Dec. 20, 1962
PROTON EXCHANGE RATESFOR WATERIN ORGANIC SOLVENTS
from all observations. In the extreme, the merence between the c d c i e n t s based on early and late points is as much as 0.3% even though the average deviation of the point by point rate coefficients based on a given set of parameters is of the order of 0.0370. Thus it cannot be concluded that rate data are correct only on the basis of a lack of trend in the point by point rate coefficients. One of the time consuming aspects of this technique is the independent determination of the conductance parameters AO and Sa. As one might expect, the parameters derived from the rate data are not very sensitive to the value of AO but they are much more sensitive to the value of Sa,the limiting slope of the A us. c'I9 plot. It is primarily S, which determines the correction to the rate data as is evident from equation 4 obtained by rearranging equation 3 (see Experimental). 10' K/Rc = 4 - Sac'/* (4) If the left hand side of (4) were a constant then obviously no correction would be necessary. If data of the optimum precision are not required one can often estimate the value of & from data in the literature and calculate S, from Onsager's relation.a1 We used this procedure to treat the rate data obtained in 50% ethanol, but one cannot use this approach unless ion association is negligible. It seems feasible to derive the conductance values from the rate data but we have not pursued this. Table IV gives a comparison of the rate constants obtained by the conductometric technique with those determined titrimetrically by Fainberg and Winstein.a2Js The reliability of the titrimetric values is estimated to be 1-2%. The conductometric values are all higher than the titrimetric (31) H. S. Harned and B. B. Owen,"Electrolytic Solutions," Third Edition, Ranhold Publishing Corp., New York, N. Y., 1958. (32) A. H. Fainberg and S. Winstun, J . Am. Cham. Soc., 18, 2770 (1956). (33)
A. H. Fainberg and S. Winnrtdn, W . ,19, 1597 (1957).
4677
values.*4 With t-butyl chloride the agreement is probably within the experimental error; but in the case of 1-phenylethyl chloride, while there is good agreement between the values in 80% ethanol, the difference increases in the more aqueous solvents. Since these two compounds solvolyze a t comparable rates, the discrepancies cannot be due to some error which is proportional to the rate. The difficulty probably is due to the decreasing solubility of l-phenylethyl chloride in the more aqueous solvents. The concentration of alkyl halide used by Fainberg and Winstein was from ten to thirty-five times that in our conductometric determinations. To summarize, we have applied the techniques of precise conductance measurements to the problem of rate determination. The reproducibility study of the solvolysis of 1-phenylethyl chloride indicates that the rate coefficient can be determined with a precision of 0.02% if one exercises the utmost care and carries out a number of runs. I n the absence of great care the limits of reproducibility may rise to 0.1% but no higher in our experience if the solvent and compound are pure. It is expected that, with further experience with this method, improvements will be forthcoming in defining more precisely the factors governing precision, if not in the precision itself. Acknowledgment.-The authors wish to express their appreciation to Mr. Earl Sexton for his patience and attention to the difficult problem of constructing the conductance cells and to Miss Joanna Dickey for frequent weighings. It is a pleasure to acknowledge many valuable discussions with Dr. E. J. Bair. The facilities of the Indiana University Research Computing Center were used for the statistical computations. (34) Often rate constants determined conductometrically are higher than the titrimetric values. See W. M. Schubert and R. G . Minton, ibid.. 84, 6188 (1960).
[CONTRIBUTION FROM TJ3B DEPARThfBNT OF CERMISTRY, UNIVERSITY OF CALIFORNIA, LOS ANCELES 24, CALIFORNIA]
Proton Exchange Rates and Hydrogen-Bonding for Water in Organic Solvents'" BY J. R. HOLMES, D. KIVELSON'~ AND W. C. DRINKARD RECEIVED Jm29, 1962 The chemical behavior of water protons in a series of organic solvents has been studied by nuclear magnetic resonance and infrared techniques. T h e shifts in the OH stretching frequencies and the n.m.r. chemical shifts of the water protons have been measured in various solvents and correlated with each other, and with hydrogen bond energies. A theory of chemical shifts due to hydrogen bonding is discussed. The equilibrium constants for water dimer formation in these solvents have been estimated from the n.m.r. data. The n.m.r. spectral line shape has been studied as a function of solvent, temperature, water concentration, and added acid, for dilute solutions of HzO-D~Omixtures with a hydrogen to deuterium ratio of one. The rate of inter-water proton exchange was determined by this technique. At room temperature, the mean exchange rate 7-1 for 1.1formal water in various solvents is (in sec.-l): 6.7 (nitromethane), 0.91 (acetonitrile), 1.0 (acetone), 1.6 (dioxane), 25 (pyridine), 8.3 (dimethylsulfoxide), 100 (triethylamine). The apparent activation energy is less than 1.5 kcal./mole for the weakly basic solvents and the reaction is approximately second order in water. The dominant mechanism in the iirst five solvents i s thought to be a direct proton exchange in a ring formed by three water molecules. The trimer concentration decreases and the direct exchange rate increases with increasing temperature; the net result is an exchange rate which is almost temperature independent. The trimer concentrations in dimethylsulfoxide and triethylamine are too low to account for the observed rates but the concentrations of OH- and protonated solvent SH + are high in these two solvents and, hence, mechanisms that depend upon OH- and S H + can become important. The activation energy for the process involving OH- is probably lower than for the one in which SH+ partakes; therefore, the OH- mechanism dominates.
Introduction
represents a preliminary investigation of water dis-
very little is h 0 W n about the behavior Of Water as a SolUte rather than aS a solvent. This study
m t e d in pert at the Southern California Regional Meeting of the A m a i m Chemical Sodety, Los Angeles, December, 1960. (b) Alfred P. Soan Fellow. (c) J. R. Holmes, D. Kivelson and W. C. DrinLud, J . Chnn. PhyJ., ST, 160 (1962).
(1) (a) SapPorted in Pprt by the R-ch
Corporation and pre-
J. R.HOLMES, D. KIVELSON AND W. C. DRINKARD
4678
VOl. 84
TABLE I GENERALSUMMARY Solvent
AVB, cm.-’
AHmix-2
kcal. /mole
- RT In K x , kcal./mole
Carbon tetrachloride 40 Benzene 76 Xitromethane 2.4b 78 -1.2 1. Acetonitrile 115 -0.7 Acetone 127 1 .05d - .5 p-Dioxane 1.6’ - .6 153 Tetrahydrofuran .7 196” Water 276 Ethyl acetate Pyridine 292 -0.65’ -1.0 Dimethyl sulfoxide 334 -1.3’ 0.2 Trimethylamine 3 58 -1.6’ a Measured in the present work; all other A v values ~ from ref. Ref. 11.
-
EH
-
EH(HIO). kcal./mole
-1.6 -1.4 -0.9 -1.2
-0.1 3.
T6-’,
7 4 -1,
sec. -1
sec. -1
3.1 0.9 (1.0)
...
sec.
...
...
3.6
2.2 6 X IO‘
0.2
0.18
... Ref. 7.
1.6
>>100
* Ref. 8.
-1
6.8 0.9 1.o
...
1.7
0.3
* Ref. 6.
Exp. r-1,
e
Ref. 9.
11 25 8.3 >100 Ref. 10.
solved in a series of organic solvents, all of which “inert” solvents, or exothermic, as with solvents are proton acceptors. Proton magnetic resonance which are more basic than water.5 Several values has been the principal tool used in this research but of AHmixm,the heat of mixing per mole of water exuseful data also have been gathered from infrared trapolated to infinite dilution, are given in Table Hydrogen bonds do not play an important and calorimetric studies. In the first few sections of this article the thermodynamic properties of the role in the solvent-solvent interactions for the liquids “dilute water solutions” are discussed. Heats of studied here. If one assumes that the non-hydromixing are related to hydrogen bond energies, to gen bonding interactions do not contribute to the infrared 0-H stretching frequency shifts, and to heat of mixing, a reasonable approximation since chemical shifts in the proton resonance spectra ; these interactions are small and probably about the polymerization constants are obtained from chemi- same for all interacting molecular pairs, then AHhxm cal shift data, and the concentrations of ionic is the energy difference, per mole of water, between species are estimated by a variety of techniques. hydrogen bonding interactions of water with water In the latter sections of the article the proton res- and those of water with solvent. Haggis, et d , 1 2 onance spectral pattern, which has been discussed have estimated the energy of the water-water elsewhere,lc has been used to study the kinetics of hydrogen bond a t 4.4kcal. per mole and the perproton exchange for water in various solvents. centage of possible 0-H hydrogen bonds formed in The results of this investigation are rather tentative pure water a t ninety. The effective water-water since the relevant experimental data are still frag- hydrogen bond energy in pure water is, therefore, mentary, but i t is hoped that the approach sug- 4.0 kcal. per mole. If one assumes that water a t infinite dilution in the various solvents considered gested will be fruitful. Infrared Shifts. -The average infrared stretching here exists principally as the hydrogen-bonded comfrequency for the 0-H bond in water vapor is about plex consisting of one water molecule and two donor 3700 cm.-’; hydrogen bonding causes a shift to molecules, the energy EH of a single water-solvent lower frequency and an increase in the width and hydrogen bond may be estimated by the relation intensity of the absorption band.2 This infrared EE = (4.0 - AHmilm/2) kcal./mole (1) shift Av, can be measured relative to the position of In Fig. 1 the infrared shifts are plotted against of the band in water vapor and is a useful measure values of E H estimated in this way; a reasonably of hydrogen bonding. The measurements have good straight line results, amazingly good when one been made on dilute solutions of water (0.01 to 0.05 considers that the calorimetric measurements are formal). Under these conditions the spectra show not very accurate and that the theory is very aponly the “associated bands” attributed to the proximate. The assumption that the infrared shift hydrogen-bonded complex of water and solvent. is a linear measure of the hydrogen bonding energy2 Values of infrared shifts measured by other^^,^ and seems to be borne out by these results. It should in the course of this work are presented in Table I. be mentioned that other estimates, drastically difHeats of Mixing and Hydrogen Bonding Ener(5) J. S.Rowlinson, “Liquids and Liquid Mixtures,” Butterworths gies.-The enthalpy change of mixing A H m i x for Scientific Publications, London, 1959. water dissolved in proton-accepting solvents is (6) D. B. Myers, Department of Chemistiy, UCLA, private comabnormally large, primarily because hydrogen munication. (7) A. L. Vierk, Z . anorg. chcm., 261, 283 (1950). bonds are broken and formed in the solution proc(8) W. C. Drinkard and D. Kivelson, J . Phys. Chrm., 63, 1491 ess. The process may be endothermic, as with (1958). (2) G. C. Pimentel and A. L. McClellan, “The Hydrogen Bond,” W. H. Freeman and Co., San Francisco, Calif., 1960. ( 3 ) E. Greinacher, W. Luttke and R . Mecke, 2. Elektrochem., 59, 23 (1955). (4) P. Saumagne and M. L. Josien, Bull. SOC.Chim. (France), 35, 813 (1958). The values reported by these workers differ slightly from those given in ref. 3, hut the discrepancies do not affect any of the present conclusions. The valaes from ref. 3 are quoted in Table I.
(9) R.J. L. Andon, J. D. Cox and E. F. G. Herrington. Trans. Faroday Soc., 58, 410 (1953). (10) J. Keuttamaa and J . J. Kindberg, Suomcn Kernisfilchti, 8 9 8 , 32 (1960). (11) I. L.Copp and D. H. Everett, Discussions Faraday Soc., lS, 174 (1953). (12) G.H. Haggis, J. B . Hnsted and T. J. Buehanan. J. Chrm. Phys., ao, 1452 (1962).
Dec. 20, 1962
PROTON
EXCHANGE RATES
I-
W5)3N ICH~)~YJ HZO
160 140
0 PYRIDINE
--
.-
4679
FOR WATER I N ORGANIC SOLVENTS
1
4 -
Nitrome thane
120
E
Y I
GIO'ifiNE
0
C? CW3CN
I tH311C0
1
i
100 , ?
8
v
80
L
a
2o
Pyridine
n .04 .06 .OS .10 Xw (mole fraction). Fig. 2.--N.m.r. shifts vs. concn. of H20.
0
.02
.12
hydrofuran in water. I n these measurements it was assumed that the tetrahydrofuran resonance is not subject to any solvent effects other than the bulk diamagnetic effect, and, consequently, that i t can be used as an internal standard. The two methods for correcting for bulk diamagnetic effects were TABLE I11 ESTIMATES OF IONIC CONCENTUTION Solvent
e,
Concentrations for 1.1 formal H20 (OH-) (HaO+) (SH+) e.s.u. K, X lorn X 1010 X 10'0 x 1018
Nitromethane 39.4 20 5 5 Acetonitrile 3 8 . 8 20 5 4 Acetone 21.4 0.2 0.8 0.3 Dioxane 2.2 0.9" 1.2 0.9 Pyridine 12.5 0.0013 120 Dimethyl sulfoxide 46.4 50 4 x 106 Water 78.5 324 From data of Harned and Fallon, ref. 29.
0.11 1 2 0 5 0 25 120.
4
x
1oc
checked for p-dioxane and acetone; the corrections evaluated by the different methods agreed to within 0.4 C.P.S. For further experimental details see ref. 14. Values of AVO,the chemical shift corrected for bulk diamagnetic effects, are presented in Table 11; some of the data were taken from the work of Cohen and Reid. l6 It is convenient to express the chemical shifts relative to that of water vapor, in which there is, presumably, negligible hydrogen-bonding interaction. The chemical shift of water vapor relative to that of liquid water, corrected for the bulk (14) J. R. Holmes, Doctoral Thesis, University of California, Los Aageles 24, Californio, 1961. (15) € DI .. Cohen and C. Reid, J . Chcm. Phyr., I O , 791 (1956).
J. R. HOLMES, D. KIVELSONAND W. C. DRINKARD
4680
VOI. 84
havior is observed for E n in the strongly basic solvents (see Fig. 1). Furthermore, crude estimates of S H + and OH- concentrations, even in solvents 400 as basic as dimethylsulfoxide, indicate that these ions cannot contribute appreciably to the chemical shift (see Table 111). Mavel’s estimates of ionic 3 concentrations probably are quite high since his z 4 100 KB’S were evaluated for S in H4O rather than for HeO in S; the dielectric constant for the latter solution is very much smaller than for the former and the effective K B will, consequently, be greatly reduced. This is discussed in a later section. Furthermore, recent evidence suggests that the AV.!~rn-~i presence of OH- ions would cause a low field shift.19 Fig. 3 . - A w us. va: AYH for CCI, and CsHr are from ref. 15; The evidence presented here suggests the need of an alternative explanation for the sign of ( b A - / b A v s ) measured value of AYH = 183 C.P.S. for HIO. in strongly basic solvents. susceptibility of liquid water, is 183.2 C.P.S.’~The Marshall, Pople and Buckinghamm have dechemical shifts AYH,relative to that of water vapor, veloped a theory which allows one to estimate of water a t infinite dilution in organic solvents, are changes in shielding resulting from the inhibition gben in Fig. 3. The chemical shifts AVH contain by an applied electric field of the diamagnetic circontributions from local diamagnetic anisotropies culation of electrons about a proton. This shielding of the donor molecule in the region of the hydrogen is a “paramagnetic” term, similar to the parabond site. These contributions are difficult to magnetic term in Ramsey’s expression for diacalculate; however, they have been estimated for a magnetic shieldingjZ1and has a Y - ~ dependence proton bonded to the n-cloud of b e n ~ e n e ~ ~ and v ‘ ~ where I is the electronic-nuclear distance. The to the triple bond of a~etylene.l*-’~ If the triple decrease in shielding varies as the square of the bond in acetonitrile is treated analogously to that applied electric field, I n a simple point charge in acetylene, one would expect an anisotropic shift electrostatic theory for hydrogen bonding, the of about -25 C.P.S.for water protons bonded to electric field due to the hydrogen bond is proporacetonitrile. Acetone, nitromethane, p-dioxane tional to E H and the reduction of the shielding tetrahydrofuran and dimethylsulfoxide should ex- should then be proportional to E H ~ .But in a hibit similar but smaller shifts. The estimated cor- simple covalent theory of the hydrogen bond the rections in AuH, arising from the anisotropic shifts, electron density about the proton increases4 with are indicated by the arrows in Fig. 3, a figure which increasing E H and the diamagnetic r-l terms in represents a plot of the chemical shifts AYE against Ramsey’s expression for the shieldingz1 increase, the infrared shifts Av,. The A m for water has been thereby increasing the shielding. The electrostatic corrected for the fact that 10% of the possible hy- theory can, therefore, be used to estimate the paradrogen bonds in liquid water are dissociatedl2; if magnetic contribution t o the shielding whereas the another estimate of this percentage is taken the covalent theory can be used to approximate the AVHwill be shifted accordingly. diamagnetic contribution. I n keeping with this Figure 3 indicates that for the weakly basic viewpoint the hydrogen bond wave function can be solvents the shielding decreases as the hydrogen written as cteqe a@cwhere the subscripts e and c bond strength increases, while for the strongly represent the electrostatic structure S. .HO and basic solvents the shielding increases as the hydro- the covalent structure (S. .H+ 0-), respectively. gen bond strength increases. Mavel” has proposed I n this description i t would appear that in all SYSs )strongly terns studied here the electrostatic structure domthat the sign reversal of ( ~ A v H / ~ A Yfor basic solvents is a consequence of the protolysis inates but that in the solvents which are more reaction basic than water the covalent structure becomes imHnO S )7 SH+ OHK B (2) portant. Of course, another way of describing the where S represents a solvent molecule and K B the variations in shielding with changes in E H is t o say equilibrium constant. The observed proton res- that the variations in the paramagnetic terms domonance would be an average of that for S. * .HsO, inate but that the variations in the diamagnetic SH+ and OH-, and the chemical shift would be terms become appreciable for strongly basic soldisplaced towards higher fields relative to solvated vents. water, S. .Hz0.18 The 0-H infrared shift is, of Equilibrium Constants for the Polymerization of course, a measure of the single species S. .HzO and Water.-Chemical shift measurements can be used would not be much affected by the protolysis reac- to obtain information about p ~ l y m e r i z a t i o n . ~ ~ - ~ ‘ tion, but the heats of mixing and the hydrogen(19) J. I. Musher, ibid., 86. I889 (1961). bond energies E H should be. No anomalous be(20) T. W. Muahall and J. A. Pople, Mol. Phys., 1, 189 (1958);
+
+
-
+
-
(16) W. G. Schneider, H. J. Bernstein and J. A. Pople, 1. Chcm. Phys. 28, 1487 (1958). (17) G. Mavel, (a) Compt. rend., 248, 1505 (1959): (b) ibid.. 949, 1753 (1959); (c) J . chim. phys., ST, 649 (1960). Mavel actually considered C?AVH/~(KB/KW), where K B and Kw apply to aqueous mlutions. (18) C. MacLean and E. L. Machor, J . C h . Phyr.. S4. 2207 (1961).
A. 0. BucHngham and J. A. Pople, Proc. Comb. Phil. Soc., W, 262 (1857). (21)
N. F. Ramscy. “Nudear Moments,” John Wiley and Sons, New York, N. Y.,1853. p. 273. (22) C. M. Huggins, G. C. Pimentd and J. N. Shoolery, J . Chcm. Phys., SI), 1244 (1856). (23) S. K. Alley, Doctoral Thesis (Chemistry), University of c.liIornia, Lus Angeles, 1961.
Dec. 20, 1962
PROTON EXCHANGE ~ T
E FOR S
WATERIN ORGANIC SOLVENTS
4681
thalpy changes given in Table I imply small negative entropy changes for most of the systems studied; the positive entropy change for the pyridine system is subject to great uncertainty as discussed above. These conclusions are, of course, tentative; the determination of K, as a function of temperature would give an independent check on these results. The determination of K , and K m was carried out at very low water concentrations. As the water concentration is increased trimers and higher polymers tend to form. The equilibrium constant K,,,'for the formation of trimer from monomer and The two species are considered to be in equilibrium dimer is probably of the same order of magnitude Approximate but somewhat smaller than K,. according to the relation trimer concentrations, assuming K m = K m ' are given in Table I1 for 1.1 formal water concentra2 M S S M& S (3) The MS, protons have a shift given by the value of tions; the true trimer concentration is probably For water concentrations A m discussed above. The Ma3 protons have a n somewhat smaller, average shift of ( ~ A v H AvH,o)/~ where AVH,O = above 0.5 formal in the solvents studied, the trimer 204 c.P.s., the corrected chemical shift of liquid concentration depends very nearly on the square of water. Because of the rapid reorientation of the the formal water concentration rather than on the molecules in solution, the observed chemical shift third power as i t would for much lower concentraAv for all water protons involved in the equilibrium tions. Mavel has estimated the equilibrium constants for formation of trimer from three monomer is an average of the individual shifts and 1.5 X for water in molecules as 6 X Ap = (%/%)(APE) -I-2(nd/%)(3A*a A*a,0)/4 (4) acetone and dioxane, r e ~ p e c t i v e l y l ~these ~ ; should where nm and nd are the number of moles of mono- be compared with the K2m values of 2.9 X lo-* mer and dimer, respectively, and n, is the number and 6.2 X respectively, that can be obtained of moles of water present, ie., nm 2nd. The for these compounds from Table 11. mole fraction equilibrium constant K , for the diUnder the assumption, discussed above, of small merization in eq. (3) can be expressed as18,22-24entropy change for water polymerization in the solvents studied, the enthalpy should lie between & = 2[b(Al)/b(n-/th)Io/(A~~ - Algto) (5) 0 and -2.5 kcal./mole. This conclusion will enter where % is the number of moles of solvent, the into the discussion of the kinetics of proton exderivatives are evaluated from Fig. 2 by extrapolat- change. ing to (nw/nJ -c 0, and the values of AVHare taken Ionic Concentrations.-The ionic species H,O +, from Table I. The limiting values of the slopes, OH- and SH + exist in the various solutions studied, the resulting values of K,, and those of the molar but i t is not a simple matter to determine the conequilibrium constants K m are given in Table 11. centrations of these ions in dilute solutions of water The most significant error in the experimental in organic solvents. The following estimates of evaluation of K,, provided the various assumptions ionic concentrations are extremely uncertain ; are justified, is the uncertainty in the determination nevertheless, they are useful, in the absence of of the slope. This uncertainty depends upon the better data, in discussing the mechanisms of proton scatter of the chemical shift measurements over the exchange. The ions arise from the reaction in eq. range of shifts measured and is estimated to be 2 and from the reaction about *20'%. The value of K , for pyridine is sub2H20 = HsO+ + OHKw (6) ject to another serious uncertainty; (AVH- AV&O)/ 4 = 10 C.P.S. but if the highly uncertain 10% cor- where K w is the equilibrium constant. If K B and rection for the broken hydrogen bonds in pure water K w are expressed in terms of concentrations rather is not made, (AVH - AvH,o)/4 = 5 c.ps. which alters than activities they are not truly constant over the K -, bv 100%. entire range of water concentrations; in fact, they ~ - ,v-The free energies, -RT In K,, for the dimeriza- depend markedly upon dielectric constant and one tion reaction of eq. 3 a t 300°K., are given in Table should write K(aq) and K(s) for the equilibrium I. Since dimerization involves the breaking of constants in solutions dilute in organic liquids and ordered S. .H bonds and the formation of ordered dilute in water, respectively. 0. -H bonds, one would expect the entropy change The quantity KB(aq) is a measure of the basicity to be reasonably small and the free energy change of the organic liquid and it has been measured for n to be approximately equal to the change in en- number of substances diluted in aqueous medium. thalpy. This latter quantity is approximately Gordy and Stanford25have found 3 reasonably good EH - EH(water), values of which are listed in Table correlation between infrared shifts A v , and the I. These values are, of course, sensitive t o the fi&(aq). This relationship can be partially underchoice of the effective energy of the hydrogen bond in stood if one assumes that the entropy cliange for water whereas the linear relation illustrated in Fig. reaction 2 is negligible and, therefore, that the dif1 is not. The values for the free energy and en- ference in proton affinity of the substance S and the OH- ion is approximately -2.3RTpKn(aq). (24) E. D. B e c k a . V. Liddel sod J. N. Sboolery, J . Md. s##~., I, 1
It is not practicable to attempt a n analysis over the entire mole fraction range of water but in terms of a simplified model the low water concentration region may be studied profitably. In very dilute solutions only two species will be considered: the monomer complex M& represented as H*.-S O 20, has been applied to a number of solvents, and the resulting Kw's are ref. 2b. give in Table 111. This procedure is not satisThe linear relationship found by Gordy and Stan- factory for substances with low dielectric constants ford then suggests that the strength of the hydrogen such as p-dioxane (e = 2 . 2 ) . Harned and FallonZ9 bonding interaction, measured by AvS, is propor- have made direct measurements on Kw in watertional to the proton affinity. In the present experi- dioxane mixtures containing up to 70 mole per cent. ments, carried out with dilute solutions of water in dioxane. Extrapolation of these data to 1.1 mole/ Pyridine organic solvents, the basicity is determined by the liter of water gives Kw(s) = 8.6 X equilibrium constant KB(s), which has not been has a small dielectric constant, 12.5, and this value of measured for most solvents and differs greatly from Kw(s) is particularly subject to error. The ionic concentrations have been estimated KB(aq), largely because of the dependence of KB(s) upon dielectric constant. No sensible cor- from these results and are given in Table 111. AIrelation, therefore, would be expected between though not much confidence can be placed in the Avs and ~ K B ( s )since the proton affinity of OH- accuracy of these figures, they represent general depends markedly upon dielectric constant and trends that are useful in analyzing the kinetic data presented below. hence upon solvent. Kinetic Data.-For very slow proton exchange The reaction the proton resonance spectra of HzO-DzO mixtures SH+ + H,O H ~ O ++ s (7) in organic solvents consist of the HDO triplet and the H20 singlet (see Fig. 1 in ref. IC). If T is the has an equilibrium constant (KwIKB). If Kw and K B depend similarly upon the dielectric properties mean life of a proton on a particular water molecule, of the solvent, an assumption which is implicit the line shapes can be calculated as a function of 7 , in Eq. 8 below, then Kw/KB should be only slightly the H-D spin-spin coupling constant A H D and the D HDO and H2O. dependent upon solvent and, hence, more or less relative chemical shift ~ H between independent of the concentration ratio of non-ionic These calculations, based upon the theories of species, (HzO)/(S). The ratio (HsO+)/(SH+) can Sack30and Anderson,31are discussed in the Appenbe estimated reasonably accurately in the various dix. Some theoretical proton resonance spectra a t solvents in the presence of strong reference acids. 40 Mc., calculated for HDO-H20 mixtures with a Values of P(Kw/KB) evaluated from (H30+)/ H / D ratio of unity and for 7 / T z>(SH+) ; measured as a function of total water concentration this would improve the linear relationship some- for concentrations ranging from 0.55 to 5.5 molar; what. If one assumes that the entropy change for r - l seems to be approximately linear in water conreaction 7 is negligible, then -2.3 l i T p ( K w / K ~ )is centration. Since the proton exchange rates for 1.1 approximately equal to the difference in proton molar solutions in acetonitrile and acetone are too affinities of H,O and S, and the linear curve in Fig. slow to affect the line shapes much, these values of 4 again stl gests that the proton affinity is propor- 7-l had to be obtained from more concentrated (28) E. A. Moelwyn-Hughes, "Physical Chemistry," Pergamon tional to t e strength of the hydrogen bonding interaction. Mavel's correlations between AVH and Press, London, 1957. r2
8
(26) H. Le Maire and J. J. Lucas, J . A m . Chem. S O L . ,73, 5198 (1951). (27) H.C.Btown and X. I. Mihon, rbid.. 77, 1723 (1953).
(29) 23. S. Harned and L. D. Fallon, J . A m . Chem. Sac., 61, 2374 (1939). (30) R.A. Sack, Mol. P h y s . , 1, 163 (1958). (31) P. W. Anderson. J. P h y r . Soc. ( J a p a n ) , 9, 316 (19.541.
LL Z = 0.80 s e c
1.0
0
.2.0 -1.0
2.0
Z =0.40 s e c
- 2 . 0 -1.0
0
1.0
2.
L A 7
.2.0 -1.0
0
AV
4683
PROTON EXCHANGE RATESFOR WATERIN ORGANIC SOLVENTS
Dee. 20, 1962
-
Z-
0.20 sec
1.0
2.0
-2.0 -1.0
0.10 sec
0
1.0
acetonitrile
-2
0
-2
2
dioxane
0
2
ethyl acetate
acetone
-2
0
2
dimethylsulfoxide
2,o
A v (CPS)
(CPS)
A
T = 0.08 sec
-2.0
-1.0
1.0
0
(1. h o l e s / liter %O)
2.0
Av(CPS)
-2
0
2
pyridine
pyridine
k T
-2.0
-1.0
0
-
1.0
0.04 sec
2.0
-2.0
AY(cPa)
~
~~~~
-1.0
0
1.0
2.0
AV(CPS)
triethylamine
~~~~~
Fig. 5.---Theoretical rate-dependent spectra; peak areas not iiormalized.
Fig. 6.-Experimental
solvent-dependent spectra.
4684
J. R. HOLMES, D. KIVELSON AND W. C. DRINKARD
solutions and the assumption of a linear dependence of 7-l upon the water concentration. Although the measurement of r is not always straightforward, particularly in spectra where the natural line widths Tz-I and field inhomogeneity are comparable to the exchange broadening, the data for T are probably good to within *25% in the range T = 0.6 to 0.2 second. The rate of exchange in pyridine is too fast to estimate r reliably by a direct comparison of line shapes. But there is a detectable broadening of the HzO-HDO line in pyridine compared with the line observed for pure H 2 0 in pyridine a t the same concentration; this broadening has been attributed to exchange. The temperature dependence of r has been measured over a 50 to 80” range in nitromethane, acetonitrile, acetone and dioxane. Within experimental uncertainty no change in r was observed; one can therefore conclude that the effective activation energy for the exchange process is very low. At temperatures of - 20’ in acetone the HDO triplet was broadened whereas the H20 line did not seem to be. This broadening might be attributed to deuterium quadrupole relaxation which becomes more important a t high viscosity, or to a slightly negative “effective activation energy” of hydrogen exchange arising, as explained below, from a negative enthalpy of trimer formation. Small amounts of hydrochloric or perchloric acid catalyzed the proton exchange of the H&HDO mixtures in acetone, but the results were not reproducible. I n order to prevent the leaching out of alkali from the glass Pyrex equipment and glassware coated with Desicote silicone films were used in some experiments. No improvement was noted. In acetone the HCl apparently adds to mesityl oxide, a material which forms by a condensation reaction, accelerated by the presence of water, and which is normally present in trace amounts even in freshly purified acetone.32 All solvents used in this work were highly purified; details are given elsewhere. l4 Exchange rates in solutions 1.1 formal in water were greatly increased (T
