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2688 A. R. OLSON N D R. J .MILLER Vol. 60aqueous solution to yield one optical form of hy-droxybutyric acid exclusively and reacts with hy-drogen ion and hydroxide ion by two other mecha-nisms to form the other optical isomer.

-0.4 I //

I@ //

j- 1 0 2 4 6 8 10

PH.Fig. 1.-Velocity of hydrolysis of malolactonic acid.80r--

- 10 2 4 ti 8 1012Fig 2.4ptical form of malic acid pro-duced by hydrolysis of (+) malolactonicacid.

w .

The j3-bromobutyric acid was prepared byJohansson's8 method. The acid was resolvedwith morphine in methyl alcohol Repeated re-crystallization of the acid yielded a product whichhad amolar rotation of +116.5' in2N perchloricacid. This solution was 0.1632M with respect tothe @-bromobutyric acid. In water alone lessthan 1% decrease was observed. ,4 0.2361 J l fsolution of the sodium salt had a molar rotationof 106.6'. The melting point of the purest acidwas44'. The 0-butyrolactone was prepared fromthis acid by Johansson's procedure.Hydrolysis of the j3-Butyrolactone.-The lac-tone was weighed in volumetric flasks which thenwere filled to the mark with the solvent used forhydrolysis. The change of optical rotation withtime and the final value reached were then ob-served using the polarimeterg described pre-

(8) Johansson, Ber., 4& 1256 (191.5).(0) Olion and Long, TH x s J O ~ A L ,16 1284 (1934).

viously. This was a Bellitlgham and Stanley in-strument designed so that 30-cm. polarimetertubes in a thermostat with glass windows could beplaced in the optical path. The thermostat washeld at 25.0 * 0.05' by means of a mercuryregular and heaters. Light from a mercury lampfiltered through copper sulfate glass and a Wrat-ten Yo. 77 filter was used for the readings withthe Hg 5461 line. Unfiltered light from a sodiumlamp was used for the sodium D lines. All read-ings were made to the nearest hundredth of a de-gree, and, except for the faster kinetic runs, themean of six to ten readings was taken as an ob-servation.Results and Discussion.-It was known fromthe work of Johansson4 that the hydrolysis of thelactone involves not only a first order reaction withwater but also a second order reaction with hy-droxide ion. In those solvents, therefore, wherea change in the hydrogen ion concentration wasapt to prove troublesome, we used buffers. InTable I we have collected the rate constants invarious solvents. Those marked with an asteriskare copied from Johansson, who used a titrationmethod for following the rate. In Fig. 3 we haveplotted the rates which haye been determined inthis Laboratory, against thepH. For the7.87 il.7sulfuric acid the activity of the hydrogen ion wastaken arbitrarily as7.87. The solid line in Figure3 is the plot of the total rate at various hydrogenion concentrations as calculated from the well-known equation for the catalytic catenary-d log, (lactone)/dl = k = kH.0 +k a ( H + ) +koH(OH-)where kH!oand koH were determined by Johans-son and kH was determined in 2 N perchloric acid.

TABLEEXPERIMENTALA I SSolvent

7 87 i?:HnSC)(2 A HC10,Water0.665 $1HzPOi-, 1.00MHPOa, PH 6.80 60 A4 HCOj-, 2.18&I

COS' pH 10Water*Water*Vi'ater *0.604 M "Os*0.0601 M HNO**0.00600 M HNOa*0.00400M NaOH*0.00200M NaOH'

Molar concn.of lactone0.288

,1685,789,1890,207.608.0600.00600,603fO599.00600.0040000200

First orderk X 10'

72127298008.08.89 . 19. 28.79.0

c - 49c - 9

Second order

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Nov., 1938 MECHANISM'F THE AQUEOUS YDROLYSISF &BUTYROLACTONE 2689The lack of agreement between some of our pointsand the solid line will be discussed in a later sec-tion in connection with salt effects. The detailsof the calculation of the solid line are found inTable11. The last column in the table is useful inconnection with the discussion in a later section.

TABLE1CALCULATEDATESd log,[lactone]- dtor k =8.5X = k = k ~ 9 0f RE(H+)+~oH(OH- )+2 X 10-4(H+)f 49(OH-).

kH (H + ) ko~(OH-1 kH lO x 1009H x 104 x 104 k X 104 k- 2 200 208.5 4.2- 1 20.0 28.5 29.8- 0.5 6.3 14.8 57.40 2.0 10.5 81.01 0.2 8.7 97.0

2 .02 8.52 99.73 *002 8.502 100.04 8.5 100.05 8.5 100.06 0.0049 8.505 99.97 .049 8.55 99.48 .49 9.0 94.58.5 1.5 10.0 85.09 4.9 13.4 63.59 5 15.0 23.5 36.010 49.0 57.5 14.811 490 498.5 1.712 4900 4908.5 0.2A change in the hydrogen ion concentration of

the solvent in which the 6-butyrolactone is hy-drolyzed produces not only a change in the rateof hydrolysis as discussed above, but producesalso a change in the ratio of the amount of (+)hydroxybutyric acid to the amount of (-) hy-droxybutyric acid in the product. In order todetermine this ratio the observed final rotationfor each run must be corrected for the opticalpurity of the initial lactone. The corrected finalrotation must then be compared with the molarrotation of pure hydroxybutyric acid in the samesolvent. The correction was obtained by com-paring the molar rotation of the bromobutyricacid from which the lactone was made with the ro-tation of the highly resolved bromobutyric acid.In Table I11we enumerate the correction factorsfor the four preparations of bromobutyric acidwhich were used in this work. In Table IV welist the molar rotations of an optically impuresampleof hydroxybutyric acid in the various sol-vents. Since the molar rotation of this sample ofhydroxybutyric acid in water was only 18.5' wehave multipliedall the experimentally determined

0-2 0 4 8 12fiH.Fig. 3.-Rate of hydrolysis of8-butyrolactone.

molar rotations by a factor to obtain the rotationof pure hydroxybutyric acid. In Table V wehave collected the data from the runs concernedwith the optical form of the product. The firstcolumn indicates the preparation of bromobutyric.acid from which the lactone was made, the second

TABLE11Prepn. of 116.5 divided byB-bromobutyric Molar rotation this molar rotationacid from which of this acid or correction factorlactonewas made in 2 N HC104 to rotationI 50.4 2.31I1 86.8 1.343

I11 104.0 1.120IV 100.7 1.158TABLEVSOLVENTSFree acid in aqueous solution, [M I z6~5.9'. Sodiumsalt, c = 0.13M, M l e 6 ~7.5" Hg 5461 calibration using5 cc. of 0.789 M acid solution of [ M I z 6 ~8.5" diluted to25 cc. with solvent, giving the concentration of P-hydroxy-butyric acid = 0.789/5 =0.1578 M in all solvents exceptwater where the original 0.789 M solution was used.

ROTAT ION^ OF HYDROXYBUTYRIC ACID IN VARIOUS

25.9Solvent a IMl:6,61 x 18.67.87N H&Od 1.12 23.6 33.1Acetate bufferAc- =0.8M , HAC= 1.03 21.7 30.4

Water 5.10 21.5 30.1PhosphatepH 6.8, 0.665 0.77 16.2 22.73.2M, H 3.85MH~POI- ,1.0MHPO,'CarbonatepH 9,2.00 M .77 16.2 22.7

Carbonate pH 10,0.6 ilk .76 16.0 22.46N NaOH .62 13.1 18.4

HCOa-, 0.72M CO,'HCOa-, 2.18M COS'(10) McKenzie, J . Chcm. Soc., S i , 1402 (1'30%).

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2690 A . R.OLSONAND R. . MILLER Vol. 60TABLE

Prepn.II11II11II1I11I11I

I11I11II V

.%v ent7.87 A H2SOa2 N He104Formate buffer, PH 2.8Acetate buffer, HAC=3.2M , Ac =0.8M , PH 3.8WaterWaterWater0.665MHzPO,-, 1.0MHPO,, fiH 6.82.00 MHCOa-, 0.72 MCOa, PH 90.60M HC03-, 2.18MCO$, fiH 100.140M NaOH6 N NaOH6 N NaOH

Initialmolarconcn.olactone0.288,1685.363,1319,113,789,1932

.1890

.118,207.140,308.249

Obsd.finalrotationof s o h [Ml::s~-0.65 - 7.5.13 2.61.36 12.51.02 27.0

0.40 11.85.10 21.54.37b 18.51.54 26.41.326 22.71.14 20.00 . 00 0 .0- .40 - 6.4- .63b -15.0- .65 - 7.0-1.07 -14.3

a I n the absenceof experimental data rotation in water was used. ndicates runs made with sodium light.the solvent in which the lactone was hydrolyzed,the third the initial molar concentration of lac-tone, and the fourth was observed final rotation.The percentages of (+) hydroxybutyric acid inthe product as calculated from the corrected rota-tions are shown in the last column of TableV andplotted against the PH in Fig. 4. Where an un-buffered solution was used an arrow shows thechange inpH during hydrolysis.

-2 0 4 8 12Fig. 4.-Optical form of hy-droxybutyric acid producedby thehydrolysis of (+) 6-butyrolac-tone.

PH.

If we assume that (+) j3-butyrolactone reactswith water molecules to formonly (+) hydroxy-

-17.32.928.830.227.028.924.829.725.422.40.0

- 7.2-16.8-16.1-16.5

Rotationof pure&hydroxy-butyricacid insolvent33.1(30.115(30.1)30.630.130.125.930.125.922.722.722.417.518.418.4

Corrected[MI X 100dividedby rotationof purehydroxy-butyric acid

- 2109698.790969698.798.098.60

-32- 6- 8- 0

Per cent.(+)form24559899.495989899.399.099.35034265

butyric acid and with hydrogen ions or hydroxylions to form only (-) hydroxybutyric acid, andif we combine these assumptions with the rates asdetermined in the preceding sections, we can cal-culate the percentageof (+) hydroxybutyric acidformed in the various solvents. This we havedone with the aid of the last column in Table I1and have plotted the results as the solid line inFig. 4. The agreement between the experimentaland calculated percentages is quite satisfactoryexcept for the point at PH of 10and the point in6 N sodium hydroxide. The agreement for thepoint corresponding to 7.87N sulfuric acid is ofcourse due to our arbitrary selection of an ac-tivity for the bydrogen ion. If we had calculatedthe activity from the mean activity rule of Lewisand Randall, the point would have come to theright of that for 2 N perchloric acid. This pro-cedure of course neglects a specific contribution tothe rate by the acid sulfate ion. That this ioncontributes to the rate ismade very plausible bythe work to be discussed later in connection withcarbonate ion.

The low rotation in the6 N sodium hydroxidemay be due to reactions producing unsaturatedcompounds such as is observed with bromo-butyric acid in alkalinesolutions.(11) Lewis and Randall, Thermodynamics, McGraw-Hill Book

Co., Inc.. NewYork,N. Y., 923, pp. 328and 357.

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Nov., 1938 MECHANISMF THE AQUEOUSHYDROLYSISF 0-BUTYROLACTONE 2691Postponing for the present the discussionof the

point atPH 10,we can conclude that the compos-ite reaction isthe resultant of the three reactions.

In Fig. 3 the point corresponding to the hy-drolysis of a 0.789M solution of the lactone inpure water shows a slower rate than that calcu-

lated fora0.15M solution. Thisis in agree-* \ / o /H *v ment with Johanssons work in which it was

found that the first order rate constants de-creased as the concentration of the lactoneI increased. We already have mentioned theH difficulty of assigning an activity to the hy-

drogen ion in the 7.87N sulfuric acid. Inaddition to this the rate also should deviate

H CHs H CHs+ -o C4-H -I- 2I I0-C-C-H\HH 4 - H 0-CO=C-] AHI

*vH

H CHa H CHs +H +*v+ H + C+ 0-C II I

O I C - -H O=C-C-HAO HIO HAH H IH

H CHa H CHn* \/H-&H 0-CI I * \/+ --O-C I +

I0- HII I0 - H

HThese reactions are written in conformity withthe principle that inversion occurs for every sub-stitution. The formation of the lactone from thebromobutyric acid must have involved an inver-sion even though there is no change in rotation,for the action of phosphorus pentachloride on(-) hydroxybutyric acid or its ester produces a(+) chlorobutyric acid12 or its ester, respectively.It is of interest to recall in this connection that(+) bromosucciiiic acid produces a lactone withnegative rotation. The lactone is in reality aninner ester. The breaking of the carboxyl oxy-gen bond under acid or alkaline conditions is inagreement with the hydrolysis of esters undersimilar conditions.13 The hydrolysis of the lac-tone by molecular water is fast enough to be ob-served. In this case it is the alcohol oxygen bondwhich is broken. Due to the fact that we usedoptically active materials, we see that the bigspeeding up of the reaction by hydrogen ions andhydroxyl ions therefore does not necessarily in-volvea catalysis of the water reaction, but ratherthe acceleration of independent, competing reac-tions. In view of these results we must disagreewith Waters,14 who states Without exceptionhydrolyses are ionic reactions. . .

(12) Fischer and Scheibler, Ber . , 43 , 1219(1909).(13) (a) Holmberg, ib id . , 46 , 2997 (1912), and (b) Polanyi and

from that calculated foradilute solution dueto the changes of the activity of water andof lactone as we go to such a concentratedsolution. These effects are likewise veryprominent in the runs with phosphate andcarbonate buffers where the salt concentra-Hzo tions are several moles per liter. Thus thevelocity of the run in the phosphate solutionisabout three times the calculated rate. Adistribution experiment using dibutyl etheras he second solvent showed that the activity

of the lactone in the phosphate solution was abouttwice as great as it was in water solution, account-ing for the major portionof the rate change. Therun in the carbonate buffer cannot be explainedin this way, for here we get not only a thirteen-fold increase in the composite rate but also achange in the optical ratio of the product. Thisratio would not be changed by a change in the ac-tivity of the lactone. Therefore, even after allow-ing for a two-fold change in the activity of the lac-tone by the salt, we find a five-fold increase in therate of the reaction with hydroxide ion and fifteen-fold increase in the water reaction rate. If wethink of the carbonate ion in solution as hydratedand write a structure for it :o :c:o:~:o:,we see that the water in this complex is interme-diate between molecular water and hydroxide ionsince the hydrogen which forms the bond is nolonger completely the property of the water.Assuming that the behavior of such a particle isintermediate between that of hydroxide ion andmolecular water, we would expect the observedchanges in the rates and products.Reactions of P-Bromobutyric Acid.--The dis-appearance of P-bromobutyrate ion in aqueoussolution at 25 gavea first order rate constant of1.09 X mn.-1. Runs which were followed

:o,.. .. ..

Szabo, Trans. Faraday Sac., SO, 508 (1934).and Sons,La., ondon,p. 282.

by Volhard titration or by change of optical rota-tion gave identical results. The rate of this re-(14) Waters, Physical Aspects of Organic Chemistry, Routledge

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2692 A. K . OLSONAND K . J .MILLER Vol. 60action at 38' was found by Johansson8 t o be0.0093. Combining these results we get .E. =1.3 X 1017e-zs~800~Rrsec.I . Later J ohans~on'~found that at 32" about 159'0 of the P-bromo-butyrate decomposed into propylene, carbon di-oxide, and bromide ion. At 25' we found a 17%discrepancy between the production of bromideion and of acid after the hydrolysis of sodiump-bromobutyrate was complete, indicating aboutthe same amount of decomposition. If all r;f thehydrolysis of the sodium bromobutyrate proceedsthrough the lactone intermediate, the optical ac-tivity of the product should be the same as thatwhich is obtained from the hydrolysis of the lac-tone. Correcting for the 15% decompositioii re-action this was found to be the case.

An aqueous solution of sodium bromobutyrateand thiosulfate ion shows an induction periodwhen the rate is followed by titration of the thio-sulfate ion. The induction period becomesshorter the greater the initial concentration ofthiosulfate ion. The limiting value for the rateappears to be the same as the rate of productionof bromide ion when thiosulfate ion is absent.The reaction therefore probably involves the pre-liminary production of lactone and bromide ion.In corroboration of this, the rate of the bimolecu-lar reaction between lactone and thiosulfate ionwas determined by following the change in con-centration of thiosulfate ion and found to be0.05liter per mole-minute The results therefore arecompletely analogous to those obtained by Longand Olson16with sodium bromosuccinate.

In solution by itself or with 2 ,I; perchloric acidthe P-bromobutyric acid loses its optical activityonly very slowly, the rotation in 2 N perchloricacid being 5,?c: of the beginning rotation aftertwo months at 25' In basic solution, however, afast bimolecular reaction with hydroxide ion oc-curs, producing ail optically inactive substance,probably crotonate ion, such as Fischer andScheibler12 ound with sodium P-chlorobutyrate.The rate constant as determined by the decrease

(16) Johansson, Bc r , 5 6 , 647 (1922).(16) Long and Olson 3 P h y $ Ckr tn , 41 , 2hi (193il

in optical activity with time was about 0.08literper mole-minute at25'.

The racemization by bromide ion was followedin approximately 0.2 N /3-bromobutyric acid and2 A' hydrobromic acid by the decrease in opticalactivity. The rate constants, uncorrected for de-crease in optical activity due to other causes, sincethis correction was small and known only in thecase of the lower temperature, were 1.27Xminute-' at 25' and 9.2 X 10-5 minute-' at39.3' as the results of a single run at each tem-perature. The rate constant can then be ex-pressed as k = 4.2 X 101'e-24~9aa/RTsec.-1s apreliminary result.

SummaryPure optically active P-bromobutyric acid has

been prepared. Its molar rotation, [M]265461,nacid solution is 116.5'. In aqueous solution thesalt gave [M ]25~~1qual to 106.6'.

The rates of hydrolysis of optically active p -butyrolactone prepared from optically active p-bromobutyric acid have been measured over arangeof hydrogen ion concentrations.

From the rates and the optical activity of thefinal hydrolysis products it has been shown thatthe mechanisms of hydrolysis by water, by hydro-gen ion, and by hydroxide ion are distinct.I t has been shown that the addition of an ion,such 11s carbonate ion, has a big influence on both

the water rate and the hydroxide ion rate. Anexplaiiation is advanced for this behavior.

Tentative values of the heats of activation forthe reaction by which P-bromobutyrate ion pro-duces lactone and for the reaction by which bro-mide ion racemizes P-bromobutyric acid have beendetermined.

The rate of the bimolecular reaction between 0-bromobutyrate ion and hydroxide ion was de-termined to be about 0.08 liter per mole-minute.

The reaction between P-bromobutyrate ion andthiosulfate ion has been shown to involve theunimolecular formation of lactone as a primarystep.BERKELEY, ALIF. I?ECEIVED JULY 15, 193s