1750
R. R. BENERITO, H. 11.ZIIFLE, R. J. BERM,AND B. M. Bz4KTA
Vol. 67
THE KINETICS OF THE ZIKC FLUOROBORATE-CATALYZED HYDROLYSIS OF 3-(EPOXYETHYL)-7-OXABICYCLO[4.1.O]HEPTANE1 BY RUTHR. BENERITO, HILDAM. ZIIFLE, RALPHJ. BERNI,A N D BETSYM. BAI~TA Southem Regional Research Laboratory, A-ew Orleans, Louisiana Received December 10,1961 Kinetics of hydrolysis of 3-(epoxyethyl)-7-oxabicyclo[4.1.0]heptane (vinylcyclohexene dioxide) catalyzed by dilute zinc fluoroborate from 25 to 75" has been investigated. Semilogarithmic plots of changes in oxirane content with time indicated pseudo-first-order kinetics. Specific rate constants for opening of the endo- or ring oxirane ( k l ) and the ezo- or vinyl oxirane ( k z ) were determined by the method of least squares. Statistical evaluation of these data gave a ratio of kz/kl of approximately 0.02 a t 25". Analysis of experimental data by the modified Swain method confirmed the assumption of consecutive first-order reaction kinetics for the opening of the two rings and also resulted in a ratio of kz/ki of 0.02. Enthalpies, entropies, and free energies of activation for both oxirane rings were calculated. Large negative entropies of activation indicate an 6x2 mechanism for both ring openings.
Introduction Certain diepoxides which are relatively stable to hydrolysis find applications in the textile industry for chemical modification of cotton^.^-^ Pad baths of these diepoxides should be stable from room temperature up to curing temperatures even in the presence of catalysts used to promote cellulose-epoxide reactions. Although the literature refers to the ease of opening of oxirane rings, there ale relatively few diepoxides, and only two monoepoxides which have reacted successfully with cotton cellulose under conditioiis of acid catalysis, and these could not react with cellulose by Hfcatalysis only. Optimum conditioiis for etherification of cellulose rather than side reactions with solvents have been found to occur with zinc fluoroborate catalysis when the epoxide to catalyst molar ratio was approximately 10, and water to diepoxide ratio was less than 100, and preferably 50. Data on specific reaction rates of hydrolysis of diepoxides (0.8 144) in the presence of dilute zinc fluoroborate (0.05 M ) Tvere not available. Thus, as part of a program of comparing the kinetics of reactions between cellulose and various diepoxides in the presence of zinc fluoroborate, a knowledge of their rates of hydrolysis and their temperature coefficients from room temperature up to 90' was needed. This paper presents such a study of the kinetics of the hydrolysis of one of these diepoxides, vinylcyclohexeiie dioxide. The rates of hydrolysis were measured a t 25, 40, 60, 75, and 90'. Enthalpies, entropies, and free energies of activation have been calculated. Experimental 3- (epoxyethyl)-7-oxabicyclo[4.1.0] heptane Materials .-The (vinylcyclohexene dioxide), was obtained from Union Carbide Corporation and was used after distillation a t 227" under 1 atm. of pressure.6 The distilled product had a n epoxide value of 1.40 (equivalents of acid per 100 g.) as determined by Durbetaki method' and a characteristic infrared absorption band a t 12.22 p . (1) Presented before the Division of Physical Chemistry a t the Southeastern Regional Meeting of the American Chemical Society, Gatlinburg. Tennessee, November 1-3, 1962. ( 2 ) One of the laboratories of the Southern Utilization Research and Development Division, Agricultural Researoh Service, U. S. Department of Agriculture. (3) J. B. McKelvey, R. R. Benerito, B. G. Webre, and R. J. Berni, J . Polvmer Sci., 61, 209 (1961). (4) R. R. Benerito, B. G. Webre, and J. B. MoKelvey, TeatiEe Res. J . , 31, 757 (1961). ( 5 ) J. Galligan, A. M. Sookne, J. T. .Jdams, Jr.. €1. Guest, and G. H. Lourigan, ibid., 30, 208 (1960). (6) The mention of trade names and firms does not imply their endorsement by the U. 8.Department of Agriculture orer similar products or firms not mentioned. (7) -4.J. Durbetaki, Anal. Chem., 28, 2000 (1956).
The zinc Ruoroborate catalyst was obtained from the Harshaw Chemical Co. as a 40% aqueous solution (d% 1.0466 g./cc.). Procedure.-For the Zn(BF&-catalyzed rate studies, known weights (approximately 5 g.) of vinylcyclohexene dioxide were dissolved in 45.00 ml. of conductivity water containing 0.5626 g. of Zn(BF& and shaken in closed flasks immersed in an oil bath thermostatically controlled to 10.05'. The pH values of the reaction mixtures, measured with a Beckman Model GS p H meter to f0.02 p H unit, were found to be constant throughout the timed reactions. The p H values, followed from 0 to 24 hr. for the reaction mixtures at 25, 40, 60, and 75", %-ere2.55, 2.55, 2.56, and 2.57, respectively. For controlled rate studies in the absence of Zn(BF4)P,known weights of vinylcyclohexene dioxide (approximately 5 g .) were dissolved in 45.00 ml. of conductivity water which was adjusted to p H 2.55 with HCl. These rate studies were performed to see if the vinylcyclohexene dioxide at approximately 0.8 M in solutions of Hf of p H 2.55 were hydrolyzed a t the same rate as in the presence of the 0.05 M Zh(BF& catalyst. The observed rates for the zinc fluoroborate-catalyzed reactions were corrected for these controlled rates. Aliquots were withdrawn with 1-ml. serological pipets at timed intervals and transferred to tared erlenmeyer flasks. Weighed samples were analyzed for oxirane oxygen by the method of Durbetaki and corrected for blank determinations including water and catalyst in every case. All concentrations were expressed as milliequivalents of oxirane oxygen per gram of solution. The HBr reagent was standardized periodically. Treatment of Data.-Cartesian graphs showing the change in concentration of oxirane oxygen with reaction time were plotted a t each of the temperatures investigated. At each temperature, there was a change in slope beyond the half-concentration point. Semilogarithmic graphs of the data resulted in two intereecting straight lines suggesting consecutive pseudo-first-order reaction kinetics. The lines were determined by the method of least squares, and their slopes were tested by the statistical test for homogeneity of regression coefficients.* Thus it was established if the two rates differed significantly. The slopes of these lines, bl and bl, then were used to calculate the specific reaction rate constants, k I and k2, of the first and second halves of the reaction-the opening of the endo- or ring and the exo- or vinyl oxiranes, respectively. A t each temperature, the point of intersection of the two straight lines correspond to a 40% loss in total oxirane oxygen, T , or to an 80% loss in diepoxide, A. Initially, kl = 2bl but a t the time of 80% loss in A, kl = 2.57b1. Therefore, for all calculations of kl, the mean, 2.28, was used as a factor. For the second line, kp = bz. The correctness of the assumption of consecutive first-order reaction kinetics was further investigated by applying the modified Swain methodg as described by Frost and Pearson.ia The tabulated values, computed by Swain and showing time-percentage reaction relationships for various relative rate constants based upon successive first-order reaction kinetics, were plotted on semilogarithmic paper. These curves were applied to the (8) J. C. R. Li, "Introduction to Statistical Inference," Edwards Brothels. Inc , Ann Arbor, JIich., 1957, p. 344. (9) C. G. Swain, J . Am. Chem. Soc., 66, 1696 (1944). (10) A. A. Frost and R. G. Pearson, "Kinetlcs and Mechanisms," John Wiley and Sons, Inc., New York, N. Y., 1953, p. 158.
Sept., 1963
ECINETICS OF
HYDROLYSIS O F 3-(EPOXYETHYL)-7-OXABICYCLO[4.1.O]HEPTANE
experimental data obtained with vinylcyclohexene dioxide, and the relative rates of opening of the endo- and ezo-oxiranes of the zinc fluoroborate-catalyzed hydrolysis were determined. The relative rates are determined by Swain from only three points of the time-percentage reaction relationships-namely, 15, 35, and 70% completion points. Jnasmuch as measurements were not made a t exactly these points during these experimental hydrolysis studies, the observed data were plotted as percentage reaction us. time curves and interpolations were made for these three percentage points which then were used in the determination OP relative rates from the plots of Swain's data. Enthalpies, entropies, arid free energies of activation of both oxirane rings were computed from the determined rate constants.
Results and Discussion The intersecting straight lines shown in Fig. 1 are typical of those obtained when the logarithms of concentration of oxirane oxygen, T , are plotted against times in those hydrolysis experiments of vinylcyclohexene dioxide in the presence of zinc fluoroborate at temperatures under 75". To obtain kl from the slope, bl, of the first experimentally determined line, T = Toe-a1t,the equation
1751
VlNY LCYCLOHEXENE DlOXl DE
1.0 B
2S.C.
t
\
Q W
I.
a
w
.I
I
1000
2-
I
I
3000
I
4000
w
z 4 P 0 X
TIME WINS.),
was used, where A. is the initial concentration of diepoxide, A, x is the concentration of A forming monoepoxide, B, and the amount of B forming the diol, C, is considered negligible. The specific reaction rate consta,nts for the opening of the endo-oxirane (k,) and the exo-oxirane (k2) as well as relative rates determined by the least squares and Swain methods a,re recorded in Table I. The rate constants obtained by the method of least squares were those corrected for the control rates. TABLE I RATE CONSTAKTS FOR OPENINGOF endo- A N D exo-OxIRAm RINGS I N Zn(BF&-CATAI,YzED HYDROLYSIS O F VIXYLCYCLOHEXENE DIOXIDE
Temp.,
"C.
cSpecifio reaction rate constants---Least squaresKi = ---Swain--2.28b1 kz = ba kl kz ( X lo4) ( X lo4) ( X lo4) ( X lo4) min.-' mi%-' min.-' min.-'
Fig. 1.-Log of concentration of oxirane oxygen, T, in milliequivalents per gram of solution us. time in minutes.
Analysis by the modified Swain method confirmed the results at 25 and 40' yielding relative rates of 0.015 and 0.018, respectively. The relative rate a t 60' was not determined by the Swain method because of the inability to obtain accurate interpolations from the experimental percentage reaction vs. time curves a t the 15 and 35% completioii points. That is, there were too few points in the experimental data lying between 0 and 35% reaction to allow accurate determination of the shape of the percentage reaction-time curve in this region. Assuming consecutive first-order reactions 61
-Relat.ive
ratea-
Least squares k%/6i
Swain kz/ICI
25 111.99 2.58 143.9 2.07 0.023 0,015 40 410.08 10.78 431.2 7.84 ,026 .018 60 695.22 61.02 ... .. ,088 .. 75 ....a 304.8 ... .. ... ... a Reaction already past S O ~ . completion after only 2 min.
.
Phillips11 attributes increased activity toward acidic reagents of the endo-oxirane over the exo-oxirane to the peculiar st,ructure of epoxycyclohexane compounds and states that the cyclohexane ring limits free rotation in such a way as t'o minimize steric hindrance and enhance reactivity of the endo-oxirane. The hydrolysis proceeded too rapidly at 75 and 90' to permit determination of k1 by either the statistical or Swain analyses. At these temperatures, and short times, the reaction had already reached 50% completion. Statistical evaluation gave a ratio of kz/kl of 0.023, 0.026, and 0.088.at 25, 40, and 60°, respectively. (11) B. Phillips, "Peracetic Acid and Derivat,ives," Union Carbide Chemicals Company, Technical Bulletin P-57-0216,New York, N. Y., 1957, p. 13.
k2
A---,B+C values of A , B, and T were calculated by use of the experimentally determined specific reaction rate constants, kl and k%,of 111.99 and 2.58 mim-1, respectively. Values of A , B, and T were calculated from the equations
(3) T=2A+B (4) Figure 2 is a plot of the calculated concentrations of A , B, and T as a function of time at 25'. The experimentally determined values of T are shown as circles. The standard error of estimate was calculated to be 0.040. Enthalpies, entropies, and free energies of activation for the hydrolysis of the endo- and exo-oxirane ring openings of vinylcyclohexene dioxide are recorded in Table 11. To illustrate agreement between statistical and Swain analyses, the free energy of activation calculated by each method is given.
According to ot her i i i vest ign t orslJ- 18 cyx)?tidt.s uiidcrro nucl~ophilic fission ; ~ n dIiydro’ysis in the pwswiw of acids by cithcr a11 8x1 or an S N 2 meclianism a\ s1ion 11
VINYLCYCLOHEXENE CIOXIDE 21.C
znieF,)E
- cAr*mr
1
1 1;\1
.(*. --(‘
s l ~ ~ v
- -+
I
-.-(‘
I
\/
I
+J12o .-(‘-- &
T
i ;
fa’t
0
IIO
1 1
(’ -4;
+ II
110 0 1 1
I1 t I
0
10
I
I
20
30
I 40
1
I
60
10
70
S\Y
TIME (HOURS).
TAB1.E
I1
ROPIICR, AXl> I”REE I’;XER(:IES OF r~CTIVATIOiY
OF 0 x 1 1 ~ 4 OSYC~EN s~ RISG
OITSISGS O F
\.lSTI.CTCI,OIIEXI~~SE
I~1Oxrl)E
ol,‘.ning
Ihtiirrlpy All*, kci*l./iiiole
Entropy Sf, c:rl./nioku dog.
endo-Oxirane e.co-Oxirane
10. 1 li.8
-43.5 -26.4
Ring
c - F r c c cnprcy nt 25”,A F*, kcsl./mole 1. C B S t sqiiiircs
Swain
23.1 26.4
23.0 26.5
The apparent cncrgics of act~ivation(or enthalpies), A H * , were calculatcd from an Arrlienius plot, over t’hc tcmpcrat.ure range at which rate constants w r e dctcrmined. iZ plot of log 76 us. 1/T yicIdcd a straight liiic, the equation of which vas calculated t)y the mctliod of least squares. l‘alues of A H * rccordrd in Tablo I1 are comparable t,o t8hoscfound for solvolysis of oxirane , ~ ~ low enthalpy rings by ot.lier i t i v c s t i g a t ~ r s . ’ ~The value for the opening of the endo-oxiranc ring of vinylcyclohexenc dioxide, 10.1 kcal./molc, is significantJy different, from the apparwt activat.ion energy for the opening of the em-oxiranc ring. Entropies of activation, AS* (Table 11),ncre cslculattedfrom the cquat.ioii
0
liO
I3y botli mccliaiiisins the reactmi 11ould follow firstorder kinetics according to the experimcrit a1 conditions of this investigation. Honevcr, orily by the Szr2 mcclianisni would the orientation factor be important and rPSiilt in a large negative mtropy of activation as it is only 11y the latter meclianism that the transition state complcx involves the bonding of one or more v-atc.r molecules. Such a mechanism VI ould produce a change in riitropy of activation of the sanw order of magnitude brought about by thc loss in translation energy of water molecules on forming the transition state complcx. The large negative values for cntropirs of activation observed in thcsc hydrolysis studies indicate an S Km~chanisrn.1~.~* ~ For comparative purposes, t h t specific reaction rato constants for tht: hydrolysis of vjI,ylcyclohe.uc.nc. dioxide (0.8 M ) at pII 2.55 in the absence of zinc fluoroborate n-ere mcasurcd at 25, 40, 60, and 73”. Tlic values of these rate conytants recorded in Table I11 show that these mtcs are mallrr than tliosc obtained in the pr(wnce of Zn(B ’4)z. The frw cncrgics of activation for thc. rcaction at 25” and at pIT 2.55 iii t l i r ahscncc of zinc fluorot)or:ttc ~ v c r cfound to h 25.4 and 30.3 k w l . mole-’ for tlio opcriiiig of tlie endo- aiid e ~ o oxi r a w ri I igs, rcspect iwly. TABLE 111 RATEC O ~ S T Z X ron T ~OIJEYISGOF TIIB endo-
(0) .is slionn in ‘I’ab!c JI, a sniallw dccwuse iii entropy of activatioii was obs(11~v(d\\it 11 tlic opming of thc cso-ring of vinylcyclohcx.rric dioxide. T h e grcatcr decrease in entropy observed in thc. case of tlic hydrolysis of t he cndo-osiraiicx ring would indicate a inore ordcrcd transition statc complcs. I l o w c v ~ r tlie , very low enthalpy obsc~vcdin tlic hydrolysis of the endooxirane ring ixwdtcd in a smallrr frec cncqy of activation, thus making the opening of the endo-ring proceed more rapidly than that of the e.ca-ring. (12) J. Iioskikiillio nnd E W h u l l ~ y ,Trans. F a r n d w Soc , 66, 813 (Iq50). (13) F. .i. J,onp, J. G. I’ntrliarcl, irnrl 1;. S. Stafford, J. Am. Chern. SOC., 79, 2362 (1957).
Tinip,, O C .
23 40 GO C r 13
AKD
em-Oxiizmis
H Y D R 0 L . l SIS OF V I Y Y L -
ClCl.OIiEXEhE I ~ I O X I D EAT
AF* = AII* - TSS*
011
11+
R I S G S IN TIYI)RO(rLN IOh-C.\T.il,YZCD
vlic~rrli is Ilic Iiydrolyds constaiit iii s:c>c.-’; AI]* ilci tlic c.nthalpy of activatioii; arid I?, K , and h arc the molar gas, Boltzmalin, and Planck constants, n~ywctivcly. 1:icc. ciicrgics of activation, AI‘’*, at 2.5” \ v ( ~ wcalculatcd from tli
