Feb. 5, 195s
REACTIONS OF
545
DIPI~ENYLDIAZOMETHANE WITH BENZOIC =2CIDS
results in the formation of a variety of products mainly as a result of free radical chain rea~tions.~e From the available evidence it seems that the thermal decomposition of methyl cyclobutyl ketone may be a unimolecular reaction. Since no significant fall-off in the rate constant was detected a t 10 mm., the pressure region of the fall-off appears to be below that of cyclobutane4 as might be anticipated for a molecule with a greater number of vibrational degrees of freedom. The frequency factor for the decomposition lies within the limits expected for a unimolecular reaction. The frequency factor A of a unimolecular gas reaction can be expressed as A = Ke(kT/h)eAsS/R
where K is the transmission coefficient and A 9 is the entropy of activation.l* From the experimental value of the frequency factor and with the assumption that the transmission coefficient is unity, one can calculate that the entropy of activation a t 400' is +4.3 cal./deg. mole. A positive value would be expected for a reaction involving the cleavage of the ring. In comparison with the thermal decompositions of cyclobutane; and ethylcyclobutane6 the activation energy for the decomposition of methyl cyclobutyl ketone is 7.5-8.0 kcal./mole lower. Although this decrease in activation energy is partially compensated by a lower frequency factor (smaller apparent entropy of activation), the methyl cyclobutyl ketone decomposition takes place a t temperatures approximately 50' lower than the decompositions of ethylcyclobutane and cyclobutane (for similar rates). I n this connection i t is to be noted that the product methyl vinyl ketone possesses some resonance energy which would not be associated with the corresponding product in the
decomposition of ethylcyclobutane or cyclobutane. The effect of resonance in the product may result in some lowering of the activation energy if the decomposition proceeds by a direct formation of methyl vinyl ketone and ethylene. As an indication of the resonance energy of methyl vinyl ketone, there is the value of the resonance energy for crotonaldehyde which was reported to be 2.9 kcal./ 1110le.~~On the basis of certain corrections for polar and hyperconjugation eff ectsZ0a higher value (7.3 kcal./mole) has been suggested recently. If the rate-determining step in the decomposition involves the formation of a biradical (by the breaking of the ring C-C bond nearest the carbonyl group), there should be more resonance in the biradical formed from methyl cyclohutyl ketone than in the corresponding biradical from an alkyl derivative of cyclobutane. The presence of any resonance in the biradical should lower somewhat the activation energy of the formation of the biradical from methyl cyclobutyl ketone. In the comparison of the present results with those from the decompositions of other four-membered ring compounds i t was observed that the frequency factor and the activation energy for methyl cyclobutyl ketone are much closer to those of cyclobutanone (k = 3.G X 10l4e-52000/RTsec.-l) than t o those of ethylcyclobutane or cyclobutane. Acknowledgments.-The authors wish to acknowledge the financial assistance of the Celanese Corporation of America a t the start of this study and the subsequent financial support of the Kational Science Foundation over the major portion of the investigation. They also wish to thank hlr. Carl 'IVhiteman for making the infrared absorption measurements.
(19) M A Dolliver, T L Gresham, G B Klstlakowsky, E. A Smith and W E Vaughan, Ti115 J O U R N A I , 60, 440 (1038). (18) S. Glasstone, K. J. Laidler and H. Eyring, "The Theory of (20) 11 h1 Kreevoy and R \V 1 a f t , Jr , % b i d ,79, 4010 (1057). Rate Processes," McGraw-Hill Book Co., Inc., New York, N. Y., ROCHESTER, NEWYORK 1941. p. 298.
[CONTRIBUTIOXFROM
THE
DEPARTMENT O F CHEMISTRY
O F TIiE
.%.
AND
hf.
COLLEGE O F TEXAS]
Quantitative Relationship between Structure and Reactivity for the Reactions between Diphenyldiazomethanes and Benzoic Acids in Toluene at 2.5' BY c. KINNEYHANCOCK AND JOHN
s. WESTMORELAND
AUGCST 26, 1957 RECEIVED Rate constants a t 25' have been determined for the reaction of dipheiiyldiazomethane (DDM) with twelve m- or psubstituted benzoic acids (XBA's) in toluene. Correlation analysis of the data yields eq. 2: log k , = -0.1023 2.5132~~ with r = 0.9947 and s = 0,0913. I n a previous article,' correlation analysis of the data for the reaction of benzoic acid (BA) with twelve m- and/or p-substituted diphenyldiazomethanes (XDDM's) yielded eq. 1: log kz = -0.1440 1.5702~~ with 7 = 0.9987 and s = 0.0442. If the structures of both reactants are varied simultaneously and the two effects are independent, it appears that the resulting data would be closely represented by eq. 4: log kp = -0.1231 - 1 . 5 7 0 2 ~ $- 2 . 5 1 3 2 ~ ~ where -0.1231 is the average of the intercepts from eq. 1 and 2, -1.570 and $2.513 are ,OD and ,OB from eq. 1 and 2, and 20 and ~ U are B the summations of U-values in the X D D M and in the XBd. Rate constants a t 25' have been determined for twenty-one reactions of X D D M ' s with XBX's in toluene. For these reactions plus two others from ref. 6, substitution of 2 0 and ~ U values B into eq. 4 yields calculated log k? values which show an average deviation of 0.084 from experimental log k2 values. For the forty-six available reactions of X D D M ' s or D D M with XBA's or BA, the analysis of the multiple ~ R = 0.9975 and s = 0.0783. The very close fit of regression yields eq. 5: log k2 = -0.1089 - 1 . 6 2 0 2 ~ ~2 . 3 7 6 2 ~with eq. 5 offers conclusive evidence that the effect of m- and/or p-substituents on the D D M is independent of the effect of m- or p-substituents on the BA.
+ -
+
Introduction Of benzoic For the reaction at 250 in acid (BA) with diphenyldiazomethane (DDM) and
with eleven m- and/or +substituted dbhenvldiazomethanes (XDDh's); it has been shown' tdat (1) C. K. Hancock, R. F. Gilby, Jr., and J. S. Westmoreland, THIS 79, 1917 (1957).
JOURNAL,
log kz = -0.1440 - 1 . 5 7 0 2 ~ ~
(1)
with a correlation coefficient Y of 0.9987 and a standard deviation from regression s of 0.0442. In equation 1, -0.1440 is the value of (log k2°)ca~cd., - 1.570 is the slope PD of the regression line, and ZUD is the summationza of Hammett's3 polar constants for the X D D M substituents. For the reaction a t 30" in ethanol of DDXI with BAland with five m- or $-substituted benzoic acids (XBA's), Roberts, et found a pB-value of 0.937 for the regression of log k2 on U B . Later, using the same temperature and solvent, for the reaction of DDM with BA and with seven nz- or p-substituted XBA's, Benkeser, et al.,b found a pB-value of 0.929 for the regression of log kz on UB. Four of the XBA's were identical to four of those that were studied by Roberts, et nl. The objects of the presently reported study were: (1) to determine the relationship between log kz and Z ~ for B the reactions of DDM with m- or p substituted XBA's in toluene a t 25", (2) to obtain kz-values for reactions between m- and,/or p-substituted XDDM's and m- or p-substituted XBA's in toluene a t 25" and (3) t o determine the relationship between the effect of varying the structure in the XDDM and the effect of simultaneously varying the structure in the XRAL Experimental
slight residual O D at t h e wave length measured. For the following reasons, i t was concluded t h a t this small residual OD was due to an uiireactivc impurity t h a t was initially present in the XDDM solution: (1) Xorris and Strain6 concluded t h a t colored solutions resulting from t h e complete reaction of 4,4'-dimethyl-DDhl with several XB.4's were due t o di-p-tolylketazine t h a t mas initially present in the reaction mixture, (2) simultaneous runs of several different XB.S's with the same XDDRi preparation yielded solutions with the same residual OD, (3) different preparations of a particular X D D M gave differelit residual OD's when reacting with t h e same XBA and (4) on standing, decomposition of the XDDM solutions mas observed and reaction of an aged XDDM solution with any XBA gave a higher residual OD than t h a t resulting from t h e use of a fresh solution of the same XDDM with the same XBA. Since non-interacting cnlored substances in the same solution give additive OD's,' in runs in which a measurable residual OD persisted after complete reaction, t h e residual OD was subtracted from each OD reading taken during the run. 1)ata corrected in this manner gave n-ell-a!igned plot 5 of log OD zieysus time.
Results and Discussion Average kz-values and corresponding ZuB-values for the reactions of DDM with XBA's are given in Table I.8 For 3,5-dimethyl-BLl,Z U B is twiceza Hammett's U-value for the 3-methyl substituent. Excluding the data for 3-methoxy-Bh and using a U-value of - 0.361 for 4-methoxy-RX, statistical treatmentga of the data of Table I yields with r = 0.99-L7 and s = 0.0913.
lOg k? = -0.1023 f 2 . 5 1 3 2 ~ ~ (3) Materials .---All of t h e XB-4's were procured froin coinTABLE I inerciat sources and, where necessary, were recrj-stallized until melting point values agreed closely with previously RATEA S D SUBSTITUEST COSSTAXTS FOR THE R E A c , r I o N S OF reported reliable values. Other materials already have DIPHEST(1,DIAZOiMETHBNE WITH SUBSTITUTED I 3 E S Z O l C ACIDS been described.' I N TOLUESE AT 25" Rate Measurements .--The general procedure has been Benzoic acid kr, , described pre2iously.' Because of limited solubility in I . mole ~1 min. - 1 Ya,,2",3 substituents toluene a t 25 , it was necessary t o reduce the initial mo3 S i t r o 4 0 . 0 +o. 710 larities of three of t h e XBX's t o t h e values innicaterl: &Bromo8.59 ,301 3-iOdo-, 0.02; 4-methoxy-, 0.01 ; &nitro-, 0.006. I n all cases, a ten-fold excess of X B h over X D D M was used. 3-ChloroT.O1 ,373 With 3-nitro-BA, matched cells with 5 cni. light paths were 3-Iodotj,G2 ,352 used because of the low initial optical density (OD). 3-Methosy0.773 - ,003" Matched cells with 1 cm. light paths were used in all of the . CjA.?'' no0 ;\'one other reactions. Due t o short half-lives. after mixing the reactants a t 25' and transferring a portion of thc reaction :j-iVZethyl. 4ot-1 - .IJW mixture t o the spectropliototneter cell, these reactions .+Isopropyl, 20t5 1.51 were followed on this sample in tlie ccll: I l D b I :ind .l-hIeth>-l.20.'i -- , 1iO 3-nitro-BA; 4,4'-dibronio-DDAI ant1 3-iiitro-B.\; 1)I)R'il 3,s-D imet li y I ,270 -- ,138 and 3-chloro-BA; D D M and 3-broino-B.\; 4,4-t!inictlloxyD D M and 3-bromo-B.4; and D D h l nuti 3-iodo-Bn. +-Butyl, 2T75 - ,197 Three or niore determinations of kz were lnatie on euch re3-hlethoxy140 - ,301' action. T h e aT7erage deviation from the 11 b Agrees n.itll vnlues of 0.040 in Caicd. from ey. 3 . K2-values exceeded 27' in onl>-the cases of t From Ref. 1. reactions: 3,3'-dinitro-I)Dhl ant1 4-lnethyl-B.~, 2.Rm~; ref. 1 and of n.642 in Kef. 10. 4-chloro-DUM and 3 - b r o l n O - ~ ~ .S.lyc. ~, Tlic inaxirnum In equation 2, -0.1023 is the value for (log deviation from tlie i m a n exceeded 35: iii only the c x e s of k?O)calcd.,+2.513 is the slope PB of the regression t h e following four reactions: D U M alii1 3-bromo-B:1, 3.6$o; DDhI and 4-t-l)utyl-B.\. 3.6%; 3,3'-rlinitro-I)D~'I line and Z ~ isB the summation of Hammett's polar and 4-nietliyI-B.\, 4.1 r { , ; 4-chloro-IlLlRJ slid ~5-l~ronio-B.l, constants for the XB-4 substituents. It is ap-
+ +
-
Q
3.1YC.
Twelve other XB.I's n.ere procured from cornniercial sources hut were not used because of low solubility in toluene a t 25'. I n geiieral, i t appeared t h a t 3-substituted B.4's were niore soluble in toluene a t 2.5' thrin were 4-substituted B:!s.' and this accounts for t h e prevalence of tllc former in Tables I and 11. In some cases, after complete reaction of an XIlI)3I with an XB.4, the solutioii had :L slight yellow color and a ( 2 ) (a) EX 1% Jaffb. Che'in kc^;^.., 5 3 , 250 ( I g i 3 ) ; ( L l 5 3 , 2 , 5 $ (1!1.5:3); ( c ) 53. 251 I l R 3 3 ) (3) I, P.F-Iammett, "Physical Organic Chemistry," M c G r a w - H i l l Book C o . . I n c . , h'ew York. h7,Y . , 1940, p. 188. (4) J , D Kuberts. E. A . RlcElhill anrl R. Armstrong, T H I S J O U K N A L , 71, 2!123 (1949). ( 5 ) R. A . Renkeser, C. 1'. I h B o e r , K. 1s. Kol,in.;ori a n d D. AT. Sauve, ibid. 78, 6 6 2 (19%iB).
parent that the data of Table I are closely represented by equation 2. By minimizing the squares of the deviations along the SuB-axis,2bequation 3 is obtained. Zurj = f0.0410 + 0.3038 log k? (3) (G) J. 1:. h'orris anrl W. H . S t r a i n , i b i r j , , 5 7 , 167 (1933). ( 7 ) 1'. D . Snell a n d C . T. Snell, "Colorimetric l l e t h o d s of Analy I n c . . Srir 1 7 0 r k , S . Y . . 1918, p. 1s. u f J . d \ ~ ~ ~ . , t n i ~ ~ r ~ The l . i t i A. ~ l , ; ~ n d\ I College of 'Texas. Jan., I! tistical Rfethuds." .It11 P;d., T h e IO\V.I S t a t e College Press, .\nirs, Iowa, I!ll('i: ( : i ) Cli:~],,0 a n d 7 , ( b ) Chali.
13. (10) A. B. Iloefelnicyer u n d C. Ii. ITancork, 'TrIrs 4716 (19%).
JC)IJKXAI.,
77,
Feb. 5 . 1958
Substitution of the log k p value for 3-methoxy-BA in equation 3 yields a U-value of -0.003. For the 3-methoxy substituent, Hamniett3 gives a U-value of +0.115 with a probable error of 0.102. In view of the large uncertainty in Haminett’s value (the prob‘ible error for 3-inethoxy is fourth largest of twcnty-nine probable errors listed in ref. 3), i t appears for the 3-methoxy group that -0.003 is not significantly different from +O.lIZ and that the former value is probably more applicable to the present reaction. Average k2-ralues and corresponding SUD and ZCB values for the reactions of XDDM’s with XBX’s (including two reactions from Norris and Strain)6are given in Table 11. TABLE I1 RATEASD SUBSTITUENT COSSTASTS FOR
THE
REACTIONS OF
SCBSTITUTED D I P H E S Y L D I A Z O M E T H ~ N E SWITH SUBSTITUTED
RENZOICACIDS I N TOLUEXE AT 2 j 0 Diphenyldiazomethane substituents 4,4’- Dime thoxy4,4’-Dimethyl4,4’-Dimethyl4,4’-Dimethoxy4,4‘-Dibrorno4,4’-Dimethoxy4-Chloro4,4’-Dimethyl4,4’-Dichloro4,4’-Dimethyl4-Chloro4-Chloro4-Chloro4- Chloro4,4‘-Dichloro4,4‘-Dibromo4,4 ‘-Dichloro4,4’-Dichloro4,4‘-Dibromo4,4‘-Dibromo3,3’-Dinitro3,3’-Dinitro3.?’-Dinitru-
Benzoic acid substituents %Bromo:%Bromo8-ChloroX-hlethoxy:%Nitro4-llethyl3-Bromo3-Methyl3-Bromo4-t-Butyl3-lIethyl4-t-Butyl4-Slethpl3 5-Dimethyl:i-Methyl:i-hIethyl4-Methyl3 , 5 - Dimethyl4-t-Butyl3,j-Dimethyl%Bromo3.5-Dimethyll-\iIethyl-
a Ref. 1. b Ref. A . ported in ref. 6 .
k2, l./molemin. 88.1
zor,
Zas
- 0 722a ,340 ,340 ,722”
t0.391 ,391 ,373 - ,003c t ,7111 - ,170 ,391 - ,009 ,391 - ,197 - ,069 ,197 - ,170 - ,138
-
?.j.flh 2 3 .ih
14.6
+ +
