Part I. Kinetics of the Vapor Phase Exchange of Radioactive Bromine Between Trichlorobromomethane and Bromine. Part II. Kinetics of the Forward and Reverse Reactions of the Vapor Phase Thermal Bromination of Chloroform. Part III. A Method of Estimating and Minimizing the Rate of a Radioactive Exchange Reaction Citation Sullivan, John Henry (1950) Part I. Kinetics of the Vapor Phase Exchange of Radioactive Bromine Between Trichlorobromomethane and Bromine. Part II. Kinetics of the Forward and Reverse Reactions of the Vapor Phase Thermal Bromination of Chloroform. Part III. A Method of Estimating and Minimizing the Rate of a Radioactive Exchange Reaction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/nysr-5c25. https://resolver.caltech.edu/CaltechTHESIS:06242025-212122769 Abstract The rate of the homogeneous vapor phase thermal radioactive exchange reaction CBrCl 3 + Br 2 * → exchange and the rates of the forward and reverse reactions of the homogeneous vapor phase thermal bromination of chloroform CHCl 3 + Br 2 ⇄ CBrCl 3 + HBr (A) have been measured in the temperature range 420-455° K. For the bromination reaction a mechanism which is consistent with all the experimental data is Br 2 ⇄ 2Br (d) (5) Br + CHCl 3 ⇄ -CCl 3 + HBr (1) (2) -CCl 3 + Br 2 ⇄ CBrCl 3 + Br. (3) (4) The rate determining steps are (1) and (4). The rate of the exchange reaction is given by k 0 (CBrCl 3 )(Br) and the equation for the rate determining constant k 0 = k 0 (T) is identical to that for k 4 as a function of temperature. The exchange reaction takes place, therefore, by the reaction sequence (d), (4), and (3). The activation energies of (1) and (4) imply that the CH bond in CHCl 3 is weaker than that in CH 4 by at least 6.6 kcal, and the CBr bond in CBrCl 3 is weaker than that in CH 3 Br by at least 11 kcal. The equilibrium constant K = (CBrCl 3 )(HBr)/ (CHCl 3 )(Br 2 ) is 1.96 at 442° K; the heat of reaction (A) is -0.9(±0.65) kcal. In a single exploratory experiment, it was observed that the exchange reaction between bromine and trifluorobromomethane is much slower than that between bromine and trichlorobromomethane. A method of estimating and minimizing the error of measurement of the rate of a radioactive exchange reaction is given. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry and Physics) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Minor Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Davidson, Norman R. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1950 Record Number: CaltechTHESIS:06242025-212122769 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:06242025-212122769 DOI: 10.7907/nysr-5c25 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17483 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 27 Jun 2025 22:45 Last Modified: 27 Jun 2025 23:17 Thesis Files PDF - Final Version See Usage Policy. 20MB Repository Staff Only: item control page

PART I THE KINE TICS OF THE VAPOR PHASE EXCFtANGE OF RADIOACTIVE BROMINE BET'f/EE N TRIC HLOROBRONlotvIBTHANE AND BROMI NE PART II Tiill KINETICS OF TI·m FORWARD AND REVERSE REACTIONS OF TRE VAPOR PHASE 11'HERMAL BROMINATIOW OP CHLOROFORM PART III A ME 1l1HOD OF ESTIMATING AND MINIMIZING THE ERROR OF MEASUREMENT OF THE RATE OF A RADIOACTIVE EXCHAWGE REACTION Thesis by John H. Sullivan In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1950 i. Norman Sullivan ACKNOWLEDGME'NTS The author grat@fully acknowledges the guidance of his research dir-ector, Professor Morman Dav1.dson, whose excellent choice of research problems and continued interest in the c ourse cf the experhnental work have done much to speed the completion of this thesis. I wish to thank Professor Don !!J. , Yost who generously . provided laboratory space and es ... sential apparatus without which part; of this work could n.ot have been undertaken. Thanks are due also to Professor Richard M. Badger for helpful advice on the construction of photometric apparatus, To my wife special thanks are due for preparing the flgures and typing the thesis. ABSTRACT ; The rate of the homogeneous vapor phase thermal radioactive exchange reaction CBrCl3 + Br2 * --7 exchange and the rs. te s of the f orward and reverse reactions of the homo• geneous vapor phase thermal bromination of chloroform (A) CBrCl3 + HBr have been measured in the te.mperature range 420...4550 K. :Ei~or the brominat:ton reaction a mechanism which is eons1s-tent with all the experimental data 1s Br2 Br~ CHCl3 -cc 13 + Br2 __,. 2Br ---- CBrC 13 +- Br • The rate determining steps are (1) and (4). ..- (d) (5) ( l) (2) ( 3} (4) The rate of the ex- change reaction is given by k 0 {CBrCl.3)(Br) and the equation for the rate determining constant ko • ko(T) is identical to that for k4 as a function of temperature. The exchange reaction takes place, therefor$, by the reaction sequence {a), (4), and (3). The activation energies of (1) and (4) imply that the CH bond in CHC13 is weaker than that in OH4 by at least 6.6 kcal, and the CBr bond in CBrCl 3 is weaker than that in CH3Br by at least 11 kcal. The equilibrium eonstant K • (CBrC13 )(HBr}/ (CHC1 3 )(Br 2 ) is 1.96 at 442° K; the heat of reaction (A) is -o.9(t0.65) kcal. In a single exploratory experiment, it was obse!'ved that the exchange reaction between bromine and tri.fluorobromomethane is much slower than that between bromine and trichlorobromomethane. A method of estimating and minimizing the error of mes.sure• ment of the rate of a rad :i. oaetive exchange reaction is given. TABLE OF CONTENTS PART I: 1 r nE KINETICS OF :!.'RE VAPOR PHASE EXCHANGE OF RADIOACTI VE BROMINE BETWErrn TRIC HLOROBROMOMETHANE AMD BROMI NE Page, A. Tri chlo1"'obromome thane and Bromine • • B. Trifluorohromomethane and Bromine • PAHT II: • • • • • l • • 7 • THE KTMETICS OP THE FORWARD AND REVisRSE REACTIONS OF THE VAPOR PI-IASE THERMAL BROMI NATION OF CHLORO- FORM A. Intr•oduotton • • • • • • • • • • • • • • • • • 9 c. • • • • • • • • • • • • • • • 10 Analysis of t he Kin t i c Data • • • • • • • • . 13 D. Determination of t ha Equilibrium Constant • • • 22 E. ~!empei~ature Dependen.-:e of Rate Constants F. Mechanism of the Reaeti on • • Exper1. mental Di souss:t on H. I. • • 25 • • • • 25 • • • • • 28 ct Photometric Determination of t he Bromination Rate ••• • • • • • • • • Appendix: Determina tion of the Chai n Brea.king • • • • • • 0 • • 30 Ste p by t h e Meth od of Stationary States • • • , 34 J. K.. Fi gures • • • • • • • • • • • • • { followi ng 4 2 ) References • • • • • • • • • • • • • • • • • • 43 'rABLE 01:41 CONTENTS ( cont.) PART III: A ME1UWD OF E:S'l'I W JATI WG AND MINIMIZING T'.ti""E ERROR OF MEASUREM.EWT OF TEtE RATE OF A RADI O~ ACTIVE EXCHANGE REACTION • Propo s i t i on$ . "' • • 45 • , • • • • • • • • • • • • • • • • • 4'7 PART I THE KINETICS OF THE VAPOR PHASE EXCHANGE OP RADIOACTIVE BROMIME BETWEEN (1) TRI• CHLOROBHOMOMl:tPHANE AND BROMINE A'.N"D ( 2) TRIF1LUOROBROMOMETHA NE AND :BROMINE -1Reprinted from THE Jo uRKAL OF C1-1DuCA L PHY SIC S, VoL 17, No. 2, 176- 181 , February, 1949 Printed in U. S. A. The Kinetics of the Vapor Phase Exchange of Radioactive Bromine between Trichlorobromomethane and Bromine NORMAN DAVIDSON AND ]OHN H. SULLIVAN Gates and Crellin Laboratories of Chemistry,* California Institute of Technology, Pasadena, California (Received July 30, 1948) The rate of exchange of radioactive bromine between trichlorobromomethane and bromine in the vapor phase in the temperature range 42O-455°K has been determined. The rate is equal to k[Br2]![CC! 3 Br ], where log 10 k(moles/liter)-! (sec.J- 1= (-33,10O(±4OO))/(4.574T)+12.75(±O.2O). The energy of activation for the elementary reaction between bromine atoms and trichlorobromomethane molecules is 10.3 kcal., and the frequency factor is 7.9X 10 10 • It is proposed that the reaction proceeds via the sequence: Br* +BrCC! 3.-BrBr*+-CCI 3, and CI,C- +Br 2*.-Cl 3CBr* +Br*, rather than by a \,Valden inversion mechanism. The observation that chloroform is formed when hydrogen bromide, bromine, and trichlorobromomethane are heated is cited as evidence for the presence of -CC! 3 radicals and for the reaction Cl 3C- +HBr->-Cl,CH+Br. The -CC! 3 radical is then more stable than the -CH 3 radical by 10 kcal. or more. The vapor pressures of liquid trichlorobromomethane are given by the equation: log1oP(mm) = (-824O/4.574T) +7.64. The exchange t"eaction Br2(g)+AgBr*.-Br 2*(g) +AgBr readily goes to completion and is the basis for a convenient semi-micro method for the preparation of radioactive elementary bromine. INTRODUCTION Hodges and Miceli 4 have very briefly reported that the exchange between bromine and carbon tetrabromide in the gas or liquid phase proceeds by a bromine atom mechanism, and that the activation energy for the elementary reaction 1s 0-3 kcal. T HE investigation of the kinetics and mechanism of the exchange of radioactivity between atoms and molecules may be expected to contribute to an understanding of free radical reactions in general in much the same ways that the study of exchange reactions between ions and molecules in solution has contributed to the theory of ionic displacement reactions in organic chemistry. 1 Wilson and Dickinson 2 observed a photochemically induced exchange between bromine and trichlorobromomethane in carbon tetrachloride solution at 76°C, suggesting that the exchange reaction is between bromine atoms and trichlorobromomethane molecules. In order to avoid the complications in the interpretation of photo-chemical reactions because of non-uniform intensity of light along the light path and because of uncertainties as to the rate of recombination of bromine atoms, we have chosen to investigate the thermal vapor phase exchange between bromine and trichlorobromomethane. 3 EXPERIMENTAL (a) Preparation of Materials * Contribution No. 1232 from the Gates and Crellin Laboratories of Chemistry. 1 L. P. Hammett, Physical Organic Chemistry, (McGrawHill Book Company, Inc., New York, 1940), p. 164. 2 J. N. Wilson and R . G. Dickinson, J. Am. Chem. Soc. 61, 3519 (1939). 3 Just at the conclusion of our experimental work we learned that Professor J. Willard and Mr. A. Miller of the University of Wisconsin were independently engaged in a stud y of the same problem. J. Chem. Phys. 17,168 (1949). The trichlorobromomethane was prepared by the reaction of carbon tetrachloride and aluminum bromide. 5 A sample boiling at 104.2°C at 745 mm was obtained by fractional distillation in an all-glass apparatus. The vapor tensions of the substance were measured using a mercury manometer in a glass vacuum apparatus. These values, p(0°) = 11 ± 1 mm, p(22°) =35±1 mm, p(24°) =38±1 mm, in conjunction with the boiling point at atmospheric pressure, imply the vapor pressure equation, log1 0f;(mm) = (-8240)/(4.574T)+7.64, and a Trouton constant of 21.8. The measured density of 1.99 g/ml at 25°C agrees with the literature values. Hydrogen bromide was prepared by the reaction of hydrogen and bromine over a heated 4 J. H. Hodges and A. S. Miceli, J. Chem. Phys. 9, 725 (1941). 5 H. G. Vesper and G. K. Rollefson, J. Am. Chem. Soc. 56, 1456 (1934). 176 ~ -2177 EXCHANGE OF Br BETWEEN platinum filament, and purified by repeated bulb to bulb distillation in vacuum. The radioactive isotope used was the 34.5-hr. Br 82 . It was prepared by irradiation of 12 liters of ethylene dibromide with neutrons from a 250mc radon-beryllium source, extracted with 400 ml of water containing 20 mg of sodium bromide, and precipitated as silver bromide, which was washed and dried. Radioactive molecular bromine was obtained by the reaction: Ag Br* + Br2--tAgBr+ Br2*. A quantity of 100-200 microliters of reagent grade bromine was distilled in vacuum into a Y-shaped vessel of ca. 50-ml volume containing the silver bromide. The tube was sealed off and heated to 160°C for several hours with occasional shaking. The radioactive bromine was then condensed in one arm of the tube. Under these conditions, there was 100 percent exchange of activity. Kolthoff and O'Brien 6 report 60 percent exchange between bromine vapor and freshly precipitated silver bromide at room temperature. This method of isolation on the semi-micro scale of radioactive bromine was selected and developed because of its convenience and because it was believed to be a method that was unlikely to introduce impurities, particularly the oxygen bearing impurities that are often troublesome in free radical chemistry. (b) Procedure for the Exchange Reactions Aliquots of Br2* (15-75 microliters) and trichlorobromomethane (100-300 microliters) were mixed in a test tube that could be attached to a vacuum apparatus by a ground joint. The mixture was distilled in vacuum through P2O 6 and condensed in liquid air with constant pumping, and then distilled into an evacuated reaction vessel of known volume. The reaction vessels had been treated with hot sulfuric acid-dichromate solution, rinsed with hot water, treated with boiling nitric acid, rinsed four times with boiling, distilled water, and outgassed by fl aming in vacuum. The volumes (ca. 80 ml) of the reaction vessels were determined by observing the weights of water required to fill them to the sealoff constriction. I. M. Kolthoff and A. S. O'Brien, J. Chem. Phys. 7, 401 (1939) . 6 CC l 3 Br AND Br, The exchange reactions took place in the dark in an oil bath, the temperature being constant to ±0.07°C. Temperatures were measured with a Chromel-Alumel thermocouple and a Leeds and Northrup portable precision potentiometer with a precision of ±0.05°C. The thermocouple was calibrated against standard thermometers to an accuracy of 0.5°C. In order to avoid possible photo-chemical exchange, reaction mixtures were stored in liquid air when not being handled. An experiment showed that there was no exchange in unheated reaction mixtures. (c) Radio-Assay Procedure After reaction, the bromine was extracted from the trichlorobromomethane with sodium nitrite solution. Mercurous bromide was precipitated from aliquots of the solution which contained an amount of bromide equivalent to 15 mi croliters of bromine. Reproducible counting samples were obtained by suction filtration of the precipitate through disks of S. and S. No. 576 filter paper mounted on a sintered glass plate. The area on which the smooth m ercurous bromide mats were formed was defined with a glass tube pressed against the filter paper. In cases where analyses were run on two aliquots of the same solution, the results agreed within the statistical counting erro r, usually about 1 percent. The activity of the bromine before exchange was determined in the same way from solutions obtained by reducing measured volumes of the liquid radioactive bromine with sodium nitrite. That the transfer of bromine into the reaction vessels by distillation was quantitative was shown by radioactive assay of a reaction mixture which had not been heated. (d) Chemical Analyses of Reaction Mixtures For the semi-quantitative chemical analyses of the reaction products reported in the cl iscussion, the components of reaction mixtures were separated and identified usin g a small glass column and the general type of vacuum techniques described by Stock 7 and Burg. 8 7 A. Stock , Hydrides of Boron and Silicon (Cornell University Press, Ithaca, 1933). 8 A. B. Burg, J. Am. Chem. Soc. 56, 499 (1934). -3N. TABLE t C d 2 a b 3 a b C 4 a b C d 5 a b 6 a b 7 a b C 8 a b C d AND I. Exchange reaction betwee n Br 2 and CCLBr. 2 [Br,J [CC IJl3r[ Expt. (moles / liter)X I03 I a b D AV IDSO N 6 .77 6.38 11.90 11.57 7. 7 I 6.55 7.30 I 2.42 I l.84 33.50 6.62 6.59 15 .1 7 7.00 7.61 7 .38 6 .94 13 .00 12 .50 10.15 6.58 6.82 10.37 I 2.42 33.45 3 1.60 35 .35 34.30 35 .65 11.30 36.0.1 36 .85 3.1.20 33.00 32 .65 32.50 26.15 24.10 13 .12 36.55 34.25 38.50 25 .80 34.95 32.50 32.70 30 .75 36.80 k(expt.) sec. T °K X x10-, 19~.3 419.10 36 .0 432.00 36. 1 4.33.80 8.95 442.85 8 .74 444.25 17 .05 445.07 4.14 4 55 .52 7.08 455.75 0. 282 0 .286 0.3 83 0 .382 0.427 0.730 0.346 0.457 0.466 0.770 0.5 48 0.534 0 .720 0.59 4 0 .754 0.287 0.294 0.576 0.685 0 .535 0 .312 0.310 0.436 0.408 k (calc .) (moles/ li ter)-½ sec . - 1 x 1o r, 2 .98± .04 3 .00 ± .04 2.92± .08 2.99± .08 9 .1 8± . 14 10.05 ± .29 11.30± .2 11.09± .2 11.05± .3 27 .1 ±1.3 26.0 ± .6 27 .2 ± .6 27 . 7 ± .8 32.8 ± 1.0 33.8 ±1.5 31.6 ± .4 31.7 ± .4 63.5 ± 1.4 65.2 ± 1.9 70.1 ±1.2 i2.8 ±1.3 7:1.3 ± 1.7 69.5 ±1.3 71.1 ±1.3 2.97 9.63 11.43 25 .1 28.2 30.3 71.4 72.6 RESULTS AND DISCUSSION (a) Analysis of the Kinetic Data An integrated form of the expression for the decrease of the activity of rad ioactive brom ine clue to exchange with trichlorobromomethane that is originall y in active is x - -a ] = -R(a, b) -a+bt. ln [( -a +1 ) b c b ab In t his relation a=concentration of elementary bromine, in units of atoms per unit volume, b = concentration of trichlorobromomethane, c = initial activity of bro.mine, x=activity of bromine after reaction for time t, and R(a, b) is the rate of exchange. J . I-1. SULL I VAN 178 concentrations of brom ine and trich lorobromomethane, respectively. An experiment in a vessel packed with glass beads, in which t he surface area was ca. 12 t imes that in an unpacked vessel, established t hat t he rate of reaction was not dependent on su rface area; the rate constants of Table I refer to a homogeneous, gas phase reaction. It was also established tha t t here were no sign ifican t side react ions t aking place. The following observations bear on t his point : (1) The weight of t he mercurous bromide precipitat e from a reaction m ixt ure was t he same within 2 percent as that from t he unreacted bromine, and in agreement with the expected value. Thus, there was no consumpt ion or formation of bromine during the reaction. (2) A mixture of bromine and trichlorobromomethane a t concentrations of 5.1 X 10- 3 and 17.5 X 10- 3 moles/liter, respectively, in a twoliter b ulb was heated to 45 6°K fo r a t ime such that more than 75 percent of t he trichlorobromomethane would have undergone exchange. After extraction of t he bromine, the organic layer was dried and fractionally distilled in vacuum. T he substance was pure trichlorobromomethane with the vapor pressures repor ted above; there was less t ha n ½ percent CC14 or other more volatile products a nd less than 1 percent of less volatile products (CCl2Br2 , C2Cl5). D istillatiqn of a known m ixture showed that less than ½ percent of carbon tetrachloride could be detected by t his means. • The variat ion of k with t emperature is described by the equation This resu lt is a consequence of the general ana lysis cl ue to McKay 9 of the rate of exchange log1ok = ( - 33 ,120(±400))/(4.574T) between two components in chemical equi+ 12. 75( ± 0.20). li briu m. Vile have tested the , hypothesls t hat th"e ex- :rhe values of t he parameters were obtai;,_ecl by a change is a reaction between bromine atoms in least squares a na lysis cif t he data of T able I. thermal equilibrium w ith brom ine gas and t ri: For this t reatment it was assumed that the temchlorobromomethane molecu les, i.e. , R(a, b) = k peratures were kno~n wit hrcertainty. T he standX (a/2)½b. Table I exhibits the analysis of t he a rd deviations in · k given in the table were obexperiments on this basis. It is evident, par- ' tained from t he assumption that t he error was ticu la rly from experiments 2, 4, 5, that the rate d ue to statistical error of counting by using a n constant derived. in this way is essentially con- analysis of errors in an exchange reaction t hat stant for fivefold and threefold va riations in t he will be published separately. 10 The comparison 9 H. A. C. McKa y, Nature 142, 997 (1938). 10 N . Davidson and J . H . Sullivan , to be published. -4179 EXCHANGE OF Br BETWEEN CCl,Br AND Br, of calculated and observed ra te constants indicates that other sources of error were significant. Br +Br*CC!a-tB r-Br*+- CC l3, (2b l) Cl3C - + Br2*-tCl 3CBr*+ Br*. (2b2) (b) The Mechanism of the Reaction Other possible reac tions of interest here a re The dependence of the rate of exchange on concentrations implies that the exchange proceeds via· th e sequence: (1) Cl3C - + BrCCl3-t Cl3CBr+ - CC1 3 (no net effect), (3) Cl3C -+Cl3CBr-tCCl4+-CCl2Br, (4a) Cl2BrC-+Br2-tCl2CBr2+Br, (4b) C!aC-+-CC!a+M-tC2Cl6+M, (5) Cl3C-+C!aCBr-tC2Cl6+Br, (6) Br+Cl3CBr-tBrCl+ -CCl 2Br, (7a) Cl2BrC- + Br2-tCCl2Br2+ Br. (76) ko Br*+ CC1 3Br-texchange. (2) The bromine atoms liberated in reaction (2) are assumed to come rapidly into radioactive equilibrium with the rest of the elementary bromine. For k 0 , the rate constant of the elementary reaction (2), we have ko=kKc-½ , where K c= [Br ] 2/ [Br 2 ] is the equilibrium constant (in concentration units) for th e dissociation of bromine. For reaction (1), t.Hm•K=46, 110 cal. ,11 t a king t.C.=0.6. 12 t.E 435•K =45,620. In addition, t.S 298 °K =25.00 e.u., 13 t.S 436°K=26.00 e.u. For the equilibrium constant of reaction (1) in a small t emperature range aro und 435°K, KP= exp(26.00/ R) Xexp(-(45,620+RT)/(RT)) a nd IC=Kp/RT = (1/ RX435°) exp((26.00-R)/(R)) exp(-45,620/ RT)= (103.69X 10-<45. 620)1(4 5741') )_ Since ko = kK c-½ ' ko = 7. 9 X 1010< ±0.201X 1o-(10. 310( ±400))/(4.574'/') moles/ liter Xsec. The activation energy of reaction (2) is 10,310 cal. The frequency factor corresponds to a mean collision diameter of 3.3A. This frequency factor is but slightly larger than the value of ca. 3 · 10 10 , which holds for severa l similar reactions of bromine atoms as tabu la ted b y Kistiakowsky and Van Artsdalen.14 The possible spec ifi c elementa ry exchan ge reactions are Br*+Cl3CBr-t Br*CC!a+ Br (Walden inversion), (2a) 11 F. R. Bichowsky and F. D. Rossini, The Thermochemistry of the Chemical Substances (Reinhold Publishing Corporation, New York, 1936). 12 G. N. Lewis and M. Randall, Thermodynamics (McGraw-Hill Book Compa ny, Inc., New York, 1923), p. 80. 13 K. K . Kelley, The Entropies of Inorganic Substances (1940), Bulletin 434 of the United States Department of the Interior, Bureau of Mines. 14 G. B. Kistiakowsky a nd E. R. Van Artsdalen, J. Chem. Phys. 12,475 (1944), Table V. (The va lues of A in Table V should be multiplied by (575)1 / 1000 to make them comparable to the freq uency factor quoted here.) The observation that there were no significant side reactions implies that reactions (4)-(7) are not of importance for the present research. The heat of the Walden inversion reaction (2a) is zero, so that it is not impossible for it to have an activation energy of 10 kcals. However, th ere seem to be no certain examples of the vVa lden inversion t ype of reaction in the free radical reactions of organic compounds. There is no evident way of proving or disproving this mechanism except by the examination of all the other possible mechanisms. The value of the C-H bond strength of methane of 102 kcal. d et ermined by Kistiakowsky and Va n Artsdalen (see reference 14, p. 478) implies that for the - CH 3 radical, t.H(j) 291 °K=32 kcal. 15 For the reaction of methyl bromide analogous to (2b): Br+BrCH3=Br2+-CH3, t.H 291 °=21 kcal. 15 If the reaction scheme (2 b) is responsible for the exchange , the C-Br bond in trichlorobromomethane must be at least 11 kcal. weaker than the C-Br bond of methyl bromide. Nevertheless, the experiment described below strongly supports the hypothesis that the exchange proceeds via this mechanism. Braunwarth and Schumacher 16 have studied the photo-chemical bromina tion of chloroform. The followin g reac tions were of importance in 16 Using the values for the hea ts of formation of CH,, H, Br, Br,, and CH,Br given in reference 11. 16 V. V. Braunwarth a nd H. J. Schumacher, Kolloid Zeits, 89, 184( 1939) . -5N. D AV IDSO N .'\ND their discussion of the results : Ea(k t,.H(k cal. ) cal.) Cl 3CH + Br-C'3C - + H Br, 10 4 C'3C-+HBr-Cl 3CH+Br, 6 (86) Br+BrCCl3-Br2+ - CCl3, 6 (261) Cl3C - + Br2-ClaCBr+ Br. 6 0 (8a) (262) Reactions (Sa) and (262) are the direct sequence for the bromination. Reaction (86) accounts for the inhib ition of the reaction by hydrogen bromide, a nd reaction (261) for the inhibition of the reaction by trichlorobromomethane. The t emperature coefficient of the rate of react ion gives the activation energy for reaction (Sa). The values for (26) were obtain ed from a study of the bromine sensitized photochemical oxidation of trichlorobromomethane.17 The inhibiting effect of hyd rogen bromide corresponded to a rate constant for reaction (86) of ca. / 0 that of (262); this ratio was ind epend ent of tempera ture , so that the activation energies of the two reactions must be the sa me. The values of t:i.H were obtained as differences of activa tion energies , they imply that CCl3H + Br2-CCl3Br+ HBr t:i.H = 4. (9) This conslusion tha t the bromination of chloroform is endothermic is somewhat surprising. Since the entropy of the reaction is probably quite small, it implies that the equilibrium in the reaction shou ld lie la rgely to the left. Actu a lly the reaction has been used for the synthesis of trichlorobromomethan e in a sealed tube. 18 Th e conclusion s of Schumacher and Braun- .. :Cl: .. I :Ql-C· : Cl· , .. .. I :Cl-C : :Cl: : Cl: J. J-1. SULL I VAN 180 worth may not therefore be entirely correct. They contain, however, the interesting suggest ion that reaction (86) t akes place at a rate com parable to that of (262) and tha t the formation of chloroform in th e presence of hydrogen bromide be used to detect - CC1 3 radicals. In an experiment in a two-liter flask the initia l concentrations (in moles/ liter) were: [Br 2] = 1.85 x 10-3, [HBr]=3.80X10-2, [CC1 3Br] =3.37 X 10- 2. The mixture was heated to 460°K for a time of about a half-time for the excha nge reaction of the trichlorobromometha ne with bromine. After extraction of the hydrogen bromide and bromine, the organic layer was examined in a Beckmann infra-red spectrophotometer and by vacuum distillation. The infra-red study revealed th e absorption bonds of chloroform; the optical density of the 3.3µ-CH fund a mental corresponded to a mole ratio of chloroform to trichlorobromomethane of 0.10. In t he vacuum distilla tion, the only fractions isolated were ch loroform and trichlorobromomethane in a mole ratio of 0.19. Th e chloroform was identified by its vapor tension ; its vapor density corresponded to a molecu lar weight of 118.4 (th. 119.4) . The observation that the rate of formation of chloroform is comparab le to the rate of the exchange reaction strongly suggests t hat t he exchange proceeds via the reaction seq uence (2 6 ) involving t he - CC13 radical. We are now engaged in a precise study of th e kinetics of the formation of chloroform definitely to settle this point. It is noteworthy that as part of the recent developments in free radical chain reactions in organic chem istry, -CC1 3 radicals, generated either from chloroform or from trichlorobromomethane, have been used as chain carriers. 19- 20 The resu lts of the present research suggest that t he carbon brom ine bond in trichlorobromomethane is weaker than the carbon bromine bond in methyl bromide. Braunworth and Schumacher's values for the activation energy a nd heat of reac tion (Sa) are much smaller t ha n Kistia kowsky a nd Van Ar tsdalen's 14 valu es for FIG. I. W. Fra nke a nd H . J. Schumacher, Zeits. f. ph ysik. Chemie B42, 297 (1939) . 18 E. Paterno, Jahresb. Forts. Chemie 24, 259 (1871). 17 19 M. S. Kharasch, E. V. Jense n, a nd W. H. Urry , J. Am. Chem. Soc. 69, 1100 (1947) . 20 M . S. Kharasch, 0. Reinmuth, and W. H. Urry, J. Am . Chem. Soc . 69, 1105 (1 947). 181 EXCHANGE OF Br BETWEEN the corresponding reaction of methane, viz. , C H4+ Br= ( -CH3) + HBr, EA= 17.8 , MI= 15.8. There is, therefore, evidence that the carbon hydrogen bond in chloroform is weaker than the carbon hydrogen bond in methane. If it is in general true that the C-X bond in CCl3X is weaker than the C-X bond in CH 3X, we may say that the - CCis radical is relatively more stable than the -CH 3 radical. It may be that this is because of either: (a) steric repulsion of the chlorine atoms in Cl3CX compounds, which is partly relieved in the Cl3C - radical because the ch lorine atoms are further apart; (b) reso- CCI,Br AND Br2 nance stabilization involvin g the structures shown in Fig. 1. This latter type of stabili za tion will be more important the more readily an electron can be removed from the ligands attached to the carbon. Judging from the present research, the extent of the stabilization of· the - CCis radical is greater than 10 kcal. ACKNOWLEDGMENT We are indebted to Professor R. M. Badger and Mr. S. Burket for their cooperation in the infra-red analysis for ch loroform. VAPOR PHASE EXCHANGE OF RADI OACTIVE BROMI NE BETWERM TRI FLUOROBHOMOMETHANE AND BROMI NE One experiment on t he vapor phase exchange of radioactive bromine between trif'lu o1"obromomethane an.a bromine ind i cated t h at t h e CBr bond in th:i.s compound is much strong er than t h at in trichlorcbr~momethane, If t he mechanism for t he exchange is t h e same h ere as for trioh lorobromometha.ne, we have • ( Thesis, pa ge 3) The data of this experiment u sing trifluorobromomethane are = ½a = ... = T (Br 2 ) (CBrF3) b 478°K 6 .0 X 10-3 mole s/1:i ter 5 .0 X 10- 2 mole s/liter t .. 7 . 32 X 104 sec • = 183 eount;a/mi:n ~ c = 19 5 counts/min . X from wh ich k' :: 2.6 x 10•6 ( moles/li ter)'·•lsec . •l • F'or compar- ison t he value of the rate constant k at 4780K for t he exchange of radioac·Uve bromi ne between trichlo1"obromornethane and bromine can be calculated from (Thesis, page 3) • If t he frequency factors for the two reactions CBrG13 + Br -0011% + Bro CBrF~ t •CF5 + Brg v Br "" are equal, w@ have ko/k~;: k/kt 1: 1o(E'•E)/(4.574T) E1 : 1'7 .5 keal . Be cause t he experirne}ltal value of x/e = 0.94 is veey close to unity , it is important to examine the precision with which x./c was m~asurecl and to appreciate th~ atfect of an er1:or in x/o on E ' • The deviation of' x/c from unity may have been dtte to chance a.lone .. to the Pandom fluctuations which occu.:r in c ounting rates as a 1.,E:H,mlt of the statistical nat;ure of radio-- active de cay. The probable error r in x/e, assumed to be due only to statisti.cal error of counting and determined from the probable er-rors in the eouJ1tin·:t rates x and c, is 0 . 015. • From the normal curve of error the probability of an error larger than 31-. oecu1. .i'ingin a statistical population of errors :ts 0 . 043. For x/c, 3:r = 0.045·, Therefo11 e with a p.1"obabili t y of (1 ~ .043 ), the values of x/o and E' a1:-e ( 0 • 94 - 0 • 04 5) ( x/C t.. ( 0 • 94 + 0 • 04 5) 1 6 kcal, 1. . E t t... 19 kcal. Thezte is a s r!lall probabil:1 ty , 0 ,007, that the random fluctu- ations of counting produced an error larger than 4r: 0.06 in x/e; the ''true" experimental value of x/c may have been x/c which g ives a lower limit 01'"' k' .: 0 and does not allow any upper 11. mi t of E' to be calculated. = 1, FART tI 1'liE' KIN'.ETICS OF THE :FORWARD AND REVERSE REAC:TI-ON$· OF THE H(YMOGENEOU:S VAPO.R. PHASE THEl~.A'L BR OMI-NATI ON OF .CIILOROFORM INTRODUCTION The determination oi' the kinetics of the forward and re- veX>se reaetions of the vapor phase thermal bromination of chlorofol'm CBrCl3 + HBr (A) was undertaken a) to furnish an experimenta l proof of a proposed meehanS.sm i'or t he vapor phase exchange 0£ radioactive bromine be t\veen. tri.chlorobromomethane and bromine,. and b) t .o redetermine values of activation ene rgies obtained by Braunwarth anrl Schurnache:r< l) in a study of the kinetics of the photobromi nation of chloroform., and b y Franke and Seb.umach.er( 2 ) in a study of the bromine sensitized photochemical oxidation of chlorof orm .. The exchange of radioactive bromine between trichlorobromo ... methane and bromine ha.s been shown to proceed vi.a the rate deter~ining step(S);(4) ( B) excha:rige • Fr om the exehange e1.:pert ment s no decision cou ld be ma.de as ·t o whe-t;her t he exchange took place by a one step Walden inversion or by a free radical me ehanism such as :Sr . + CBr *Cl,;, i) + Br2 «· (4) CBrCl3 + Br 1!- • (3) -cc13 Br 2 * -+ -CCl"" ..'? The kinetics of reaction (A) show t ha t the react ion in t he re • ver se directi on,!.!• t he reaction of hydrogen bromide with tri - - ehlorobromometha.ne, takes place via the sequence Br 4 CBrCl 3 ...cc 1 3 + B:r2 - - - > CHC l3 ~ Br (C) In this pa.per the rate constants for (B) and (C) are shown to be equnl a.n d to be the same fune ti ons of the tempera tu:r•e. 11::1.e radioactive ex.change reaction must therefore take place by t he free ra.diee.1 mechanism, reactions (4 ) and (3). Activation energies reported by Braunwarth and Sehumach.erCl} and by Franke and Seht:imaeher ( 2 ) g!. ve an end otherm.ic heat of reaction for the bromina.tlon of chloroform and are at variance with t h e values reported l1ere and in a previous paper< 5). '11he activation energies deter-mi.ned her·e indicate the bromination of chloroform to be exotherrr.i c, in agreement; wi.th the observation of Schwab and Lober(6) that the equilibrium c onstant K ; ( HBr )(CBrC l3}/( Br2)(CHCl3) decreases id t h inc1,.ea.sed te mperature. The kinetics of tr e thermal bromination of chloroform ie sa:bisfactort ly explai.ned by a raeehani sm propoaed by Braunwarth ana Schumacher for the photobromination. EXPERIMENTAL a) General experimental method l111e rate constants were determined from the d:ti,e ct; 1 measurements of t he initial and final a mounts of bromine in ea.eh reaction s ystem.. One reaction aystern or run gave one datum, to be u sed 111 calculating the value of a rate constant . b) Preparation of materials The chloroform was prepared by washing Eastman Kodak white label chloroform with co ncentrated sulfuric acid, t hen dilute sodium hydroxide fo ll owed by several porti ons of distilled water< 7 >. The ehlorofo1"!>m was dried in the dark over potassium carbonate. Fractional distillation in the dark in an all glass apparatus gave a middle f'raction oi' about 300 ml . from a total o:f 700 ml . The bromine used was Merck reagent grade, dried over phosphorus pent oxide. The hyd:Pogen ·bromide and trichlo1~obromomethane were prepared and purified as deserlbad in a previous paper( 4 ). All four reactants were stored in vacuum l:tne storage bulbs kept at t h e te mperature of acetone di-.y ice mix.tures. c) Procedure for t he reactions The reactants were dried, degassed, a.nd distilled into r eaction vessels in the vacuum system shown i n I•'igure 1. In fillin g the reaction vas'sels an aliquot of e1 ther ch loro:form or t1--ichlorobromometha:ne was distilled through a tube containi ng solid potassium hydroxide and phosphorus pentoxi.de into the tube A. A po!'tion of this aliquot was tested f or chlorine in the case of trichlor.obromomethane or ehlorine and phosgene in the chloroform,. These testa, us ing starch iodide solution and barlu.m hydroxide solution wore always negative. pipets., From A, using mi cro- (50 -300 mi eroliters) calibrated to deliver chloroform, an aliquot was pi petted into t he glass tube B which was attached to the vacuum line with a ground glass joint . The liquid was degassed and dried by vacuum dis·billa.tion through t h e P2 o 5 tube and condensation in the liquid ...air trap C duri ng cons t a nt p1..1.mping . With t he bromine storage bulb at o° C bromine vapor was nllowed to fill t he volume D at room tempera t ure at the vapor tension of liquid bromine at o° C. The vapor was de gassed by cu sti llation i nto the trap C dur ing constant pumping . 1'he bromine 1 and halogenated methane mixt ure was then distilled .f'rom C into the reaction vessel of known volume . In1.tia1 concentrations of bromine in the reaction vessel$ were determined by f illing blanks before and after filli ng the reaction vessels and ti.tratj.ng the bromine in these us ing a starch iodide solution and standard t hiosulfate solution , Amounts of hydrogen bromide distilled trom the hydr ogen bromide st or .a ge bulb were measured in the known volume E wi t h the gas at room temperature and at a p1"essure measured on the . ,,C.Qll£it;t a.nt volume mer(}u.ry manometer . After di stille.tiolt,.J'lit the hydrogen bromide onto the bromine- halogenated .methan$. 11:ixt ure .a in the 1•eaction vessels~ the vessela were sealed off at a p1"esswe of a.b out 10.-4 to 10-5 mm. of mercury whil~ und@r c on- etant pumping . The density of ch lorofor m i s given as a function of temperature in t he International Criti cal Tables. The density o:f tri ... chlor"obromometha.ne is given at 15°c; densities at other temperatures were calcu lated assuming t h e d@nsity to ·v ary with temperature as does that of carbon tetrach loride( 8 ) _ Deli wn:·y volumes of t he mlc ropipets we r e assu.med to be t he same f or ch loroform and tri chlorobromometba.ne. The volume E was determined by a Boyle's l aw comparison to a bulb, (ca. 120 ml .) 1 t he volume of which was determined by weighing the bttl b f:i.lled with water on an analytiea.1 balance . In the Boyle's law comparis on car bon dioxide was used as t he gas and f)ressures were measured on the constant volume manometer .. The reaction vessels had been tr•eated with hot sul furic acid-diehromate solut i on, rinsed with water., treated. with boi ling nitri c acid., rinsed four ti mes with h ot water and outgassed by flam1.ng in a vacuum. The volumes (ca. 80 ml.,) of the reaction vessels were determi ned by observing the weights of' water required to fill them to the seal- off constriction , The reaetions took pla.c e in the dark in an oil bathi! the temperature being con stan·t; to ,!"O. o7° c. Temperatures were m.e asured with a Chromel-Alumel thermocouple and a Leeds and Northrup _o~ta.ble pr·e cision potentiometer with a precision of .:o.os° C, The thermocoupl e was calibrated age.in.st standard thermon:ieters to an acou?tacy o:f 0 . 5° C. In order to avff:tc1 pos- sible photochemical reactions, reaction mixtures were stored in liquid air when not being handled, At the e11.d of a reaction the l"ea.etion vessels were chilled in liquid air, era.eked open, and the reaction mixture t i trated fo1. . bromine using potassium iodide ana standa:r>d 0..,02 N t h iosulfate solution ... • A comparison of the bromine con tent of a blank titrated i mmediately aftel" di a·t lllation to t hat in a re .. action mixture kept at liquid air temperature for 24 h ou r s sh owed no reaction in the reaction mixture. AUALYSI S OF THE KINETI C DATA a) '.rhe r•ate of the .forwa:t•d react.ion in the absence of' added hydrogen bromide and trichlorobromomethane The rate of the forward reaction CBrC1 0 + HBr has been found to be proportional to t h e ch loroform concent1"s.tion and to the square root of t he bromi .n e concentration; t he react:i.on is 1.nh1b1ted by hydrogen bromide and the rate is sati.sfa.etor:i.ly dese1,.ibed by the equati on (l) For runs using reaction systems :ln which the initial concentrations of hydrogen bromide and trichlo:robromemetha.ne were zetto a.no (CHCl 3 ) >> ( Br 2 ) this equation has 'been integrs:ted assuming the concentrations of chloPotorm, a.nd of bromine and hydrogen bromide in the inhibition term, to be constant during the run at the average values define.a below·. (2) where k 2 /k5 1:: Inhibition constant {CHC l s )a :Z {(CHC l3) 0 + (CI:I Cl3 )r)/2 (Br 2 }a. ( HBr ) a • ... (( Brz ) o + ... (HBr)r/2 (Br 2 )r)/2 • Subsorlpt s o, t:, and a on t he reactants: refer to initial:t final, and ave1--age concentrations. In these runs the decrease in t he chloroform concentration during the run a.mounted to about only 2% of the initial values; the changes in (UB:r) and {Br 2 ) are si gnificant eompared to the ini t i al concentrations, of course, but since k 2 /k3 =. «040 {see late:r) and for all t he se l'.'uns ( HBr)r/( Br 2 )f < o.60, the use o:f average va lues in t h e in- hi bi tion term produces er1"'ors .in kf which are small compare d to experimen t al errors. That equations ( l)- and (2 ) desoribe the rate may be aeen from Table l; variations fou~••·-i'old in initial 'b~omin.e concentrations and two-fol d in in1 tie.I ebloro.f'orm c.o nefJntNitions have . no e.ffec t on calculated value.s of kr-• From the df p$ndenee of the ziate on. eonce.n trations the rat.e _d.e,termining elemtn.1ta:.r y reaction, mus,t be one .between triehlorobr.omomethane and b!'om:tne. atQm~ in ·t hermal equilibr ium wit-h bromin& molecul es,.. - The ex. pePimental data i.n the.s.e reaet1ons aJ:>e not s1.1:,ff!eien·tly precise to sho\v the dependence of tile :riate on the .inhibition · term, {.i + k2 (HBP )/k3 (:s~2)) • 1 wJn.ich varied but little from 0~,98 ln all these ~uns; h owever,. a;s will be shown later, the rate express ion fo-r t h e forward r«tact1on in the p P,t1Hles1ce of appree:table tni tial eoneent?J$.tions of hydrogen bl'omide is strongly dependent upon thl s teI'm-. · Table ! Rate of the Forward Reaction Run . { Br 2 ) 0 . (CHC1 3 ) 0 kf moles/ liter la kf {moles/ liter )•½sec ,•l x10!3 :x103 xlo 6 x106 0 . 452 b o ♦. aee 38,4 51 . 15 20 . 61 20.92 20-76 2a o.746 l. 752 1. s u; i2~l5 30.15 31.•,25 19,70 20.85 20 . 25 . 1.200 15.59 15. 97 b C 3a. b e 1. os1 2._1oa 15.73 20 . 20 441.81 19. 50 19. 23 19 .• 87 ...1e,... '.Pable I (continued) Run ( Br2)0 { CHC 1 ) 0 3 moles/1:lter x.103 x10 3 6a l.351 b 2.098 C 2.082 2.165 d Sa b C d e lla b C ox 442.05 28i,90 30,07 2.070 1.977 1.448 1.411 1~358 28.65 27.40 1.994 27 . 70 1 •.425 l.36:3 30.40 30 .. 92 30 .:LO tcr x'-06 xl06 20 . 23 20 .03 20.oa 20.03 20.09 2 . 972 2.995 3.040 419.98 C d l .4.07 e 1.471 29 . 65 30.96 301!10 3.015 3 .040 3 . 025 455.06 57.7 58.2 455.06 58 .2 57.8 58 .4 57.8 57.8 57.3 29.10 28.60 17~7'1 kt . /1 i.•t· er )•½ sec · .. oi!>l •( mo l es 29 . 00 2.092 2.028 2.200 12e. b b) 29.00 29.12 T 57 .8 The rate of the rever se reaction The rate of the reverse reaction GHC1 3 + Br2 is :. ropo1"tional to t he trichlorobromomethane concentration, to the square root of t he bromine concentration, and to an inhibition te1"m which involves the ratio of the bromine concentrati on to the hydrogen bromide concentration ,. v;tz. • ( 3) In all t he l"uns on the reverse l'"ea.ction the init ia l con centrations of h ydrogen bromide and of trichlorobromom.ethane were large compared to that of b1,.omlne. rrhe concentrations of' hydrogen bromide and of tri chlorobromoo1ethane were t reated as c on.$tants in in ... tegrat:t ng e qt1at'io11 (3) s ince the percentage change in t h ese dur 1.ng any run wa.s amall compa red to the perce ntage ch..ange in is then J ( :Bx-2) o1 ~ :: ( HBr ) a ( CBttC1 3 )a,t (4) where (HBr)a, = (( HBr ) 0 + (HBr} t )/2 ( CBr Cl3)a :: ( ( OCl5Br ) o .. (GCl 3Br)1J/2 • At a gi ven te:mpera:ture ; five ct> six runs were made ( Table II h Using the data from these runs equation (4} 1 c ontaining the two unkno~rn.s ~ and kz/ k 3 , was solved by the t r.:tal and error substi tuti on of likely values of k 2/k 3 • Five or s ix individual values -o f ~ ( one for each run) and an -avenige value ka, w~re oalculated for e.ach trial valuia of kg/ka• That value of k 2 /k3 whicb. gave a minimum sum of the squar•ed devi ations .of the 1n- di vidual va.luea of kr from their average value kr was taken to be t he correct one. The value s o.f kz. and k2/ks as determined in thi s way from equation (4) and given in Table II are constant f or two-fold variations in bromine , hydrogen bromide, and tr1ch lorob1. . omome thane initial c oncem tra ti ons. The rate dete1...... mining s tep ia a.gain a zteaction of bromine atoms in thermal equilibrium with br•omine molecules, in th1 $ case with trich loro- bromometha.ne molecules . The value of ¾/ks used in calculating kt in Table I w·a.s taken f1?om Table Ir . •18• Tabl$ II Rate of the Reverse Reaction Run ( Br2t, ( CBr0lzb ( :HBr )(:) moles/liter ... :x1ov xJ.O3 x103 11.48 12. 25 20 . 90 23. 50 22 . 13 35. 90 38.45 28 . 85 33.05 31 . 20 0.552 0.541 o. 570 o . 576 1 . 350 16. 06 14.75 24 . 30 33. 55 1 . 482 24 . 90 23 . 50 24.78 14 . 42 5a 0. 532 b o . 56'7 C d e 9a. b C d e lSa. 1.240 1 . 395 1.515 b o . 557 C 0~598 14'1 b l.;360 0 . 540 C c) o . 587 15 . 72 22 . 79 13 . 99 23.68 T O'fC 442.07 22 . 21 25,. 55 25.20 k2/k3 25 . 48 .0405 3.65 .0408 7 5 .'7 . 0392 25.€;5 !3 . 64 420 . 10 21 . 40 36. 90 $6.10 3? ~35 kr 25 . 50 25.50 'S7 .30 39 . 10 kr ( moles/1. )•·lsec-:-1 x106 x105 3.66 3 . 64 3.675 :3.64 '75 . 6 455 . 06 32 . 45 19.94 34 . 20 '75 . 8 75.6 75 . '1 76.2 75 . 0 Determination of the ratio, k9/ k3,- from the inhibiti on of t he forward reaction by added hydrogen bromide. Several runs were made with the f ol;'\vard retac ti on st.t"ong ly inhibited by hi gh concentrations of hydrogen bromide. The ini tial concentration of trich lorobvomomethane and t he initial ra t e of the reverse reaction in t hes@ runs were zero; h owever, because kr is larger t han k.f by a factor• of about 10 and b$- eaus e the concentrations of hydrogen bromide were high in all these runs, the small amounts of trichlorobromomethane ( /\., l x 10- 3 mole s/11 ter) produced by the forward rieac ti on were enough to make the average rate of the reverse reaction a.bout 10~ of that of the forward reaction . With the rate of t he reve:rse reaction now comparable to the rate of the fol"we.rd reaction,. t h e rate expression i s By rearranging, th~ rate ean be expressed ~s a .function of k.r, kg/k 31 and the :r-a.ti o k.rk3 /k!»k2_,- • •d{ Br 2 )/dt ; . l -_ ~ _ -. kt ~2 (HBr )/ ( -) k3 Brg ( ' 1 (CRCl:;) (Br2) 2 ( 6) • (1IBr){OBrCl5) /( Bl'g)½(!<rkl'Jl'krk:!~ • • As shown latet• the ratio krks/krk2 is the e quil1bn1um constant of reaction (A) .for a proposed mechanism that s:atisf'ies the kinetic s, (HBr){CB:rOl:;)/( B~2)(CHCl3) = K :; l<tks/k:rke • (7) Treating the high concentrations ( HBr ) and (CHC 13 ) .a s eonsta11ts equation (6) can then be :tntegrat$d to give k2/k3 ::: _ krNt ... 2 [ ( Br2)9½ .. (Br2}1-~ ) M (HBr )a 1 Nf.1! • log [ (B~2-)Q½ - iJ][ <Br -· 2 -)r½ - -+ ( Br 2 ) 0 l + -~ ;¼] • l (8) ( Bx•2 .>:r½ ... ~ where 1) ( HBr)a/K M :: [ K(GHCl3)a/01~r)a + 1 ) (B~2>a • N' =- ( (cHCl3)aK/(HBr)a + The equilibri um constant K* given in Table III; has been calculated by substituting values of' kt' from Table I and values of kr and ¾/k3 from Table II into equation (7). Table lII The Equilibrium Constant from the Ratio of Rate Constants K 420.0 3. 015 s.ae . 0408 2jj01 442 . 07 20.1 25 . 48 •.0403 1.sa 455,. 06 5'7 . 8 75,.7 ,.0$92 1.95 Using these values of K, and the values of kr determined from the f orward reaction , equatlon (8 ) was used to ealeula:te the values of k 2/ k3 given 1:n Table IV. Thie calculQtion of k2/ k 3 is no·t an example o.f nbegging the guest1ontt . In. equation ( 8 ) k2/k3 ls sensi t i v-ely dependent on k:r {a 11& error 1n kr gl ves a 3% .error in k2 /k3 ) and insensitively dependent on K {a 1% error i n K give e a 0. 2% error in kfa/k3). Table IV The Ratio k2/k3 :from the Inhibited Forward Reaction Run (Br 2 ) 0 (CHC15 ) 0 (HBr) 0 (moles/11ter)xlo 3 T OK k-r ~108 k2/k3 kz/k3 4e. b 2 .1'75 28 .25 27 . 50 28. 45 18 •.85 441 .• 68 19 . 8'7 .0556 .0276 .0334 9 . 92 . 03170 27 .25 32.15 14.65 . 0425 .0435 C "la b e d e 2.105 2. 176 1.962 2 •.31'7 2.265 2. 023 2.247 2'7 .• 80 30 . 90 24 . '70 27 . 45 33. 35 37.25 2 . 064 28 . 67 28 . 35 26 . 82 1 . 933 rr. 34 17.10 26ii96 2. 041 9 . 63 31 . 45 10a 1 .252 b 2.168 e d a - 30.10 19 . 25 31 .20 29 . 67 442.07 419 . 98 20 . 1 3.015 . 0444 .0422 . 0416 . 0385 . oJ95 . 0394 . 0387 . 0391 . 0428 . 0390 The low values of k2/ks of Run 4 a.re a result of poor ex""' pePimental technique rathe:v than of insufficient co:t"'I"EH3POndenee between t;he equations deser-lbiri..g ·the kinet1.ca and the actual kinetics of the reactions . In Runs 1-·• 4 bromine-,.halogenated methane mixtures were pipetted into the tube Band then dlS• t .i lled; the uncertainty in the bromine . concentrations in t h ese runs is mueh larger th1;m that in lateJ? runs in whieh the method of filling reaction vessels described un<ier "~pe1..,imenta1u was used. The values of k2/k3 as calculated from t he i.nhibited for. ward r$act1on , Runs 7 and 10., agree wi thi.n experimental e:rror with those .¢ .alcula.ted from the reverse reaction {Table II ) • d} Side reactions and surface effset. Two experiments in two-liter bulbs established tha.t there were no sign:L fieu. n.t side re.actions. I n ea.ch expEn•iment frac- tion.al distillation after reaction showed less than 1% of the " products to be leas volatile eompounds {CC12Br2,. C2c1 6 ) . The se experiments are d.escribed on pages :3 and 5. The agree - ment of' the values of k 2/k3 detevmi~ed .from the forws.1"d (Table IV) with those dete~mined from the reverse reaction (Table II), and the agreement of' the directly measured equilibrium const.ar;rt K ( see later) with the valua of K calculated from the ratio of t he rate constants also indicate that there were no significant side reactions. Experiments on both the for-1.vard and reverse reactions in vessels packed with beads with. a total surface area of£!.• 6 times that in unpacked vessels established that the rates were independent .o f the sur face area.. DETERMI1'!ATI01J OF THE EQUILIBRIUM CONSTANT The experimental deter.minat:ton of an equili.brium constant b y a chemi cal analysi s of :reaction s ystems usually means the value of the constant 1s bracketed between two limiting values obtained from reaet;ion s ystems wh ich ap9i•oach t he equilibr:tum ·state :from both t h e forwa1..d and the re verse directi.ons. How• ever·, the equilibrium constant may also be determined fr om the net rate of a reaction in either d:ireetlon if the forward and reverse rates a.re comparable. For t h e brominat;ion of chloroform let A and B represent the concentrations of chloroform and tri• ehlorobromomethsme in a reaction system CB1~ 13 + f!Br B • The rate of disappearance of bromine is given by krA(Br2)i --------- ____!trB( Br2)½______ .,,.___--:, l + k3 (Br2}/k!{ HBr) .... I f the concentrations of chlorof0~m and trichlo.robromomethane, A anu B, a.re large compared to t he concentrations of bromine and hydrogen bromide ., the percentage change in A and B during reaction ls small compared to t he percentage change in (Br2 ) and (HBr). Por such reaction systems t he rate equati on can be integrated treating A and B as constants~ If also the initial concentrations of a.11 the rea.eta.nts are almost at their equi• lihriu.m values_. the inhibition term (1 + k2 (I:IBr)/ks( Br 2 may be taken to be eonSftan t during a reaction~ J. 1 Using these assumptions the rate equa tion ean be integr-ated to give t = 2K •.. . ( ( Br2) 0½ . - (Br2):r½ + 1.1s{Br2 )etlos1o kt(KA + B) l . ( B.r2 )_0 ½ . . ( Br. 2>e½~ - (Br2)f½ .• .,. ( Br2). e½~j ( . . . . . J... • • • • .=!,. •• • •. l + k2 { HBr ) a/k5 { Br2 ) a 1 ~(B:Pg) 0 2 + (Br2 >ea { Br 2 ) f12 ... ( Br 2 ) ei J ~ a ( { Br2) 0 + (HBr ) 0) / (:kA • B J (Br2 >e or., 1n order to simplify ealeulations t " k r i : \ B) f (BI>:i)i ~ (Br2Y' + 1,15( Br 2 ) 6 ½iog10 ( Br2>0¼ - ( BP2 ) ei ( B.r-2)/1!_· + ( t~l'2)e2 1 ( . • 1,, _ [ (Br ) 2 + (B1• ) 2 2 0 2 6 ~ (Br2 }:rz • ( Br- 2 )es 1 • . ·. . . J ' 1 t k2 (I1Br ) a.fk3 { Bf2) a • ro, Here the reactants ave now given not in con:eentl~ations but in moles and vis the volume of the reaction vessel in liters.. The sub$cripts o, f, e,, and a on the react;anta indicate initial, final , equilibrium., and ave;a:,age values. The equilibrium constan.t , K, is in this equation .an implicit function of t he experi men- tally determinable quantities, t, kr, k2/k3 t and the concen• tra ti ons of t he r•eao tan ts " Reaction systems weve prepared in which ·the c oncentrations of the 1"eacta.J1ts fulfilled t h e Conditions under which the dif:fe ren.tial rate equation (9) was integ rated . After t•eaction '11he time$ of 6 ... 10 h ours these \"!ere analyzed for brorr.d.ne. values of K given in Table v we1"e ealcu...tated fr om equation (10) b;r tri al and error ..,. by substituting l ikely value s of K until the equati on was aati s f:i.ad., Th:e t:trne, t .,. is a sensitive f-t.motion of K; a change of 1 p~J."t i n 200 in K produces a ehange in t of 10 ud.nu te s in ~85 ( Run l ) * and a change of 50 min:u te s i n 64 0 ( Run 2) ~ I n Table V a comparison ot the valtt$ of Kt = (Imr) :r< CBr o1 3 ) :el <Br 2 ) r< OBO J..3 ) :f for each 1?un w:t th t .h e value$ of Kand K0 = { H'.8r) 0 ( CBrCl5 ) 0 / ( Br2) 0 ( GI1Cl3} 0 .fo:r" the aaro.e run show s that the eoncent:ratlons of th£¾ l"$.aetants changed very l i ttle f~om their i ni tial values over a 6 ... 10 h our- :J?eaction time; the systems were 4 t hereto1°e., ◊lo se. to their e q_uillbrium states . The a11erage value of lC 1:n. '1\t.ble V :l a 1,.95 wh:teh agree s well \d th the value ea.lculaued from the ratio of rate constants , K i l.96 a.t 442 ,11r07{t}l{ ( Table III ),. Table V Measurement of" th0 Equili bri um Const.ant at One Temperature 1! :: 442 ,0'JOK kr. . ~ 20.. 1 x 10 ~6 Run v CHCl3 CBrOl3 ( HBr)0 ( Br2) 0 ( Brz)f' K0 :u.ters - - - - - mill ,.mo,l e s - - - - - 15a . 0753 b ~or154 C . 0767 d . 0783 e .o~a1 16a . 084'7 p .• 08 32 e ·~0868 d . 0841 - e ,0833 2 ~257 2. 257 2 . 2'5'7 2 . 257 2.257 1 , 505 1 . 505 1.505 1 . 505 l.505 . 908 . 908 .oos ,908 . 908 . 593 . 593 . 593 . 593 , 593 .-657 . 657 .1057 . 1057 .,552 . ;;1.051 ,555 .105'7 , 596 . 1057 .50 6 .,1055 , 521 . 541 . 561 .4! 418 . 1055 .1055 . 10 55 .1055 .,1113 , 1128 2 .• 50 .10112 2 .. 10 2 . 10 2. 27 .. 1079 .1097 . 1058 . 1065 , 1066 . l 08f5 . 1002 2 . 50 l . 89 l . 95 2~..02 2.,.06 2 . 33 2.29 1. 9'7 2.()7 1 .• 99 2,06 1 . 96 1 . 98 1 ,. 885 1 . sr1 1 . 9$ 1 . 89 2 . 15 1 . 99 2 . 10 l . 95 2 . 02 1 . 57 1 . 89 l,.68 1. s 9 '.l?EMFERA'11URE DEPENDENCE OF R.1,\TE CON8 1l1AriTS T11e variations of kt and Kr with temper,a ture are deser1bed by the equ~tions The parameters in the se equations were determined graphically by plotting kt and kr e.gainst 1/T on an e xtended scale• Prob• able $rrors, r,. of ~ :f and kz- at the extremal temperatures were calculat@<'i from the individual values of k.r and kr at these tempe:ratui:-es. The errors in the parameters are those resulting from t he ~.ssum.ption of errors of 0. 1°c :tn each of the ex• trema.l temperatures and errors of 2r ink.rand kr .. these errors tf\ken a s to give e maximum ei"ro:r in the aeM.va.tion energies . The temperature de pendence of the illh.ibition constant , k 2 / kz , is too small to be deterrrdnad .from the p1?ecit!li on of the result,$. The trends shown in Tables II and IV a.1~e in opposite directions . "fhe data in the tables indicates that over the temperature range 420-.455°c k 2 / k 3 = . 040 .!: , 002 . A mechanism for reaot1on (A),. eonststent with the de-... pendence of the forwsvd t:111.d reverse rates on aoncentrations , is one si milar to that proposed by Braunwarth and Schumacher ( l ) fo:r. the photohromination of chloroform. 1 •26• 2Br + M (d) ---+ RBr + •CC13 (l) HBr + ..CCl5 ~ CHCl:5 Br { 2) Br2 + .- cc1 3 ~ c:arc1.,, + Bl? ( 3) Br2 ...cc13 (4) M (6) M + Br2 Br + CHCl3 Br + CBrClez. V M + 2Br ----+ Br 2 + "+ -t Reaction {2) aceo'Ullts for the inhibition of the forward reaction by hydrogen bron1ide; reaction (3) shovrn the reverse reaction to be i :nhibi ted. by bromine. The inh:tbi tion terms ( 1 + kg( HBi") /k3( Br2)) •l and { l + k3( Br2} /ka(P'J3l,,)) ~l are the fractions of ... cc13 riadicals wh ich are reacting at a:n:y t i me to gi ve trichlorobromome'bhane and chloro.f'o1')m reepectively. App J.i,.. cation o.f the method of stationary states to this mechani sm re• sults in the general rate equation (5) which is in a greement with all the experimental data;- ( t,) where the rate constants ~or the elementary reactions are kl l. i: kt l<e • 1a k4 :: ~ lee-½ and Kc :: kd/k5 :: ( Br} 2 /( Br 2 ), Setting the rate equal to zero in equation (5) yields K = ( HBr }( CBrC 13) /( Br2 )( CHC13) : k1 k 3/k2k.4 • For renc ti on ( d) h l:1 291 OK : 46 , 110 eal J ( 9 ) taking ~ Cv : o . 6,. ( lO) Li E4560 K :; 45., 620• In addition, i\S2980K = = 25.00 ~. u ., (ll ) 6 84.350K 26 . 00 e.u, Fo:t> the equilibrium constant of reaction {d) in a SI-nall temperature range around 435°K, i~ ·:; 8 26 .·00/R 8 -(45 1 620 + Rt )/RT Kc ::: Kp/RT Since kl :: 10S:J.3l( ! 0 . 15) 10~(9,220( ± 300 } )/4 . 574T k4.:: 1010. 86 ( t 0 • 15) 10- (10tl20( ± 500) )/4 . 6'74T • and Th$ activation energies or reactt'ons (1) and (4) a.re E1 ::, 9 ;220( :. 300) kcal . E4 :: 10;120( ~ 300) kcal ., The frequency fact or of reaction (1) is smaller bys. factor of 10 than those tabulated by Kistiakowsky and Van A.rtsdalen (1 2 ) for .$ im:i.lar reactions of bromine atoms with methane and methyl brom1.de. C~rres.ponding to the frequency ;factors given~ the mean collision di.a.meters, s, calcul ated from are s 1 = 0 . 5A, 0 s 4 = 3 . 1A • 0 A plausible e xpl anatio.n of the low frequency factor for (1) is a steric hindrance effe c t caused by the la.P-g e chlorine atoms on ehloroform; urtfortunately,. fre- quency factors Ol" collision diameters for any t:iimilar reaction {Y ,. X are halogens) are not reeorded in t he literature fot• eomparison., The equation for k4 as a f'Unct:ton ot· temperature is 1den- tic~l within experimental error to toot determined for k 0 and Tin the exch~nge of radioactive bromine between bromine and trie~lorobromomethane (page 4)~ exchange log1oko =: -10,,310( :t 400 ) /4.674T + l0.9( :!: 0.20) • R.e action (4) is therefo~e the rate detel,')rnin:tng step in the radi oactive exchange reacti on which must ·take plac·e !!!.. the sequence ( d) , ( 4) , and ( 3) • DI SCUSSION Kistiakowsky and Van Artsdaien< 12 ) have determined the CH bond strength in methane to be 102 kea.1. t h e ...cHs radieal .1 H(t) 29 1oK This implies t hat for = 32 kca1.{l3) For reac t ions of methane and methyl bromide analogous to reactions (l) and (4): E( act.) A H291 OK 21 The activation energies for t he elementary reactions Br + OHC1 3 ~ HBr + • CCl5 Br + OBrCl 3 ~ Br2 + • CCl3 El = 9 . 2 kcal . E4 =- 10 . 1 kca.1 . indicate t here f ore tha t t he CH bond in CHC l3 is weaker t han t he CH bond in CH4 by at least 6.6 kcal . and t hat t he CBr bond in. CBrCl:5 is weaker than the CBr bond in CH3Br by ~t least 11 kcal. These :results are in disagreement with those reported by Braunwarth and Schumacher<l) from a study of the photochemical broraina.tion of chloroform. E (act.) A H kcal ,. kcal. •OCl3 lO 4 Br + CHCl3 ~ HBr + HB:t> + - CCl3 ~ OHCl3 Br 6 Br2 + - CC13 ~ CB~Gl3 + Br 6 Br + ~ Br2 + CBrCl3 + ...cc1 3 (l) (2) 0 6 (3) (4) The (1.cti va.tion energies for ( r,) and (4) were obtained by these authors from the kinetics 0f the bromine sensitized photoohem... ieal oxi dation of triehlorobromomethane,.< 2 ) In the bromination of chloroform the ratio k2/k3 = 0 . 14 v1as independent or tempev- ature, so that 'the activation ~nergies of (2) s.:nd (3) must be equal . The values of AH were obtained as differences of acti vation energiea and i mply that A H : 4 kcal., In t his work , the activation ene1?gi es E1 and E4 , t he t e mperature independence of k2/k3, and t he errors in E1 1 ·E4 ~ and k2/k3 gi ve D H : E1 - E4 = -o.9( ± o.65) kcal. where the probable erro1'" o . 65 :: 10•:5( 5oo2 + aoo2 + 500Brl • . ... . The diff Grence between the results reported here and those of Braunwarth and Schumacher lies mainly i n the values of the aetivation energy for reaction (4) . The overall reaction from which E4 was obtained by F'rs.nke and Schumacher( 2 ) is complex and it m~y be that the mechan1. sm from which E3 and E4 were determined is incorrect . Schwab and Lober ,< 6 ) in a study of the earbon e.a talyzed thermal brom1.nation ot ch loroform have shown the reaction to be exothermic; the equilibr ium constant decreases a.s the temperature is inereaserl . PHO'l10:METRIC DETFJtMINATIO?i OF THE BROMINATI ON RATE An att empt was made to follow the rate or bromination of chlorof orm photometric.ally. A thermostated an<I heavily insu• lated cylindrical oven, 6H in inner diameter and about 12« long ,. was constructed . To reduce temperature gradients a variable s pe,e d blower circulated a ir within the oven. Five reaction ab- sorpti on cells, 1 cm. in diame ter and 10 ems. long , were held parallel to the axis of t he oven on a !'otat§,ble rack. The re.ck , movable ~o.m outside t he oven, could be rotated to bri ng each reaction cell into ali gnment with optically pol ished windows in the ends of t he oven (Figure 2). Light t i ght shutters ke pt the interior of' the oven dark except when mea sure ment s were ta.ken . 'l'he light s ource wa.s a n AH4 mercury arc l amp ; Corni ng . 0 glass filt ers t}~5120, l/403 , and #3484 isolated 1.;he 54 60A mercury line ( Fi gure 3 ), whi ch gave con"t"eni&nt optical densitiee with the bromine concentrations used ., Th~ relati ve light trans- mit tances in Pi gu_e 3 wer·e measured on a Beekmann spectrophotomo eter using a band widtb o:f l.75.A., A vari able slit was uaed to adjust t he intehsity o.f the light beam. Relative (small) light 1ntensi ties ,vere mea sured by a photomultiplier tube , the 01.1tput from wh ich was determined by measuring t he potential dro p across The optical p.ath was completely- enclosed and was defined from the slit to the photomultiplier tube housing by diaphragms~ According to Urn1ston and Badger , ( 14 ) "a very appreciable f:,aetion of the bromine molecules excited by light in the visible region of discr$te absorption dissociate w;l thout collision by other molecules" • In order to be free of' any eompl:t.cat1ons due to photochemical dissociation of bromine molecules ·bhe average eoncentt>ation of photochemically pr•odu,eed bromine atoms had to be n&gligible compared to the ceneent:ration of bromine atoms in thermal equ:tlibri.um with bromine :molecules~ Based on ·the results of Rabinowitcb and LehmanCl5} on the rate of recombination of bP01uine atoms, a calo.uls.t-ion of the per-m:tssible upper limit of the light intensity indieated ·that it would be necessary to u se a. sensiti.,,e photomulti plier tube to measure li ght intenait1e$ ; Using an RCA 929 PMT, a light beam through the JJ>eaotion cell eould generate a current output of a.bout 10 .. 50 ti mes the PI:liT dark current without appreciably distrubinc:; the a:verage bromine atom eoncentration - if the pressure within the cell were about one atmosphere . Although the Br concentration might increase by one-i'i.fth its value duri ng a measurement of the optical density of the reaction system, a calculation showed the 1~ecomb ination :rate to be hi gh enough to bring the . eoncentr•a tion down to with:tn one or two percent of t he therr•~£tl value within a few minutes~ Since the measurement of an opt lcal dens·ty t ook only a mi nute , t he time average value of the bromine atom concent;i:,ation oven.. a period of an hour could be Qonfined to within one or two percent of the thermal value if but a few measurements were taken an the Rabinowitch and Lehman showed t hat bromine a.toms eombine only o:n ternary col.lisions; the rate of ;recombination is proportional to the total pressure . To work with pressures ap• prec~ably lower t han one atmosphere in the :reaction cells appre-ared to be experi mentally u..nfessible • With a pressure of one-..tenth atmosphere the half life of the bro:mi.ne atoms would be g 1..,!!Hil.ter by a factor o:r 10; in order to kee.p the bromine atom concentration near the thermal equilibrium value the light beam intensity would have to be redu.ced to a value near "the limiting sensitivity of the photomult:tplier tu.be. :f-rel:lminary measurements on the appera.tus indicated that the precision of the results which would be obtained in de~ termining rats constt'ilnts and activation energies of the order of 30 k:oal. ~rnuld be s maller than that des:trable . 'fhe temper ... ature difference between any two reaction cells in the furnace was about 1°c and variable. 'rhe resulting uncertainty in de - t:01"mi ning an over .. all activation energy of about 30 kc al. would be about 1.5 kc a.l.; in the activation energ y of inte1~est :h ere, a difference of two la:.t•ge valu,e s, E A/ (33•23) kcal.t t h :ts would be an undesirably . large percentage error. 'To be independent of slow changes w1 t h time in the mercury arc intensity or phototube sensit;ivity; relative li ght in- tenst ties were measured. The output from the PMT for a re- action cell in the l .i ght path ws.s compared to that obtained with nothi ng i n t he light path immediately before and after the cell m@a su..rement. rrhe optical densities of the eell windows were known a nd optical densities of reaction mixtures could be determi ned i n this way w1.th a preoieion of about one percent, but with diff iculty ., '.Phe curr ent output of a photomultiplier tube is strongly de pendent on the poeition of the ligh t beam on the photo-s ensitive ce.t h ode~ Alt hough thi$ positi.on-sens:ltivity was considerably reduced by placing tracing paper light ...cH.:t"f using screens in f ront of both t h e A.B'.4 lamp and the PMT, the variation s of the PMT output _p1,,oduced by the mercu:ry e.~c W$.VOl:\ ing in i.ts quar•tz e nvelope made the me4lsu ren:ient of even ~elati ve iutensi ties diff icult; . Because or fluctuation s in the positi on and the in- tensity of the me~cury arc only aver~ge values of optical dens i t i es were precise to one pe1"ce11t., these obta ined by averaging t hree or. foul" mea~ur¢ments taken over a tedious ten minu te period. Each separate met-umrement of an optieal density - blank , reaction cell, blank - took t hree minutes. A 6 volt t ung sten filament la.mp powered by a. storage bat t ery gave a heam of constant intensity., but a band ,vi dth which would allow Beer 's le:w to be used eould not be isolated by f:i.lters ( F'igure 3) • Bees.use of the temper ature gradients in the oven and the fluctttta t ions in the mercury arc t his method of following 'the reacti on was discarded in .favor of the less elegant but more a.ccu.rate meth od descri bed unde r• 0 Ex pe r1me nta l 11 • APPENDIX DETI!~HMI NA'I'I ON 01" 1rHE CR.AI N BREAKING S~PEP BY THE METHOD OF STATIONARY STATES In the eha:tn reaction mechanism + M ~ 2Br + M (d) CHCl3 + Br ~ • OCl:.; + HBl'> {1} + B:r2 - CCl5 + HBr ~ CRC13 Br (2) ...cc1 3 + Br 2 ~ CBrCl3 + Er {S) CBrCl3 + B:r ~ •CCl3 -t- Br 2 (4) the following reactions are possible ehai n 'breaking steps 2Br + 2 •CCl:3 M ~ B:ra + M ( 5) ..... M ~ C:a016 + NI ( 6) ~ 02Cl0 {7) ~ CBrCl5 + M (8 ) 2 ...CClz, ~cc 1 3 T Bt• + M Es.eh of these chain. breaking step s 1Pth e n corabined with t he chain formirig .mech a1'lism, ( d ) through (4),, gives a separate eom:plets reaction mechanism. Fom."' dif.fere nt rate equations fol" t he over- all r eaction a.re deri ved by the application of the met hod of stati onary state·a to ea.oh of these f our hypotheti cal reaction mechanisms (below)• Three of these rate equations , based on -,. (6), (7) 1 and (8) as the chain breaking step s., do not agree with t he rate equa tion de1"1ved from the e xperimental data; but that derived by t he method of~ stati one.Py states asaum1 ng (5) as the chain breaking ate p l!, the experiment al rate e quati on on page 19. Because the numbers of vibrational degrees of t'l?eerlom in hexe.chloroothane and triehlo1"t,bromomethane are larger than that in brominet the f:ree ::r>adlca.1 recombination rate constants k.0 and ka should be larger than k5; the P$Conib:tnation react:tcn of -,,CGl3 radicals may actually btJ tbe fast bi moleeular rea.ction {7), However; the vates of (6), (7), &nd (8) must be :small com... pared to that of the dominant chain b~EHaking step (5); since only (5) g:l.ves a P$.te equation. eons:tstent with the experimenta.l data., 'llhe stationary state eoneentration of ..cc13 1,..e.dicals must:, theref'ore, be small eompared t ,o t he stationary state eoncentration of bromine atom.$._ I, If the reaction mechanism is Br2 -+- M ---4 CHCl:3 -+- Br ;,,CCl3 .... Br2 f 2Br -+- then ( letting R ii M + M (d) •0013 + HBr ( l} ( 2) Br (3) (4) Id (5) Br 2 ~ + --CCl 0 } the stationary state eoncen trat1.on of bromine a.toins is g:lven by d{Br)/dt:: 0 : 2ka( B1.. 2)( M) - 2k5( Br• ) 2 ( M) - k 1 ( RH ){ Er ) - k 4 ( RB1•)( B1" ) + kg{R)( HBr} + k5(R )( Br 2 } • Let the last four terms= A. Then, d( Br)/dt =: 0 ::- 2kd{ Br 2 )( M) - 2k 5 { Br.)2( M) + A d(R}/dt : 0 ~ -A {Br) : (R) +-- 2Br CBrCl5 + ) __,. { F"'"C( Br2) :: ( Br) k1{ &"9:) + ~(RBr) kg( HBr) -t- k3(Br2) • ...fl(Br2 )/d·t;: k3{Br2)(R) ""'·k4 (RBr)(Br) :; k {Br2 HBr) k1(RH} + k4_(R6r) ~ k 4 (Br)(RBr) • 3 . ~(ID3r) +kz(nr2 ) Afte:t' substitution of {Bv). = VKc(Br2) and a rearl:'angement of terme, k4 Koft( Brel#(RBr) . l -t • k3(BI'2)/k2fHBP) Th1s :ts the experimen~al rate equation (5) on pag~ l9 with kf ;; k 1 K0 ½ and ltr = k4Kci • The:refo~e the mechanism above is :tn complete agreement ,,1th the experimental data. Reactions (6), (?); and (8) lead to s 1tinetica very diff.e~ent fttom that · ex:pe1"imentally observed, aa shown below. l his fact, ta.ken w1 th 11 the a.ssttmptton th.at t he rate eonstants for ( 6) and (8) are at least as large as J: 5 , indicates that reaction (5) 1.s the dom• inant cha!.n breaking step only because the stationary state oon- centl:'at:loD of ...cc13 radicals is lower than that of' the bro• mine atoms, The chai11. lengths for botb the f-'.)l'Wa.J:"d and reve1•se re .. a ,:; tions can be calculated. chain length= For the forward 1.. oaction; d RBr) . dt d Br dt -... k1(RH)(Br) 2kd(Brz){ I\1 ) • I n measu:r.~ing t h e ra t es :i.n t h e .forward direction k2( HBr)/k5( Br2) '.( l •. Si nc e 2lta( B~ 2 )( M) e, 2k 0 ( Br)2( M) 1 • The bromine a.tom reeombination rate eo:i.i.stant k5 wa.s measured by Rabinowi tch and Lehman wi,t b helium as M;· k5 1itfJ):))•2secj•l.(l5) = 3 x 109 ( moles/ :B"'o1"' eh loiio.form eir bromine as M., t h e work of Hl l f erding and Steiner indicates t hat k 5 would be greater by a fa.ct or of about l.O; k 5 = 3 x 1010 .( lo) Using t h is and t h e followi ng experi mental values t ypical of t he mea•su.rements made ( M) ::: 20 x 10~3 moles/liter {lU:t) : 80 X 10•3 { Br 2 ) ,;: 2 X 10"'" 0 k 1 = 6 x 104 (mole.s /liter)""lsee . -1 we have chain length (forward direetion): 7.5 x 104 • The chain in the reverse d:lrectlon is longer because k4 N lOk1 • Chain length = d(RH)/dt d( B1~)/dt :: k4{ RBl'.') l 2k5{ !l) VKe ( Bt-2) Typ:l cal ex pe1~1mental conoentr a t i o:ns whi ch wer•e u sed and me a- sur ed value s of -the r a:t e c onstant,:r e.re { M) : 40 x 10...s w.oles/11. to!' (RBr) # 20 x 10""3 { H}Jr) ( :;i 20 X 10"':5 2} e 1 X 10•5 k4 = 6 i 10° ( mole s/U. ter) •·1 eec ~ ... 1 (435°IC) 6.,3 x 10-20 mole.s /11. ter (4350K) K0 : k:;/kz : 25 from. which eha.:t:n length (reverse ,.ur-eet1on ) ~ .... M ~ CHCl:; + '.Br ) 13/t'9. 2Br + {d) -i>CCl;, + HB:v ( 1) (2) CBrOlo + Br (3) (4) M ( 6) "" •0~13 + B~g 2 ..oc1 3 + m ) ( r-- 1\,1 ~ then, l etting R = ..cc13 and A C2Cl6 + = k2 ( RH HBr) -+ k3(R)( Br2) • k 1 (RH)(Br) ... k4(R:Br){Br), the stationary state concent!'ations of bromine atoms and - CCl3 t>adicals are given by d( Br)/dt: 2ka( Br2)( M) + A: 0 d(R)/dt from wh ich (R) : ... 2k6 (R)2(M) - A ; . 0 = (kd/1t6 )~(Br 2 )½ (3¾i/k6 )~( Brz ) ½[ k 2 (HBr) + k3 ( B~ { Br ) :. 2ka(Br~)OO + k1(RH) + ~(RBr) The r0.te in the for-ward dil"ection is ...a( Br2)/dt ::: d{ RBr)/dt -~ k3(Bl"g )( R) .... k4( RB:r)( Br) . After substitution of the expressi ons f'or ( R) s.rld {Bl'-') the rate is -d{ Br2)/dt - k4 (RBr) .l. 3/z. = k5(ka/ke)li(Br2) 2kd ( Brg )( M) + ( kd/k6 r~· ( Br2) ½[k2 ( HBr) • • k1(RU) t lq(RBr) + k3 ( Br2 > ] " >) . When the reverse reaction ea.n be neglected, i~ , the initial concentration of' trichlorobromometb.ane is zero, the rate ◊f the forward reaction is ·-d-( Bt- )/dt : k3{;ka/k6 )i"( Brg,3'2- • 2 The rate of the forward reaetion is negligible compared to the reverse rate when (!{Br ) >> (RH } and ( HB:r) >> ( Br 2 ) . vera$ rate is t hen given by . . * . . l. o( Brg)/dt: kg(kd/k6) .. ( HBr)( B:v2 ) fa ~Phe Pe• • These rate equ.,ations are very different from t hose derived from the experimental data. 1 and 1ndieate that Pe,aetion ( 6) is un• 5.mportant .compared to reaction ( 5) as a cha.in breaking step . As stated previously , it is ,rery probable t hat k 6 ?'- k 6 ; if lt 6 .?.. 1-t , the reason t hat t he rate of ( 6) is small compared to 5 the rate of (5) must be that (R)/( Br) < l. III. If the recombination of ...ccl3 radicals t:ak es place by the bimolecular reaction (7) ,., a mecha..nism based 011 t his re ... action as. t he sole chain breaking ste p yields the following rate equations which are similar to thos e de1"i ved in II. •d ( Br 2 ) / dt = k3( ka/k7 )"f( IW ) i- ( Br2Yl ( fot•waI1d rate) d( Br 2 }/dt ; k2(ka/k7 )ft( r;1)'t( HBr )( Br2 )i" (rever se rate) The lack of agreement between the ,s e equati ons and the exper i- mental data indic.flltes that (7) is not an i mportant chain breaking step in the actual reaction mechanism. If. reaction ( 7 ) we1'."e the sole ch ain bm~aking step, the reaction run would be neg l .:tg'ible and ttn obse1')vable. d(C 2c16 )/dt ~ k 7 (R)2 =k 7 { k a/k 7 ) (Br2 ) ( M) : k 5Kc { B:P2 ) { M) c 2c16 ,w k 5K0 (Br2 HM) x t x v "'1•3 x 10•10 moles produced. IV ., If the reiiction mechani sm 1s Br 2 + .M CHCl3 + Br ..cc13 + 131:'2 ...cc1 3 + Br + M ----+ 2Br T"- -cci3 --+ t-- + M { d) + HBr (1) (2) ~ CBrCl:3 + Br (3) (4) ~ CBrCl 3 + M {8 ) -- the stationary state concentrations of bromine atoms and - cc1 3 ra..dicals, letti ng R = .;.CC 13 , are g:i.tten by d( Br)/dt : 2ka(M)(B;c,g) + k2(U )( HBr) + k3{RHBr2) • k1 (RH)( Br) ... k4( RBr)( Br ) -.. k3 (R)( Br)( M) : 0 d(R)/dt : • k2(R)(HBr) • k3(R)(Br2> + k1{:HH)(Br) + k4(RBr)(Br ) • k3(R)(Br){ M) : 0 from which The bromine atom concentration (Br) is obtained as a function of the measurable c oncentrations by $ubstituting this ex... pre ss:lon for (R} into d (R)/dt = o. terms., Aft er' a rearrangement of rl(R)/dt ::: 0 := (k1 ( RH ) + k 4 ( m r)) ( Br )2 - kd( Br2){ M)( 1:3r) • Letting { Br) (k2 ( HBr) + k3 ( Bre )) {Itg/ks) ( Br2) : 0 k 1 (RH} + k (RBr) 4 ;: D;; and ~ ka { Br2) ( M) + ii. k (HBr) + k ( Br ) 2 3 2 : E, V k:22( Bra )2 ( M) 2 + 4ED( ka/ks )( Br2 ) 2D • The i'~acticn under the square root s:igr1 is }) ) 1; us ing the va.lues of the coneent:t·at:tons g :'i. ven on page 37 and t he follmv ... lng values of the rate eonstants kd ~ Kck.5 = 2 x 10-9 (moles/1iter)•2sec.""l k 3 ""'· 10° {moles/liter)~lsec.•l k9 3 x 1olO (moles/liter) .. 2 sec ...l = 5 x 104 ( moles/liter)"" 1 sec ♦-'"' 1 k4 r 6 .x 105 (moles/liter)• 1 see,• 1 k1 A, the value of the .t'raetion is about 1011 .• The bromir..e atom concentration is therefore ( Br )~ k 4 ( B·.... 2 ) ( 'It~) 2D l\_ x !?(~•)fa' '"'J:'.lv . -<1c__k__r..,..~C-Br__>½_t_i~-) 0 8 2 :: .( kd/ka)\ E/D)fa( Brg)i • The rate in the forward direction is When the initial concentration of trichlorob:vomomethane 1.s zero the reverse rate is negligible compared to the forward rate which 1.$ :: k5(BI'2) ( kg/kg) (Br,a)/(:Br) • : k3(k4/k9)i • 'h f . k1(RH) . l k 2 (HBr) ·•· } k5(Br2 ) = k3(kd/ka)½k1½(Rn}i(Br2)2 .. . .. . . . .... • ( l + . k20IBr)/k3(Br2) )'½ When (RBr) >> (RR) an.cl (HBr) >) (Br2 } the :rate of the revc,:rttse reaet:1.on is d(Br2)/dt : ~(RBr) (Br) :: q(RBrHka/ks}½ f k2(F{Br) + k5(B:r3) } '1-z.. (Brg)½ k 1 (ml) + k4 (RBr) l = (k4ka/ks) 'i(RBr)½(Br2)½(k2{HBr) + k3(Br2) )½ • Since these equations are inconsistent with the experi- mental data, reaction (8) is not an important chain breaking step. To vac. To vac. B 1l P205 D C Vessel Reaction A 11 E P205 I~ 81 I § ; I Lo ::EI I +> ~ I I S::+>I al Cl) I I g I~ --, I I CHCl3 Manometer r-W:afety Storage Bulbs CBrCl3 I KOH Figure 1.· Apparatus for filling reaction .v essels. Br2 Cf.) To vac. I 1-P- ll:> I l.\) Figure 2. Light Filters I determination of bromination rates. Optical path in apparatus for photometric l_!lotor_J I Blower ,-----, I Optical Diaphragms Light Diffusirg ~ Screens .1 ~ 80 i:i::: CD r-4 cd .µ ,,, 5380 .,,,,,,,, / Figure 3. _ _ _ _ ..;;1..,,. 5300 20 ~ 40 " f.t 8 1@ 60 +> +> @ CD 0 100 I I I I 0 5460A I .wavelength I I I I / / .:r--- ..... ....... "' 5540 ....... ' ' '' #4 03, and #3484 Corning glass filters. Isolation of the 54~0A Hg line by #5120, / I I I I --- Tungsten auto lamp - - AH4 lamp ' 5600 "''' I 0 I (\) I-P- REFERENCES v. Braunwarth and H. J. SehumacheP, .Kolloid Zeits . ~~184 ( 1939 ). w. Franke and H. :J. Schumacher, ze:tts . r . physik. Chemie l34_2 , 297 (1939) • .A. A. Mi ller :and J . E. Willa.rel ., J. Chem. Phys . 17, 168 (1949). - Norman Davidson and Johu 11. Su.111 van:, J . Chem . Phys . ll, 11s <1949). Referenee 4 but see also Referenee 3 in which different parameters are given !'or the exchange rate constant ko • ko(T ). • G. Schwab and F .,. Lober, Zei ts. t . phystk • Chemie i\.186 1 321 ( 1940) 0 • • • A. Weissberger and E. Pr-oskauer, oraa.ni~ Solver1,ts ( Oxford, The Clarendon Pres.s 1936) page l.53. a. Inter11ational Critical Tablee Velum~ 3, pa ge 28 ,. 1r. fh Biehowsky and Ii'\ • P . Rossini; The Thermooh~mist!"_x. ot: tl',le ChemicB\1 Substance,g (Reinhold Publishi ng Cor .... porat:ton New ~ork., 1956). · 10. G. N. Lewis and M. Randall, r hermodJ:!lamic$ ( McGraw - Hi l l Book Company , Inc., lllew York 1923) page ti"a . 11. K . K., Kel l ey, T"ne Entrqp~es of I7torganic ~ubstances 12. G. B. K:t stie.kowsky and 1~. R., Van Artsdalen, J . Chem. Phys., l2 1 475 (1.944) . (The Vflues of A in Table V (1940), Bulletin 434 of t he United Stated Department of the Interior, Bureau of Mines. should be mul ti plied by {575)t/1000 to make them com~ parable t o t he freque ncy tac terrs quoted here . ) Using the values for t he hea:ts of formation of CH4 , H, Br, Br 2 , and CH3Br given in Reference 9. 14. J . Ur ms.ton and R. M. Badg er , J . Am. Chem. Soc . 56 1 343 ( 1934 ) • E. Rabinowi teh and n. L. Lehman, Trans. l•'araday Soc• 31, 689 (1935). 1a. - a. See It. Holle.fson and M. Burton, Photocll&roistrt'. and the Meehaniem of' Chemical Reactions' (Prentice 'lia~l!ne. ffew York)page 164. •• PART III A METHOD OF ESTIMATING AND MINIMIZING THE ERROR OF MEASUREMEJIJT OF THE RA TE OF A RADIOACTIVE EXCHANGE RF.ACTION -45- . [Rep rinted from the J ournal of the Ame ri can Che mical Society , 71, 739 ·(1949).] ·~ X ~ = - dins= E(a / b,s) s O's d In z A Method of Estimating and Minimizing the Error of Measurement of the Rate of a Radioactive Exchange Reaction BY NORMAN DAVIDSON AND JOHN H. SULLIVAN It has been explicitly pointed out by several authors that for a radio-active exchange reaction between two components in chemical equilibrium, the activity of either component varies in a simple exponential manner with time. 1 • 2 We present here, as a consequence of this analysis, a method for: (a) the estimation of the error, due to the error of radioassay, in the rate constant for the exchange reaction, as a function of the extent of exchange; (b) the selection of the optimum degree of exchange to mini.mize this error. 3 For the case ·where the rate is measured by the decrease in. the ~ctivity of the component that initially contained all the activity, the integrated rate expression is • ·''· .•::· In[(~+ b 1)~:~]· ,,,,;··-R(a,b)·~ .+ b t . ....(1) c , b . . • . ab - In this relation: a is concentration of component A that initially contained all the activity ; b is concentration of initially i&active component B; c is initial activity of A; xis activity of A at time t and R(a, b) is the rate of exchange For very short times of reaction x will be almost the same as c and the error in the rate large r: ,, long times of reaction, the components will ; ,e almost in equilibrium with respect to the clistrihution of activity which will then change but little with time. It is often the case that the: errors in a, b, t are small compared to the errors of radioassay in x and c. Set z = x/c ands= R((a + b)/ ab)t. The variables is dimensionless and proportional to two factors : (I) Rt, the total number of concentration units (i . e.. atoms/ cc. or moles/liter) that have undergone n:utual exchange, and (2) the term (a + b)/ab (Displayed in the form s = Rt/ b + Rt/a, it is evident thats is the sum of the number of exchanges per atom of a, and the number of exchanges per atom of b). Then _ d In~ = I + (a/b) exp(s) = E(a / b,s) d In z s . (2 ) The relation rr. = lds/dz\rr, holds for the standard deviations, <rs and ""• of s. and z, because of the assumption that the error ins is due entirely k the error in z. 4 Then (1) McKay, Nalure, 14.2, 997 (1938). (2) Duffield and Calvin , THIS JOURNAL , 68. 557 (194A'. (3) Roseveare. ibid. , 58, 1651 (1931) bas applied similat a r l(uments to the problem of estimating and minimizing the error in the rate constants for chemical reactions. (4) Sec, for example, Marge nau and Murphy The Mathematic• ot Physic• and Chemistry ," D Van Nostrand Co. , New York, N . Y., 11143 o 49K (3) For rrz,(rr,./z) 2 = (o-x/x) 2 + (rrc/c) 2 ; the standard deviations of the activities may be due to statisti- · cal counting errors or may be manipulative errors determined by reproducibility tests. . It is often the case that the fractional error in x,(rrx/x), is a constant; this is roughly true, for example, if the error is principally a counting error and one counts all samples to the same number of counts, or if the error is a manipulative error in preparing chemically identical samples for radioassay. For such cases, the minimum of E locates the point for minimum error ins (and hence in the rate function R). Knowing the value of s corresponding to the minimum value of E and using a preliminary value of R, the optimum t may be chosen. 14 I I I . I 12 I I I I I I I 10 I I I ,;;;- ~ 8 6 ~ "' .<::,. '-- 4 ~ iJ:l 2 1 3 5 s. Fig. 1.-Error funC'tions for ~xchange reactions. The minimum of the error function, E, may be found by solution of the equation: s - I = (b/a) exp(-s). It will generally be more useful to construct a family of curves like those in the figure so that the error in s will be known for any s (or z). Estimates of the standard deviation in s obtained in this way are useful, for example as weighting factors in averaging data or in least squares treatments of data on the variation of rate of exchange with temperature or ionic strength. For such applications, the function E is useful even when the fractional error of radioassay is not constant. For these cases, knowing rrx as a function of x and hence (for given a and b) as a function of s, one could construct the function, E(s)o-x(s)/ x(s), and thus select the point of minimum error. For the usual case where rrx/ x does not change too rapidly with x, it may be sufficient to select by inspection a point in the region of the minimum of the E(s) curve without making the more elaborate calculations required to select the optimum point. PROPOSlTIONS l. A consideration of the relative :rates of possible chain brtak1ng steps in the thermal bromination of chlorofoJ?m. leads to the following values of r ,a te cons tan ts am activation ene:rgies for r&actions ( 2) and ( 3) BBr + ... QCl3 + Br ( 2) + (3) Br2 + -0013 . CBrOl.3 Br > 5 X 106 Eaet. (. 5 keal. k2 8 k3 ) 10 2. OROl3 E . act, < 5 keal. On the basis of' the aetivatiom energies given above for reactions (2) and (3) tho OH bond. in OHC13 is at least 6.6 and at most 11.6 kcal. weaker than the CH bond in CH4 , and the CBr bond in OBrGl3 is at least 11 and at most 16 keal. weaker than the OBr bond 1n CH3 Br.(l) 3. The photochemical rearrangement of N-ehloroac e tanilide in the solid stato observed by Porter and Wilbur{2) and the thermal rearrangement of liquid benzoylchloroaminobenzene observed by Cha.ttaway and Orton< 3 ) at:te not satisfactory proof of a dir$ct intramoleeular interchange of atoms.( 4 ) A photo- chemical rearrangement of these compounds occurring in a dilute inert solution solidified as a glass would be proof of an intramoleeular process. 4. .I'he ma~ked decrease 1n th.e resistance of a palladium 1 o.xide .film caused by proton recoil might be utilized as a simple neutron speatrometer by interposing various thicknesses of a non ... hydrogenous material between the source of' recoil protons and the oxide film. ( 5) • 5. In the 1.n v,stigation of the kinetics of the phosphorus tribromide catalyzed conversion of white phosphorus into red the large solvation effects during precipitation of' the red phosphorus could be considerably di.minished by studying the rate in a. solution of the tribromide and white phosphorus in an inert solvent. A dependence of the rate on the phosphorus tribromide eon.centra.tion might be obtained in this way. ( 6) a. Additional evidence for the weak bonding of o2 mole• oules to form o4 could be given by an attempted exchange reaction between 0218 and 0 2 16 • 7. In a study of a ehain reaction, the absence in a re- action system of a compound which would be formed in a partic• ular chain breaking step is sometimes taken as an indication that this chain breaking step is not present.(?) This reason- ing is fallacious; the amounts of' sueh compounds may be unobservable.(8) A more sensitive indication of the ehain break- ing mechanism is the overall rate equation. 8, In a thermal he.log~na.tion r•actio:n a square root dependence or the rate on the halogen concentration does not necessarily indicate the rate determining step involves halogen atoms in thermal equilibrium with halogen molecules. A steady stata eoncentration of halogen atoms appreciably less than tb.e equilibrium value may give the same rate equation. 9. Inves t~ gat1ons .o f the photolysis of formaldehyde indicate that two primary steps, HCHO + b.v co HCHO + hv CRO + H + 1l2 may take place in the de,~ompo,sition to carbon monoxide and hydrogen~ ( 9 ) The Pela ti ve importance of these two steps can be determined by the photolysis of a mixture of DODO and HCHO. lO. Athle'l,ies for the g:raduate student would be unobtrus- 1 vely, effeeti vely, amd ehefaply eneoura.ged by the athletics department of Oal. Teeh. if school purchased athletic equipment were assigned to the vari ous divisions for graduate student and faculty use. I believe the ready availability of this equipment would be of cons:1,derable benefit to the health, general well bein g , and the social life of the graduate students at Cal. Tech. REPERD.OES l. '!'heals, page 2~• 2. o. W. Poi,\er and P • . Wilbur, J. Am. Ghem. Soc. 4_9,.· 214$ •.(·1927) . ( • - a. 4• s. F:. D., Obatta:way and K. J. P. Ort<>n, J. Co.em. Soo.·- 75, 100 ( 1899 ),• •, . .· G, . I .. Ro.; Llets C">~ and M._. aurton, _Pn:o to e1'e~1s t,lltJ. ,M5! _th•flh,obflnis1'i ,!?£' .01\em&~al . Reaotiona, , ( Pren tlce ffall;7'ew '¥'ork :f§J§) page ~-x. . . .' . . . -~ . B.__ R~ Gosslok, Pliye_. Rev. '7'1 • 897 ( 1950) .• / 6 • . H.·• ., s.Jfb.n·s·t on,_ Tb.ea1s, Oe.litomia Institute ot Teehno... log-, 1947 ... • . 7. 'J. One 1nstane•h' s:. -A • Taylor and w. E. Ban son, J. Ohem. !• 42-l ( 1939)'. llhifs, ♦, 8. f.p.eaia; P•$• 40 .. 9. I. w.. R.• $teac1e, Atomic and Free 3a41ce,:l, ReaQtions, (fi,tnhol4 l?ubl.isning corporation "1946) page 1'.'1$:" •