CHARLES CERJANAND RONALD E. BARNETT
1192
The Viscosity Dependence of a Putative Diffusion-Limited Reaction by Charles Cerjanl and Ronald E. Barnett* Department of Chemistry, Unisetsity of Minnesota, Minneapdia, Minnesota
66466 (Received December 90,197'1)
Publication costa assisted by the National Science Foundation
Variation of viscosity using water-glycerol mixtures appears to be a useful method for studying diffusionlimited reactions in aqueous solution, especially for reactions in which the rate-determining diffusion-limited step is preceded by unfavorable equilibria. In one such reaction, the hydrolysis of 2-methyl-A*-thiazolineto give S-acetylmercaptoethylamine and N-acetylmercaptoethylamine, the breakdown of a neutral intermediate to give the thiol ester is diffusion limited for pH values greater than 2. The diffusion-limited step is proportional to the reciprocal of the viscosity, while equilibria and nondiffusion-limited steps are relatively unaffected in going from water to 60% glycerol.
Introduction In the formulation of reaction mechanisms for carbonyl and acyl group reactions it is often assumed that simple diffusion-limited proton transfer steps are too fast to be rate determining, and that breaking or making of bonds to carbon is concerted with proton transfer for general acid and general base catalysis. 2-4 However, in recent years evidence has accumulated for several carbonyl and acyl group reactions that the rate-determining step may be diffu~ion-limited~-'~ or have intermediates which are not at equilibrium with respect to simple proton transfer^.^^^'^ It seems likely that many other carbonyl acyl group reactions may also for some reaction conditions be limited by a simple proton transfer step not involving making or breaking of bonds to carbon. It would be desirable to have a technique by which one could readily determine whether the ratedetermining step for a reaction is diffusion limited even if preceded by an unfavorable preequilibrium without having to resort to rather elaborate methods and a r g ~ m e n t s . ~ - ~ , ~One ~ - ' property ~ which should be characteristic of a diffusion-limited reaction is an inverse dependence on the viscosity of the medium. Equilibrium constants and nondiffusion-limited processes should be independent of viscosity. One way of increasing the viscosity of aqueous media is to add glycerol. Water and glycerol form relatively ideal mixtures, 15s1* glycerol has a relatively high dielectric constant (42.5), and water activity seems to be linearly correlated with water mole fraction,I6 so this system looks promising for continuous variation of viscosity. In this paper we apply the viscosity variation method using aqueous glycerol to a reaction for which there is indirect evidence that the rate-determining step for some conditions is diffu~ion-limited.~,~ Experimental Section Materials and Methods. Reagent grade glycerol was used for all experiments. 2-hlIethyl-A2-thiazoline (Eastman) was redistilled before use. Carbon dioxideThe Journal o j Physical Chemistry, Vol, 76, N o . 8,1979
free glass distilled water was used throughout. Viscosity measurements were made with a Cannon-Fenske viscometer. The initial ratio of thiol ester to amide formed in the hydrolysis of 2-methyl-A2-thiazoline was determined as previously described.6 Spectroscopic measurements were made with a Beclcman DU spectrophotometer with a thermostated cell compartment. The temperature was maintained at 25.0" with a circulating water b8th. Results and Discussion The hydrolysis of 2-methyl-A2-thiazoline proceeds by way of a neutral intermediate which partitions to give S-acetylmercaptoethylamine and N-acetylmercaptoethylamine. Below pH 2 approximately equal amounts of thiolester and amide are produced, with the ratio of products being independent of pH."3'* As the (1) National Science Foundation Undergraduate Trainee, Summer 1971. (2) M.L. Bender, Chem. Rev., 60, 53 (1960). (3) 9.L. Johnson, Advan. Phys. Org. Chem., 5 , 237 (1967). (4) T . C. Bruice and 9. J. Benkovic, "Bioorganic ,Mechanisms," Vol. 1 and 2, W.A . Benjamin, New York, N. Y., 1966. (5) R. E. Barnett and W. P. Jencks, J. Amer. Chem. Soc., 90, 4199 (1968). (6) R. E.Barnett and W. P. Jencks, ibid., 91, 2358 (1969). (7) R. K. Chaturvedi and G . L. Schmir, ibid., 91, 737 (1969). (8) R.E.Barnett and W. P. Jencks, J . Org. Chem., 34, 2777 (1969). (9) 1%. J. Zygmunt and It. E. Barnett, J . Amer. Chem. Soc., in press. (10) R. E. Barnett and W. P. Jencks, ibid., 89, 5963 (1967). (11) R. E.Barnett and W. P. Jencks, ibid., 91, 6758 (1969). (12) L. D.Kirshner and R. L. Schowen, ibid., 93, 2014 (1971). (13) D.G.Oakenfull and W. P. Jencks, ibid.. 93, 178 (1971). (14) W. P. Jencks and K. Salvesen, ibid., 93, 1419 (1971). (15) R. H. Stokes and It. A. Robinson, J . Phys. Chem.. 70, 2126 (1966); R. A. Robinson and It. A. Stokes, "Electrolytic Solutions," 2nd ed, 1959, pp 241-245. (16) L. L. Schaleger and C. N. Richards, J. Amer. Chem. SOC.,92, 5565 (1970). (17) 1%.B . ,Martin, 5. Lowey, E. L. Elson, and J. T . Edsall, ibid., 81, 5089 (1959). (18) R. B . Martin and A. Parcell, ibid., 83, 4830 (1961).
1193
VISCOSITYDEPENDENCE OF DIFFUSION-LIMITED REACTION
pH is increased above 2, however, the fraction of thiolester drops to near zero. This drop is not a result of a conversion of initially formed thiol ester into amide,5v6 and so must be a result of a change in rate-determining step in the partitioning of the intermediate formed in (3) thiazoline hydrolysis. The S to N transfer reaction of S-acetylmercaptoethylamine has also been s t ~ d i e d . ~ , ~ , ’ ~ and ui the radius of the molecule.23 By combining eq There is a neutral intermediate in this reaction, and a 2 arid 3, eq 4 is obtained. For nonspherical molecules change in rate-determining step occurs at the same pH at which the fraction of thiol ester formed in thiazoline kab = c/q (4) hydrolysis drops 0 f f . ~ 0 ~ The data for thiazoline hy2/aza~be2N(ua a b > drolysis and the S to N transfer reaction could not be C = fit into a single mechanism which excluded simple pro1 0 0 0 W a U b exp zaxbe2) ton transfer steps from being rate determining.6n6*20 &Tuab The mechanism shown in eq 1has been proposed to exthe expression should have the same general form. plain the data.5*6 The crucial part of the mechanism Assuming the mechanism of eq 1it can be shown that is the interconversion of X i and X+, a process which is k - 2 / 1 ~ ~ ~is 0+ given by eq 5 where ~ H $ o +is the seconda simple proton transfer and presumably diffusionlimited in the thermodynamically favored direction.21 order rate constant for the protonation of Xk t o give X+, f” is fraction of products formed as the thiol ester By the mechanism of eq 1 the interconversion of Xk
[ (
kq
CH3 S
X’
and X+ is the rate-determining step above pH 2 in the S to N transfer reaction and is responsible for the drop in thiol ester formation from thiazoline hydrolysis above pH 2. The evidence for this mechanism has been discussed e l s e ~ h e r e . ~This ! ~ mechanism ultimately depends on being able to show that there must be at least three s e q u e n t i a l steps, all of which can be rate determining under appropriate conditions in the S to N acetyl transfer reaction. For most reactions such detailed kinetic information cannot be obtained. The arguments for rate-determining, diffusion-limited steps in thiol ester h y d r o l y s i ~and ~ ~ ~amide hydrolysis12 are indirect and not completely definitive. The rate of a diffusion-limited reaction should be inversely proportional to the viscosity of the medium. If k a b is the second-order rate constant for an encountercontrolled reaction of a and b, then the rate constant is given by eq 2, where xae and xbe are the charges of a and b, Da and Db are their respective diffusion coefficients, k is Boltzmann’s constant, B the dielectric constant, and Cab the reaction distance.22 If the reactants are approximated as spheres, their diffusion coefficients are given by eq 3, where 71 is the viscosity of the medium
X+
+
it
N
X
in strong acid, and K is the hydrogen ion concentration Jc-2 _
kHsO+
-_ K 1 - f”
~
(5)
for which f = 0.5f”. In Figure 1is shown the dependence off on the hydrogen ion concentration as the concentration of glycerol is varied from 0 to 60%. I n strong acid the rate-determining steps in partitioning of the intermediate in thiazoline to give thiol ester and amide are pH independent and not diffusion-limited according to the mechanism of eq 1. If varying the glycerol concentration has little effect on nondiffusion-limited steps and on equilibrium constants, then f” should be independent of the glycerol concentration. The effect on glycerol on f” is shown in Table I. As the glycerol concentra(19) R. B. Martin and R. I. Hedrick, J . Amer. Chem. Soc., 84, 106 (1962). (20) R. B. Martin, R. I. Hedrick, and A. Parcell, J . Org. Chem., 29, 3197 (1964). (21) M. Eigen, A w e w . Chem. Int. Ed. Enol., 3 , 1 (1964). (22) P. Debye, Trans. Electrochem. Soc., 82, 265 (1942). (23) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” Wiley, New York, N. Y., 1961, p 271. The Journal of Physical Chemistrg, Vol. 76, No. 8,19Y2
1194
CHARLES CERJAN AND RONALD E. BARNETT
1 7
0.6
0.5
-1,21---1
4
0.7
-1.4
t
-1.6
-1.8 Y
01-2.0 0
-1
0
1
-Log[H’],
7 M-
4
I 00
Figure 1. The effect of acidity on the fraction of thiol ester formed in thiazoline hydrolysis a t 25’ for water (a), 10% glycerol (A),20% glycerol ( W ) J 307, glycerol (v)J407, glycerol (0),50% glycerol (A), and 60% glycerol (D).
1-f”
- k-zv
c
I
0.2
I
I
I
I
0.6 Log Irlirlot
0.4
I
I
, I
I
0.8
1.0
- 1’).
Table 1: Effect of Glycerol on the Formation of S-Acetylmercaptoethylamine in the Hydrolysis of 2-Methyl-Az-thiazoline a t 25’ K
%
x
108,
glycerol
f”
M
0 10
0.480 0.420 0.388 0.383 0.371 0.352 0.325
2.32 3.01 4.64 6.92 8.20 14.8 24.2
20 30 40 50 60
(6)
diffusion-limited, and so should be independent of viscosity, a plot of log [K/(1 - f”)]vs. log (v/vo), where 70 is the viscosity of pure water, should be a straight line with a slope of unity if in fact the mechanism of eq 1 is correct and interconversion of X+ and X f is rate determining when the hydrogen ion concentration is less M . Such a plot is shown in Figure 2. than about The slope is 0.94, which is in good agreement with eq 6, and is further confirmatory evidence for the mechanism of eq 1. It is highly unlikely that the observed effects of glycerol on the partitioning of the intermediate formed in thiazoline hydrolysis are due t o medium effects on nondiffusion steps and equilibrium constants. I n support of this it should be observed that (a) the effects of glycerol on f” , which include both rate and equilibrium effects, are small and (b) the pK, of P-cyanoethylpiperidine hydrochloride is virtually independent of the medium up to 70% glycerol.26 Variation of viscosity by addition of glycerol appears to be of considerable potential usefulness in distinguishing diffusion-limited processes from nondiffusionThe Journal of Physical Chemistry, VoE. 76, No. 8,1972
I
Figure 2. The viscosity dependence of K/(1
tion is increased from 0 to GO%, f” varies from 0.480 to 0.325. This is a small change and can probably be largely accounted for by the effect of lowering the dielectric constant on the equilibrium constant from X to X+. The dielectric constantz4of GO% glycerol is GO. However, K/(1 - f”) should be proportional to the viscosity, as can be seen by taking HA = ~ C H ~ O C and combining eq 4 and 5 to obtain eq 6 . Since kF2is not
K
-I
-26
limited ones in aqueous solution. Reactions of reactive carbonyl compounds with good nucleophiles to give zwitterionic intermediates, which must be converted into neutral intermediates before breakdown t o products can occur, may very well behave as does the S to N transfer reaction of S-acetylmercaptoethylamine, with interconversion of the zwitterionic and neutral tetrahedral intermediates being rate determining, for some conditions. For this to be possible, expulsion of the nucleophile from the zwitterion to give reactants should be quite rapid. I n the case of the S to N transfer of X-acetylmercaptoethylamine I C - ~ is G.6 X lo8 sec-l. I n the hydrolysis of methyl X-trifluoroacetylmercaptoacetate, a reaction which is also probably diffusion limited,*r9 the rate constant for the expulsion of water from IL zwitterionic intermediate has been esti(24) A. A. p 29. (25) A I .
Newman, “Glycerol,” Morgan-Grampion,London, 1968,
M. Kreevoy and J. Dolmar, J . Phys. Chem., in press.
1195
SOLUBILITY AND PARTIAL MOLARVOLUMEOF DISSOLVED HELIUM mated to be greater than 3.8 X.lOIO sec-l. Reactions such as oxime and Schiff base formation, ester aminolysis, and amide hydrolysis may quite likely be diffusion limited for appropriate reaction conditions. For example, a zwitterionic intermediate is probably formed in oxime formation. Reimann and Jencks26have estimated that the rate constant for the expulsion of hydroxylamine from the intermediate formed with pchlorobenzaldehyde is about lo9sec-l. Since elimination of water to give the oxime must occur from the neutral intermediate, conversion of the initially formed zwitterionic intermediate into the neutral one may be
rate determining for some conditions. I n problems such as this kinetic methods quite often may not provide sufficient information to decide whether a reaction is diff usion-limited, while variation of the viscosity of the medium using water-glycerol mixtures should provide the answer quite readily. Acknowledgment. I wish to thank Professor Maurice Kreevoy for many helpful discussions and Mr. John Dolmar for making the viscosity measurements. (26) J. E. Reimann and W. P. Jenoks, J. Amer. Chem. Soc., 88, 3973 (1966).
Solubility and Partial Molar Properties of Helium in Water and Aqueous Sodium Chloride from 25 to 1000and 100 to 600 Atmospheres1 by Gregory E. Gardiner and Norman 0. Smith* Department of Chemistry, Fordham University, New York, NEWYork 10@8
(Received August 6, 1971)
Publication costs assisted by the Ofice of Research Services, Fordham University
The solubility of helium in water was measured a t 50 and 100' at pressures from 100 to 600 atm. The results differ systematically from the only previous data. An explanation for the discrepancy is offered in terms of meniscus corrections. The solubility of helium over the same pressure range in 1 and 4 m NaCl a t 25, 50, and looo was also measured. The applicability of Henry's law to the results is considered in detail. A pressure dependence of the partial molar volume of the dissolved gas is proposed. For solutions of helium in water and in 1 m NaC1, the compressibility of the dissolved gas, defined as ( - l / ~ ~ O ) ( b ~ ~ / b P ) passes ~ , x , ,through zero at 25-30'. The relevance of such a compressibility to the structure of the solution is discussed. A set of isobaric solubility measurements a t 200 atm in water is reported and the solubility of the gas shown to pass through a minimum at 28.3'. The thermodynamic quantities related to the solution process are derived. Calculation of the partial molar volume of helium in water as a function of temperature shows that it also passes through a minimum near room temperature. The variation of the temperature of minimum solubility with pressurejs treated semiquantitatively. The effect of added EaCl on the temperature and pressure dependence of V Zis discussed. Salting-out coefficients are reported for the NaCl solutions. Generally these decrease with increasing salt concentration and the Setschenow relation is not strictly valid.
The solubility of helium in water and sodium chloride solutions is a topic of special interest to the physical chemist. As a key to understanding the structure of water and aqueous solutions, the solubility of noble gases has found wide usee2 Helium is ideal for this purpose since, because of its small polarizability, interactions with the solvent are expected to be virtually negligible and its effects on water structure almost purely those arising from excluded volume phenomena. In the fields of geochemistry and oceanography, interest in helium is widespread: special attention has been given to its solubility in water and the effects of added salt, temperature, and pressure on the solubility.
Though many studies have been made of the solubility of helium in water and salt solutions at atmospheric pressure, data on its high pressure solubility in water have been reported only twice in the p a ~ t . ~ , ~ The first of these is the more extensive, covering the (1) Taken in part from the Ph.D. dissertation of G. E. G. Portions of this paper were presented before the Metroohem 69 Regional Meeting, New York, N. Y., May 1969,and the 158th National Meeting of the American Chemical Society, New York, N. Y., Sept 1969. (2) See, for example, H. 8 . Frank and M. J. Evans, J. Chem. Phys., 13,507 (1945);W. Kauzmann, Advan. Protein Chem., 14, 1 (1959). (3) R.Wiebe and V. L. Gaddy, J . Amer. Chem. Soc., 57,847 (1935). (4) H.A. Pray, C. E. Sohweikert, and B. H. Minnich, Ind. Eng. Chem., 44, 1146 (1952). The Journal of Physical Chemistry, Vol. 76, N o . 8,1.978
