kept in the dark under refrigeration during the course of the investigation. kH20
+
(8) T. S.Morrison and N. B. Johnstone, J. Chem. SOL.,3141 (1954). (9) R . E. Robertson, R . L. Heppolette and J. M, W.Scott, C a n . J . Chem., 37, 803 (1959). (10) R . L. Heppolette, R. E. Robertson and J. M. W. S c o t t , unpublished work. (11) R . E. Robertson, Can. J . Chem., 31, 589 (1383). (12) R . E. Robertson, i b i d . , 33, 1536 (1955). (13) K. T. Leffek, J. A. Llewellyn and R . E. R 0 b e r t s o n . J . A m . Chem. SOL.,8'2, G315 (1960).
~ o )
TEMPERATURE DEPENDENCE OF SOLVENT ISOTOPE EFFECT
April 20, 1961
DzO (99.8%) was obtained from Atomic Energy of Canada, a single stock solution containing 0.002 111. KBr backing electrolyte being used throughout the course of the study. In Table I, rate data for the hydrolysis of isopropyl bromide in DzO for a range of temperatures RATEDATAFOR
THE
TABLE I HYDROLYSIS OF ISOPROPYL BROMIDE IN DEUTERIUM OXIDE
Temp., " C .
k i , set=.-' X 105
nn
kD20/kn20
80,005 74.829 69.988 64.812 59.894 54.967 49.974 44.872 39.995 35.038
212.9 i 0 . 2 129.6 zk . 2 79.54 i ,003 46.19 zk .04 2 6 . 8 5 i .03 15.30 =k .014 8.473 =k .002 4.475 + ,002 2 . 3 7 0 xk ,002 1.206 i ,001
4 3 3 4 3 4 5
0.789 ,788 ,787
.784 . 782
.
r-?
i l l
,772 4 . 767 4 ,760 4 ,752 n is the number of parallel runs from which the average values of kl is determined.
are given with the average deviation from the mean of n parallel runs. The temperature dependence of these rate data were fitted by a least squares calculation to the following empirical three constant equation Log k = - 10,000.619/T - 31.8624 log T 106.83054 (2) Deviations from this equation are of the order of the experimental variations found for the n individual rates a t a single temperature and show no systematic variation which would suggest that further terms should be included. Since the deivations are small and random, the use of the above form of empirical equation seems justified even though some other equation might prove equally good.I4 Combining equations 1 and 2 gives the expression
+
log
~ D ~ o / ~= H ~-693.707/T o
-
4.4867 log T
4- 13.29353 (3)
from which the corresponding values of kD20/kH20 for the experimental temperatures in Table I can be found. Clearly the change in k D z O / k H 2 0 with temperature for a single compound is very similar to the trend shown through a series of halides of different reactivity, though the range of the variation is limited by the fact that the investigation was not extended below 35'. The value of kDzo/kH20for 4' calculated from equation 3 is 0.677; the value found for t-butyl chloride a t the same temperature was 0.695. l5 Reasoning from solubility characteristic^,^ we should have expected a lower value for the chloride unless some specific factor introduces small alterations in the ratios. Such specific differences which presumably contributed to the scatter in the halide ratios in our earlier publication3 are eliminated here and hence a more detailed examination of the temperature dependence of the k D 2 0 / k H 2 0ratio is possible. The trend in kDlo/kHro values (Table I) shows a significant temperature dependence in the range (14) F. S. Feates and D. J. G. Ives, J . Cizern. SOL.,2798 (1956). (15) P. M. Laughton and R. E. Robertson, Can. J . Chem., 3 4 , 1714
(1956).
lS35
35-80' confirming the conclusion of Laughton and Robertson3 but a t variance with the conclusion of Swain and Bader5 for temperatures above 18'. Their conclusion was based partially on nonkinetic evidence that the structural difference between the two media remains constant above this temperature. This conclusion seems very doubtful in view of our results and does not necessarily follow from the evidence cited by them. Thus the Baker viscosity relation16 is applicable over a very restricted range of temperature, and its failure a t lower and higher temperatures is consistent with a decreasing structural difference with increasing temperature. While the librational frequencies (Table I, ref. 5 ) they report show marked change between 10 and 2 5 O , these results come from different laboratories and would be more convincing if there was one temperature in common with the earlier investigation of GiguPre and Harvey. l7 If librational frequency contributes but 17% to the difference in heat content13 and the heat capacity term for H20 and D20 show very small trends with temperature over the range of interest, then conclusions drawn from calculation of relative heat contents with respect to the temperature dependence of the structural difference are unconvincing. The question of whether there is a rapid change in relative structure (and hence in ti^ Fs) in the region 0-20' has not been explored here but indirect evidence weighs against such a conclusion. In our study of the hydrolysis of methyl benzenesulfonate'?; isopropylbenzenesulfonate, tosylate and methanesulfonatelO; and methanesulfonyl chloride and benzenesulfonyl chloride13 there is no indication in dAH*,'d2' of a more rapid change in the structural stability of water a t the lower temperatures. For these reasons we set aside the arguments advanced by Swain and Bader concerning d(kD20/ka20)/dT and our earlier assumption4and proceed to examine the reasons why ko,olkHzo might be expected to vary with temperature over the entire experimental range. CDmposition of the Solvent Isotope Effect in Hydrolysis.-As a convenience for examining components of k D 2 0 / k H 2 0 the formal separation is made AF* = (F*R+ + F*x- + F * I ) - ( F s -+ Fi) where R + and X- refer to the solvent associated with the quasi-ions in the transition state, S to the solvent in the initial state solvation shell and I to the solute The isotope effect due to a change in medium will be given by the difference ndicated , assumption beng made by the operator 6 ~ the that ~ M ( A F I *- A F I ) is negligible. Str ctly, the +* not only solvent isotope term ~ M F Rincludes effects but also any possible secondary deuterium isotope effects arising from differences in the 0-H bond as a result of nucleophilic interaction. As we shall show presently, this factor is small, if not negligible, and the main source of the effect is still to be related to 6 h l F s and this in turn to the rela(10) (17) (1956). (18) (19)
W. N. Raker, J . Chem. Phys., 4, 291 (1936). P. A. GiguPre and K. B. Harvey, Can. J . Chern., 34, 798
J. D. Bernal and G. T a m m , S u t u r e , 135, 229 (1936). R. E. Robertson, unpublished work.
1836
R. L. HEPPOLETTE AND R. E. ROBERTSON
1'01. 83
tive difference in structural stability of the two illustrated in Table I, arises in the same way as media as suggested in our earlier papers. dAH*/dT for the physical processes cited above The structural nature of water has been discussed if due allowance is made for differences associated repeatedly and no agreement appears to exist with the changes in structure of water caused by as to the exact description. Iyhether it approxi- the presence of solutes. mates to the idealized tridymitic and quartz\Vhen a weakly polar molecule is dissolved in like structure Bernal and Fowlerz0put forward as a water, i t creates asymmetry in the field of contiguous working hypothesis?' or the more recent poly- water molecules leading to a loss in librational hedra of PaulingZ2or the string-bag hypothesis of freedom, i.c. an increased restriction to rotation Pople with bendable hydrogen bonds23 or the about the 0-H axis as a result of an increase in fluttering cluster theory of Frank and M-en,24 nearest neighbor water-water interaction. Indeed, it is sufficient for our purpose that relative struc- the thermodynamic parameters characterizing this tural stability be recognized as determining, to a process are determined in the main by this inlarge degree, the characteristics of aqueous solu- creased water-water interaction rather than by tions and differentially (equation 5 ) between DzO water-solute interaction. The enthalpy of soland H20, providing a source of the solvent isotope vation is negative and decreases with temperature, effect. Since no general agreement has been i.e., having large positive heat capacity values conreached as to which of the above hypotheses is sistent with the description outlined above and dispreferable, it would seem premature as well as cussed in greater detail by Eley,:j3 Frank and unnecessary to be more specific here, particularly EvansI3* Glew and Moelwyn-Hughes,:35 Rohon when we must add to our considerations the fur- and Claussen36 and others.j.28,zg If the solute ther uncertainties attending initial and transition contains centers providing a possibility for soiiic state solvation. Calculations based on an investi- degree of hydrogen bonding, then loss of librational gation of t h e temperature dependence of dielectric freedom noted above as characterizing the forniarelaxation, viscosity and self-diffusion lead Sax- tion of an aqueous solution of non-polar molecules ton,z5 Collie, Hasted and Ritson26 and \Tang2' will be reduced, the entropy ill be less negative to conclude t h a t a common energy barrier of 4-5 than for a less polar molecule and the heat capacity kcal. was associated with the rate-controlling effect less positive. Obviously there is the posstep in the disruption of water structure. Fur- sibility for a range of initial state solvation shells thermore, in such physical processes, where the with varying stability characteristic of the polarity moment of inertia relating to rotation about the of the solute and as a corollary, with varying degrees 0-H axis is d ~ m i n a n t , ~ D20 , ~ ~ .invariably ?~ shows of relative structural stability as between solvation evidence of greater structural stability than HzO. by D20 and HzO. Thus the much stronger interThus Conway30 calculated that (H*o?o- H*H,o) action between sulfonates and water compared for dielectric relaxation was 300 cal. and a similar with halides and water leads to corresponding value was to be expected3] and was found for vis- reduction in the relative structural stability of the cosityY2based on data of Harday and Cottingdon.6 initial state solvation shells about the former. I n both calculations, A H * was found to decrease Solvation parameters for the halides9 predict an with rising temperature with a coefficient of about increase in water-water interaction about isopropyl -30 cal.;deg. Since structural stability as used bromide relative to bulk water while the presence here is the physical consequence of the difference of more basic oxygen atoms in the sulfonate may between structure forming from dipole-dipole lead to a decrease in structural stability in the interaction and the structure breaking of thermal initial state solvation shell compared to bulk water. activation; as the latter increases the residual must Laughton and Robertson concluded in an earlier decrease both absolutely and differentially as paper4 t h a t such differences in stability of initial between H 2 0 and D20 whatever model of water we state solvation shell 6 ~FS 1 largely determine GxilF*. choose to adopt. This conclusion differed from t h a t of Pritchard \Ve have previously assumed the source of the and Long37 who assumed the major terms to be solvent isotope effect to be associated with the 6afF*x- or of Swain, Cardinaud and Ketley38who double difference in relative initial state structural expected 6bl F*R to make important contributions stability and here make the further assumption to GbfAF*. From equation 5 our assumption t h a t the temperature dependence of ~ D ~ o / ~ H , orequires , that
-
(20) J. D. Bernal a n d E. Fowler, .I. Clzein. P h y s . , 1, 315 (1933). (21) J. D. Bernal in "Hydrogen Bonding," edited by Hadzi, Pergnmon Press, New York. S . Y.,1959, p. F. (22) I b i d . , p . 1. (2:1) J. A . Poyle, PI'OC.R o y . S o c . (I.oizdon), 8206, l l i 3 (1951). (21) II. S Frank and Wen-Yang Wen, Disc. F a r a d a y Soc., 24, 133 (1CGi)
(2.j) J . A . Saxton, Pvoc. Roy. SOC.( L o i i d o n ) . A213, 473 (1952). ( 2 6 ) C . H. Collie, J. B. Hasted and D. I f . Ritson;Pvor. P h y s . Soc., 60, 14.5 (1948). (27) J , H . Wang, J . P h y s . Chem., 58, (i8li (1954). (28) J H . W a n g , C. V. Robinson a n d I. S. Edelman, J . A m . Cheiii. S o r . , 7 5 , 4 G O (19.53). 7roiz.r. F a r a d a y Soc., 53, 1578 (1957). a y , C'aii. J . Ciiem., 37, 613 (19.59). (31) E . H . G r a n t , J. Cheiiz. Phys., 26, 1,575 (1967). (:in) R. E . Robertson. S. Sugatnori a n d S . H a r t m a n (unpublished c:\lculations).
S>fFS
>> (G\iF*S- $- G > i F * K - )
(6)
This requirement would appear to neglect such well known differences in solvent isotope effect for aqueous solutions of ions as shown by relative heats of solvation39and relative solubility in D2O (.1:1) D. D. Eley, T i o i z s . P a r a d a y .Sot., 40, 184 (1944). (3.1) H. S. F r a n k a n d h'l.W Evans, .I. Chem. P h y s . , 13, 507 (151451. (35) D. K , Glew a n d E . A XIoelwyn-Hughes, Disc. Fnvadny Soc , 16, 1.50 (1953). (36) R. F. Bohon and \V. F. Claussen, J . Ani. Cheiii. Soc., 73, 1.571 (19.51) i.37) J , G . Pritchard and I' A . L m g , i b i d , 78, 6008 ( 1 9 , X ) . (38) C. G. Swain. R Cardinaud and A . D . Ketley, ibid., 77,
TEXPERATURE DEPENDENCE OF SOLVENT ISOTOPE EFFECT
20, 1961
and H20.40 In the latter, the solvent isotope effect appears to be of the same magnitude for ions and for some non-electrolytes in apparent conflict with the above inequality. The anomaly disappears when it is recognized t h a t major contributing factors to this isotope effect may be related to initial state differences in the two bulk media. The factors determining k D , o / k H , o stem from the property of neutral molecules (the initial state, here) to increase the structural stability of the solvation shell relative to bulk media thus enhancing solvation differences while singly charged ions of intermediate size break down structure and so tend to reduce this difference. Bernal and FowlerIs appear to have been among the first to recognize this property of ions to "raise the structural temperature" of water, a view subsequently supported by evidence from viscosity41,42infrared,5,43dielectric dispersion44 and diffusion rates.2as45 Even so, characteristic differences were observed with changing size and charge, in each physical parameter, and the fact that a greater degree of scatter in the k D 1 o / k H , O values was not observed in our survey of the alkyl halides3 is consistent with inequality above. If there is a charge of 0.8e or greater on the developing anion,g a similar charge must be associated with the cationic moiety or vicinity with a corresponding decrease in the structural stability of initial state solvation shell, and hence ~ M F *will be small compared with 6hlFs. Because there is ample evidence for differences in the degree of overlap between oxygen of water acting as a nucleophile and different alkyl groups for a given series13 and for different displaced groups for the same alkyl group,46a corresponding variation in &IF* might be anticipated from a secondary deuterium isotope effect because of corresponding differences in the loosening of the 0-H binding in the transition state. In Table I1 corresponding values of kDpo,'kHnofor the hydrolysis of methyl and isopropyl esters are arranged in the order of increasing covalent bond formation in the transition state for the methyl compound. While the order
1837
i
0.65
0.75
0.80 Relative fluidities,
0.85 +D,o/@H~o.
Fig 1 -A correlation of kinetic solvent isotope effects for t h e hydrolysis of a series of esters with the Corresponding values for the relaxation process in bulk water: A, isopropyl TABLE I1 bromide; B, methyl bromide; C, isopropyl benzenesulfoA COMPARISON OF SOLVEKT ISOTOPE EFFECTS FOR METHYL nate; D, methyl benzenesulfonate. AND ISOPROPYL COMPOUNDS HYDROLYZIXG IN WATER Temp., "C. Anion
60 Bzs.
60 Mes
90 C1
80 Br
80 I
Methyl Isopropyl
0.905 (0.94)
0.94 (0.94)
0.78 0.75
0.81 0.79
0.816 0.767
(isopropyl)> k D , o / l k H 2 0 (methyl) is consistent with a contribution to &F* from a secondary isotope effect as noted above, this simple hypothesis would require an increasing difference kD20/kHz0
(40) F. T. Miles, R. W. Shearrnan and A. W. C . Menzies, S a l t w e ,
138, 121 (1936). (41) W. 51. Cox and J. H . Wolfenden, Pvoc. R O Y . SOL. ( L o n d o n ) , 8 1 4 5 , 47.5 (1934). (42) 11. Karninsky, Disc. F a v a d u y Soc., 2 4 , 171 (1957). (43) D. Williams and W. Millett, P h y s . Rw.,66, 6 (1944). (44) G . H. Haggis. J B. Hasted and T . J. Buchanan, J . Chem. Phys., 2 0 , 1452 (19,jZ). ( 4 j ) 0. Y . Samilov. Disc. F a r a d a y Soc.. 24, 141 (19.57) (16) S. H a r t m a n and I
