EFFWT OF SOLVEXTS ON SPECIFIC RATE5
881
The results of our experiments, whilst agreeing with thosc of previous workers over most of the range of salt concentratioris hitherto studicd, show that in more dilute solution the reaction shou normal primary salt, efl’ect. This implies, for a reaction between ions of opposite sign, a decrease in the velocity constant with increase in ionic strength. llobinson and Stokes ( 5 ) have shown that the mean activity coefficient of hydriodic. acid in aqueous solution at 35°C. has a minimum value at p = 0.2, which suggests that the normal primary snlt, effect would be expected only in solutions more dilute t,han this. The results in figure 4 are in complete agreement with this. At ditrerent timcs suggestions have been made that the Brpinsted theory does not atlequately account for the salt. effects observed in reaction rates, but careful investigation has steadily reduced the number of apparent escept,ions. One of t,hese exceptions was removed by a recent paper by Wyatt and Davies (6), who showed that in the reaction between hromoacetate and thiosulfate ions the anomalous salt effect in t’heprescnce of cations of high valence was due to incomplete dissociation of the salts. We believe that our work has removed another supposed exception and that there are in fact no exceptions to the Brgnsted theory, which must be accepted as the basis for the study of all ionic reactions. REFERICSCES (1) (2)
(3) (4) (5) (6)
U R ~ ~ S S T E L IJ, .
S . :2 . physik. Chem. 109, 169 (1922); Chem. Rcvs. 5, 231 (1928). H A R C O T R T , A. V,,ASD ISssox, W . : Phil. Trans. Roy. SOC. 157, 117 (186i). ~ E B H A F Y K Y ,14. A , , A N D h f O H A M M A D , .4.: J . Am. Chem. S O C . 65, 3977 (1933). ~ E B H A F R K Y H. , A , , A S D M O H A M M A I ) , A , : J. l’hys. Chem. 38, 857 (1934). I~OSINSON R,. A . , A S D S T O K E S , R . H . : Tritns. Faraday SOC. 45, 612 (1949). WYATT,1’. A. H . , A S D DAVIES, C. W . : Trans. Faraday Soe. 45, 774 (1949).
THE SOLJ’EST DEPEXC’DESCE OF SPECIFIC RATES TRE.iTED AS A PROBLEM IK ACTIVITY COEFFICIENTS] ERNEST GRUXWALD Department of Chemistry, The Florzda State Uniuersilu, Tallahassee, Florida Received August 10, 1960
riccording to the transition-state theory (9), the effect of solvent on the specific rate k at infinite dilution is given a t constant temperature by the equation:
Presented before the Symposium on Anomalies in Reaction Kinetics which was held under the auspices of the Division of Physical and Inorganic Chemistry and the Minneapolis Section of the American Chemical Society at the University of Minnesota, June 19-21, 1950.
882
ERNEST GRUhWfiD
In equation 1 ko is the specific rate in the reference solvent, the f’s are the distribution coefficients (2) or degenerate activity coefficients (5) referred to the reference solvent for the reactant species R or the transition state *, and the n’s are the exponents of the concentration terms in the rate equation:
u =k
n
c;3
I t is clear from equation 1 that the variation of k with solvent is a problem in the variation with solvent of degenerate activity coefficients. The problem is solved if and when extrathermodynamic relationships are discovered, giving f as a function of solvent for stable molecules. Since transition states are to be treated like ordinary molecules (9, the extrathermodynamic laws will also apply to f*. Perhaps the best-known extrathermodynamic basis for predicting the variation of k with solvent is the postulate (20) that values of f can be separated into factors 81, 82, * * for the individual groups in the molecule, and into a factor, I , for charge (postulate 3). e ,
f = 91.9,
a ’ .
I
(3)
The thorough work on the solubility of amino acids in the system ethanol-water (3) lends a measure of direct experimental support to equation 3. Values of log f over considerable ranges of amino acid structure are given as the sum of an electrostatic term characteristic of the zwitter-ion dipole and inversely proportional to the dielectric constant of the medium, and of a specific term proportional to the molal volume of the amino acid (3). Postulate 3 predicts the solvent dependence of ratios of activity coefficients to be especially simple. Consider the series of compounds AZ, BZ, AZ’, RZ’, consistingof the electrically neutral radicals A, B, and the functional groups Z and Z’. It follows from equation 3 that e ,
9
e ,
e ,
According to equation 4,ratios of the type fA./fAz, depend on solvent only and are independent of the nature of the A radical. Hammett. Deyrup, and Paul (10) have shown that equation 4 is valid for neutral bases and their conjugate acids in media of high dielectric constant over a remarkable range of structure, and this work has been later extended to include even such solvents as anhydrous formic acid and nitromethane (10, 16). When postulate 3 is applied to the problem of specific rate in various solvents, equation 5 is obtained. The g-type activity factors drop out altogether, because the transition state consists of the sum of the reactant structures.
Equation 5 has been the explicit or implicit basis of many attempts to understand the variation of rate with solvent. Hughes, Ingold, and coworkers (12)
,
EFFECT OF SOLVENTS ON SPECIFIC RATES
883
consider only the change in electrical charge upon forming the transition state. Predictions are made on the basis that the charge has been increased, has been decreased, or has become more diffuse in the transition state. More quantitative approaches based on electrostatic theory (1) predict linear relationships between log k and various functions of the solvent dielectric constant for reactants containing charges or systems of charges. There is by now a considerable body of evidence indicating that the range of applicability of equations 4 and 5 is rather limited. There is evidence of long standing that equation 4 fails to fit for Z = -COOH and Z' = 4 0 0 - in the system ethanol-water (8, 14, 15), butanol (19), dioxane-water ( l l ) , methanolwater (15); for Z = -qHNHCONHCO and Z' = -CH(COOH)NHCHO in the system ethanol-water (13); for Z = -N
I I
I
and Z' = -NH+ in the systems
I
ethanol-water and methanol-water (14, 15). The list could be extended almost at will by examining the available data for other functional groups in solvents of intermediate dielectric constant. Electrostatic theory based on equation 5 results in predictions which are not generally in harmony with experimental facts. The theory predicts in every case that k is a single-valued function of the dielectric constant of the so1vent.l The theoretical predictions are thought to be most nearly valid in solvents of high dielectric constant, perhaps greater than 40. Therefore test studies are frequently made in mixed solvents containing water and a second component such as ethanol, acetone, or dioxane. It turns out in a number of cases (1, 4) that apparent agreement between theory and data is obtained for any one twocomponent solvent system, but that plots of k us. dielectric constant do not coincide for the various solvent systems. Thus k is in general not a single-valued function of the dielectric constant. It is unfortunate that the'solvents of high dielectric constant available for the testing of the electrostatic equations are also excellent solvating media. Therefore treatment of the solvent solely as a dispersion medium will not lead to valid results. This fact is widely recognized, and the concept of a microscopic dielectric constant, effective for reactants and transition state but differing from the macroscopic dielectric constant by unknown amounts, has been introduced (4). This concept lends flexibility to the electrostatic equations and is valuable in elucidating the nature of solvation. Considerable success is achieved in fitting rate and equilibrium data ( 5 , 6, 7, 18) if equation 6 is substituted for equation 4.
According to this equation, functions of the type log f A Z / j A Z # are proportional
' Westheimer and Shookhoff (17) have used the concept of an effective dielectric constant in a not entirely analogous situation. Even to this higher approximation, k is a single-valued function of the dielectric constant of the solvent.
884
ERNEST GRUNWALD
rather than equal. The parameters mA, VZB are independent of solvent, and the function Y Z , ~is , independent of A , B,. . ., and assumes characteristic values for each solvent and functional group couple Z-Z'. A function of the type Yz,zt has been termed an activity function ( 5 ) .Empirical values of Y for Z = -COOH and Z' = -COO-
and for Z = --S
l
I
and Z' = -SH+ are available in the sys-
1
I
tem ethanol-water ( 5 , G), and it is possible on the basis of equation G to predict the solvent dependence of dissociation constants for carboxylic acids and ammonium-type acids with a probable error of only 0.03 in p K A . Equation G has been applied successfully to fit the specific rates of unimolecular-type solvolysis of alkyl halides and esters over wide ranges of rate, solvent, and structure (7, 18). In this type of solvolysis, the rate-determining step involves the heteropolar dissociation of the halide or ester RX, and in the transition state, the R-X dipole moment has been greatly increased (12). Since the group X may be varied over wide ranges, it appears that fRXIfRX. = ~RX//RX., but the empirical activity function Y applicable in this case does not depend solely on dielectric constant. Preliminary indications are favorable as to the applicability of equation 6 to other ionic reactions involving different charge types REFERENCES (1) AMIS: Kinetics of Chemical Change i n Solution, especially Chapters IV and VIII. Macmillan Company, New York (1948). (2) BJERRUMA N D LARSSON: Z. physik. Chem. 127,358 (1927). EDSALL,A N D WEARE:J. Am. Chem. SOC.66, 2271 (1934). (3) COHN,MCMEEKIN, LAIDLER,A N D EYRING:The Theory of Rate Processes, pp. 1G11,419-23. (4) GLASSTONE, McGraw-Hill Book Company, Inc., New York (1941). (5) GRUNWALD A N D BERKOWITZ: J. Am. Chem. SOC.,in process of publication. (6) GRUNWALD A N D GUTBEZAHL: Unpublished research. (7) GRUNWALD A N D WINSTEIN: J. Am. Chem. SOC.70,846 (1948). (8) HALFORD: J. Am. Chem. SOC.59, 2939, 2944 (1931);66, 2272 (1933). Physical Organic Chemistry, pp. 115ff ., 127ff. McGraw-Hill Book Company, (9) HAMMETT: Inc., New York (1940). (10) HAMMETT AND DEYRUP: J. Am. Chem. SOC.64,2721 (1932). HAMMETT A N D PAUL: J. Am. Chem. SOC.66, 827 (1934). (11) HARNEDA N D OWEN:The Physical Chemistry of Electrolytic Solutions, Chapter XV, p. 529. Reinhold Publishing Corporation, New York (1943). (12) HUGHES:Trans. Faraday SOC.97,603 (1941). (13) MCMEEKIN,COHN,A N D WEARE:J. Am. Chem. SOC.67, 626 (1935). A N D MIZUTANI: Z. physik. Chem. 116, 135 (1935). (14) MICHAELIS Z. physik Chem. 116. 350 (1925);116, 318 (1925). (15) MIZUTANI: J. Am. Chem. SOC.87, 23 (1945). (16) SMITHA N D HAMMETT: (17) WESTHEIMER A N D SHOOKHOFF: J. Am. Chem. SOC.62, 269, 1892 (1940). JONES,A N D GRUNWALD: J. Am. Chem. SOC.79. 2700 (1951). (18) WINBTEIN, J. Am. Chem. SOC.67, 2289 (1935). (19) WOOTENA N D HAMMETT: (20)ZUCKERA N D HAMMETT:J. Am. Chem. SOC.61, 2791 (1939).
