PRIMARY SALT EFFECTS I N REACTIONS I N WHICH THE SUBSTRATE IS NEUTRAL NICHOLAS N. T. SAMARAS Department of Chemistry, Yale University, New Haven, Connecticut Received September 30, i932
It has been suggested by some authors (1) that the primary salt effects in reactions between an ion and an uncharged molecule are governed solely by the changes in the activity coefficient of the catalyzed molecule producei by salt addition. However, as already pointed out by Harned and Akerlof (2), experimentally determined values of fB, the activity coefficient of the neutral substrate, account for neither the order nor the magnitude of the velocity constant variations in salt solutions. In this brief communication a new method of approach will be discussed. Harned (3), in calculating the activity coefficients of hydrochloric acid in HC1-MC1 solutions, has employed the equation
-
logf = - *354 d?T 1 A d2CT
+
+ 2B,.c, + 2B’.c,
B’ is an empirical constant characteristic of the salt. Butler (4)?by considering the mutual salting-out of ions obtained an expression which may be used in the interpretation of the B constants. Carrying this idea further we may look upon the B’ constant as determining the displacement, or salting-out, of the acid by the salt-inasmuch as in an HCI-MC1 solution we have the displacement of hydrochloric acid not only by its own ions but also by the ions of the added salt-and use the Debye and MacAulay (5) expression to represent this part of the activity coefficient. A comparison of the proposed expressions for B and B‘ leads immediately to the relation
a, the mean ionic radius, is defined by
As the values of B‘ have been computed by Harned from thermodynamic measurements by means of equation 1, it is possible to test equation 2; 437 THB JOURNAL OF PHYSICAL CHEMISTRY, V O L . XXXVII, NO. 4
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NICHOLAS N. T. SAMARAS
the agreement is quite satisfactory. Although it is doubtful whether B and B’ as determined empirically from equation 1, are independently correct, and whether the Butler, and the Debye and MacAulay equations separately express completely these constants, equation 2 may be taken to be valid, as any other factors that may enter will be common to both B and B’; the recently published thermodynamic data of Hawkins (6) also support this equation, in spite of the fact that the B and B’ values given differ somewhat from those of Harned. It is also interesting to note that B’, being a partial, must be related to the B constants of both the salt and the acid; this relation for HC1-MC1 solutions, using the data of Harned (7), is found empirically to be a very simple one.
4-B, B’;I B, 2
The introduction of the B’ constants, as calculated from equations 2 and 3-the ionic radii values are those calculated from crystallographic data @)--in the interpretation of primary salt effects, for the type of reaction considered, has led to interesting results, it being possible to account for the salt effects in all but one of the reactions examined. Because of the complexity of the problem, no strict theoretical justification can be given for this linking. We may, perhaps, regard the salting-out of a strong, highly soluble electrolyte as its displacement from the neighborhood of the ions of the added salt and therefore as its increased ability to collide with the substrate molecules to form the complex capable of decomposition. Further, it can be shown, from the empirical relation for a uni-univalent electrolyte
+
B, B’= Ba 2
together with the expressions for B and B’, that the displacement coefficient may be also regarded as the change in the dielectric constant, provided that the mean of the 6’s (iis the molal lowering in the dielectric constant) as well as of the a’s (defined by equation 3) for the catalyst and the salt is employed; this explanation would be in accord with the suggestion of Harned and Samaras (9). It is known from experimental data that for reactions between an ion and an uncharged molecule the interionic-force term of the Debye and Huckel expression does not appear, the logarithm of the rate constant varying linearly with the salt concentration (the concentration of the catalyst being fixed) up to very high concentrations (6 or 7 N );if, of course, both the ions of the catalyst exert a catalytic effect, this term does enter. The results of the present investigation are summarized in table 1. That the characteristic factors by which the displacement coefficients
TABLE 1 Expressions for the primary salt effects REACTION
SALT EFFECT
CATALYST
Cane sugar hydrolysis (i). .......... H + Acetylchloroaminobensene transforH+ and C1mation (ii) ........................ Cyanamide hydrolysis (iii) .......... H + Hydrogen peroxide decomposition I(iv) ..............................
log k = (interionic-force 3B'.n, R' effect) log k = 2BI.n. R1'
+
Ethyl acetate hydrolysis (vi) . . . . . . .
+
+
+ R"'
log k = 2Ba.na 4B' na R"' 3
Diacetone alcohol decomposition (v) ...............................
+R
log k = 3 B ' - n ,
OH-; cation also? H+
+
Z
log k = (interionic-force RrV effect) - 2B'.na log k = ).logf., RV
+
+
R is a constant independent of the salt but characteristic of the reaction. The term involving B' is in each case the displacement coefficient of the catalyst. The salt concentrations are from about 0.4N to the highest concentration for which data are available. The salt effects are represented very satisfactorily by the expressions given. (i) The salt data for this reaction are those of Kauts and Robinson (lo), and for k the medium effect in pure hydrochloric acid &e., for the slope of the log - vs. T Z H C ~ nHCi line) those of Worley (11). (ii) The empirical equation used by Akerlof (12) has been simply rewritten. k
(iii) The values of the slopes of the log- vs. n.,lt lines as given by Grube and ko
Schmid (13) have been used. As neither the B constant for nitric acid nor the ionic radius of the nitrate ion is known, equation 2 cannot be employed, and the assumption has been made that the displacement coefficients of nitric acid in HNOa-MNOa solutions are the same as those for hydrochloric acid in HCl-MC1 solutions, which is perhaps justifiable as in the hydrolysis of sucrose i t is found from the data of Worley that the medium effect for nitric acid is exactly the same as that for hydrochloric acid. (iv) Harned and Samaras (9) have shown that for the hydrogen peroxide decomposition the salt effects can be interpreted by the B constants of the added salts; Boata~. Bsalt although BKI is not known, b y using the empirical relation B' = 2 together with equation 2, its value may be calculated to be nearly zero (which seems t o be borne out also by activity coefficient curves), so that the partial B', which includes both the B for the catalyzing electrolyte and the B for the salt, will in this case involve B , alone. (v) The B"s employed are those of Harned and Akerlof (7a), as the calculation from equation 2 cannot be carried out, since the radiiof the hydroxides are not known. The catalytic data are those of Akerlof (14) and the agreement obtained by using the equation given in the above table is remarkably good up to 6N salt concentrations. (vi) Robinson (15) showed that the square root of the activity coefficient of the ethyl acetate accounted for the salt effects; it is possible, although highly doubtful as the order for the various salts is different, that logf, is related to the B' constant. As this is the only one of the reactions examined for which the salt effects are given b y t , we must regard i t for the present as complicated by an unknown factor or factors . 439
+
440
NICHOLAS N. T. SAMARAS
are multiplied appear to be whole integers, as seen from table 1, must not be regarded as significant, in view of the uncertainty of the values of many of the fundamental quantities involved; all that may be claimed is that the B’ constants account quite well for the greatest part of the salt effect. If we agree with Bronsted (16) and Bjerrum (17) that some kind of a complex is formed, we should expect to deal with a ratio of two displacement coefficients, so that for a reaction between an ion and an uncharged molecule and for uni-univalent salts we shall have, k
log- = 2[Bi’ ko
- BZ’J-nr
(4)
It may be shown that if the susceptibility, a,of the complex is greater than that of water, then the slope of equation 4 is positive and greater than 2Bi’; similarly, the negative sign in the diacetone alcohol reaction may be ac~ O . scheme is by counted for on the assumption that L ~ ~ < ~ Y O H < C Y HThis no means new, as the Bronsted (16) expression, assuming that A in equation l, which involves the so-called mean distance of approach of the ions, is the same for the catalyst as for the complex, would lead to log
k
- = [ai -
ko
Bz
+ aBI*n,
(5)
Equation 5 differs from equation 4 in that it involves the activity coefficient of the uncharged molecule; it should be pointed out, however, that the values of OB, as determined from solubility measurements, are not of the same order as the B’ constants, and it consequently appears that the kinetic factor F , given by the well-known expression, 2,
= k.
CiCB.F
does not involve the activity coefficient of the neutral substrate. A comprehensive and detailed examination of this field leads one to the realization that an exact theoretical treatment is impossible a t present, not only because of the inherent complexity and obscurity of the problems of chemical reactivity and highly concentrated solutions, but also owing to the paucity, if not complete absence, of reliable data on such fundamental quant’ities as the dielectric constants of salt solutions. Nevertheless, it is hoped that the viewpoint presented here, supported as it is by experimental data, may be of some value in the final analysis of the problem. The writer is indebted to Professor H. S. Harned for valuable assistance and information.
SALT EFFECTS WITH NEUTRAL SUBSTRATE
441
REFERENCES (1) SCATCHARD: Chem. Rev. 10, 237 (1932). GROSS:Monatsh. 63-64, 445 (1929). (2) HARNEDAND AKERLOF:Trans. Faraday SOC.24, 666 (1928). (3) HARNED:J. Am. Chem. SOC.48, 325 (1926). (4) BUTLER:J. Phys. Chem. 33, 1015 (1929). Physik. 8. 26, 22 (1925). (5) DEBYEAND MACAULAY: (6) HAWKINS:J. Am. Chem. SOC.64, 4480 (1932). (7) HARNED AND ~ E R L O F : Physik. Z. 27, 411 (1926). HARNED: J. Am. Chem. Soo. 61, 416 (1929). (8) PAULINQ: J. Am. Chem. SOC.49, 765 (1927); that for the H+ is the one given by BRAGG:Phil. Mag. [6] 40, 169 (1920). AND SAMARAS: J. Am. Chem. SOC.64, 9 (1932). (9) HARNED (10) KAUTZAND ROBINSON: J. Am. Chem. SOC.60, 1022 (1928). (11) WORLEY:J. Chem. SOC.99, 349 (1911). (12) ~ K E R L O F : J. Am. Chem. SOC.49, 2955 (1927); the equation used by ikerlof as given in this paper contains two typographical errors. (13) $RUBE AND SCHMID:Z. physik. Chem. 119, 19 (1926). (14) AKERLOF:J. Am. Chem. SOC.48,3046 (1926). (15) ROBINSON: Trans. Faraday SOC. 26, 217 (1930). (16) BRONSTED:Chem. Rev. 6, 231 (1928). (17) BJERRUM:2. physik. Chem. 108, 82 (1924); 118, 251 (1925).
