3498
W. F. SAGER AND CALVIND. RITCHIE
was 3 "V and the ferric chloritle solution was 5YGferric chloride in 0.1 N hydrochloric acid. The aqueous stock hvdroxylamine solution was prepared by neutralizing a 28% hydroxylamine solution (w./v.) with an equal volume of 14% sodium hydroxide solution (w./v.). This solution was buffered with an equal volume of a solution made by mixing 4 parts of 0.1 M sodium acetate solution and 1 part of 0.1 X acetic acid. The resulting stock hydroxylamine solution was usable for over a week if kept under refrigeration. Kinetic Measurements.-All experiments were carried out in aqueous solutions adjusted t o a calculated ionic strength of 1.0 M with KCI. The hydroxylamine and imidazole served as their own buffers in the p H range employed. The buffering capacity of all solutions was great enough t o assure against pH drift during the studies. The concentration of hydroxylamine was sufficiently large, as compared t o lactone, so that pseudo-first-order kinetics were always obtained. The pH of each kinetic run was routinely determined a t 0 and m time. Imidazole Catalyzed Lactone Hydrolysis a t 78".-The hydrolysis of approximately 0.02 M solutions of lactone were followed a t two PH's (6.45 and 6.83) and a t two imidazole Concentrations (0.5 111 and 1.0 M ) at each pH. The kinetic procedure employed was a modification of that of Lippmann and T ~ t t l e . ' ~ One-ml. aliquots of the aqueous lactone-imidazole solution were pipetted into 15 X 135 mm. screw-cap (neoprene lined) Pyrex vials. The tightly capped rials were thermostated a t 78". T o determine lactone concentration at the desired time intervals, tubes were periodically removed from the 78' bath and quenched in an icebath. Two ml. of the buffered hydroxylamine stock-solution was introduced and the tube heated a t 100" for 1 hour (to prevent evaporation of the water solvent the tubes were capped with marbles). The hydroxamic acid ferric ion complex was then developed by introducing t o the cooled solution 1 ml. each of the stock hydrochloric acid and ferric chloride solutions. The absorbance was measured at 540 mp. The reactions were followed t o 50% of completion with a minimum of ten points (tubes). The pseudo-firstorder constants (kohl) were obtained from the slope of the plot of log [O.D.i/O D.t] against time. The catalytic constants for imidazole were obtained by plotting k,b,-k, (where k, is the solvolytic constant in the absence of imidazole) against IMT ( K a / ( K s a u ) ) . Hydroxylaminolysm of Lactones.-One-ml. aliquots of the aqueous lactone (0.01-0.02 A!!) hydroxylamine solution were pipetted into screw-cap vials (vide supra) which were tliermostated a t 30" (f0 01'). For the general base catalysis studies the imidazole (0.20-1.20 X)was included in the hydroxylamine (0.40-0.80 M) solution. Tubes were withdrawn from the water bath a t appropriate time inter-
+
(15) 1'. Lippinann and
[,.
C. Tuttlc, J. B i d . Chem., 169, 21 (1943).
Vol. 83
v d s and quenched 1 ) ~ ' tlic additioti of 2 in. of 3 -1' HCI. T l ~ c
hytlroxamate ferric ion complex color developed instautly O H addition of 2 ml. of the stock ferric chloride solution and the absorbance was determined spectrophotometrically as before. The hydroxylaminolysis reactions were followed t o 75'3" completion employing 12-13 readings (tubes) plus final readings in duplicate. The pseudo-first-order rate constants (kniis)wereobtainedbyplottinglog [O.D.,/O.D., - O.D.,] w. time. Precise first-order plots were invariably obtained. D 2 0Solvent Kinetic Isotope Efect .-The rates of hydroxylaminolysis of 6-valerolactone were determined in DgO by the same procedure followed above, taking care that all solutions remained anhydrous. I n the determination of an the glass electrode correction formula of Fife and Bruicel6 was employed. The ion product of deuterium oxide a t 30" was calculated to be 0.224 X 10-14 from the values K D , ~= 0.154 X lo-'* (25"),17K,v = 1.47 X (30°)&and K , = 1.008 X (25")18 by assuming that the change in Kn0o from 25 t o 30" is proportional to the change in K, from 25 to 3oo. pK Determinations.-The pK's of hydroxylamine ant1 imidazole were determined by the method of half-neutralization and serial dilution maintaining a calculated ionic strength of 1.0 ill (KCI) a t 30". The apparent pK,' values did riot change on dilution. Using the determined values of ,OK,' it was possible to calculate accurately ( d ~ 0 . 0 2pH unit) the desired composition of all reaction solutions. Thus, final adjustment of reaction solutions to the desired PH was not necessary. The PK,'of hydroxylamine in D.0 agreed with the value predicted from the equation of Li1@within 0.05 PK unit; see Table I for the determined dissociation constants. While the pK2' values for H&"H in HgO and DuO are too large to be determined with any accuracy by the half-ncutralization technique,20 they were shown t o be far beyontl the range of pH employed in this study. Thus, the species H?SO$could only be present in trace amounts.
Acknowledgments.-This work was supported by grants from the National Science Fouti(1ation and the Kational Institutes of Health. We wish to thank Professor F. A. Long for stiiiiulating (liscussions. (16) T. H. Fife a n d T. C Bruice, J . Phys. Ciiem.. 65, 1070 (l!)[jI). (17) R. W. Kingerley and V. K. L a M e r , J. A m . Chetib. Sof.. 63,3 2 i O (1941). (18) H. S. IIarned and R. A. Robinson, T i a i i s . F i l r a d d y S O L . , 3 6 , 973 (19.10) (19) N. C. Li, Abstract of paper prescnted t o t h e .Z C. S . hleclillf in St. Louis, Mo., March 21-30, 1961, Llivisioii o f Phys. Chem., Paper 14. (20) P. Dallingcr a n d F. A. Long. J . A m . Chert&. SOL.,81, 1050 (1959).
The Interrelation of Reaction and Substituent Constants and the Role of Electronegativity in Linear Free Energy or Enthalpy Relationships BY W. F. SAGER AKD CALVIN D. RITCHIE RECEIVED SEPTEMBER 14, 1960 An equation is derived relating the reaction constant p with tlie substituent constants of the groups iuvolvcd it1 rcactioti.; The relationship between electronegativity and subwhich are not complicated by variable resonance or steric interactions. stituent constants is discussed. Application of tlie equation is made to the linear free energy relationships of Grunwald and Winstein and of Swain and Scott, as well as to reactions involving ambident groups.
In recent years, increasing progress has been made toward solving the troublesome problem of separating the interlocking factors which govern reaction rates and equilibria. The Harnmett equation, which allows the separation of steric and other factors within aromatic series, has had a major influence on the development of structure-reactivity correlations.' Extended insight has been gained from the
work of Taft, who, by separation of polar and steric factors, was able to show the existence of linear free energy relationships in the aliphatic series. (1) L. P.H a m m e t t , Chem. Revs., 17, 125 (1935); H.H.Jaffk i b i d . , 63, 191 (1953). (2) For a recent review of t h e development and applicability of t h e T a f t equation, see R. W. T a f t , Jr., in M. S. Newman, "Steric Effects in Organic Chemistry," John Wiley and Sons, Inc., N e w York. h'. Y , 1959, p . 550 tt.
3499 ELECTRONEGATIVITY IN LINEARFREEENERGY OR ENTHALPY I
