General vs. Specific Acid-Base Catalysis in Strong Mineral Acid

General vs. Specific Acid-Base Catalysis in Strong Mineral Acid Solution. Aromatic Decarbonylation1. W. M. Schubert, and Philip C. Myhre. J. Am. Chem...
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April -5, 1955

=~ROMATIC DECARBONYLATION IN STRONG ACID

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cyanate. The copper salt of 2-mercaptoethyl t h i ~ c y a n a t e ' ~ After filtration to remove the decolorizing agents, water was added until the hot solution became slightly cloudy. was made by the reaction of the copper salt of acetoacetic As the solution cooled, a precipitate formed which was reester with ethylene dithiocyanate in absolute ethanol. Trimethylene dithiocyanate4 was prepared from trimethylprecipitated in the same manner several times, until a constant melting point of 105-107° had been obtained. This ene dibromide and potassium thiocyanate. P-Mercaptoethyl acetate,14 b.p. 62-66' (16 mm.), was made from 2substance gave a n analysis close to t h a t calculated for ethylene sulfide polymer. A n a l . Calcd. for (CzHaS),: C, 40.0; mercaptoethanol and acetic anhydride. Cysteine hydrochloride, 1,2-diniercaptoethane and 2-mercaptoethanol were H , 6.7; S, 53.3. Found: C, 39.4; H , 6.3; S, 53.1. commercial materials. An authentic sample of ethylene sulfide polymer14 was Tests for Thiocyanate Ion Evolution. ( a ) Mercaptans.made by dissolving 1 g. of 2-mercaptoethyl acetate in 5 ml. .4 small volume (about 3 ml.1 of redistilled cvanoaen chloof absolute ethanol and adding 3 ml. of 2OY0 sodium liydroxride was added to a solution of about 0.1 g. o f t h e substance ide. After one hour, a few ml. of water was added and the to be tested in 2-3 ml. of mater or ethanol-water. After a mixture was filtered. The solid thus obtained was precipifew minutes, the solution was made alkaline by the addition tated several times from solution in X,N-dimethylformof aqueous sodium hydroxide (with care, in the case of cysamide, as described in the preceding paragrap?, a n d finally washed with ethanol and ether, m.p. 108-109 . teine hydrochloride, to raise the pH above 9). On acidification of the mixture and addition of a few drops of 5-3070 ( b ) In Aqueous Acetone.-Ethylene dithiocyanate (0.5 aqueous ferric chloride solution, a deep red color indicated g.) was dissolved in 3 ml. of acetone. Three milliliters of the presence of thiocyanate ions. Positive tests were ob- 2053 aqueous sodium hydroxide was added, the mixture was shaken well and 20 ml. of water was stirred in. After tained with 1,2-dimercaptoethane and cysteine hydrochloride, and a negative test with 2-mercaptoethanol. 15 minutes, the oily globules of ethylene sulfide tkat had ( b ) Organic Thiocyanates and 2-Imino-I ,3-dithiolane .formed were extracted with ether and the aqueous 1a:;er was The previously described procedure was followed with omisseparated and treated with 0.5 g. of semicarbazide hydrosion of the cyanogen chloride. Positive tests were obtained chloride in saturated aqueous solution. The pH was rewith ethylene dithiocyanate, methylene dithiocyanate, the duced to 8 by dropwise addition of dilute hydrochloric acid copper salt of 2-rnercaptoethyl thiocyanate and 2-imino-l,3and the solution was permitted to stand several hours. dithiolane, and a negative test with trimethylene dithiocyThe precipitate of hydrazodicarbonamide, a standard deanate. rivative for cyanate,l5 was isolated by filtration and airIdentification of the Products of Reaction of Ethylene Didried, m.p. 253-256", literatureL6m.p. 254-259'. thiocyanate with Base. ( a ) I n Aqueous Ethanol.-Ethylene Acknowledgment.-The authors are pleased to dithiocyanate (0.1 g.) was dissolved in 25 ml. of 95% ethanol. acknowledge the interest and encouragement of Two milliliters of 0.2 S sodium hydroxide mas added and the Dr. Albert A. Kondritzer, who made i t possible for solution was allowed to stand two hours, after which 1 ml. of 6 11.1 sulfuric acid was introduced. -4fter addition of 20 ml. this work to be carried out. of water to the mixture, the precipitate was filtered off, dis(15) F. J. Welcher, "Organic Analytical Reagents," Vol 11, D. solved in hot S,S-dimethylformamide and decolorized with Van Nostrand Co., I n c . , New York, N. Y . , 1947, p. 454. a small amount of charcoal and diatomaceous filter aid. (13) E. P. Kohler, A m . Chem. J . , 22, G7 (1899). ( 1 4 ) 1,. W. C. Miles and L. S . Owen, J . Ckenz. Soc., 817 (1952)

[CONTRIBUTION F R O M THE

(16) N. A, Lange, "Handbook of Chemistry," 8th e d . , Handbook Publishers, Inc.. Sandusky, Ohio, 1952, p. 558.

ARMY C H E M I C A L C E S T E R . hlARYLAhTD

DEPARTMEKT O F CHEMISTRY

O F THE UNIVERSITY O F i%'ASHISCTON]

General os. Specific Acid-Base Catalysis in Strong Mineral Acid Solution. Aromatic Decarbonylationl BY W. M. SCHUBERT AND PHILIPC. M Y H R E ~ RECEIVED h

T9, 1957 ~

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Isotope effects have been determined for the decarbonylation of 2,4,6-triisopropylbenzaldehyde in 71-99% D2SO4-D20 and for 2,4,6-triisopropylbenzaldehyde-d, (ArCDO) in 72-967, HzSO~-HZO. T h e results are in complete agreemerit with the general acid-base catalysis mechanism of successive bimolecular proton transfer steps previously proposed. In accordance with expectation, based on steric grounds, a step involving proton transfer from solvent acids to the aromatic ring is rate controlling in the higher HzS04 percentages and largely rate controlling in the lower HzS04 percentages Conclusions of general significance are: (1) general acid-base catalysis in non-dilute H z S O has ~ been demonstrated : (2) agreement with HO- log ([B]/[Bjstoioh) = constant, over a limited acid range, is not a the Hammett acid catalysis equation, log k o b s d sufficient criterion for the assignment of mechanism; (3) the mechanism of successive bimolecular proton transfer steps assigned to the decarbonylation may give agreement with the H a m e t t equation under the condition t h a t acid and/or basic catalysis constant ratios are the same as for indicator bases; (4) additional evidence t h a t aromatic electrophilic substitution in general proceeds via an intermediate has been obtained.

+

The following bimolecular mechanism has been proposed for the replacement of the formyl group by hydrogen t h a t occurs when 2,4,6-trialkylbenzaldehydes are treated with strong mineral acid (e.g., 60-10070 H,S04).3.4 In these equations, H A i refers to solvent acids ( i e . , H30@ and HzS04) and Ai refers to solvent unbases (ie., HzO and HSOde), with the charges (1) Presented a t t h e Symposium on Aromatic Substitution, 130th National l t e e t i n g of t h e American Chemical Society, Atlantic c i t y , N J , September, 1956 (2) Du Pont Pre-doctoral Fellow, 1956-1957 (3) W. M. Schubert and R . E Zahler, THISJOURNAL, 7 6 , 1 (1955). (4) W. 51.Schubert and H. Burkett, ibid , 7 8 , 61 (1956).

specified. This mechanism m7as found to be consistent with all of the experimental facts amassed including the changes in kobsd with percentage sulfuric acid for 2,4,G-trimethyl-, triethyl- and triisopropylbenzaldehyde, and the isotope effects for deuteromesitaldehyde (MesCDO) in 60-10070 D,S04-Dz0.4 Disagreement with the experimental facts was found for each of a number of other mechanisms considered, including the genera1 Hammett mechanism and t e r m o k u l a r mechanisms. In terms of this mechanism, the observed deuterium isotope effects with deuteromesitaldehyde

~

~

11. 81. SCHC‘BERT AND PHILIP C. A ~ Y I ~ R E

17.56

(MesCDO) in sulfuric acid solutions and with mesitaldehyde in deuterosulfuric acid solutions require that in low mineral acid concentrations (59-70% H,S04) step 3 be rate-controlling and step 2 be an established equilibrium, whereas in high acid concentrations (S5-100~o H2S04jsteps 3 and 2 forward be competing rate controlling steps of comparable r n a g n i t ~ d e . ~This means that in the lower H2S04 concentrations, D- is appreciably greater than v3 (where v is velocity) and in the higher H?SOI concentrations, D - ~ is comparable to u,$. H O H O@

\ /

\/\

C

H

rapid equilibrium

(1)

H O

\(!! H

I

R

R (BH@*) (steady state concn.) ( 2 )

H O

\ II C

H

I

R

1

R

1.01.

so

(compared to step 3) may be due, a t least in part, to steric factors T h a t is, there may be a greater increase in steric strain in step 2 reverse than in step 3 with the bulkier bisulfate ion; i e . , the proton being abstracted in step 2 reverse lies a t a considerably more hindered position than the proton being abstracted in step 3. If such a steric factor plays a role in reducing the relative effectiveness of bisulfate ion in step 2 reverse for mesitaldehyde, then it mould be expected that the relative effectiveness of bisulfate ion would be reduced even further iii step 2 reverse for 2,4,6-triisopropylbenzaldehyde. This should result in a further slowdown of step 2 reverse relative to step 3 in the high acid percentages, perhaps enough to make step 2 forward largely rate controlling. Furthermore a very large reduction in the relative catalytic effectiveness of bisulfate ion in step 2 reverse would impart a behavior approaching specific oxonium ion catalysis to the decarbonylation of 2,4,G-triisopropylbenzaldehyde. We have studied the decarbonylation of 2,4,6-triisopropylbenzaldehyde-dl (ArCDO) in 7 2 4 6 % HzS04, and of the ordinary aldehyde in 71-9970 D2S04-D20in order to determine whether these expectations could be realized. Experimental 2,4,6-Triisopropylbenzaldehyde-dl.-The method used in the preparation of mesitaldehyde-dt was applied to the preparation of 2,4,6-triisopropylbenzaldehyde-dl(ArCDO) .‘ The isotopic purity of the aldehyde was checked by infrared analysis. To obtain maximum resolution of the spectrum, a special spectrophotometer equipped with a calcium fluoride prism was used.’ A comparison of the aldehydic C-E (4.75, 4 . 5 5 ~ )and C-H (cn. 3.5, 3.6~)stretching bands iiidicated that the aldehyde was a t least 90y0 ArCDO. The preparation of other materials is described in previous p~blicstions.3~~ Kinetic Method.-The spectrophotometric metliod for determining the first-order rate constants, using a Beckman D U instrument fitted with a constant temperature bath, has been described previously.3 The temperature was controlled to 1 0 . 0 5 ” .

Such a slowdown with increasing H2S04 concenResults tration of step 2 reverse relative to step 3 was Basicity Determinations.-The ultraviolet specrationalized as follows: Both 2 reverse and 3 involve proton abstraction from the same species, trum, a t room temperature, of 2,4,6-triisopropylBH*@, by solvent bases. However, the proton benzaldehyde-dl was identical to that of the ordibeing abstracted in 2 reverse lies a t a different site nary aldehyde in several percentages of sulfuric than the one being abstracted in step 3; therefore, acid, including 64.4%, in which the amounts of free there is no per se reason to expect the relative cat- base and oxygen conjugate acid of the substrate alytic effectiveness of HSO& to t h a t of H,O to be are about the same. Therefore, the ordinary and the same in the two steps (see e.g., references 5 and deuteroaldehyde have experimentally identical 6). Provided t h a t k--2HrO/k3H%O is sufficiently basicity. The extent of conjugate acid formation of greater than unity and k- 2 H S O l e / k 3 H S O , 0 has a value around unity or less (and presuming ~ H % O 2,4,6-triisopropylbenzaldehydein D2S04-D,0 us. > kHSo,@) then i t should be found that: (1) in the that in the corresponding percentage sulfuric acid low mineral acid percentages (59-70% H2S04),in was determined spectrophotometrically a t room which the concentration of water exceeds that of temperature, as was done for mesitaldehyde. bisulfate ion, step 2 should be an established I t was found that conjugate acid formation is more equilibrium and step 3 rate controlling; (2) in the nearly completein D2S04. Thevalueof Ho(H2S04)high acid percentages (85-100% H2S04),in which Ho(DnSO4) using triisopropylbenzaldehyde as the the population of bisulfate ion greatly exceeds t h a t indicator base was found to be 0.3 in the region of of water, step 2 reverse should be slowed relative to 65.lOj, HzSO4. This compares with the value of 3 and, consequently, 2 forward could then become 0.35 found for mesitaldehyde in 59-70y0 acid.4 The greater “acidity” of deuterosulfuric acid as partially rate-controlling in competition with 3.* A reduction in the catalytic effectiveness of bi- against sulfuric acid is illustrated in Fig. 1. Rate Results.-For the determination of the sulfate ion (relative to water) in step 2 reverse first-order rate constants the plot of log (D- D,) us. (5) L. Zucker and L. P. Hammett. THIS JOURNAL, 61, 2785 (1939). (6) R. P. Bell, “Acid-Base Catalysjs.” Oxford Universlty Press, London 1941, Chapter VII.

(7) We wish to thank Dr. David F. Eggers, Jr , for the use of his npparatus and his help in interpreting the result5.

AROMATICDECXRBONYLATION IN STRONG ACID

April 5, 1938

17.57

time was linear within k0.05 of log (D - 0,). The plot was made for a t least two wave lengths in each separate run. The reaction was followed in all runs to i5-90% completion. The maximum deviation was h4y0 and the average deviation was =!=2%. The rate constants obtained are given in Tables I and 11. TABLE I FIRST-ORDER RATE CONSTANTS FOR TION

DECARBONYLA2,4,6TRIISOPROPYLBESZALDEHYDE-dl IN HzS04 AT 80" THE

O F 2,4,6-TRIISOPROPYLBENZYLALDEHYDEAXD

1.32,1.29 1.31,1.29 2.00,2.02 1.87 2.30 2.20 0.558O 0.542" 2.36,2.30 2.29,2.36 3,24' 2.45 3.60' 2.83,2.81,2.82 79.0 3.49 2.93 77.4 2 . 70b 2.12 72.5 a D2SOa-D2C). * Previously r e p ~ r t e d . ~

96.8 93.4 90.9 90.9" 89.8 84.9

1.01 1.07 1.04 1.03 1.01 1.32 1.27 1.18 1.27

TABLE I1 FIRST-ORDER RATEC O N S T A N T S FOR

Acid,

%

99.0 95.5 93.5 90.9 00.9" S6. ti 80.0

kosad

DzSOd

0.146

,306 .478

x

AT

THE DECARBOXYLATION

D2S04-D~o AND I N

80"

i o 3 SeC.-' HzSOI

0.723 1.51 2.00,2.02 2.30 2.20" 3.05b 3.70' 2,33b

310

330

350

A, ml.c.

Fig. 1.-Spectrum of 2,4,G-triisopropylbenzaldehyde: upper curve, in 65.1% D2SOp-D20; lower curve, in 65.1%

H~SOI.

(>85%) the ratio of observed rate constants, kArCHO/ is practically unity; i . e . , there is practically no isotope effect for the decarbonylation OS 2,4,Btriisopropylbenzaldehyde-dl. Table I1 reveals that the decarbonylation of the hydrogen aldehyde proceeds a t a considerably slower rate in DzS04-DzO solutions than in corresponding percentages of HzS04.8b The maximum in kHzSo,/kDgso,is 5.0, in 9956 acid. and declines slowly as the mineral acid percentage is decreased. The kArCHo/kArCDO ratio of unity in greater than S5yo H2S04 indicates that a step involving cleavage of the aldehydic C-H (or C-D) bond (;,e., step 3) is not detectably rate controlling. The large kH,SO,/kDzso, ratio indicates that a step involving proton transfer from solvent acids (ie., step 2 ) is a t least partially rate-controlling. The two results taken together, then, lead to the conclusion that in the higher percentages of mineral acid (>85y0), step 2 forward is practically completely rate-controlling. This means that the velocity of step 3 considerably exceeds the 1-elocity of step 2 reverse. Under these conditions, the general rate expression 4 reduces to equation 5 . 4 kArCDO,

O F 2,4,6-TRIISOPROPYLHENZALDEHYDEI N

HzSOa

290

~ H Z S O ~

~ D P S O ~

5.0 4.9 4.2 4.1 4.1"

[B] in HzSOa [B] in DzSO,

2.0 2.0 2.0 2.0 2.0" 2.0 2.0 1.6"

,558 ,542" ,772 4.0 ,9j2 3.9 3.2 70.7 ,752 These runs made 011 %,~,B-triiso!,rop?.lbeiiz~ldeliyde-d (.lrCDO). Previously r e p o r t e ~ i . ~ Assumes the degree of oxygen conjugate acid formatiou to be the same at 80" as a t rooni temperature.

'

Discussion The general rate expression for the inechanism assigned (equations 1, 2 and 3 ) is given by equation 4.

Equation 4 is derived assuming only that the carbon conjugate acid, BH*@, is in steady state con~ e n t r a t i o n . ~This equation applies when either step 3 or step 2 forward is rate controlling, or when both are rate controlling, although it may be simplified in the former Equilibrium I is established instantly and the extent of it is readily measured.sa I t plays no direct role in theprocesses leading to the decarbonylation products, but acts only to reduce the concentration of B, the reactive substrate species in step 2. Examination of the rate data of Table I reveals that in the higher sulfuric acid percentages ( 8 ) (a) I n this respect t h e behavior of 2.4,R-trialkylbenzaldehydes is like t h a t of other typical oxygen bases, s u c h a s acetophenone. T h a t is. in mineral acid media in which t h e conjugate acid ultraviolet peak is experimentally detectable, t h e peak is fully formed by t h e time the spectrum is measured, and probably in a much shorter time.

The expression for the isotope eiTect for deuteroaldehyde in HzS04 is equation 6, where BD refers

to free deuteroaldehyde. Since the hydrogen and deuteroaldehydes have experimentally identical basicity, [ B ] / [ B D ] = 1. Furthermore, it is reasonable to expect k2, for each proton so1ven.t acid species to be practically the same for the deuteroaldehyde as for the hydrogen aldehyde. Also, i t is reasonable to expect fB,/ftrzi = fBD,/fDtrzx for (8)(b) There is no exchange of aldehydic deuterium during decarbonylation a s shown b y t h e following experiments: P.B,A-triir,opropylbenzaldehyde-dl (300 mg.) was treated a t POo with 85y0 a.nd 95% HzS04, respectively (30 ml.), for a sufficient length of time t o allriw decarbonylation t o prnceed tn from one i n t w o half-lives; l h e aldehyde recovered from each reaction mixture had an infrared !;pectriini identical t o starting aldehyde, including t h e pri>minent C-D stretching bands a t 4.75 and 4.85 p .

1758

W. &I. SCHIUBERT AND PHILIPC. MYHRE

each i in all the sulfuric acid percentages. Therefore, for step 2 forward rate controlling, the expected kArCHO kArCDO ratio is unity, as observed. %3th step % forward rate controlling the expression for the isotope effect in deuterated mineral acid its. protonated mineral acid for hydrogen aldehyde is given by equation 7 .

1701. so

from mesitaldehyde to 2,4,6-triisopropylbenzaldehyde, and more so than does k m s o 4 e / k 3 H z o . For 2,3,G-triisopropylbenzaldehyde in the lower mineral acid percentages ( the isotope effects indicate that step 2 forward is largely rate controlling; for mesitaldehyde in step 2 reucrse rclatizie io 3 is reduced in changing k D , , for each i. Secondly, since equilibrium 1 lies from mesitaldehyde to 2,4,B-triisopropylbenzaldefurther to the right in DsS04-D?0 than in H&304, hyde (i.e., k- 2 H , o i / ' k s H 2 0 less for triisopropylbenzthe ratio [B] in H?SO?'[B] in D2S04is greater than aldehyde). This conclusion is in agreement with unity; experimentally this ratio is equal to 2.0. the prediction that steric strain in the transition Thus the direct isotope effect in the rate-controlling state would act to slow down step 2 rwerse relative step, 2 forward, is half of the experimentally ob- to step 8 . served k H 2 S o aik D z s O l ratio. Unpredictable differIt should be pointed out that the ratio it- %, 'c3 = ences in a H A i f B 'ftr2i L I S . U U A , B :ftrsi, presumably Z k - l i ! L ~ i f B H * @ j t r t , 'Zkai!LAifBH*', Jtra1 lliay Vary small, also could modify the isotope effect. with mineral acid percentage (and aldehyde strucI t seems clear that the isotope effects in >S5% ture) for reasonsother than k- 2 H s o 4 9 / k - 2H20 less than mineral acid are completely consistent with step 2 k s H s o 6 3 k 3 I I 2 o . Thus even ifthe solvent basic species forward rate controlling in these percentages. should have the same velatiae effectiveness in step 2 reThis is further confirmed by the observations that verse as in step 3 (ie., k - - 2 ~ ~ 0 4 3 / k - - ~ = 2 0 k:wsorO k A r C H o , ' k A r C D O is unity in 90.9y4)D2S04-D20(Table k j H 2 0 ) , changes in the ratio ftr,> /ftrZl with acid perI ) , and t h a t k H t s o I , i k D 2 S o i in 90.9yo acid has the centage and with aldehyde structure would produce same value for d r C D O as tor XrCHO (Table 11). changes in ZL v3. Hon-ever, we believe i t is highly The isotope effects in the lower mineral acid per- unlikely that the activity coefficient ratio of such centages, iO-S3Cjc, are consistent with step 2 similarly constituted transition states would vary in fovward being a t least largely rate-controlling. the extreme fashion necessary t o change the ratio However, the k d r C H o ~ A ~ Cratio, D ~ though near uii from a value considerably greater than unity unity, is greater than unity by an amount sig- to a value considerably less than unity.$ nificantly greater than the experimental error. General Catalysis, Specific Oxonium Ion CatalyFurthermore. there is a noticeable decline in the sis and the Hammett Mechanism.-The Hammett k H 2 S o I k D , S o 4 ratio that is not all attributable to "uniniolecular" mechanism, equations 8 and 9, is the decline in the ratio [ B j i n H~SO,; [BIi, D ~ S O ~ . clearly excluded for the aromatic decarbonylation This may indicate that in the lower acid perceii- reaction by tlie expriniental facts, including both tages step 8 has entered to a slight extent as a rate- the isotope effects for mesitaldehyde4 and 2,4,6controlling step. If i t is assumed that k A r C m triisol)rol)vlbelizaidehyde and the change in kob,d kxrcuo would be exactly unity if step 2 forward were over a \',,idc range of sulfuric acid percentage for completely rate-controlling and the isotope e,ect nicsital tlehyde . 2 4,(itriethylbenzaldehyde and 5,on the deuteroaldehyde in step 3 has the value of 3 4 , (i-triisopropylbenzalciehyde. Nevertheless, kobsd (the niaxiiiiuiii \-slue iii the step 3 isotope efiect ob- for niesitaldehyde iii about 7tj-!)5ch sulfuric acid, served for niesitaldehydc was 2.S),4 then about a which rcpresents a goodly portion of tlic total 157& contributioii of step 3 to the rate-contro!liiig range of suliuric acid iii which tlie reactioii was processes would be rcr~uirecl to make i r . ~ ~ I Ic ~ studied ( 5 ! ) - l O V , ~ ~ , chaiiges in a manner consistent k.krCDO = 1.25. This amount of contributioqi of i.e., equation 10 or with the I-laiiiiiiett ~iicchaiiism~; step 3 would also act to reduce the ohserved 11 is lollowed. Since this mechanism cannot bc ~ I ~ ~ ' k Ds2 soo l~ ratio , by about 0.Ci. [!I) 1:or a discussion of activity coeilicient ratios i o cuncentratcd 2,4,6-Triisopropylbenzaldehyde LIS. Mesitalde- culfuric :kcid see: N . C. Den" and R. W T a f t , Jr. THISJ O U R N A L , 7 6 , hyde.-For 2,4,6-triisopropylbenzaldehyde in 1 :I'.l5&1, a n d N C. Deno and C Perizzolo, ibid, 79, 1315 (1957). > SS% mineral acid the isotope erTects indicate (10) I,. f. Hammett, "Phy,ical Organic Chemistry," McGrawHill Rook Cm, Inc , New York, S . Y , 1940, Chapter IX that step 2 forward is practically (11) Equation 10 I S the proper equation t o use when the substrate controlling; for mesitaldehyde in base, B. I S in,erluilibrium with appreciable amounts of other species." isotope effects indicated that both When the o n l y uther substrate species present in appreciable amounts aiid step 3 are rate-controlliiig steps of comparable I > the r o n j u p t e :tcid, &Ha, equation 11 is equivalent t o equation ~iiagnitude.~This means that when the substrate l O . ' 3 \Vhrn thc suhstrdte is practically all in t h e form of t h e free theti [ R ] = [li]itoich a n d Ka//zo