PSU CHEM 408 - The Effect of Structure upon the Reactions of Organic Compounds

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9G LOUIS P. HAMMETT Vol. 59 [CONTRIBUTION FROM THE DEPARTMENT OF CHEMISTRY, COLUMBIA UNIVERSITY] The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives BY LOUIS P. HAMMETT The effect of a substituent in the meta or para position of the benzene ring upon the rate or upon the equilibrium of a reaction in which the reacting group is in a side chain attached to the ring may be represented by a simple formula which is valid within a reasonable precision in a surprising variety of cases. -RT In K + RT 111 Ko = AF = A/d2 (g + Bs) K is a rate constant or an equilibrium constant for a substituted reactant, KO is the corresponding quantity for the unsubstituted reactant, AF is a free energy change or its kinetic analog, d is the distance from the substituent to the reacting group, D is the dielectric constant of the medium in which the reaction occurs, and the quantities A, B1 and B2 are constants independent of tem- perature and solvent. Of these A depends only upon the substituent and its position in the ring relative to the reacting group (with one exception, the two values necessary for the para nitro group), while Bl and Bz depend only upon the reaction. The most important practical feature of equa- tion (1) is the separation of the effect of a substitu- ent into two constants, one of which depends on the substituent, the other upon the reaction. For this corollary of the equation the linear loga- rithmic relationships between equilibrium and rate constants which have been noted by myself1 and in wider variety by Burkhardt, Ford and Singleton2 offer a verification which has so far been made only qualitatively and by graphical methods. A more significant test may be made by obtaining a set of values of the constant A for various substituents from some suitable reaction or reactions, and determining quantitatively the precision with which these constants may be made to fit the data for all available reactions. For this purpose equation (1) may be rearranged to the form log K = log KO + up The formula is (2) where u = -d/2.303 R P = (2 + B,) (1) Hammett, Chcm. Rev., 17, 125 (1935). (2) Burkhardt, Ford and Singleton, J. Chem. Sod., 17 (1938). u is a substituent constant, dependent upon the substituent; p is a reaction constant, dependent upon the reaction, the medium and the tempera- ture. Since the only data available consist of values of the up product, it is necessary to assign an arbitrary value to some one u or p. The choice of a value of unity for the p constant in the ionization equilibrium of substituted benzoic acids in water solution at 25’ was determined by the large amount of accurate data availabe from the recent work of Dippy and co-~orkers.~ On this basis the difference between the logarithm of the ionization constant of a substituted benzoic acid and the logarithm of the ionization constant of benzoic acid gives the value of the u constant for that substituent. With the nucleus of u values thus provided, p values have been derived by least squares methods for other reactions, and from these in turn u values have been obtained for substituents whose effects upon the ionization constant of benzoic acid are unknown or inaccur- ately known. After any new u value was ob- tained it was used for the calculation of subse- quent p values, so that the order of the calcula- tions, which is that of the key numbers in the Tables, is of some significance. The criterion of the validity of equations (1) or (2) for any reac- tion is the precision with which the previously de- termined values of cr together with the experimen- tal values of log K satisfy the linear equation (2). As a measure of this precision I have used the median deviation of the experimental points from the best straight line, the “probable error” of a point.4 The results of such calculations for all the reac- tions I have been able to find are given in Tables ‘I, I1 and 111. Table I contains the values of the substituent constants u together with the symbol of the substituent, a key number to indicate the reaction from which the value was obtained, the number of reactions n for which data on the effect of this substituent are avaiIable, and the probable (3) (a) Dippy and Williams, ibid., 1888 (1934); (b) Dippy, Wil- liams and Lewis, ibid, 343 (1936); (c) Dippy and Lewis, ibid., 844 (1938) (4) Wright and Hayford, “The Adjustment of Observations.” D. Van Nostrand Company, New York, 1908, p. 132.Jan., 1937 STRUCTURB AND REACTIVITY OF BENZENE COMPOUNDS error r of the log K values calculated for this sub- stituent for these reactions. The data on reac- tions 28, 35, 36, 37 and 38 were not included in calculating the probable error because there was reason in these cases to doubt the accuracy of the measurement or the theoretical applicability of equation (1). Table I1 contains the p values for the various reactions together with a key number for the reaction, the best value of log KO in equa- tion (2), the number of substituents n for which data are available, and the probable error r of the calculated values of log K. Table I11 contains brief descriptions of the reactions and literature references under the key numbers previously used. In the descriptions E means that the data used are the equilibrium constants of the reaction described, R that they are rate constants. TABLE I SUBSTITUENT CONSTANTS Constant -0.660 - ,268 - .25 - .229 - .211 - ,205 - ,170 - .161 - .159 - .144 - ,069 - ,047 ,000 + ,009 + ,062 + ,115 + .15 + .I7 + ,237 + ,232 + .2ifj + ,337 + ,352 + .3i3 + ,391 U Source 2 1 3 4 31 21" 1 2 2 2 1 2 1 2 1 1 3 3 I I 2 1 1 1 1 + ,640 26,2i + ,678 26,2i + .ilO 1 + .ii8 1 +I ,000 4 +1.2i :I No. ,of reactions n 2 21 6 1 1 1 33 3 3 1 21 1 36 3 7 7 2 9 3 1 24 11 5 8 19 17 1 1 21 I5 4 8 Probable error r ... 0.077 .lo5 ... ... ... .040 .060 .023 ,038 .034 .22 ,066 .116 .lo2 ,040 , 040 . 0i3 ,083 ,039 ,041 ,035 ... ... ... ... ... ,069 ,066 ,042 ,053 A statistical factor of 2 was used in calculating the value of 8. &Naphthalene derivatives. To be used for the reactions of all benzene derivatives except those of aniline and phenol. To be used for the reactions of derivatives of aniline and phenol. Reaction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29


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PSU CHEM 408 - The Effect of Structure upon the Reactions of Organic Compounds

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