Grunwald the Correlation of Solvolysis Rates

8/3/2019 Grunwald the Correlation of Solvolysis Rates

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846 E K N ~ S TKUNWALDND S. WINSTEIN Vol. i oth e time of reilloval of the first tube aftu attainment oftemperature.The infinite ti ter of bromide ion agreed well with th eexpected as indicated by the equivaleni weights of the CY-bromopropionic acid samples. The infinite ti ter ofbase was usually unreliable by a few per cent., probablydue t o reaction of the glass. Soft glass tubes were usedin the experiments with methanolic solutions, and Pyrextubes were employed for the aqueous runs.I n the ruiis with high bast concentration, the reactionwas followed chiefly by titrat ion for bromide ion. Withthe low base concentrations, titration was carried out forboth base and bromide ion except where bromide ion wasadded in large amounts initially. When added sodiumperchlorate the rate constants based on the two titrationsagreed closely (Table 11). With added sodium nitrate,the rate constants from bromide titration were steady butthose based on base tit ration were lower and drifted down-ward. In run 21 with 0.5 M added sodium nitrate, thebase consumed during a run averaged 98.8 * 0.7% ofthe bromide ion produced, while the analogous figure was96.6 f 1.5% for run 19with Madded sodium nitrate.

SummaryThe hydrolysis and methanolysis of sodium a-

bromopropionate in the presence of sodium hy-droxide or methoxide was investigated in solutionsof varying ionic strength a t 64.04. A kineticanalysis reveals that both the bimolecular andunimolecular specific reaction rate constants, kzand kl , respectively, increase with ionic strength.

The variation of k1 with change in solvent andionic strength is discussed in terms of a rate-deter-mining ionization either to the zwitterion I1 (spe-cific rate kc) , or the a-lactone I (specific rate kb).An unambiguous decision regarding the reactionmechanism is not possible from the salt and sol-vent effects alone.

I I1However, the sign of these effectsand related evi-dence, particularly the high reactivity of a-bro-mopropionate ion compared to isopropyl bromideand the contrast with a-bromoisobutyrate ion, areconsistent with the rate-determining ionizationsymbolized by ka.The ratio of rate constants for reaction of theintermediate in the solvolysis of a-bromopropion-ate ion with bromide ion and solvent, kBr/ks, de-rived from measurements in solutions containinghigh bromide ion concentrations, is 2.0 in metha-nol and 0.76 in water.Los ANGELES4, CALIPORNIA RECEIVEDUN E 11, 1947

[CONTRIBUTION FROM THE CHEWISTRY DEPARTMENTF THE UNIVERSITY O F CALIFORNIA, LOS ANGELES]The Correlation of Solvolysis RatesBY ERNESTRUNWALDND S. WINSTEIN

One of the important mechanisms (A) or sol-volysis1.2 of alkyl halides involves more than enestage and is at present best formulated as involv-ing a rate-determining ionization (equation 1) to acationic intermediate. The rate constant k~R X + R + f X -

depends on the so-called ionizing power of thesolvent, and it is possible from such rates to ar-range solvents in a relative order. For examplesubstitution of the unimolecular types proceedsslightly more rapidly in acetic acid than in abso-lute ethan01.~The rate is increased by addition ofwater to alcohol or partly aqueous acetone or diox-ane.S2 Further , substitution is about as rapid informic acid as in 50% aqueous ethanoLSThe question arises whether it is possible toassign to each solvent a definite number Y whichis a quanti tat ive measure of its ionizing power indetermining K1. In this article is reported ascheme for correlating unimolecular solvolysis

(1)ki

(1) (a) Hughes, Trans. Far. Soc., 87 , 611 (1941); (b) Dostrovsky,(2 ) Hammett, Physical Organic Chemistry, McGraw-Hill Book(3 ) Winstein, Grunwald, Buckles and Hanson, THISOURNAL, 70,(4) Winstein, Hanson, and Grunwald, i b id . . TO , 812 (1948).(6) Dootrovsty and Hughes, J . Ch cm. Soc., 166, 171 (1946).

Hughes and Ingold, J. Chcm. Soc., 173 (1946).Co., Ne w York,N. Y., 940, pp . 166 8.816 (19481.

rates with the aid of such a set of Y values and asimple functional relationship between k1 and Y.Also, the theoretical implications of the methodare discussed.In addition to the solvolysis mechanism A thereoccurs solvolysis in neutral and acidic solvents bya process or processes (B, ate constant k,) orwhich the nucleophilic character as well as theionizing power of the solvent is important. Thebest understood concerted process is the so-calledbimolecular substitution in which a solvent mole-cule plays a role such as that of a pyridine mole-cule in the Menshutkin reaction. One of the im-portant problems for the proper understanding ofsuch subjects as reactivity, stereochemistry ofdisplacements and rearrangementsIb is that ofsorting out the fractions of solvolysis proceedingby mechanisms A and B.The scheme for correlating solvolysis rates al-lows one to make deductions regarding the rateby process A and therefore the fraction of solvoly-sis by mechanism A. This application of themethod is being actively pursued and the proce-dure is illustrated in tne present article for isopro-pyl p-bromobemenesulfonate.A Quantitative Measure of Ionizing Power.The Y Fqctioa.-The specific solvolysis rates Kfor a number of halides which, t h e accumulation


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Feb., 1945 THE ORRELATION OF SOLVOLYSIS RATESTABLE

S~LVOLYSISATES OF SOMEALIDES N D Y VALUES OR SOLVENTST p p . .

(CH3)sCCI 25.0Compound C.

CH&!HCICH==CHg 25.0

(CH3)sCCHIBr 95.0

(CsHs)nCHC1 25.0

WsCHClCHt 50.0

SolventAbsolute EtOH90% EtOH, NH,O= 0.26280% EtOH, N H ~ O 0.44870% BtOH, NH*O= 0.58260% EtOH, NH*O= 0.68450% EtOH, NH,O= 0.76540% EtOH. NH,O= 0.82980% (CHaIiCO5% (CHJKO, NH~O0.98748.61wt. % H 2 0 n dioxaneH20-MeOH, NH,O= 0.000Hz0-MeOH, NE,O = 0.070H20-MeOH, = 0.175Hz0-MeOH, = 0.230H20-MeOH,NH*O= 0.282H20-MeOH, NE,O= 0.346HpO-MeOH, NR%O 0.432HaO-MeOH, NH,O = 0.497H2OeHCOOH~AcOH, 0.025 M KOAcAcOII-AcsO, N A ~ O H 0.042EtOH90% EtOH80% EtOH76.5% EtOI-T, NH,O= 0.50195% (CHa)zCO, N H ~ O 0.17890% (CHJzCO, NHZO 0.31380% (CHa)zCO, NHZO 0.50670% (CHa)zCO, NHZO 0.637EtOHHzO70% EtOH50% EtOHHCOOHEtOH90% EtOH80% EtOH90% (CH312CO80% ( C H W O70% (C?&)zCOEtOH80% EtOHMeOH '80% (CHJzCO60% (CHdzCOAcOH, 0.2M KOAc

0.017M KOAc

60% EtOH

50% Et013

E' ,kcal.25.9723.0622.9222.622.82:5.0

22.9"26.4326.4"23.0"22.822.5"21.722.720.820.8"23.5"23.5"29.0

19.621.021.9"21.421.7'21.8"21.5"

k(sec.-1)9.70x 10-81.73 x 10-89.24x 10-4.07x 10-51.27x 10-43.67X lo-'1.29 X lo-*1.94 X 10-62.57 X 10-21.81x 10-48.20 x 10-71.75 X 10-64.33x 10-07.14 X lo-'1.13 X 10-62.12 x 10-65.28 X lo-'9.75 x 10-53.3 x lo-'1.1 x lo-'2.13 x 10-74.77 x 10-93.63 x 10-43.76x 10-31.10 x 10-45.15x 10-4

5.69 X 10-67.14 X 10-65.22 x lo-'2.10x 10-01.27 X 10-68.8 X 10-91.14X 10-18.1 X lo-'1.54x 10-79 . 2 ~ 10-74.90x 10-41.53 x 10-05.30 X 10-51.72 x lo-'4.60 X 10-67.24 x 10-53.20 x 10-45.85 x 10-71.64x 10-47.06X 10W1.44x 10-64.19 X 10-63.9 x 10-6

Ref.Table I1666666678,llb8,Table I188888889aTable I1Table I11OC1Oa10a10d1Oa10b1Oeloa1Oella1 allb55510f12b12b10e1Oe10e1312"13131314

847

Y-1.974-0.7270.0000.6441.1391.6042.1513.4491.292-1.052- .722.-0.329-0.1120.0880.3610.7571.0233.562.08-1.633

-3.287

- .402"-1.549"- .527'0.205'

-3.377d- . 797d-0.945d

0 Value used by the authors. Rate constants have been reported" a t 15.0' ranging from 2.0X 10-4 o 3.9X 10-4Rate measurements in formic acid a re complicated by decomposition of the sol-e Obtained by extra-sec.-l.ventgb,e into carbon monoxide and water.polation from the plot of log kBuC* s. NH,O sing the datao.' in aqueous acetone.

An average value was used.e From t-butyl bromide. d From benzhydryl chloride.

(8 ) Hughes, J . Chcm. Soc., 255 (1935 ). Proskauer. "Organic Solve nts," Clarendon Press, Oxford, 1935,(7) Swain and R m , HIS OURNAL, MI, 658 (1946).(8) Olson and Halford, i b i d . , 69, 2644 (1937). (10) a) Bateman, Cooper, Hughes and Ingold, J . Chcm. Sot..(9) (a) Bateman and Hughes, J . Chrm. Soc., 935 (1940); (b) 925 (1940); (b) Cooper and Hughes, ib id . , 1183 (1987): (c)Hughes,

Bateman and Hughes, i b i d . , 940 (1040): (c ) Weissberger an d Ingold, Masterman and McNulty, ib id . , 899 (1940); (d) Petrenko-

p. 145.


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Vol. 7048 ERNESTGRUNWALDND S. WINSTEINTABLEI

FIRST-ORDURovvoLysis RATE CONSTANTST 70.0". FOR I-BUTYL HLORIDEN D PINACOLYLN D ISOPROPYL p -BROYOBENZENESULFONTESCompound Solvent

(CHi)sCCl AcOH-97.5% ACZONA,OH 0.042ACOH-O.l% A s 0

EtOH

MeOH80% EtOH"

(CHs)rCCH(OS02 AcOH-97.5% Ac2OCd-IJWCH3 N A ~ O H0.042

AcOH-80.3% Ac2ON A ~ O H 0.294ACOH-O.l% Ac~O

EtOH

MeOH

80% EtOH(CH&CHOSOI AcOH-97.5% Act0

C&Br NAoaa = 0.042AcOH-~O.~%c~ ONA.OH= 0.294AcOH-O.l% Act0

EtOHMeOH80% EtOH

gz40.342.312.0419.2519.60'18.43'52.1637.2552.16*37. 25b19.2137.4033.4619.4024.7122.6134.2927.6016.5512.377.16

19.8212.065.879.94

12.8430.6536.7221.8128.3342.6626.7224.1023.1623.3118.1511.3511.93

(ROAc)i v M19.0715.6724.6324.5424.8924.9160.235.060.235.058.558.519.918.99. . .. .. . .

24.87. . .. . ... .. . .. . .. . .. . .. . .. . .22. 2gd10. 25d. . .. . .. . .

25.03. . .. . *....... . .

k, e c - 1(1.620 * 0.048) X ( 0 - 6(1.625 * 0.048) x 10-8(7.12 * 0.12) X lo-;(7.45 * 0.10) x 10-5(8.78 * 0.17) X lo-'(8.91 * 0.20) x 10-7(3.19 * 0.03) X 10-6(3.12 * 0.03) X(3.82 f 0.07) X 10-7(3.69 * 0.07) X lo-'(2.07 * 0.07) X lo- '(2.10 * 0.03) x 10-41.51 X

(11.49 * 0.15) X11.66 X 10-6(7.89 * 0.11) x 10-5(2.734 * 0.026) X lo-'(2.742 * 0.033) X lo-'(2.811 * 0.022) X 10-9(7.02 * 0.10) X(7.01 * 0.13) X(3.19 * 0.06) X lo-'(3.15 * 0.05) X lo-'(3.29 f 0.05) X lo-'(1.369 f 0.018) X lo-$(1.386 * 0.017) X lo-'1.30 X lo-'1.50 X1.46 X lo-*(8.45 * 0.11) X(6.98 * 0.08) X lo-'(7.41 == 0.07) X(2.64 * 0.04) X lo-'(7.28 * 0.16) X lo-'1.73 X lo-'1.67 X lo-'

(7.09 * 0.09) x

(6.90 * 0.05) x 10-5(7.34 0.08) x 10-4

Data at 34.85'; E* = 26.43 kcal./mole. * Data a t 34.43O; E +i = 25.97 kcal./mole. c From data of Hughes.'d R, = 3.61 X lO- '~ec.-~hP1.of evidence indicates, react by the unimolecular-type mechanism A, are summarized in Table Itogether with the values of the correspondingArrhenius activation energies,E *,wherever avail-able. The solvolysis rates for any one compoundhave been corrected to one temperature with theKritschenko, Ba., 61, 862 (1928): (e) Bateman, Church, Hughes,Ingold and Taher, J . Chem.Soc.,979 (1940); (0 ughes, Ingoid 8ndTaher. ib id . , 949 (1940).

(11s (a) Young and Andrens, THISJOURNAL. 66,42 1 (1944); (h)Winstein and Grunwald, ibid., 10 , 828 (1948).

(12) (a) Ward, J . Chcm. Soc., 446 (1927); (b) Ward, ib id . , 2186(1927).(IS) Hughes, Ingoldand Scott, ib id . , 1201 (1937).

(11) Bt.iaarnrsd Hmnamatt, TBXUORRNAL, 6 9 , Z S W (191)7),

aid of available values of E * or else on the basis ofreasonable estitnatesof E *. The values of E * forany one compound are fairly insensitive to solventchange and all values of E * hover near 22 kcal(Table I). It is therefore possible to estimate E Awith sufficient accuracy since the corrections madeare small. Even an error of 2.0 kcal. in E * wouldcause an error of no more than 0.079 in log k for a20' correction.Supplementing the data in Table I are the sol-volysis rates k we have measured for t-butyl &lo-ride and a-methylneopentyl p-bromobenzenesul-fonate, (CHI)aCCH(OSOIC&J3r)CHa, in a num-


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Feb., 1945 TIIECORRELATIONF SOLVOLYSISATES S49hcr of solvents. These mcasrirements are sum-innrized in Table I I .Inspection reveals a simple quantitative rela-tionship among the various solvolysis rate con-stants. Thus, when the values of log k for anyone compound in a number of solvents are plottedagainst log k of some other compound in the samesolvents a stra ight line is obtained. This linearrelationship is illust rated for a number of com-pounds in Fig. 1.

- 2 - 1 0 1 2 3 45 + log kBUC'.Fig. 1.-Plots of log k os. log kBuC': I, t-butyl bromide

25.0'; 11, a-methylallyl chloride, 25.0'; 111, a-methyl-neopentyl p-bromobenzenesulfonate, 70.0O ; IV and V,neopentyl bromide, 95.0, nd n-butyl bromide, 59.4 ',both v s . t-butyl chloride, 26.0"; solvents: 0, HzO; 0 ,EtOH-H20; 0, MeOH-HtO; V, ACOH-AC~O; A,acetone-HiO; 63, COOH.

The linear plots illustrated in Fig. 1 indicatethat log Put* (EuCl = t-butyl chloride) satis-fies the requirements for a useful quantitativemeasure of ionizing power of a given solvent.However, log kBuC1varies with temperature and isusually a negative enti ty of a n inconvenient orderof magnitude. It is convenient to define Y byequation 2, where kBuCl and k,Buc' are the rateconstmts of'

Y = log P " C ' - og k0B"C't-butyl chloride a t 25.0' in the given solvent andin "80%" ethanol, respectively. By virtue of thisdefinition, U is zero in ' i80~0" thanol, a solventoften employed and of intermediate reactivity,and Y varies from ca. +4 to -3 for the mostcommon solvolyzing media. Although 25.0'' ischosen as he reference temperature for computing

(2)

values of Y it is clear from the near constancy ofE& in various solvents tha t any other referencetemperature would give an almost identical setof Y values.The linear relationships illustrated in Fig. 1combined with the defining equation 2 for Y leadto equation 3 for the variation of solvolysis ra teconstant k with solvent for these compounds. In

log k = nzY + log K Othis equation, m and log K O are parameters, al-though physically K O s the solvolysis rate constantin "80%" ethanol. Equation 3 is the basis ofthe quantitative scheme for correlating solvolysisrates.In Table I are summarized values of Y for anextensive series of solvents. Y values for all sol-vents except the acetone-water mixtures were cal-culated from the available data for t-butyl chlo-ride a t 25.0' (Tables I, 11). In order to obtain Yvalues in the la tter solvent mixtures the parame-ters m and log K O were evaluated for t-butyl bro-mide and benzhydryl chloride from dat a a t 25.0'in ethanol-water mixtures, and Y was calculatedfor various acetone-water mixtures with the aidof equation 3, using the available values of log kfor these compounds. Two different sets of Y areobtained in this way, of which one (from t-butylbromide) is used for aliphatic compounds whilethe other (from benzhydryl chloride) is used witha-phenylethyl chloride. Acetone-water mixtureswere the only solvents where it was found neces-sary to use two different sets of Y n order to cor-relate all rates of unimolecular-type solvolysisscrutinized by the authors to date .The functional relationship between Y and thecomposition of mixed solvents is apparently not

(3)

0 0.5 1" 2 0 .

Fig. 2.--Plot of Y us. mo1e:fraction of water (Nn@) or:X, Ha0-MeOH; 11,HIO-EtOH.


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Vol. 7050 ERNEST RUNWALDN D S. WINSTEINsimple. Plots oi Y vs. weight % or volume % ofwater in aqueous ethanol and methanol haveconsiderable curvature. The plot of Y os. iriolefraction of water, N H , ~ ,s more nearlylinear forthese systems as illustrated in Fig. 2. The latterobservation is useful for purposes of interpolation.

The parameters ttz and log k, in equation 3 havebeen evaluated for a number of compounds by themethod of least squares, using the values of k andY in Tables I and 11. The results are summarizedin Table I11 together with the probable error ofthe fit,lS r . The fit is satisfactory, particularlysince the values of k often vary by 3 to 6 powers often, the mean value of r for the whole table beingless than 0.05. The probable errors in m are ofthe order of 0.05 or less.TABLE 11T y w

1 &Butyl chloride 25 .0 1 .000 -5 .031 . . .2 t-Butyl bromide 25 .0 0.917 -3.476 0.026:J Neopentyl bromide 95.0 .712 - .248 ,059i a-Methylneopentylp-bromoberizene-sulfonate 70.0 .706 -2 .837 .096

chloride 25. 0 .894 -6.314 .052

CORRELATION OF SOLVOLYSIS RATESN VARIOUS SOLVENTSN O . Compound c . 711 logko

5 a-Methylallyl6 Benzhydryl chloride 25.0 .757 - .779 .0047 a-Phenylethylchloride 50.0 1.195 -3.808 ,072S n-Rutyl broinide 59.4 0 .392 - .972 ,02675.1 0.331 -5.419 .034

The value of k for HOAc, 0.2 M KOAc (Table I ) ,was not included smce no value of Y is available at suchhigh acetate concentration. From the above data k =1.74 x 10-6sec.- at 0.025 M KOAc (Y = -1.633) inreasonable agreement with the value in Table I.Equation 4 gives the variation of m with teinpcr-ature T. This is slight since for most solvents the

dn i E* - E:H P.303 Y -d Tdifference between the activation energy E * andthe activation energy EO in 80% ethanol issmall for unimolecular-type solvolysis (TablesT T T \I, Ll).

Theoretical Interpretation. The ActivityPostulate.-Application of the Bronsted theoryto the variation om k1with solvent for unimolecular-

type solvolysis leads to equation 5 where K is thespecific rate in the s tandard s tat e of unit activityand A andfz are the activity coefficients of reac-tant and transition-state. In the case of dilutesolutionsl6 of non-electrolytes i t is useful to refer(15) Margeiiau and1 Murphy, Mathemat ics of Physics and

Chemistry, D. Va n Xoslrand Co., nc.,New York, N. Y.,943, p502.*&(I@ Lewis and Randall, Thermody namics , McGraw-Hill BookCo., Inc., New York,N. Y.. 1923, Chapter XX.

all activity coefficients to the gas phase so thatequation 5 reduces to 6. Jn this equation H A andH Z are the Henrys law constants16 of reactantand transition-state.Coniparisoii of equations (j arid 3 lends tu Twhich implies a liiienr rtl:itionship, 8, hetweci i

k i K = (HA/K?) (6)

I ~ A kolog -- = mY + log -f I 2 (7)log ( I - . . A /H ~ )nd log (HB,;) for any two com-

pounds A and B solvolyzirig by the unimolecular-type mechanism in a series of solvents. This de-duction calls to mind the ob~ ervation~hat thereexists an even simpler linear relationship, shownin equation 9, between log ( f ~ / f ~ a + )or any two

conjugate acid-base systems B and B in a seriesof solvents.The success of equation 3 for correlating sol-volysis rates of the unimolecular type may be dueto the validity of a general relationship regardingratios of activity coefficients. For systems under-going similar changes of the type AZ3 Z, BZ+BZ, etc., the postulated general relationship maybe expressed by equation 10, p and f l being par-ameters.

In the case of solvolysis by mechanism A thechange AZ ---t AZ is from the dissolved halide orester to the partly ionized and strongly solvatedtransition-state molecule. Equation 3 and thus bis successful for variations in the ionizing group toinclude chloride, bromide and bromobenzenesul-fonate. Also, the change XZ -+ AZ is not re-stricted entirely to the A-Z bond. For example,resonance will diffuse any positive charge of thealpha carbon atom in the transition state to theortho and para positions of an alpha phenyl group.Even in aliphatic cases the positive charge will bespread. Now evidently equations 3 and 8 hold forconsiderable variation in the R part of the sol-volyzing molecule KX but further work is neces-sary to clearly outline the scope and limitationsin this respect. The nccd for two sets of Y valuesfor aqueous acetone mixtures is one of the liniita-tions which has already appeared.Solvolysis of &Butyl Chloride.-The solvolysisrate of t-butyl chloride in a range of mixedaqueous solvents has previously been correlatedby Olson and HalfordBwith the aid of the fugac-ity rate equation 11 where pw and pa are vapork =i ( k , 9, + k. P ~ ~ ~ B U C I

pressures of water and alcohol, respectively. Thiseqbation, which empirically fits the rates but not(11)

(17) Ref. 2, Chapter IX.


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Feb., 1948 THECORRELATIONF SOLVOLYSISATES 851the products, l8 is based on assumed bimolecularreactions between halide and water or alcohol butit is set up according to an activity rate formula-tion, the respective terms not being divided by theactivity coefficients of the corresponding transi-tion states. Actually higher order'* fugacity rateequations lit the rates at least as well as equation11. Scrutiniziiig the data with our present ap-proach, seeking generalizations regarding activitycoefficients involved, we find that log k is a linearfunction OF log HBuCl for the range of solventstreated by Olson and Halford. Equation 12 fitsthe da ta a t 25.0' for all partly aqueous solvents(including also water and methanol) (Tables I,11, IV, ref. 8) with a probable error of 0.06. Thus,only two parameters are necessary.The linear relation expressed in equation 12indicates, according to equation 6, that a linearrelation exists between log H&CInd log H B ~ C Inthe solvent range involved. This linear relationtakes the form shown in equation 13.

log W C ' = 1.232 log H B ~ c ~9.811 (12)

log H& C I = -0.232 log HB ~ C IConstant (13)TABLEV

25.0'HENRY'SLAWCONSTANTSOR t - B U m CHLORIDE ATlo-' RBuCI,Solvent mm .HOH 5 x 108EtOH 1.09 *0.09HOAc, 0.025 M KOAc 1.23 t0.05HOAC - AQO, NA~OH0.042

While there are indications tha t linear log-log re-lationships between the activity coefficients ofnon-electrolytes are fairly general,l9 the linear log-log relation expressed by equations 12 and 13 fort-butyl chloride and its solvolysis transition statebreaks down when one proceeds to the morepoorly ionizing solvents such as absolute alcoholor acetic acid-acetic anhydride combinations.The plot in Fig. 3 of log kBuC1 s . bgHBuC1 a t 25.0'illustrates the linear relation for one range ofsolvents and the large departure for the slowersolvents mentioned. Even with the departurefrom linearity the curve is smooth. However, asmooth curve is not necessarily to be expected and.this feature may be fortuitous.Further insight into the above-described situa-tion is derived by reference again to equation 6.A s shown in equation 14, (logH13,cl-log KBuC' ) is ameasure of log H&CI,nd this quantity is plottedagainst log kBuC1 n Fig. 3 . It can be seen that inthe partly aqueous solvents where equation 12

0.786 * 0.020

log H&CI- og h = log 1 1 ~ ~ ~ 1og kB"C1 (14)

(18) (a) Bartlett, TEIS OURNAL, 61, 1630 (1939); (b) Winstein,ibid., 81, 1635 (1939); (c) Bateman, Hughes, and Ingold, i b id . , 60,3080 (1938); (d) Bateman, Hughes and Ingold, J . Ckcm. Soc., 881(1938).(19) Grunwald, Dissertation, University of California a t Los

Angeles, Calif., 1947, sections 6, 17.

holds the variation in kBuClis due largely tochanges in I I B ~ c ~ . n the other hand, in thepoorer ionizing media the variation in KBuC1 is duelargely to changes in H&cI.I I " " " '

I+

- 3 - 2 -1 0 1 2 35 + og kBuCI*

Fig. 3.-Plots of log HBuC'nd (log HiBuC1 log K )against log kBuC1,25.0': 0 , Hz0-EtOH; 0, Hz0-MeOH;8 , H20-dioxane; V, AcOH-AclO; A , HaO-acetone;

Solvolysis of Isopropyl pBromobenzenesul-fonate.-For the simple secondary alkyl com-pound, isopropyl p-bromobenzenesulfonate,without essentially prohibitive steric hindranceto nucleophilic attack on carbon such as evi-dently obtains in the case of pinacolyl p-bromo-benzenesulfonate, the nucleophilic character ofthe solvent is very important. The first-ordersolvolysis rate constants k for isopropyl p-bromo-benzenesulfonate are summarized in Table I1 andinspection reveals the contrast with the othercompounds treated successfully by equation 3 .For example, the rate constant in ethanol is muchgreater than in acetic acid although the Y valuefor acetic acid is the higher. This contrast is dueto the fact that ionizing power and nucleophiliccharacter of solvents do not go hand in hand. In-stead of the rates in all solvents being manageabletogether it is now necessary to differentiate be-tween basic solvents and others.Quite a satisfactory understanding of the sol-volysis rates of isopropyl p-brompbenzenesulfon-ate may be reached on the assumption tha t solvol-ysis proceeds by both mechanism types A andB, B being slight or negligible in the acidic typesolvents such as acetic acid or its mixtures withacetic anhydride and serious in the inore basicsolvents.In the acetic acid-acetic anhydride solvents theplot of log k for isopropyl p-bromobeiizenesulfon-ate against log K' for pinacolyl p-bromobenzeiie-sulfonate gives the least squares line shown inequation 15,theprobableerrorl6beingO.1 6. The

log k = 1.204 log k' + 0.031straight line fit is not as satisfactory here as in theother cases, possibly because the acetolysis is notcleanly of the unimolecular type (k = kl). I t isnot out of the question t ha t acetic acid can func-

0, Hz0.

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852 ERNEST RUNWALDND S. WINSTEIN Vol. iotion in solvolysis by mechanism B. While theaddition of O.O%h< potassium acetate to glacialacetic acid gives no serious change in first-orderrate constant the addition of 0.01M potassiumacetate to the solvent rich in acetic anhydrideproduces a predominantly bimolecular reaction.However, the slope of the line represented byequation 15 is reasonable for solvolysis largely byinechanisin A . The value of 1.204 combined withan m value of O. iOG for piriacolyl p-bromobenzene-sulfonate (Table 111) corresponds to 0.550 for min the case of the isopropyl ester.Assuming k = kl in the acidic solvents, equation15 allows one to estimate kl in the nucleophilic al-coholic solvents;. These estimates are listed i nTable V along with k, (4. z. , k - kl) an$ the per-centage of solvoXysis by mechanism A, 100k l / k .

TABLESOLVOLYSISF ISOPROPYL-BROMOBENZENESULPONATET

70.0 IN NUCLEOPHILICOLVENTS10kl Calcd. Calcd. Calcd.Sol vel1 t sec. - 104kl IO+. I O O R ~ / BEtOH 2.64 0.108 2.53 4 .1MeOH 7.31 6 .68 6.63 9 .380% EtOH 17.0 3.86 13.1 22.7It is interesting that k , in the small range ofcomparably nucleophilic alcoholic solvents is fitby a linear equation of the same type as 3, equa-tion 16 fitting the da ta in Table V with a probable

101: 6, = 0.360 Y - 2.857error of 0.046. I n these solvents the rate of sol-volysis by mechanism B seems to depend on thesame properties of the solvent which control therate of the A type, the slope m, however, beingquite small.It is an especially satisfactory feature of theassumed way of accounting for the solvolysis ratesof isopropyl p-bromobenzenesulfonate that theslope in equation 16 is so small andso nearlyequalto the one which is derivable for n-butyl bromide.There is reason to believe that the latter halidesolvolyzes exclusively by mechanism B in alco-holic solvents, and Bird, Hughes and IngoldZ0 avesupplied rates of solvolysis in various aqueousethanol and methanol solvents.21 Using theirdata a plot of log k against log kBuCl is linear as il-lustrated in Fig. l and equation 3 fits the data wellas summarized in Table 111. The values of m inaqueous methanol a t 59.1 and aqueous ethanola t 75.1 are 0.392 and 0.331, respectively. In

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(20) Bird, Hughes and Ingold, J . Chem . SOC., 55 (1943).(21) In the case of n-butyl bromide, the fugacity rate equation 11has been found b y Bird, Hugh es and Iagold*o to fit both rates and

products. It must bir noted that R may be expressed a s the ratio ofthe vapor pressure of halide to either it s mole fraction or its molarity.Olson and Halfordha,ve used mo le fraction as is also done in the pres-ent article, and Bird, Hughes and Ingoldlo have used molarityHowever, because of differ ences in molar volumes of various mixedsolvents, if the use o l molarity furnishes a fit for the product com-positions, the me of mole fraction cannot furnish such a fit. A re-calculation of the data of Bird, Hughes and Ingold, using molefraction in evaluating H . sbovs that equation 11 will fit the rates hutno t the products.

fact, values of nz are also auite simi1aP for otherprinlary halides apparent]+ solvolyzing by mech-anism B.Experimental and Kinetic Part

Mataials.-The t-butyl chloride was Eastman Kodakeo. White Label grade, b. p. 51.2 (752 mm.), n Z 6 D1.3520.a-Methylneopentyl alcohol, b. p. 120.0-120.3 (754mm.), was prepared by Miss Anita Stiran from t-butylmagnesium chloride* and acetaldehyde.a-Methylneopentyl ~-hroniobenzenesulfonatc I andisopropyl p-bromohenzenesulforiate I1 were preparctl il lCQ . 50T0 yield in 0.05mole batches from the correspo!itliiigalcohols and p-bromobenzenesulfonyl chloride in pyridineby conventional methods.z4 I crystallized upon pouringthe pyridine reaction mixture into ice-cold 6 N hydrochloricacid and was recrystallized several times from petroleumether (b. p. 60-80); m. p. 53.2-53.5; equivalent weightfrom quant itative solvolysis: calcd., 321 2; found, 323.2(in acetic acid), 320.1 (in 80% ethanol).An a l . Calcd. for ClaH170sSBr: C, 44.86; H, 5.34.Found: C, 44.99; H, 5.49.

I1 separated as an oil upon pouring the pyridinereaction mixture into 6 N hydrochloric acid. The oil wasseparated with the aid of GU. 40 ml. of carbon tetrachlorideand the solution was dried over anhydrous potassiumcarbonate. After evaporation of the solvent at roomtemperature the viscous residue was induced to crystal-lize. The solid was purified by reprecipitat? underpetroleum ether (b. p. 00-80); m. p. 32.334.1 . Equiv-alent weight from quantitative solvolysis : calcd. 279.2;found 282.1 (in acetic acid), 278.3 (in methanol). Anal-ysis for carbon and hydrogen was unsuccessful becauseI1 decomposed rapidly on heating.Solvents.-Synthetic methanol, containing less than0.030/, of water by the miscibility temperature withcyclohexane,*6was used.Ethanol was dried by the ethyl formate methodz6 andcontained less than 0.02% of water by Robertsonsparaffin oil test.1680% ethanol was prepared by adding 317.5 g. ofconduct-ivity water to 1000 g . of ethanol.Acetic acid containing 0.0142 M (0.1%) acetic an-hydride by Kilpis anthranilic acid analysis* was pre-pared as described in a previous a r t i ~ l e . ~To 379.0 g. of Baker and Adamson Reagent Gradeacetic anhydride, equivalent weight 51.20 * 0.06 byhydrolysis and titration with standard aqueous base tothe phenolphthalein endpoint (mole fraction of aceticacid 0.042), was added 80.6 g. of acetic acid containing0.1 wt. of acetic anhydride to give a solvent of equiva-lent weight 52.63 * 0.06 (mole fraction of acetic acid0.294).Inorder to prepare solvents containing potassium acetatethe Baker and Adamson Reagent Grade salt was driedto constant weight in a tared glass-stoppered flask a t110 in u u c w and dissolved in the desired weight of sol-

vent.Kinetic Measurements.-Rates were meas-ured by the usual sealed ampoule technique.Titrations were made on 5-ml. aliquots from 5-nil. microburets. For the measurements inethanol, methanol and S O ~ o ethanol, titration(22) Winstein and Grunwald. unpublished work.(23) Puntambeker and Zoellner, Organic Synt hese s, Vol. 23,

John Wiley and Sons, Inc., New York, N. Y., 1943, p. 510.( 2 4 ) Winstein, Grunwald and Ingra ham, THISJOURNAL, 0, 821(1948).(25) Jones and Amstell, J . Ckcm. SOC.,1321 (1930).(25) Robertson, Laboratory Pra ctice of Organic Chemiatry,(27) Kilpi, Suomcn Kcmis f i l chf i ,18B. 19 (1940); C. A . , 86, 2446Macmillan Co., Ne w York,N. Y., 1943, pp. 178, 295.

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Feb., 1948 THECORRELATIONF SOLVOLYSISATES 853for acid was camed out with 0.05 N sodium hy-droxide using brom thymol blue as indicator.Titrations in glacial acetic acid and mixtures ofacetic acid and acetic anhydride were performedas described previouslyaJ4 except th at 0.05 N p -toluenesulfonic acid was substituted for perchloricacid in the solvents containing large amounts ofacetic anhydride. Reactions were usually fol-lowed to ca. 75% completion. Reaction mixtureswere prepared gravimetrically except for the rate-runs involving t-butyl chloride where initial con-centrations were obtained from the "infinite" ti-ter of acid and/or from Volhard titration for chlo-ride ion. In order to avoid errors due to the vola-tility of t-butyl chloride, the vapor space above thereaction solutions in the ampoules was kept quitesmall.The observed kinetics were fist-order withinthe experimental error of 1-2% in k over the rangeof concentrations investigated except for the sol-volysis of isopropyl p-bromobenzenesulfonate(RX) in 4.2 mole yoacetic acid in acetic anhydridein the presence of potassium acetate. A represen-tative set of experimental data is shown in TableVI. These data were fitted satisfactorily by equa-tion 17 which assumes a simultaneous first-ordersolvolysis and second-order reaction with potas-

-d In (RX)/dd = kl + Rl(K0Ac)sium acetate. Using the data obtained during thelatter part of the ru n where the potassium ace-tate has been neutralized, k1 was calculated fromthe slope (obtained by the method of least squares)of the linear plot of log (RX) vs . time, t. The de-rivative, -d In (RX)/dt, was then obtained a tvarious concentrations of potassium acetate froma large-scale plot of In (RX) v s . t with the aid of atangent meter. Substitution in equation 17 gavesatisfactorily constant values for kz. The averagevalue of k2 for this and a duplicate run was (3.61 *0.07) X see.-' M.-l

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TABLE IACETOLYSISF' I s o p R o p n #-BROMOBENZENESULFONATE(RX) IN 4.2 MOLE% ACETIC CID N ACETICANHYDRIDE

AT 70.0'

0.011.620.730.9554.170.5103.1-120.1143.1

36.72 22.28 . .26.89 12.45 5.8422.74 8.30 4.4719.20 4.76 ..15.68 1.24 1.9414.25 . . . ..12.05 ... . .11.02 . . . ..9.62 ... ..Equilibrium in the System t-Butyl Chloride,t-Butyl Acetate, Hydrogen Chloride.-In analogywith the report of Steigman and HammettI4 fora-phenylethyl chloride, t-butyl chloride solvolyzesin initially neutral acetic acid to give an equilib-

rium mixture according to equation 18. The rateof establishment of equilibrium is considerablyfaster than the rate of solvolysis in the presence ofpotassium acetate. For example, a t 40.0' cu.977' of the equilibrium concentration of hydrogenchloride is produced from a solution of t-butylchloride within 28 hours whereas the solvolysis inthe presence of potassium acetate is only ca. 207'complete within the same period.The pertinent equilibrium data are summarizedin Table VII . The data were obtained by thesealed-ampoule technique described for the kin-etic runs. The equilibrium titre of hydrogenchloride was constant within experimental rrrnrover a period of several days.

TABLEI1ACETATE,HYDROGENHLORIDE

t-BuC1 + HOAC = t-BuOAc + HC1 (18)

EQUILIBRIUMN THE SYSTEM &BUTYL HLORIDE, & B U T Y LInitial WCI)IOSM T, C. 10'M K a158.3 60.2 8.12 * .2 2.3 X lo381.8 40.0 4.15 f .2 4.5 X l o 3

I-BuCI at equilibrium81.8 60.2 6.02* 0.2 2.1 x 103158.3 40.0 5.65 * .1 4.8x 103Measurement of Henry's Gaw Constants.-Approximate Henry's law constants were de-termined as follows: A 500-rnl. standard-taper round-bottom flask equipped with a gradu-ated dropping funnel and an outlet tube leadingby way of a T-joint to a manometer and an oilpump was placed in a thermostat and evacuateduntil the pressure was below 2 mm. A knownvolume of standard solution of t-butyl chloride inthe appropriate solvent was introduced carefullyfrom the dropping funnel and the increase in pres-sure read. Room temperature was maintainedabove tha t of the thermostat to avoid condensa-tion of the vapors. A typical set of experimentaldata is given in Table V I I I . In computing themole fraction of t-butyl chloride, allowance wasmade for the materials in the known vapor space.

TABLEI11ACID CONTAINING.025 M POTASSIUMCETATE,5.0'

0.0000 16.0 * .

a K = (t-BuCl)/(t-BuOAc)(HCl).

HENRY'SAWCONSTANT OF I-BUTYL CHLORIDE IN ACETIC10-* , mm.BUCI p, mm.0

.0338 53.6 1.13.0359 59.1 1.22.0293 52.3 1.26.0137 33.5 1.29a p = pressure increase due to the solution.The Henry's law constant of t-butyl chloride inwater was estimated from the vapor pressure anda rough determination of the solubility of the hal-ide in water (cu. 3 X

SummaryM ) .

For compounds which appear to solvolyze by a


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VO l . 'To54 ERNST ERLINER ND FRANCES J. BONDHUSrate determining ionization, plots of the logarithmof the first-order rate constant k in various sol-vents (either from the literature or here reported)against log k for t-butyl chloride are linear.A set of values of the so-called ionizing power,Y, efined by the equation

Y = log kBQCl - og k p l(kBUcl and koBu'21being solvolysis rate-constants fort-butyl chloride at 25.0' in the given solvent andin SOY0 ethanol) has been set up for a number ofsolvents includmg water, methanol, ethanol, aque-ous alcohols, formic acid and acetic acid. Thesolvolysis rate constants (varying sonietimes bysix orders of magnitude) are fitted by the equationlog k = mY + log K O

with a mean probable error of less than 0.05 in thecases of t-butyl bromide, neopentyl bromide, a-methylneopentyl 9-bromobenzenesulfonate, a-methylallyl chloride, a-phenylethyl chloride andbenzhydryl chloride.The observed linear relationships, interpretedon the basis of the Bronsted equation, lead to theequation

log --fA =-A log& + constantfh mB

for the relationship among the pertinent activitycoefficients(f~,2, tc.) for any two compounds Aand B. It is postulated that linear logarithmicrelationships among ratios of activity coefficientsof this type may be quite general.The solvolysis of t-butyl chloride is discussed interms of the Bronsted equation. It is shownthat, to a good approximation, log f&c1 varieslinearly with logfBUa in the partly aqueous sol-vents and tha t in these solvents the variation in kis due largely to changes infBuC1. On the otherhand, in the more poorly ionizing solvents changesin k are attributable mainly to changes in f & ~ .The reported method of correlating unimolecu-lar type solvolysis rates is useful in elucidating thenature of the solvolysis of materials the rates ofwhich depend markedly on the nucleophilic char-acter of the solvent. For isopropyl p-bromo-benzenesulfonate the rates of solvolysis in aceticacid and acetic acid-acetic anhydride mixturesfurnish estimates of unimolecular solvolysis ratesin ethanol, methanol and aqueous ethanol. Theactual solvolysis rates are considerably larger inthe lat ter solvents, the fractions of unimolecularsolvolysis being low.Los ANCELES 4, CALIFORNIAECEIVEDUGUST 15, 1947

[CONTRIBUTION FROM THE MARION DWARDSA R K LABORATORYF B R Y N MA W R OLLEGE]Hyperconjugation. 11. The Competitive Bromination of Benzene andt-Butylbenzene

BY ERNST ERLINER ND FRANCES. BONDHUSWhen benzene and t-butylbenzene in an equi-molecular mixture in 92% acetic acid are allowedto compete for an insufficient amount of bromine,the corresponding brominated hydrocarbons areformed in proportions which show that the ratioof the rates of bromination at 25' is about 115:1in favor of t-butylbenzene. At 45' the ratio isabout 72 :1. 'Therefore the bromination of ben-zene requires a higher energy of activation thanthe bromination of t-butylbenzene.' Since underthe same conditions toluene is brominated about

four times faster than f-butylbenzene,2*ahe rateof bromination of toluene appears to be about465 times faster than th at of benzene. Valuesfor the individual rates of chlorination of toluene(1 ) The bromination of difierent aromatic compounds is probablyanother case in which the differences in rate are primarily due to dit.

ferences in the E term of the Arrhenius equation (Scheffer andBlanks-, Rcc. Iros. chim., 46, 522 (1928); Bradfield and Jones, J .Chcm. SOC., 006 1928)); i:e.,the relationship (log k i / k a )n = T:/TI(log k i /ka )Ta should. hold. In the competitive bromination of tolu-ene and I-butylbensene the calculated ratio at 45 " is 3.70 (found,3.80 ); in the present bromination the agreement is less satisfactory(calculated ratio n l 4.5': 86.7. found: 71. 8). This may be due toirregularities on account of the greater difference in rate.(2 ) Berliner and Rondhus, T i m JOURNAL, 8, 2355 (104G).(3) De 111 M n r r :itmI Iertsnn, . Chc,~ r . o r . , ?7!) ( 1943 ) .

and benzene iix the ratio a t about 345,a,4whereasin nitration with acetyl nitrate toluene reactstwenty-three times faster than benzene.6The difference in the rates of bromination oftoluene and t-butylbenzene was explained by no-bond resonance of the Baker-Nathan type,2B8*6which involves carbon-hydrogen bonds, but themuch greater difference between t-butylbenzeneand benzene clearly cannot be accounted for bysuch resonance, since no a-hydrogen atoms areavailable for conjugation.' On the other hand,it would be hard to see how the inductive effect,which, on the basis of the Baker-Nathan theory,should be operative in the absence of hydrogenatoms, could alone account for the great activationand strong ortho-$Jura directive influence of thet-butyl group, particularly since inductive effectsof alkyl groups are conceded to operate through arather feeble relay mechanism. The definitionsthat make the Baker-Nathan type of resonance

(4) This ratio is for 80% acetic acid; the ratio of the rate of( 5 ) Ingold, Lapworth, Rothstein and Ward, J . Chcm. Soc., 1959( 0 ) Baker nnd Nathan, i b i d . , 1840 (1!)3.5).(7) Baker, i h i d . , 1150 (1939).

chlorination of I-butylbenzene and benzene is 110.( I 931).

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Grunwald the Correlation of Solvolysis Rates