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Kinetics of the reaction between formic acid and permanganate in queous acid solution. Taylor, Sandra Margaret 1958

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KINETICS OF THE REACTION BETWEEN FORMIC ACID AND PERMANGANATE IN AQUEOUS ACID SOLUTION by SANDRA MARGARET TAYLOR B.A., University of Br i t i s h Columbia, 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of CHEMISTRY at the UNIVERSITY OF BRITISH COLUMBIA We accept this thesis as conforming to the required standard Members of the Department of Chemistry THE UNIVERSITY OF BRITISH COLUMBIA Ap r i l , 1958 i i ABSTRACT The kinetics of the oxidation of formic acid by permanganate in aqueous perchloric acid solution, i.e., 2Mn04" + 3HCG0H + 2H+ —-» 2Mn02 + 3 C 0 2 + 4H20 were studied in the temperature range 15 to 35°C. The variables examined included the reactant and hydrogen ion concentrations, ionic strength, the presence of various metal ions, and solvent and reactant deuterium isotope effects. The reaction appears to proceed through two independent paths in which the rate-determining steps are bimolecular reactions of permanganate with formic acid and with formate ion, respectively. The kinetics are thus of the form -d |Mn04"] / dt = [Mh04~] [H C O O H] (k A + k BK ± / [ H + ] ) where k A and kg are rate constants of the two bimolecular reactions involving formic acid and formate ion, respectively, and K± i s the ionization constant of formic acid. The Arrhenius expressions for the rate constants were found to be k A = 1.1 x lO^exp. (-16400/RT) l.mole^sec" 1 and kfi = 7.8 x 109exp. (-13000/RT) l.mole~ 1sec~ 1. The formate ion reaction exhibits a large deuterium (HCGO":DCOO~) isotope effect which suggests cleavage of the C-H bond in the rate-determining step. The i i i absence o f a c o r r e s p o n d i n g i s o t o p e e f f e c t i n t h e f o r m i c a c i d r e a c t i o n s u g g e s t s t h a t i t proceeds by a d i f f e r e n t mechanism. (but n o t A g + , Cu***", Ce"1"*" or Na +) was found t o c a t a l y z e t h e r e a c t i o n , p o s s i b l y by a mechanism i n v o l v i n g +•4" a FeMn0 4 complex. P r e v i o u s i n v e s t i g a t i o n s o f t h e f o r m i c a c i d -permanganate system have been c o n f i n e d t o l o w e r a c i d i t i e s t h a n the p r e s e n t one, and o n l y t h e f o r m a t e i o n c o n t r i b u t i o n t o the r e a c t i o n had been d e t e c t e d . I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . ~ Chemistry Department o f _ The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver S, Canada. tot* ^ 16, 1 9 5 8 . iv TABLE OF CONTENTS Page INTRODUCTION 1 I. General 1 II. Previous Kinetic Work Leading to the Present Investigation 2 EXPERIMENTAL METHODS 6 I. Materials 6 II. Preparation and Standardization of Reagents 6 III. Kinetic Measurements and Analytical Determinations 8 RESULTS AND DISCUSSION 11 I. Stoichiometry of the Reaction 11 II. Kinetics of the Reaction:Effeet of Reactant Concentration 11 III. Effect of Hydrogen Ion Concentration . . . . 19 IV. Evaluation of K^, the Ionization Constant of Formic Acid 25 V. Effect of Temperature on the Reaction . . . . 30 VI. Effect of Ionic Strength 36 ¥11 . Effect of Metal Ions 3« VIII. Deuterium Isotope Effects . . . . . 44 CONCLUSIONS I. Mechanism of the Formate Ion Reaction . . . . II. Mechanism of the Formie Acid Reaction . . . . III. Ferric—Catalyzed Reaction . . REFERENCES v i LIST OF TABLES Tabl e Page I . S t o i c h i o m e t r y of the R e a c t i o n Between Mn04" and HCOOH 12 I I . Evidence f o r Second Order K i n e t i c s 15 I I I . Dependence of the Rate on P e r c h l o r i c A c i d C o n c e n t r a t i o n 22 IV. Temperature Dependence of the I o n i z a t i o n Constant of Formic A c i d 26 V. Dependence of k^ and kg on Temperature . . . . 27 V I . K i n e t i c Parameters f o r the R e a c t i o n 34 V I I . Dependence of Rate on I o n i c S t r e n g t h 37 V I I I . E f f e c t o f S o l u t i o n Composition on the Rate . . 39 IX. Isotope E f f e c t s on the Rate 4-6 X. Rate Constants i n V a r i o u s I s o t o p i c Systems . . 49 X I . R a t i o s of Rate Constants f o r V a r i o u s I s o t o p i c Systems 50 v i i LIST OF FIGURES Figure Page 1. F i r s t Order Rate Plots at Constant HCOOH and Varying MnO^ "" I n i t i a l Concentrations . . . 13 2. Typical Rate Plots f o r Reaction i n Solutions Containing Different (Excess) HCOOH Concentrations 16 3 . F i r s t Order Rate Plots at Constant I n i t i a l Mn04~ and Varying HCOOH (Excess) Concentrations 17 4. Plot of Pseudo-First Order Rate Constants (k 1) Against HCOOH Concentration 18 5. F i r s t Order Rate Plots at Constant HCOOH and Mn04 I n i t i a l Concentrations and Varying HCIO4 Concentration (30.1°C) 20 6. F i r s t Order Rate Plots at Constant HCOOH and Mn04 I n i - f c i a l Concentrations and Varying HCIO4 Concentration (35.0°C) 21 7. Plot of Apparent Second Order Rate Constants ( k " ) Against [H*] at Different Ionic Strengths 24 8. Plots of Second Order Rate Constants ( k M ) Against 1 / [ H 4 ] at Several Temperatures . . 28 9. Dependence of on Temperature 29 10. Arrhenius P l o t Showing Dependence of k A on Temperature 31 v i i i F igure Page 11. Arrhenius Plots Showing Dependence of k g l ^ and kg on Temperature . . 32 12. P lo t of k " Against 1 / [ H F ] Showing Ef fec t of Varying Ionic Strength on k A and kgK^ . . . 35 13. F i r s t Order Rate P lo t s Showing E f fec t of F e + + + Concentration on the Rate (k c ) 41 14. P l o t of Apparent F i r s t Order Rate (k c ) Against F e + + + Concentration 42 15. P l o t of Rec iproca l of F e + + + - Catalyzed Rate Against Rec iproca l of F e + + + Concentration . . . 43 16. P lo t s of Apparent Second Order Rate Constant ( k " ) Against 1 / [ H + ] (or 1 / [ D + ] ) for the Isotopic Systems 47 ACKNOWLEDGEMENT Sincere thanks to Dr. Halpern for his whole-hearted assistance and guidance, to Mr. Connor for making N.M.R. measurements, and to N.R.C. for financial aid. 1 INTRODUCTION I . General Considerable progress has been made i n recent years toward the understanding of the k i n e t i c s and mechanism of simple oxidat ion-reduct ion react ions i n aqueous s o l u t i o n . Some ox id i z ing agents whose react ions have been examined i n (20,54) (12,13,14) +.(15,51) some d e t a i l are A g + , Cu , Hg , ++ (15,5D - (18,32 ,47,54,57) +++ (17) (16) Hg 2 , Mn0 4 , T l , 0 2 and _ (14,25,41,42) Ci;20r/"". Among the reducing agents subjected to (12,23,54) , 1 6 _ (1,17 ,21 ,25,32, study have been H 2 , U ( IV) , HC0 2 , 41,42,46,57) (56) benzhydrol , and other simple organic (5,7 ,10,20 ,31 ,34 ,53) m u , • a , ^ species . The present study of the reac t ion between HCOOH and Mn0 4 i s another cont r ibut ion to t h i s general f i e l d . The choice of t h i s p a r t i c u l a r r eac t ion was based, i n p a r t , upon the fo l lowing cons iderat ions . 1. The k i n e t i c s of the reduct ion of Mn0 4 by various organic substances and by molecular Hp have been (32,54,56,57) thoroughly inves t iga ted . A comparison of the react ions of H 2 and of HCOOH was considered to be of p a r t i c u l a r in te re s t i n view of c e r t a i n s i m i l a r i t i e s between the two molecules. Both are two-electron reductants with (28) very s i m i l a r oxidat ion p o t e n t i a l s . 2 2. I t was ant ic ipa ted that the stoichiometry of the r eac t ion would be simple and c lear cut ; the reduct ion product of Mn04~ being exc lu s ive ly Mn0 2 , and the oxidat ion products of HCOOH, exc lu s ive ly H2O and C 0 2 . 3 , The k i n e t i c s of the reac t ion between HCOo"" and (19,32, Mn04~ have previous ly been invest igated i n some d e t a i l 57) . I t was hoped, by extending these inves t iga t ions to higher a c i d i t i e s , to e s t ab l i sh a l so the k i n e t i c s of the reac t ion between undissociated HCOOH and Mh04~. In view of the important effects which various metal ions have been found to exert on severa l other oxidat ion-reduct ion (12) react ions , i t was proposed a l so to explore such ef fects i n t h i s r e a c t i o n . I t was a lso hoped to obtain some information about the mechanism of the reac t ion through an examination of k i n e t i c isotope e f f ec t s . I I . Previous K i n e t i c Work Leading to the Present Inves t iga t ion Among the ox id i z ing agents whose react ions with + J 5 D aqueous HCOOH have been k i n e t i c a l l y examined are Hg"*^" , • ^ ( 5 1 ) . ^ J 1 ^ 6 ) MW (21,32,57) H g 2 + + , Ce"*"4* , T1+++ and Mn0 4 -The react ions of HCOOH with H g + + , Kg2++ and C 6 + + + have been postulated to involve a one-electron t rans fer from HCOO" to the oxidant r e s u l t i n g i n formation of formyl r a d i c a l (HCOO*). These react ions are apparently second-order k i n e t i c a l l y . The estimated Arrhenius frequency factors for these react ions 3 were abnormally high for bimolecular rate-determining steps l«f 10 -1 i (1,46,51) (Hr? - 10^ 1-mole s e c ~ x ) . For the r eac t ion between HCOOH and T l + + + simple k i n e t i c s have been observed, and a mechanism was proposed invo lv ing formation of a complex (T1»HC00H ) which decomposes i n the r a t e - c o n t r o l l i n g step + " ' + ( 1 7 ) to form the products , T l , C02 and H . A number of k i n e t i c inves t iga t ions have a l so been made of the reac t ion between MnOa, and HCOOH (or HCOo ) . (22) (35) (19) H o l l u t a , Or lov , Hatcher and West, and l a t e r , H i l l , (21,32,50) Mann and Tompkins studied t h i s r eac t ion i n neut ra l and s l i g h t l y ac id s o l u t i o n . The o v e r a l l k i n e t i c s observed mm mm were of second o r d e r : f i r s t order i n W11Q4. a n <* i n HCO2 j and the a c t i v a t i o n energy and frequency fac tor of the reac t ion were evaluated. I t was found that the rate of ox idat ion was independent of pH when the a c i d i t y was low enough to ion ize most of the formic a c i d . HCOO" was observed to be ox id ized much more r a p i d l y than HCOOH, and a primary s a l t ef fect ind ica ted that the r eac t ion involved two s imi lar ly-charged ions . The mechanism proposed involved oxygen transfer from MnO^ to HCO2 , wi th subsequent decomposition of the act ivated species to CO2 and O H - . More r e c e n t l y , Wiberg and Stewart examined the k i n e t i c s of the reac t ion between MnO^" and HC0o" i n bas ic (57) 2 s o l u t i o n , and found s i m i l a r r e s u l t s . The rate was found to be subs tant i a l ly independent of pH, and HCO2P reacted more r a p i d l y than HCOOH. Through the use of O 1 ^ - l a b e l l e d 4 MnC-4" i t was determined that considerable amounts of oxygen i n the CO2 product came from Mn04~. However, a large deuterium isotope e f f e c t (7.4) was also observed. These re s u l t s suggested that the oxidative mechanism involved simultaneous oxygen transfer from MuC^ "* to HCC^", and hydride transfer (or si m i l a r process) from HCC>2~ to MnC>4*". Several possible mechanisms were considered. The reduction of Mn04~ i n aqueous solu t i o n by H 2 was (2) f i r s t reported i n l859« K i n e t i c studies of t h i s reaction (23) were made i n 1911 by Just and Kauko, and more recently by (54) Webster and Halpern. The reaction proceeds by simple second-order k i n e t i c s and apparently involves Mn(V) as an intermediate. An in t e r e s t i n g feature of t h i s reaction i s i t s marked s u s c e p t i b i l i t y to c a t a l y s i s by Ag +. I t has been suggested that the catalyzed reaction proceeds v i a a Mn(VI) intermediate. Some k i n e t i c measurements have also been made (24) on the reduction of MnC^- by CO. The reaction i s f i r s t order i n each species. The observed rates of oxidation of CO are of similar magnitude to rates of H 2 oxidation, and the apparent a c t i v a t i o n energies are s i m i l a r . (29) Reactions of Mn04~ with various organic substances (3,10,40,53) have been examined, including ethylenes, (7,47) (5,34,44,47) (3D carbonyls, alcohols and acids. I n i t i a l attack by Mn(III) or i t s complexes (MnX2+) i s postulated f o r the oxidation of oxalate, followed by f a s t reduction i n ( 3 D several stages to form Mn(II). Oxidative attack of 5 enolized aldehydes and ketones by Mn(III) has also been (7) suggested. However, the majority of permanganate reactions are believed to proceed v i a conversion of MnC>4~ to Mn(V) (as I n O ^ or MnO^~), either by two electron (or hydride ion) transfer from the substrate to MnCvL", or by (8,32, transfer of an oxygen atom from MnO^" to the substrate. 37,40,43,48,54,57) On the basis of i s o t o p i c studies Wiberg and Stewart have suggested mechanisms f o r the permanganate (43,56) oxidation of benzhydrol involving simultaneous oxygen and hydrogen t r a n s f e r . A number of these considera-tions are relevant to the present i n v e s t i g a t i o n . 6 EXPERIMENTAL METHODS I. Materials Baker and Adamson HCOOH was r e d i s t i l l e d twice to remove impurities. KMn04 was an Analar product of high p u r i t y . This reagent was dissolved In d i s t i l l e d water and heated at the b o i l i n g point f o r several hours followed by f i l t r a t i o n to remove Mn02. Reagent grade HCIO4 from Merck (6l%) and from Baker and Adamson (70%) were employed. Other chemicals were of reagent grade. D i s t i l l e d water was used throughout. Deuterium oxide (99«5$ i s o t o p i c a l l y pure) was obtained from Stuart Oxygen Co.; the isot o p i c p u r i t y was confirmed by N.M.R. measurements. I I . Preparation and Standardization of Reagents Solutions of KMh04 w e r e standardized against anhydrous sodium oxalate. HCOOH and HCIO4 solutions were standardized with carbonate-free NaOH solutions of known concentration. A Fe(C104)o solution was prepared as (30) follows: to a soluti o n containing 100 gm. FeCl^, a solution of NaOH(6N) was added slowly with s t i r r i n g . The pre c i p i t a t e of Fe(OH)^ was p u r i f i e d by r e p r e c i p i t a t i n g from HCIO4 and washing several times. The s o l i d Fe(0H)3 p r e c i p i t a t e was added to 200 ml. HCIO4 (6l%) and t h i s mixture refluxed for 12 hours, a f t e r which the hydroxide was 7 completely dissolved. Fe*4"4" i n the resulting Fe(C10 4)^ solution was determined by adding excess I" (10^" -free) and titrating the I 2 liberated with standard thiosulphate. The acidity of the FeCClC^)^ solution was determined potentiometrically using a Beckman H-2 pH meter. Deuterated Formic Acids DCOOD and DCOOH were synthesized using the (44) procedure described by Stewart: Oxalic acid dlhydrate (126 gm., 1 mole) was equilibrated several times with D 2 0 . Glycerol (10 gm.) was twice equilibrated with D 2 0. After complete equilibration, the deuterated oxalic acid (dideuterate) was slowly added to the heated glycerol, and catalyzed decarboxylation of oxalic acid occurred. The reaction mixture was continuously d i s t i l l e d , and after purification the product of DCOOD in D 20 contained O.85 moles DCOOD (Q$% yield, 93 ml. containing .00914 equivs. per ml.). DCOOH was prepared by diluting a small quantity of the DCOOD - D 20 solution with H 2 0. The isotopic purity of the DCOOD - D 20 solution was found to be over 99$> using N.M.R. de t ermination. Deuterated perchloric acid was prepared by equilibrating HCIO4 (165 gm., 70% HCIO4) five times with 30 ml. D 2 0 , excess water being removed by d i s t i l l a t i o n under reduced pressure after each addition of D2O. An examination 8 of i t s N.M.R. spectrum showed i t to be 85*5$ i s o t o p i c a l l y pure. The f i n a l solutions employed i n k i n e t i c experiments were d i l u t e d to 1 M with D2O, and thus had an is o t o p i c purity of over 98$. I I I . K i n e t i c Measurements and A n a l y t i c a l Determinations The rates of the reactions were measured by the following methods: A. Spectrophotometric Method A blackened glass reaction vessel of 100 ml. capacity, containing known amounts of HCOOH, HCIO4 and NaCK>4 solutions, was immersed i n a water bath thermostatically controlled to *0 .05 ?C. A separate vessel containing KMn04 and another containing d i s t i l l e d water'were also allowed to come to the same temperature. An aliquot of KMn04 was subsequently pipetted into the reaction f l a s k , and the reaction mixture made up to 100 mis. by adding water. At appropriate times, samples of the reaction mixture were with-drawn, quenched by cooling to 0°C, and centrifuged to remove Mn02. Mn04" concentrations were measured using a Beckman D.U. Spectrophotometer at the Mn04~ peak wavelength of 522 nu(. This method was found to be unsatisfactory because of d i f f i c u l t y i n removing a l l c o l l o i d a l Mn02 from the samples by centrifugation. Optical density measurements were inaccurate because of t h i s . 9 B. Ferrous-Dichrornate T i t r a t i o n Method As i n the preceding method, samples from a s ingle reac t ion mixture were withdrawn at su i table t imes, cooled to 0 ° C , and centri fuged to remove Mn0 2 . A l iquot s of each so lu t ion were quenched with a known quan i t i ty of ferrous sulphate. The quenched solut ions were back- t i t r a ted with standard dichromate, using sodium diphenylamine sulphonate as the i n d i c a t o r . Aga in , d i f f i c u l t y i n removing a l l MnC-2 from the samples was experienced, and the ind ica tor proved unsat i s factory i n cases where a large amount of Mn04~ had been present i n the sample. However, r e su l t s obtained using t h i s method agreed at leas t q u a l i t a t i v e l y with those obtained using the fo l lowing method: C . Iodide-Thiosulphate T i t r a t i o n Method Brown glass r eac t ion ves se l s , a l l containing known quant i t ie s of HCOOH, NaC104 and HCIO4 were immersed i n the thermos ta t i ca l ly -cont ro l l ed water bath. A so lu t ion of KMn04 a l so was heated i n the bath, and subsequently, a l iquots of KMn04 were p ipet ted in to the reac t ion f l a s k s , which were shaken to ensure uni formity . Each reac t ion mixture was qu ick ly quenched at the required time with an excess of K I . The I 2 l i be ra ted was t i t r a t e d with standard sodium t h i o -sulphate so lu t ion using s tarch i n d i c a t o r . This method proved to be most s a t i s f ac tory because instantaneous quenching could be achieved, and analys i s for 10 Mn04~ does not necess i ta te removal of Mn02. Quenching time d i d not exceed two seconds. Concentrations of KI and ^28203 so lut ions were sui ted to reac t ion concentrat ions , and ranged as fo l lows : KI - 0.025W to 0.5N; Na2S203 - C O I N to 0 .1N. Uncerta inty at the end point d i d not exceed 0.003 m l . of C O I N t h i o -sulphate for most of the t i t r a t i o n s . Experimental ly measured rates were reproducible to wi th in 5$ i n most cases. Reactions were conducted i n the temperature range 15 to 35°0; most of the experiments being conducted at 3 0 °C . The reac t ion rate was found to be unaffected by glass wool (evidence for homogeneous character) and by l i g h t . (These re su l t s are shown i n Table VI I I . ) A c i d i c solut ions of the separate reactants (HCOOH and MnO^") were found to be s t ab le . Ion iza t ion constants for DCOOH and HCOOH were determined over the temperature range 15° to 36°C by measuring the pH of so lut ions of known HCOOH - HCOO" concentrat ion r a t io s (concentrations ranging from 0.2 to 0.05 M) with a Beckman Model G pH meter. The i o n i c strength was maintained constant at 1.0M with NaC104. 11 RESULTS AND DISCUSSION I . Stoichiometry of the Reaction When HCOOH was present i n excess, Mn04~ was found to be reduced q u a n t i t a t i v e l y to Mn0 2 . (Table I . ) Further reduct ion of Mn02 by HCOOH was slow. When MnO^" was present i n excess, that amount of MnO^." reduced to Mn02 was found to be two-thirds of the i n i t i a l HCOOH concentrat ion. Further reduct ion of Mn04~ was slow and could be neglected i n the time taken for the k i n e t i c experiments. Results are shown i n Table I , page 12. These observations are consistent with the expected stoichiometry of the reac t ion represented by: 2Mn04~ + 3HC00H + 2H+ — » 2Mn02 + 3C02 + 4H 20 1 I I . K i n e t i c s of the React ion: E f fec t of Reactant Concentration A ser ies of experiments was made i n which the concentrat ion of HCIO4 was maintained at 0.601M. The i n i t i a l concentrat ion of Mn04" was var ied from 0.0004M to 0.0016M while the i n i t i a l concentrat ion of HCOOH was i n large excess ( O . O 9 7 O M ) . Ionic strength was maintained constant at 1.0M by the add i t ion of N a C K ^ . T y p i c a l f i r s t order rate p lo t s (the reac t ion i s pseudo-f i r s t order s ince the concentrat ion of HCOOH which i s i n large excess i s e s s e n t i a l l y constant through-out the react ion) are shown i n Figure 1, page 13. No 12 TABLE I STGICHIOMETRY OF THE REACTION BETWEEN Mn0 4 r AND HCOOH Temperature = 30.1°C Ionic strength = l.OM Expt. No. I n i t i a l Cone. (Mxlo3) HCIO4 Mn02 formed Mn04" HCOOH (M) (M/Lxl03) A 3 1.002 97.0 0.601 0.948 A 5 0.502 97.0 0.601 0.486 A6 0.252 97.0 0.601 O.25O Rl 40.18 10.29 1.02 6.76 R 2 40.18 10.29 1.02 6.84 R4 40.18 10.29 1.02 6.80 13 Figure 1 F i r s t - Order Rate Plots at Constant HCOOH and Varying MnO- I n i t i a l Concentrations, HCOOH--0.097GM. HC10 — O ^ o i M . J —1.0 M. Temperature—30.1 C. 14 observable change In the slopes was apparent over the range of I n i t i a l Mn04"* concentrations employed. The re su l t s showed the reac t ion to be f i r s t order i n Mn04"" under these condi t ions . A second ser ies of experiments was conducted i n which the i n i t i a l Mn0 4~ concentrat ion was maintained constant at 0.0010M, while the i n i t i a l HCOOH concentrat ion was var ied from 0.00 to 0.1212M. Solut ions were 0.601M i n HCIO4 and the i o n i c strength was he ld constant at 1.0M using NaC104. The r e su l t s of these experiments are shown i n Table I I , page 15, and Figures 2 and 3» pages 16 and 17 r e s p e c t i v e l y . The pseudo-f i r s t order rate p lot s (Figure 3) were again l i n e a r ; however the slope var ied with the HCOOH concentrat ion . Pseudo-f i r s t order rate constants (k f ) were found to be d i r e c t l y propor t iona l to the HCOOH concentrat ions . (See Figure 4.) Thus the o v e r a l l k i n e t i c s are seen to be of second order ( f i r s t order both i n HCOOH and i n Mn04~), i . e . , -d[Mn04~] = k ' ! [Mn04"] [HCOOH] 2 dt When the concentrat ion of HCOOH remains e f f e c t i v e l y constant during a given experiment, t h i s reduces to -d [Mn04"] = k* [Mn04~] 3 d t -where k' = k " [HCOOH] . In these and subsequent experiments, values of k ' , and hence 15 TABLE II EVIDENCE FOR SECOND ORDER KINETICS Temperature = 30.1°C Ionic strength = l .OM Expt . No. I n i t i a l Cone. (M) k ' x l O 4 k " x l o 3 Mn0 4 " HCOOH HC10 4 sec""*' l-nf^s ' J l 0.0970 0.601 - -S i 0.0004 0.0970 0.601 5.10 5.25 »1 .0010 0.0970 0.601 4.87 5.02 Mi .0010 0.0970 0.601 4.90 5.05 R l .0016 0.0970 0.601 4.90 5.05 K l .0010 - 0.601 - -U l .0010 0.0485 0.601 2.45 5.06 Ml .0010 .0970 0.601 4.90 5.05 N i .0010 .0970 0.601 4.87 5.02 T l .0010 .1212 0.601 6.18 5.06 1 16 F i g u r e Oo5oo .400 H I u •p •H H I © H O 1 J .200 0 . o — 0 — 0 — 0 — 0 — 0 - 0 — C o ~ A " O " V 0 .00 M HCOOH O.OJ+85 M " 0.0970 M 11 --- 0.1212 M " A. 2lf0 720 960 1+8 0. Time (seconds) Ty p i c a l Rate Plots f o r Reaction i n Solutions Containing D i f f e r e n t ( E X C E S S ) HC0©H Concentration. I n i t i a l MnO"— 0.0010 H . HC10 —0 .601 M . i i — 1 .0M. T 3 0 . 1 °C. k 17 Figure 3 » 1 o I I I to o H ,1|00 0 . o A O V — 0 . 0 0 0 M HCOOH — o.oi(.85 M " 0 . 0 9 7 0 M " - - - 0 . 1 2 1 2 M " 1 214-0 1 1 9 6 0 I4.8O 7 2 0 Time (seconds) -F i r s t - Order Rate r i o t s a t Constant I n i t i a l MnO and k -V a r y i n g HCOOH ( E x c e s s ) C o n c e n t r a t i o n s . I n i t i a l MnO • 0.0010 M. HC10 — 0 . 6 0 1 M. JJ --1.0K. T * - - 3 0 . 1 P C . 18 319 of k f l were determined from the slopes of pseudo-first order rate plots of the type shown in Figures 1 and 3» III. Effect of Hydrogen Ion Concentration To determine the effect of hydrogen ion concentra-tion on the reaction, a series of kinetic experiments was conducted as follows: the i n i t i a l HCOOH concentration was maintained at 0.0970M, and the i n i t i a l Mn04~ concentration at 0.0010M. The HCIO4 concentration was varied from 0.10M to 1.202M. Ionic strength was maintained at 1.0M, where possible, by the addition of NaC104. In these experiments, the pseudo-first order rate constants were found to vary with H* concentration as shown in Figures 5 and 6, pages 20 and 21 respectively, and in Table III, page 22. The measured rates steadily decreased with increasing HCIO4 concentration, approaching a f i n i t e limiting value at high H4* concentration. (Figure 7.) In Figure 8 , a plot of k M against 1/ [H +3 i s seen to be linear. Similar relationships were obtained at several other temperatures. (Figure 8 and Table III.) In an attempt to explain this pattern of kinetic behaviour the following mechanism has been proposed: 1. HCOOH, in aqueous solution, ionizes in an equilibrium process to form HCOO" (formate ion) and H+* viz HCOOH K i ^  HCOO" + H + 4 \ .- . where i s the ionization constant for HCOOH at a particular 20 Figure 5 t O 1.202 M HC10 Time (seconds) F i r s t - Order Rate Plots at Constant HCOOH and Mn© k I n i t i a l Concentrations and Varying HC10 Concentration. I n i t i a l MnO. —0.0010M. HCOOH — 0.0970M.1/ — 1 . 0 M . T--30.1 C. 21 Figure 6 Q - - - 1.029 M HC10 • — 0.257 M " Time (seconds) Firast- Order Rate Plots at Constant HCOOH and MnO I n i t i a l Concentrations and Varying HC10 Concentration. I n i t i a l MnO- —0.0010M. HCOOH—0.0970M. U — 1.0M. T—35.0 TABLE I I I DEPENDENCE OF THE RATE ON PERCHLORIC ACID CONCENTRATION -Ionic s t r e n g t h - l.OM Temperature I n i t i a l Cone. (M) 1/ H + k'xlO 4 - k''xlO^ (°C) Mn0 4" HCOOH HCIO4 (M*"1) s e c " 1 l - m " 1 s ~ 1 15.6 O.OOIO O . O 9 8 9 1.029 0.973 1.17 1.18 15.6 0.0010 0.0989 0.2573 3 .89 3.27 3.3-1 15.6 0.0010 0.0989 .I690 5.90 4.57 4 .61 15.6 0.0010 0.0989 .1029 9.73 7 .38 7.46 22.8 0.0010 O.O989 1.029 0.973 2.03 2.05 22.8 0.0010 0.0989 0.2573 3.89 5.40 5.46 22.8 0.0010 0.0989 .1698 5.90 8.01 8.22 22.8 0.0010 0.0989 .1029 9.73 12.6 12.7 25.8 0.0010 0.0970 1.029 0.973 2.57 2.64 25.8 0.0010 0.0970 0.2569 3.90 7.57 7 .28 25.8 0.0010 0.0970 .1696 5.90 10.3 10.6 25.8 0.0010 0.0970 .1028 9.73 15.7 16.2 30.1 0.0010 0.0970 1.202* O.833 3.57 3.68 30.1 0.0010 0.0970 0.6010 1.67 4.90 5.05 30.1 0.0010 0.0970 .3004 3.33 7.97 8.22 30.1 0.0010 0.0970 .1202 8.33 17.5 I8.I 32.7 0.0010 0.0989 1.029 0.973 4.58 4.63 32.7 0.0010 0.0989 0.2573 3.89 11.5 11.6 32.7 0.0010 0.0989 .1690 5.90 16.0 16.7 32.7 0.0010 0.0989 .1029 9.73 25.8 26.1 35.0 0.0010 0.0970 1.029 0.973 5.12 5.26 35.0 0.0010 0.0970 0.2573 3.89 I3.6 14 .0 35.0 0.0010 0.0970 .1690 5.90 19.1 19.7 35.0 0.0010 0.0970 .1029 9.73 29.7 30.7 • I o n i c s t r e n g t h = 1.2M. 23 temperature. In strongly acid solution, most of the formic acid w i l l exist as the undisspciated HCOOH molecule. The equilibrium concentration of HCOO" i s given by [HCOO"] = K i [HCOOH] / [H+] 5 where ^HCOOHJ may be approximated by the t o t a l formic acid concentration. 2. Mn04~ reacts with both HCOOH and HCOO", i n bimolecular rate-determining, steps, i . e . Mn04~ + HCOOH k A > intermediates 6 Mn04~ + HCOO" kB > intermediates 7 where k& and kg are second order rate constants for the oxidation of HCOOH and HCOO" respe c t i v e l y . (The nature of the intermediates w i l l be discussed l a t e r . ) Hence the t o t a l rate of reaction i s given by = k A [HCOOH] [Mn04~] + kB [HCOO"] [Mn04~] 8 Substituting for [HCOO~] from equation 5 and rearranging, the rate expression becomes -d mofi = [HCOOH] [Mn0 4 j (k A + k BK ±/ [H+]) . . . . 9 •d |5n04 c Lt dt Thus i t i s seen that 11 k = k A + k g ^ / [H+] 10 and k' = [HCOOH] ( k A + kgK^/ [H+]) 11 At any temperature a p l o t of k " against 1/ [H+J should Figure 1 0.00 1.00 [ H + ] ( M ) Plot of Apparent Second- Ord®r Rate Constant (k") Against [ii +] at 2.00 Di f ferent jonic Strengths. Temperaturo--30.1°C. 25 then be l i n e a r with a slope of kgKj_ and an intercept of k A. Such plots for various temperatures are shown i n Figure 8, page 28, and were used to obtain the values of k A and kgK^ l i s t e d i n Table V, page 27. Values of kg were then calculated using separately measured values of Kj_, l i s t e d i n Table IV, page 26. IV. Evaluation of K±, the Ionization Constant of Formic Acid (18) In 194-3, Harned and Embree determined % values f o r HCOOH using electrochemical methods. These measurements were conducted i n solutions having i o n i c strengths up to O.25M. There appeared to be a s l i g h t increase i n with increasing i o n i c strength, i n keeping with the predictions of the Debye-Huckel theory. Since the present k i n e t i c investigations were ca r r i e d out i n solutions of A{ = 1 . 0 , values for i n 1.0M NaclO^. were determined potentiometrically using a Beckman G pH meter. Kj. values were observed to be about three times greater than those previously reported at low i o n i c strengths. (Table IV.) However, the same type of temperature dependence (although much more pronounced) was found, (Figure 9) with a maximum i n Kj_ occurring at about 25°C. Similar maxima i n have been observed at 25°C fo r acetic and propionic acids. 26 TABLE IV TEMPERATURE DEPENDENCE OF THE IONIZATION CONSTANT OF FORMIC ACID Acid Temperature (°C) Reported* K± (M/L) Experimental** K± (M/L) HCOOH 15.2 1.750xlO~ 4 4.12xl0 - 4 HCOOH 20.9 1 .767x l0 " 4 5.7 x l O " 4 HCOOH 24.7 1.772X10" 4 6.2. x l O ' 4 HCOOH 29.9 1.768xlO" 4 5.6 x l O " 4 HCOOH 36.1 1.740xl0" 4 4.2 x l O " 4 DCOOH 29.9 - 8.0 x l O " 4 (18) ' •Harned and Embree, 1934. / \ <.i0.01M **Mean of two measurements at d i f f e r e n t [HCOOH] / [HCOO^ r a t i o s , = l.OM. 27 TABLE V DEPENDENCE OF k A AND k B ON TEMPERATURE Temperature k A x l 0 3 k g ^ x l O 3 * 4 . K i x K T kB °C °K l-mole-^sec"*^ sec"*1 M/l l-m"^" 1 15.6 288.8 0.450 0.718 4.25 I.69 22.8 296.0 0.881 1.22 6.05 2.01 25.8 299.0 1.15 1.59 6.20 2.56 30.1 303.3 1.70 1.95 6.04 3.23 32.7 305.9 2.15 2.47 4.95 4.99 35.0 308.2 2.69 2.87 4.45 6.46 •Experimental values from Figure 9. Figure 8 29 Figure 9 30 Y. E f f e c t of Temperature on the Reaction An Arrhenius plot f o r k A i n the temperature range 15.6° to 35.0°C i s shown i n Figure 10, page 31. The slope corresponds to an apparent a c t i v a t i o n energy E A of 16.4 kCal mole" 1. Using t h i s value and the experimental values of k A , the Arrhenius frequency fa c t o r A A was estimated to be l . l x l O ^ l i t r e - m o l e ^ - s e c " " 1 (corresponding to an entropy of a c t i v a t i o n A s A of -19.3 eu.). Although a plot of log kjjKji versus 1/T gave a good straight l i n e (Figure 11, page 32) , the Arrhenius p l o t for kB (based on values of % measured at d i f f e r e n t temperatures) showed pronounced curvature (Figure 11). I t seems l i k e l y that t h i s i s an apparent e f f e c t a r i s i n g from a systematic error i n the determination of the temperature dependence of K^. This i s suggested by the f a c t that the magnitude of the apparent temperature dependence of K-« i s much greater than that found (18) by Harned and Embree (at i o n i c strengths up to 0 .25M i n which range there was no i n d i c a t i o n of an increase i n t h i s magnitude with i o n i c strength). Furthermore i t would be most unl i k e l y that the dependencies of log kg and log on 1/T were both non-linear and that the departures from l i n e a r i t y were exactly compensating to account for the resultant l i n e a r i t y of the log kB&± vs. 1/T p l o t . I t i s believed that while the pH method used i s s u f f i c i e n t to y i e l d approximate K± values, more refined methods, such as those employed by (18) Harned and Embree would be necessary to measure the 31 F i g u r e 1 0 3 . 2 0 3 - 3 0 . 3 3.14-0 3 . 5 0 1 / T K 1 0 Arrhenius Plot Showing Dependence of k. on Temperature. A Ionic s trength.— 1 . 0 M. 32 Figure 11 • U U j I I T> .t 3.20 3.30 3 3 4 0 3.30 1/ T x 10 Arrhenius Plot Showing Dependence oif k K on Temperature ( ° K ) . (Right Ordinate) B i Arrhenius P lo t Showing Dependence of k on Temperature ( ° K ) . (Left Ordinate) B Ionic strength 1.0M. 33 temperature dependence p r e c i s e l y . However, the maximum i n at 25°C which was observed both i n the e a r l i e r and present measurements appears to be r e a l ; hence for the purpose of determining kg i t seems safe to assume that the heat of i o n i z a t i o n of formic a c i d ( A ^ ) i s zero at t h i s temperature. Using t h i s assumption, a value of 13.0 kCal/mole i s obtained for Eg from the slope of the log kBK± v s . 1/T p l o t . This corresponds to the value estimated from the slope of the kg Arrhenius p lo t at 2 5 ° C (See Figure 11.) The Arrhenius frequency factor Ag was estimated to be 7.8x10^11tre mole " 1 sec"-*-, corresponding to an entropy of a c t i v a t i o n ASg* of -15.3 eu. (A Summary of Temperature Parameters i s shown i n Table V I , page 34.) The uncer ta int ie s i n E A and Eg are estimated to be l o . 5 and - 2 . 0 kCal/mole r e s p e c t i v e l y . The uncertainty of A s A i s estimated at -1.5 eu. The absolute uncertainty of K^, and hence of ASg* are d i f f i c u l t to estimate. However, the values of the k i n e t i c parameters determined above are i n (32) reasonable agreement with those reported by Tompkins (Eg = 11.8 kCal/mole* ASg* = -20.8 eu.) on the basis of measurements at lower a c i d i t i e s and i o n i c s t rength . The value of 2.30 l . m o l e " 1 s e c " 1 found for T = 25°C and A{ - 1.0M, compares with the value of 3.00..m" 1s7 1 reported by T o m p k i n s ^ 2 at yCf = .O859M and the value of 0.927-.0l5-l-m~1s~1 reported 34 TABLE VI KINETIC PARAMETERS FOR THE REACTION Reaction E A A s k (Cal/mole) (l-mole'-^sec" 1) (eu) (l-mole'^-sec" 1) HCOOH+ 7 : ~ ~ q — — — Mn04""-* 16,400 l . l x l O 9 -19.3 kA=l.lxlO^expj(-l6400/RT) HCOO"+ Q Mn0 4"-» 13,000 7.8x10* -15.3 k B=7.8xl0 9exp(-13000/RT) 35 Figure 12 30.0 H I H I W C o o © ra ra © H °? © U •P •H H 20.0 o H 10.0 0.00 0.00 A " " 1 ' 0 M A ^ 7 _ - _ 0 .5 M " O --- 2 .0 M " 2.50 5..C0 7.5P 1 / [ H ^ (M ) Plot of k" Against 1/ [E*} Showing E f fec t of Varying Ionic Strength on k and k K • Temperature — 30 .1°C. A B i 36 by Stewart at A{ = 0.2M. ( A l l at 2 5 ° . ) * VI. E f f e c t of Ionic Strength Varying the i o n i c strength of reaction solutions from 0 .5 to 2.0M by changing the NaClO^. concentration had no detectable e f f e c t on reaction rates over an acid concentration range of 0.10 to 2.1M. Results of these measurements are summarized i n Table VII, page 37 and i n Figures 7 and 12. The absence of an i o n i c strength e f f e c t on k A i s not surprising since k A r e f e r s to a reaction between an ion and a neutral molecule. The absence of an apparent i o n i c strength e f f e c t on the formate ion contribution i s probably due to the f a c t that the measurements were made i n the region of high i o n i c strengths where i o n i c a c t i v i t y c o e f f i c i e n t s tend to be f a i r l y independent of i o n i c strength. At low i o n i c strengths, kn (32,57) 3 has been reported to increase with i o n i c strength i n accordance with the predictions of the Bronsted-Bjerrum theory. VII. E f f e c t of Metal Ions The addition of C o C C l O ^ , AgC104 and Cu(G10 4) 2 had no effects on the rates of reaction (Table V I I I ) . Considering the marked c a t a l y t i c a c t i v i t y which Ag + exhibits i n the •Kinetic calculations of E, A andAs* employ the standard Arrhenius and Eyring rate equations: k = A exp.(-E/RT) . ± k = KkT/h exp. (AS* /R) exp . ( - A H /RT) 37 TABLE VII DEPENDENCE OP RATE ON IONIC STRENGTH Temperature = 30.i°c I n i t i a l Cone. (M) k'xlO 4 k " x l o 3 Mn04" HCOOH HC104 NaC104 (M) sec*"x O.OOIO 0.0970 1.20 - 1.2 3.57 3.68 0.0010 0.0970 0.601 .40 1.0 4.90 5.05 0.0010 0.0970 0.300 .70 1.0 7.98 8.22 0.0010 0.0970 0.120 .88 1.0 17.6 18.1 0.0010 0.0970 2.06 - 2.1 2.65 2.73 0.0010 0.0970 1.03 1.0 2.0 3.45 3.56 0.0010 0.0970 0.257 1.7 2.0 9.10 9.39 0.0010 0.0970 0.170 1.8 2.0 12.6 13.0 0.0010 0.0970 0.103 1.9 2.0 20.3 20.9 0.0010 0.0970 0.451 . 0 5 0 .5 6.37 6.55 0.0010 0.0970 O.238 .26 0.5 9.55 9.84 0.0010 0.0970 O.I63 .34 0 .5 14.0 14.5 0.0010 0.0970 0.108 .39 0 .5 18.6 19.1 . 38 (54) reaction of MnO^" with H 2 i n aqueous solution, t h i s i s of i n t e r e s t . The addition of Fe(0104)3 w a s observed to increase reaction rates to a considerable extent. That Fe*++ displays true c a t a l y t i c a c t i v i t y (rather than " t r i v i a l " c a t a l y t i c a c t i v i t y a r i s i n g from the oxidation of HCOOH by Fe4"4*4", followed by the reoxidation of Fe4*4" by Mn04~) may be shown by the following evidence: In acid s o l u t i o n containing HCOOH and Fe*" M, but no Mn04", the concentrations of HCOOH and F e + + + remained constant fo r several hours. When MnO^ /" i s added, reaction s t a r t s , and the rate of t h i s reaction i s proportional to the concentration of F e M 1 . Furthermore, during t h i s reaction the Fe H concentration remains constant. Acceleration of the reaction by Fe''' i s i l l u s t r a t e d i n Figure 13, page 41, and i n Table VIII, page 39. I f the pseudo-first order rate constant k c i s plotted against concentration of Fe , the r e s u l t i n g curve i s found to l e v e l o f f at high Fe concentration. (Figure 14, page 42.) This behaviour i s consistent with the following i n t e r p r e t a t i o n : Fe +' M' i n aqueous solution i s assumed to associate with Mn04 to form a complex FeMn04 (there i s no evidence for t h i s but analogous complexing of Fe with HSOA and ClO^ has been reported): Fe"1""" + Mn04" K c > FeMnO^ 12 39 TABLE VIII EFFECT OF SOLUTION COMPOSITION ON THE RATE Temperature = 29.9°C Ionic s trength = l .OM I n i t i a l Cone. (M) k ' x l O ^ k r t xl0.3 MnO^~ HCOOH HClOj^ Added M a t e r i a l s e c - 1 l - n f ^ s " 0.0008 0.0989 1.017 - 3.70 3-75 0.0008 0.0989 1.017 - 3.60 3.65 0.0008 0.0938 1.022 .001M Cu(C10^) 2 3.S3 3.76 0.0008 0.0938 1.022 .010M Cu(Cl0^) 2- 3.1|£ 3.67 0.0008 0.0939 1.022 .010M Co(C10^) 2 3.57 3.80 0.0008 0.0939 1.022 .001M AgClO^ 3-50 3.72 0.0008 0.0939 1.022 .010M AgClO^ 3.H-6 3.71 0.0008 0.0989 1.017 .0017M Fe(010^ )3 5.13 5 .20 0.0008 0.0989 1.017 .007^M Fe(C10h_)3 6.73 7.16 0.0008 0.0989 1.017 .0170M Fe(C10^) 3 7.^2 8 .00 0.0008 0.0989 1.017 glass wool 3.37 3.58 0.0008 0.0989 1.017 exposure to l i g h t 3.67 3.70 4G The e q u i l i b r i u m constant f o r t h i s process may be expressed as K c = [ F e M n O ^ J 13 [ F e ^ 4 ] [MnG 4 "J S i n c e [ F e + + 4 ] i s i n l a r g e excess over JMnO^ ."*] i t may be approximated by the t o t a l Fe'*" c o n c e n t r a t i o n . I f the o v e r a l l r e a c t i o n i n v o l v e s independent r e a c t i o n s of MnO^" and of F e M n 0 4 + + w i t h HCOOH (or HCOO'), the r a t e equation w i l l be of the form: Rate = k G [Mn0 4"J = k' [Mn0 4"] + k* [ F e M n O ^ ] . . . 14 where k 1 i s the apparent r a t e constant f o r the r e d u c t i o n of uncomplexed Mn0 4~ ( u n c a t a l y z e d r a t e ) and k" i s the apparent r a t e constant f o r r e d u c t i o n o f FeMnO^j4"*" ( c a t a l y z e d r a t e ) . Rearranging equation 14 give s Rate = k' [Mnp4~] + (k* - k') [FeMnO^4"4] . . . . . . 15 ( t o t a l ) S o l v i n g f o r [FeMn0 4 + +] i n equation 13 g i v e s [ F e M n O ^ ] = K c [ F e + + + ] [m0^total)/(l + K c . . l6 Hence equation 15 w i l l become Rate = k* [Mn0 4'J ( t o t a l ) + (k* - k') K c [ F e ^ [Mn04"3 1 + K c [Pe*"**] 17 and k c = k' + ( k * - k 1 ) K c [ F e + + + ] / ( l + K c [ F e + + + ] ) 18 Figure 13 41 I 1 1 1 1 a 0. 2J4.0 If80 720 960 Time (seconds) F i r s t - O r d e r Rate Plots Showing E f f e c t of P e * + + Concentration on the R a t e ( k c ) . HCOOH O .O989 M. I n i t i a l MnO^--0.0008M. HC104—1.0171-1^  —1PM. T—29.9 °C 42 Figure lij. 0.00 1.60 0.80 2 [•Fe+*«Jx 10 M Plot of Apparent F i r s t - Order Rate (k ) Against c Fe**"* Concentration. Ionic strength — 1.0 M. Temperature — 29.9°C. 4 3 Figure 1$ xa •a 8 I 6000 I 1+000 20 00 l -600 0.00 200 1) 1+00 l/Oe+*+3(MT ) Plot of Reciprocal of Fe***— Catalyzed Rate Against Reciprocal of Fe**f Concentration. Ionic strength—1.0 M, Temperature—29.9 °C. 44 Rearrangement of equation 18 gives 1 1 + 1 . . . . 19 k c - k' (k* - k') K C [ F e + + + ] (k* - k') According to t h i s , a plot of 1 , against k G - k 1 should be l i n e a r with an ordinate Intercept of 1 , , and a slope, _^ 1_ . The pl o t i n Figure 15 i s ~ k (k"' - k ) K C consistent with t h i s i n t e r p r e t a t i o n , and yiel d s values of k 1 = 3.65xlO- 4sec - 1j k*"" = Q.^OzlO'^seo"1; and K C = 273 l i t r e / m o l e . Here k' and k* are apparent rate constants only, since the dependence on the HCGOH concentration i s not considered i n the above rate c a l c u l a t i o n . The above value of KQ i s not unreasonable f o r the 4*4* formation constant of a complex such as FeMnO^ . However, there i s no corroborating evidence for the existence of t h i s complex. For example, the addition of 0.017MFe did not produce any detectable change i n the absorption spectrum of a 0.0002M Mn04" solut i o n . The proposed explanation f o r the 4-4*4-c a t a l y t i c e f f e c t of Fe must therefore be considered as very speculative. V I I I . Deuterium Isotope E f f e c t s To obtain further i n s i g h t into the mechanism of the reactions, an inv e s t i g a t i o n was made of the k i n e t i c isotope effects a r i s i n g from the substitution of reactant (HCOOH) and solvent (H2Q) hydrogen by deuterium. Measurements of the *5 k i n e t i e isotope e f f e c t (HCOOlDCOCTrates) have been previously (58) reported for the HC00~-MnC>4~ reaction (also Aebi, Buser and Luthi, Helv. Chim. Acta., 112:944.1956). Pour series of experiments were conducted. Series a ) . Reactions i n which the reductant was HCOOH; the solvent, H 2 0 ; the ac i d , HCIO4. Series b). Reductant, DCOOH; solvent, H 20; acid, HCIO4. Series c ) . Reductant, HCOOD; solvent, D 20; acid , DCIO4. Series d). Reductant, DCOOD; solvent, D 20; acid, DCIO4. A l l experiments were made at i o n i c strength of 1.0M by the addition of NaC104, and temperature was maintained at 29.9°C I n i t i a l Mn04" concentration was always 0.0008M, and perchloric acid concentrations were varied within each series from 0.1 to 1M. Linear f i r s t order rate plots were obtained f o r each s e r i e s . The experimental r e s u l t s are summarized i n Table IX, page 46. Pseudo-first order rate constants (k') were used to calculate k'' values and these were plotted against 1/ [H*] (or 1/ [D +]) as i l l u s t r a t e d i n Figure 16, page 47. For each series a f a i r l y good straight l i n e could be drawn, and k^ and kgK^ determined as described previously. The i o n i z a t i o n constant % for DCOOH i n H 20 was determined potentiometrically to be 8.0X10""4" m o l e / l i t r e 46 TABLE IX •ISOTOPE EFFECTS ON THE RATE Temperature = 29.9°C Ionic strength = l.OM Solvent Formic Acid F.A. Cone. Mn0 4 ~ Acid A c i d Cone. k'xlO 4 k' ' x l 0 3 (M) (M) (M) sec J" l-m~ 1s~ 1 H 2 0 HCOOH 0.1029 0.0008 HCIO4 1.20* 3.52 3.42 H 2 0 HCOOH 0.1029 0.0008 HC10 4 0.330 7.93 7.71 H 2 0 HCOOH 0.1029 0.0008 HC104 .155 14.7 14.3 H 2 0 HCOOH 0.1029 0.0008 HC104 .111 19.9 19.3 H 2 0 DCOOH 0.1005 0.0008 HC104 1.11* 1.92 1.90 H 2 0 DCOOH 0.1005 0.0008 HC10 4 0.300 3.07 3.05 H 2 0 DCOOH 0.1005 0.0008 HC10 4 .150 4.13 4.12 H 2 0 DCOOH 0.1005 0.0008 HC10 4 .107 5.38 5.35 D 2 0 HCOOD O.IO36 0.0008 DC10 4 1.51* 2.60 2.51 D 20 HCOOD O.IO36 0.0008 DC10 4 0.350 6.72 6.48 D 20 HCOOD O.IO36 0.0008 DC10 4 .162 12.3 11.9 D 20 HCOOD O.IO36 0.0008 DC10 4 .112 17.3 16.7 D 2 0 DCOOD 0.1253 O.OOOB DC10 4 1.03 2.15 1.72 D 2 0 DCOOD 0.1253 0.0068 DC10 4 .590 2.80 2.23 D 2 0 DCOOD 0.0888 0.0008 DG10 4 .296 2.22 2.50 D 2 0 DCOOD O.O888 0.0008 DC10 4 .216 2.88 3-24 •Ionic strength > l.OM. 20.0 Figure 16 47 16. 0-12.CJ 8.0Ch l+.OO o.ool 0, o A O V - HCOOH i n H 0 2 - HCOOD i n D 0 2 - DCOOH i n H 0 2 - DCOOD i n D 0 2 1 1 1 2.50 ~ J T O O " 7.5o 1/ C lit] pr 1/ [ D ^ (M"») 10. Plots of Apparent Second- Order Rate Constant ( k « ) Against V [ H J or i / [ D 4 . ] f o r the I ao topic Systems.^ --1.0M. T--29.9 48 (Table IV) and hence kn for series (b) was calculated. ( 3 3 , 3 6 ) Butler and co-workers have determined i o n i z a t i o n constants for HCOOH i n D 20 to be about one-third of K± i n H 20 under the same conditions, or K±(D20) = 0.340Ki(H 20) 20 This r e l a t i o n s h i p was employed to estimate f o r HCOOD and DCOOD i n D 20, and hence kg for series (c) and (d). Table X, page 49, l i s t s the values obtained f o r k A and kg for series (a) to (d). Obviously (within experimental accuracy) su b s t i t u t i o n of the hydrogen attached to carbon i n HCOOH by deuterium has l i t t l e e f f e c t on k A, and hence i t appears that cleavage of the C-H bond probably does not play an important r o l e i n the rat e - c o n t r o l l i n g step of the oxidation of HCOOH. This i s applicable i n H 20 as well as i n D 20, as i s seen i n Tables X and XI. Ratios of k A (A) and (C) are approximately unity i n the two solvents, showing that rates of oxidation of undissociated HCOOH are unaffected by deuterium s u b s t i t u t i o n i n either solvent. Moreover, apparently there i s very l i t t l e solvent isotope e f f e c t on k A; values i n H 20 being close to those i n D 20 for HCOOH and DCOOH. This i s seen by examining r a t i o s (B) and (D), Table XI. Hence i t seems that H-0 bonds of the solvent also do not play an important part i n the oxidation r a t e - c o n t r o l l i n g process. On the other hand, oxidation of HC0O" i s observed to be greatly affected by deuterium s u b s t i t u t i o n . In H 20, 49 TABLE X RATE CONSTANTS IN VARIOUS ISOTOPIC SYSTEMS System k A x l 0 3 kgKiXlO 3 K j X l O 4 kB l-m'^-s"1 see" 1 m/1 1-Ifl-lg-l HCOOH i n H 20 1.69 1.94 5.6 3.50 DCOOH i n H 20 1.60 0.40 8.0 0.50 HCOOD i n D 20 1.50 1.74 1.9* 9.1 DCOOD i n D 20 1.57 0.348 2.7* 1.29 •Calculated from K^DgO) = 0.340^ ( ^0 ) (36) • 50 TABLE XI RATIOS OF RATE CONSTANTS FOR VARIOUS ISOTOPIC SYSTEMS JSC- / DC-Reaction ^O/^HpO KH 2 0/ D 2 ° k D 2 % 2 ° k D~ AD" H2O/ D 20 ,,H,lC00"H,,+Mn04Z> 1.06(A) MH,,C00"+Mn04"_> 7.0 (E) 1.13(B) 0.38(F) .974(C) 7.1 (G) 1.04(D) 0.39(H) 51 reactions of HCOO~ are 7«0 times f a s t e r than reactions of DCOO" (Table X and r a t i o E, Table XI), i n agreement with the values of 7 . 4 and 6-10 previously reported by Wiberg and (57) Stewart, and Aebi, Buser and Luthi (Helv. Chim. Acta., 112 :944.1956), r e s p e c t i v e l y . In the solvent D 20 the r a t i o ^ H C O Q - ' ^ D C O O " I S y*1' ( R a t i o G» T a D l e X I ) > Indicating that i n forming the activated complex cleavage or weakening of the (11,26,27,55) C-H bond occurs. Also, a noticeable solvent isotope e f f e c t i s seen for the HCOO" oxidation. Oxidation of HCOO" i n H 20 i s O.38 times that i n D 2 0. S i m i l a r l y , oxidation of DCOO" i n H 20 i s 0.39 times that i n D 2 0. (Ratios P and H, Table XI.) Apparently H-0 bonds of the solvent play some part i n the rat e - c o n t r o l l i n g step. The experimental uncertainties of k A and kg are estimated to be as follows: series (a) -2%; series (b) ±3$; series (c) ±10$; series (d) ±15$. The large possible error i n the l a t t e r two series are due to the very small,slopes: these are r e f l e c t e d i n large uncertainties i n kg. 52 CONCLUSIONS I. Mechanism of the Formate Ion Reaction The observed entropy of a c t i v a t i o n ( A s g = -I5eu.) i s within the normal range f o r 1bimolecular reaction between two similarly-charged ions. The occurrence of a deuterium isotope e f f e c t implies C-H bond weakening or breakage i n the r a t e - c o n t r o l l i n g step. The present observations are consistent with those of Aebi et. a l . (Helv. Chim. Acta., 112:944.1956), and Wiberg and (57) Stewart. The r e s u l t s imply a hydride transfer to Mn04~ during the r a t e - c o n t r o l l i n g step. However, Wiberg and Stewart have also shown that oxygen from MnOA- appears i n the COo (57) * product i n t h i s reaction. Hence a combination of the two processes i s probable. Possibly the t r a n s i t i o n complex i s a c y c l i c species, e.g. 0" 0 s C N ;0 MnOo" In forming t h i s activated complex the C-H bond w i l l be greatly weakened, r e f l e c t e d i n a deuterium Isotope e f f e c t . Subsequent decomposition of the activated complex may proceed i n two ways: a) complete cleavage of the C-H bond, with transfer of hydride ion to Mn04*" forming HMn04~ b) cleavage of the O-Mn bond; and hence transfer of a Mn04~ oxygen to the C0 2 product 53 or to the solvent. Formation of other types of c y c l i c t r a n s i t i o n intermediates w i l l also be consistent with the observed behaviourj f o r example, complete cleavage of the G-H bond i n the rate-determining step to form a "cage** type of t r a n s i t i o n species: 0 = C B~ MnO " v ^ 3 ^0 ' i n which hydride ion may subsequently be transferred to Mn04"*, or else the O-Mn bond i s broken, oxygen appearing i n (57) C0 2. Possible intermediates i n the reaction mechanism (8,37,47) are Mn(VI) and Mh(V), both of which would be expected to react r a p i d l y under the experimental conditions to give the observed products. The l a t t e r species i s considered more l i k e l y on thermodynamic grounds: HCOO" .+. Mn04" -> Mn0 4 = + C0 2 + H°. . . A H ° = +20i6KCal . . . A F ° = +23.4IfCal HCOO" + Mn04" Mn0 4 i + C0 2 + H +. . .AH° = -56.8KCal A F ° = -31.9KCal 21 22 A H 0 values used here f o r MnO'7 and MnOf were those 4 (48) evaluated by Symons i n basic so l u t i o n . Other values were (28) obtained from Latimer. Formation of a H atom i n equation 21 i s considered energ e t i c a l l y inconsistent with the observed a c t i v a t i o n energy (Eg = 13 kCal/mole). However, the formation 54 of Mn(V), as shown i n equation 22, seems p o s s i b l e . This species has been postulated for t h i s r e a c t i o n , and for the (56,57) reac t ion between MnO^ and benzaldehyde. Furthermore, s ince Mn(V) can be regarded to form e i ther by a two e lec t ron (or hydride ion) t rans fer from HCOO~ to MnO^"* (to give HMn0 4 ~), or by oxygen t rans fer from MnO^" to HCOO"" (to give MnCs~ or a re la ted spec ie s ) , t h i s postulate i s consistent 5 (57) with the i so top lc observat ions . I I . Mechanism of the Formic A c i d Reaction Under the condit ions descr ibed, oxidat ion of undissociated HCOOH apparently does not involve C-H bond cleavage i n the r a t e - c o n t r o l l i n g step, as ind ica ted by the absence of a deuterium isotope e f f e c t . Pos s ib ly the mechanism of ox idat ion proceeds by oxygen transfer from MnO^" to HCOOH, or by e lec t ron transfer from HCOOH to Mn0 4 ~. This i s an i n t e r e s t i n g demonstration that ion ized and unionized forms of a substance may react by d i f f e rent mechanisms. The entropy of a c t i v a t i o n (As^ = -19 eu.) i s abnormally low for a bimolecular r eac t ion between an ion and a neutra l molecule. A s i m i l a r l y low A s i s observed for the reac t ion between H 2 and M n O ^ i n s o l u t i o n . This suggests that Mn0 4 " may be involved as an intermediate , r e f l e c t e d i n a t r a n s i t i o n state which i s more h i g h l y hydrated than the reactants because of a greater charge. That Mn(V) and not Mn(VI) i s formed i n the r a t e - c o n t r o l l i n g step i s supported thermodynamically: 55 HCOOH + Mn04~ Mn0 4 = + C0 2 + H + + H ° . . . . A H ° = +20.6KCal A F ° = +28.5KCal . . . . . . . . 23 HCOOH + Mn04~ — » Mn0 4 S + C0 2 + 2H + A H° = -56.8KCal A F ° = -26.8KCal 24 Again, formation of Mn(VI) accompanied by formation of a H atom i n equation 23 leads to a value of A H ° (and A F ° ) which appears inconsistent with the observed a c t i v a t i o n energy (16 kCal/mole), while formation of Mn(V) by equation 24 appears to be energetically p l a u s i b l e . I I I . F e r r i c — C a t a l y z e d Reaction In view of the observed a c t i v a t i o n energies, and the comparably large energy required to form H atoms, i t i s suggested that formation of Mn(V) rather than Mn(VI) i s more probable i n the uncatalyzed reaction schemes. From an examination of equations 21 and 23, i t might be predicted that formation of Mn(VI) would be favored by the presence of another species which r e a d i l y accepts an electron (or combines with a H atom). The c a t a l y t i c a c t i v i t y of F e + + + i n t h i s reaction may be due to i t s f u l f i l l i n g t h i s r o l e , so that the rate-determining steps of the catalyzed reactions can be expressed as 56 ++4" mm ' ++ 1, J, — Fe + Mn0 4 (or FeMn0 4 ) + HCOOH — > Fe + Mn04~ + C0 2 + 2H where A H ° = -41.1kCal A F ° = -37.9k.Cal 25 F e + + + + Mn04" (or FeMnO^) + HCOO" — » F e 4 * + Mn04~ + C0 2 + H + where A H ° = -41.1kCal A F ° = -43.0kCal 26 Here the energetics of formation of Mn(VI) are apparently favorable, since A H ° and A F ° for both reactions are negative. This mechanism i s analogous with the proposed mechanism for Ag + c a t a l y s i s of the reaction between Ho and -C54) + Mn04 where Ag acts as a hydrogen atom acceptor, and hence energetically promotes formation of Mn(VI). I t i s of inte r e s t that Ag + apparently does not catalyze the reaction of Mn04" with HCOOH or HCOO". Fe*4"1* has also been reported to cause a s l i g h t (54) increase i n the rate of the H2-Mn04 reaction which was attributed to induced decomposition by Mn04" rather than to c a t a l y s i s . In view of the present study, i t would be of interes t to examine t h i s e f f e c t further. 57 REFERENCES 1. C.E.H. Bawn and A.G. White, J . Chem. S o c , 339.1951. 2. M.N. Beketoff, Compt. Rend., 48:442.1859. 3. J . Boeseken, Rev. Trav. Chim., 47:638.1928. 4. B.E. Conway, Electrochemical Data. E l s e v i e r Publishing Co., New York, N.Y., 1952. 5. C F . C u l l i s and J.W. Ladbury, J . Chem. S o c , 2850.1955. 6. M.L. Delwaulle, Compt. Rend., 192:1736.1931. 7. 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