.- I. THE KINETICS AND MECHANISM'DFTHE'V . _ ,_ DECOMPOSITION OF AQUEOUS summons OF THE — PENTACYANOCOBALTATE (”HON A = H. THE KINETICS OF THE FORMATION OF COBALT (IH) PRODUCTS FROM THE REVERSIBLE OXYGEN CARRIER, n- PEROXOTETRAKIS (HtsanAm) DICOBALT (I H ) ’ Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY CHARLES S. SOKOL 71970 'HhSHS LIBRARY Michigm State ’ f' U112 csit“ a -1‘ X .{-:",W v'v This is to certify that the thesis entitled I. THE KINETICS AND MECHANISM OF THE DECOMPOSITION OF AQUEOUS SOLUTIONS OF THE PENTACYANOCOBALTATE(II) ION II. THE KINETICES OF THE FORMATION OF COBALT(III) PRODUCTS FROM THE REVERSIBLE OXYGEN CARRIER. u-PEROXOTETRAKIS(HISTIDINATO)DICOBALT(III) presented by Charles S. Sokol has been accepted towards fulfillment of the requirements for Ph.D. Chemistry degree in <252515l-‘5wuvdaahaésif" Major professor DateW‘ ”1'70 0-169 ABSTRACT I. THE KINETICS AND MECHANISM OF THE DECOMPOSITION OF AQUEOUS SOLUTIONS OF THE PENTACYANOCOBALTATE(II) ION II. THE KINETICS OF THE FORMATION OF COEALT(III) PRODUCTS FROM THE REVERSIBLE OXYGEN CARRIER. u-PEROXOTETRAKIS(HISTIDINATO)DICOBALT(III) BY Charles S. Sokol The kinetics of the decomposition of the pentacyano- cobaltate(II) ion in aqueous solutions at low ionic strength has been investigated. The reaction is second order with respect to the pentacyanocobaltate(II) ion. The activation energy is 9.84 i 0.27 kcal/mole in the temperature region of 25-500 and is more than twice that previously reported. It was found that the discrepancy in the activation energy is due to the large ionic strength dependence of the de- composition reaction. As the ionic strength increases, the Co(CN)53- ion forms ion pairs with the cations in solution. As the concentration of the ion pairs increases, the apparent activation energy decreases. Limited evidence in support of the postulated monomer- dimer equilibrium of the pentacyanocobaltate<11> ion has been observed. As the concentration of this ion decreases from 0.17 u, there is a slight spectral shift. LK‘I . K'JIJEJ ya Inop§ .vivbbb . N ry— ‘0 ‘AJ Q pynfloun‘ ,,‘ U...“ . Otis, 'Ddo. CA, Ovun ‘V I a. ~_ I.~v I... ‘u "CH. ‘5‘ «on .c -- S s 1 I R Oa‘t I' \ s. .A‘ r- ~ -‘.4¢e ‘ V Charles S. Sokol The kinetics of the slow formation of the bis(histi- dinato)cobalt(III) cation from the reversible oxygen carrier, u-peroxotetrakis(histidinato)dicobalt(III)has been investi- gated. -From the dependence of the rate of formation of the product on the histidine concentration, the equilibrium forma- tion of small quantities of the tris(histidinato)cobaltate(II) ion is proposed, when the histidine to cobalt(II) ratio is. greater than two. Spectrophotometric and kinetic evidence is given for the formation of u-superoxotetrakis(histidinato)— dicobalt(III) ion in low yield when cobalt(II)-‘I histidine solutions are oxygenated. The most likely mech; anisms for the formation of the bis(histidinato)cobalt(III) cation are discussed and the mathematical equations for these mechanisms are derived. Least squares calculations for determination of rate and equilibrium constants could not conclusively confirm the mechanism for the formation of the bis(histidinato)cobalt(III) cation due to the presence of the Superoxo complex. Evidence is given which suggests the possible auto- catalytic activity of the bis(histidinato)cobalt(III) cation in its formation from the peroxo oxygen carrier. ‘vaa—v :- 1'; “gouty... I. THE KINETICS AND MECHANISM OF THE DECOMPOSITION OF AQUEOUS SOLUTIONS OF THE PENTACYANOCOBALTATE(II) ION I II. THE KINETICS OF THE FORMATION OF COBALT(III) PRODUCTS FROM THE REVERSIBLE OXYGEN CARRIER. u-PEROXOTETRAKIS(HISTIDINATO)DICOBALT(III) BY Charles S. Sokol A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1970 To my wife Myra and my parents Leona and Adolph. ii ACKNOWLEDGMENTS The author expresses his deep gratitude to his wife, Myra, whose patience and understanding made this possible. The author is very grateful to Professor Carl H. Brubaker, Jr. for his continued assistance and encouragement throughout the work. The author thanks Dr. R. S. Schwendeman and Dr. J. L. Dye for their helpful suggestions. The financial support from the Atomic Energy Commission is gratefully acknowledged as is the moral support from friends and coworkers. iii R L IN" I. I. II. III. IV. TABLE OF CONTENTS ‘ INTRODUCT ION . O O O O C O O O O O O O O O O O HISTORICAL . . . . . . . . . . . . . . . . . . A. B. C. Cobalt Synthetic Oxygen Carriers . . . . . The Pentacyanocobaltate(II) Ion . . . . . . The Cobalt-Histidine Oxygen Carriers . . . THEORETICAL . . . . . . . . . . . . . . . . . A. B. C. G. H. I. J. -Estimation of K4a and K4 Linear Least Squares . . . . . . . . . . Non-linear Least Squares . . . . . . . . . Mathematical Equations for the Decomposition of Pentacyanocobaltate(II) . . . . . . . . Mathematical Equations for the Formation and Decomposition of u-Dioxygentetrakis- (l-hiStidinatO)diCObalt o o o o o o o o o 0 Calculation of Ligand Concentration During the Formation and Decomposition of u—Dioxygentetrakis(l-histidinato)dicobalt . .Numerical Method Used to Solve Equation 87, the Newton Method . . . . . . . . . . . . . .Numerical Method Used t0°Solve Equation 78. .Computer Programs . . . . . . . . . . . . . b O O O O O O O . + . . . Correction of COL2 (L = hlStldiEe) Absorb- ance Due to the Presence of CoI . . . . . aq EXPERIMENTAL . . . . . . . . . . . . . . . . . A. B. C. D. ~Preparation of Reagents . . . . . . . . . . Analytical . . . . . . . . . . . . . . . . rEx erimental Procedure for the Study of the Co CN)53' Decomposition . . . . . . . . . . Experimental Procedure for the Study of the Cobalt—Histidine-Oxygen Reaction . . . . . iv Page 11 14 14 16 23 24 33 36 4O 41 42 46 48 48 52 53 57 .313 OF C avg 31' i'" TABLE OF CONTENTS (Cont.) V. Page -RESULTS AND DISCUSSION . . . . . . . . . . . . 60 A. The Decomposition of Co(CN)53— . . . . . . 60 B. The Formation of Cobalt(III) Products from the Oxygen Carrier, u-Dioxygentetrakis- (histidinato)dicobalt(III) . . . . . . . . 71 REFERENCES 0 O O O I I O O O O O O O O O O O O 112 APPENDIX C O O O O O O O O O O O O O O O O O O 120 A. Derivatives for the Non—Linear Least ,Squares Calculation . . . . . . . . . . . . 120 B. .Derivative for the Ligand Concentration Calculation . . . . . . . . . . . . . . . . 127 C. Computer Programs .4. . . . . . . . . . . . 129 1. Linear Least Squares . . . . . . . . . 129 2. Non Least Squares Calculation Program . 133 3. Non-linear Least Squares Calculation . 137 F“! '1 [a H C III. IV. VI . TV '1) H w~ lde thE LIST OF TABLES TABLE Page -I. Preparation of the COL; solutions (2:1 histidine to cobalt ratio) . . . ... . . . . 51 II. —Rate constants for the decomposition of Co(CN)53' as a function of temperature . . . 62 III. Possible oxidation states of Co and H in CO(CN)5H3- o o o o o o o o o o o o o o o o o 66 IV. Activation energies for reactions similar in mechanism to the decomposition of aqueous CO(CN)53- o. o o o o o o o o o o o o o o o o 68 V. Data of L. Zompa for the formation of COL2+ from (C0112 )202 o o o o o o o o o o o o o o o 75 VI. Data showing the de endence of the formation of CoL2+ from (Congzoz on the cobalt(II) and oXygen concentration at a 2:1 l-histidine to cobalt ratio at 25°C . . . . . . . . . . 77 VII. .Experimental data in support of the catalytic nature of CoL2+ in the decomposition of (COLZ )202 o o o o o o o o o o o o o o o o o 80 VIII. .Data in support of the catalytic nature of C0L2+ in the decomposition of (C0L2)202. . . 81 IX. -A typical set of calculated and experimental data that shows K3.: 1.4 x 104. . . . . . . 84 .X. -A comparison of the calculated data from Table IX and data calculated with K3 = 1 to show that a value of K3 2 1.4 x 104 signifi- cantly changes [C0L2+]calc only for ligand to metal ratios of greater than 2 . . . . . 86 XI. Values of k5a and k5 which result in almost b identical sets of values of [COL2+]calc for the mechanism including equation 49 . . . . 89 vi LIST CF '32-. Ca II. II (”a LIST OF TABLES (Cont.) TABLE XII. XIII. Page Values of kSa' and k5 which result in b almost identical sets of values of [C0L2+]CalC for the mechanism including equation 50. . . 90 Calculation of number of moles of Oz initially II II = absorbed per 2C0total(initial) for Cot 1.2 x 10-2! and pure 02 gas (at 25°C). 0 = 6 K4a 'K4b 7.2 x 10 . . . . . . . . . . . 97 vii nyfi' . s9» 10. 11. 12. 3.: ’V Plot SClut thESE FIGURE 1. 10. 11. 12. LIST OF FIGURES Possible structures for the pentacyano— cobaltate(II) ion . . . . . . . . . . . . . . Geometric representation of the Newton method for numerical solution of equations . . . . . A block diagram of computer program “Deriv” . IA block diagram of computer subroutine "CoScalc" . . . . . . . . . . . . . . . . . . -Special mixing cell . . . . . . . . . . . . . Comparison of visible and near uv spectra of aqueous Co(CN)53' kept in darkness and in daylight for 2 hours and 15 minutes after preparation . . . . . . . . . . . . . . . . . Comparison of visible and near uv spectra of aqueous Co(CN)53‘ kept in darkness and in daylight for 48 hours after preparation . . . Second order rate plots for the decomposition of the pentacyanocobaltate(II) ion . . . . . Arrhenius plot for the decomposition of the pentacyanocobaltate(II) ion . . . . . . . . . The visible and near uv spectra of monomeric aqueous K3[Co(CN)5] and dimeric K6[(CN)5CoCo(CN)5] in a nujol mull . . . . . ~Enlargement of the spectra near 625 mu of the first three observations during the 50° kinetic experiment of the decomposition of Co(CN)53‘ . . . . . . . . . . . . . . . . . . Plot of absorbance versus time of the quenched solutions which shows the acid attack on-- these quenched solutibns . . L ... . . . . . viii Page 10 37 43 44 49 54 55 61 63 72 73 87 LIST OF FIG'. F131. 13. P13: 14. Pitt 15. &SA. LIST OF FIGURES (Cont.) FIGURE Page 13. Plot of experimental values of [C0L2+] and least squares values of [CoLz lcalc versus time for the mechanism including equation 49. 91 14. Plot of experimental values of [CoL2+] and least squares values of [C0L2+]calc versus time for the mechanism including equation 50. 93 15. .Absorbance versus time of cobalt-histidine solutions oxygenated with various gases . . . 99 16-19. Visible spectra of solutions of (COL2)NO3 . . . . . . . . . . . . . . . . 102- 109 ix 'dmm I'm . I w— n F‘r- .I LII _'..‘-n ‘Fq H . IftoouVVLM 6..“ 4.: .;~_ ‘ “W" béu- ' y . . . ‘-'-’;Y""v~e o-p- “' '5... ... -.. 37516375 “" I a‘ has ‘_ .b Nth Lemsey. ‘ ‘ s" p , I “ Ye“ “lent "' ' :""::I;€L I. INTRODUCTION In the last 15 years, much work has been done on the kinetics and mechanisms of inorganic reactions.1 Prior to this time, the majority of investigations sought only to determine the stoichiometry and thermodynamics of the kinetic systems that were investigated. A typical experiment involves the measurement of the concentration (or some property of the system that is pro- portional to the concentration) of one or more of the re- actants or products of the reaction as the reaction proceeds. Mechanistic investigations are usually performed at constant ionic strength and are always performed at a con- stant temperature since the ambient temperature will drastic— ally affect both rates of reaction and equilibria. However, there are reactions in which ion pair formation will signi- ficantly alter the reaction rate and therefore, these reac- tions will be significantly affected by the presence of an "inert" electrolyte. In these cases, it is much more impor- tant to keep the ionic strength as low as possible than to keep the ionic strength as constant as possible. Spectrophotometric methods of analysis can be very convenient where they can be applied. Generally, spectro- photometric methods of analysis do not give better than 1 pr. IN 7" "l '5. ‘H -b .. . . annoy-sw- *Y‘ ’ unvevn- '6-“ . DF‘R‘VAHHP 0 § . ~~-~.L.A. 4:..v u . S i n) q"? ( ) f Y m p -4 0 av ‘ . RF Ma ~ h‘ ‘AIEA§--CG II) 2 one percent accuracy.2 In order to be able to use the spectro— photometric method, it is necessary to know, for all reactants and products, the molar absorptivities in the region of the Spectrophotometric investigation. Then, at any wavelength, the total absorbance will be the sum of the absorbances of all chemical species present. I .Lt ‘ietular 02-: 2c a, It.“ I I . HISTORICAL A. Cobalt Synthetic Oxygen Carriers The first synthetic oxygen carrier, diamagnetic u- peroxodecamminedicobalt(III), was prepared by Fremy3v4 in 1852 by oxygenating an aqueous ammoniacal cobalt(II) solu- tion. Prior to the start of the twentieth century, several diamagnetic and paramagnetic oxygen bridged compounds were. prepared.‘5'10 Then, around the turn of the twentieth century, Werner, the father of modern coerdination chemistry, prepared many cobalt complexes including additional oxygen bridged species.’ He also established the octahedral geom— etry about the cobalt atom in these compoundsfi'll‘i8 Interest in synthetic oxygen carriers was renewed by the possible use of'Hhese compounisfor oxygen fixation19 and as models for the investigation of the reversible oxygena- tion of hemoglobginfi‘m'21 Recently, extensive research on synthetic cobalt oxygen carriers has been performed.21'"",6 Several cobalt(II) complexes react with, and absorb, molecular oxygen according to the fOlIOWing equation: 2COIILgX + Oz < > L5C002C0L5 + X . f Two series of cdbalt oxygen carriers can be formed. One 3 series is 9 c; .- harver v... - "' :me: car 2 b‘ 35““ qualt O}? L .4 series is diamagnetic and the other series is paramagnetic. Werner9 showed that the diamagnetic binuclear cobalt ammonia oxygen carrier is the ion [(NH3)5COOZCO(NH3)5]4+ . Werner described the above ion as containing two cobalt(III) ions. This required that the oxygen bridge be peroxide, 022-. The above ion can be oxidized24 to a paramagnetic ion [(NH3)5C002C0(NH3)5]5+ . A detailed discussion of much of Werner's work can be found in reference 27.; There are other members of each series. 11 28. The ligand can be ethylenediamine, diethylenetriamine, cyanide29 and various amino acids.26 There can be additional ligands in the bridge.3°’32 In the case of amines as ligand, the diamagnetic oxygen carriers are red and the paramagnetic oxygen carriers are green. The paramagnetic oxygen carriers have one unpaired electron and a magnetic susceptibility of 1.7 B.M.26 Werner had characterized the paramagnetic oxygen car- riers as being peroxo—cobalt(III.IV) species. This nomen- clature continued in general use.30 However, it was shown by esr that cobalt atoms were equivalent in the amine,33:34 cyanide,35'33 histidine37 and some dibridged35 cobalt oxygen carriers. The fifteen line esr signal results from the equal influence of the two cobalt atoms (59Co - 100% abun- dance - I = 7/2) on the unpaired electron. The two series of cobalt oxygen carriers were then called "diamagnetic :Hrect and s An inve5= 3E§€C carrw - 's'a . (I) m r) ’. J . (D l (7' n .‘v' —~"Yec frgm t 5 peroxo" and "paramagnetic peroxo" complexes.24i32:33:39 Linhard and Weigel4O stated that Werner's formulation of OIII IV for the paramagnetic oxygen carriers was in— IIIQZ-COIII. As will be seen below. C Caz-Co correct and should be Co Linhard and Weigel were correct. An investigation of the cobalt ammine paramagnetic oxygen carrier had incorrectly shown that the Co-O-O—Co was a gigfboat type configuration.41 Dunitz and Orgel42 had discussed the electronic structure for a linear Co-O—O-Co arrangement. Brosset and Vannerberg43 and others44 favored a structure with the O-O axis perpendicular to the Co-Co axis. Vlcek45v46 also postulated the perpendicular structure. He stated that the greater stability of the paramagnetic oxygen carriers relative to the diamagnetic oxygen carriers was due to the fact that the electron re- moved from the diamagnetic carriers to form the paramagnetic carriers came from a Co-Oz-Co antibonding molecular orbital. While Vlcek's structure was incorrect, his explanation of the relative stabilities of the paramagnetic and diamagnetic oxygen carriers probably was correct. ‘A detailed discussion of these structures mentioned above can be found in reference 47. Recent X-ray studies of some ammonia and ethylene— diamine binuclear cobalt oxygen paramagnetic and dia— magnetic oxygen carriers showed that for the diamagnetic oxygen carriers. the Co-O-O-Co bonds are'"Z" shaped with Co-O—O bond angles of 110 to 1130 and an 0-0 bond distance 251.47 to I. 6 of 1.47 to 1.48 £48.49 and the Co-O-O-Co bonds are also "Z" shaped for the paramagnetic oxygen carriers with Co-O-O bond angles of 117 to 120° and an O-O bond distance of 1.31 to 1.36 3.39'5°'53 ‘The 0-0 bond distances for the diamagnetic 02 carriers are within the range of 1.49 i 0.02 R which is expected for peroxides54 and the 0-0 bond distances for the paramagnetic Oz carriers are within the range of 1.32 to 1.35 A which is expected for superoxides.55 The Co-O-O-Co dihedral angle is approximately 0° for the paramagnetic oxygen carriers and approximately 146° for the diamagnetic oxygen carriers.: Thus, the configuration of the oxygen in the diamagnetic oxygen carriers is similar to hydrogen peroxide.56 .The striking similarity between the esr of the para— magnetic amine and cyanide cobalt oxygen carriers indicates that they are isOstructural.35 The equivalence of the two cobalt atoms in the para- magnetic oxygen carriers, the presence of a peroxo group in the diamagnetic oxygen carriers and a superoxo group in the paramagnetic oxygen carriers showed that the two series of oxygen carriers should be formulated as follows: L5CoIIIOZZ-COIIIL5 (diamagnetic) and L5CoIIIOZ-COIIIL5 (paramagnetic). Thus, all binuclear cobalt oxygen carriers are now con- sidered as containing two cobalt(III) ions and either a peroxo or a superoxo bridge. 3 ‘-~n Hwy-r Ir 1......6 CV“. N ‘ .... . ‘qu ' ',- Sufi . CW9 . t. l 9 Carrie: was I 5. s “:5: 6. b C E 1 ~. 7 Earlier research had incorrectly shown that the absorp- tion of oxygen by ammoniacal cobalt(II)57 and other cobalt(II) amine complexeszsvss, to form the oxygen carriers, was fairly slow. However, recent stopped-flow studies proved that fieoxygen carrier was formed rapidly.59v60 B. The PentacyanocobaltateLII) Ion When cyanide ion is added to a solution of a cobalt(II) salt, a brown precipitate of Co(CN)2 is first formed that redissolves to form a green solution61 when the cyanide to cobalt ratio reaches five to one.62"'66 The maximum heat evolution also oCcurs at this ratio.67 This pentacyanocobaltate(II) ion is of interest not only as an oxygen carrier29'68'59 but also as a hydrogena— tion catalyst. In the last ten years, this ion has been investigatedextensively.71r72 It has been shown that the cobalt species present in solutions containing excess cyanide ion is actually Co(CN)53' rather than Co(CN)6"—.°1I73 However, it could not be determined whether this ion was five coordinate or contained a water molecule in the coordin- ation sphere. The violet solid which is in equilibrium with the aqueous green CQ(CN)53- solution may be precipitated by the addition of ethanol.62 Whereas the green Co(CN)53- ion is paramagnetic with one unpaired electron and a magnetic moment of 1.72 B.M.,°2I74 the violet solid is diamagnetic.52v 75'7“ Although the solid violet compound was reported to be I.- ' a :xplex, [cgz In 1942 I n}! fl"\ 3- t... \b.‘ 5 a1;_ v:6. “~0 0i one «IEEEI-i.2:e 8 K4C0(CN)6 in the earlier literature,77'79 it has been shown to be a hydrated8° (probably a tetrahydrated72) dimer of the Co(CN)53' ion, X6[C02(CN)10]. It has been suggested that the solid dimer contains a metal—metal bond81 (which would explain the diamagnetism) as in the more recently determined structure for the analogous meflud isocyanide complex, [C02(MeNC)10](ClO4)4.32 In 1942, Iguchi83 noted that aqueous solutions of Co(CN)53‘ absorbed molecular hydrogen in the approximate ratio of one atom of hydrogen per atom of Cobalt and that the rate of heterogeneous hydrogen absorption was greatest with a Co:CN ratio of 1:4.5. The product of this hetero- geneous absorption was later assumed to be the colorless hydrido species Co(CN)5H3'.84 This was confirmed by nmr studies which showed the existence of Co—H bonds in reduced aqueous solutions of the pentacyanide.81 The solid mixed sodium-cesium salts of the Co(CN)5H3“ ion have recently been synthesized.85 Mills and coworkers found that aqueous solutions of Co(CN)53‘ "aged" and lost their paramagentism at a rate paralleling the loss of reducibility (i;g., the loss of the ability to absorb H2 bubbled into the solution) and a hydride intermediate was proposed.86 Both the original Co(CN)53' and the reduced solutions were found to catalyze the heterogeneous D2(gas)-H20( ) hydrogen exchange. liquid The "aging" of these solutions was first thought to be due to dimerization but it was shown to be due to homogeneous absorption of hydrogen from water to form the above mentioned sgecies .37 . E . [3233;626:115 p! m 1‘; ‘Q‘.Ei as C: 5.1 tits, My m .uged Cut t :‘Iucture .9 :67! L3 and C in. - “on Site . p‘w. “table 1 Ta “‘6: . equi. CE: .- ta... e1. ~\ I. ....e - lutEI 2p In. 13 eSt “L“:le .94 9 hydrido species.7° In earlier literature, the reduced or "aged" solutions were thought to contain a cobalt(I) species.87'88 Thus, Co(CN)5H3’ is produced by both the homogeneous and the heterogeneous absorptions of hydrogen. The heterogeneous absorption of hydrogen by Co(CN)53' is reversible and as the temperature is increased, the equi- librium shifts toward the evolution of H2.89r9° On the basis of the similarity of solution spectra of the pentacyanocobaltate(II) ion with some corresponding alkyl isocyanates which are known to be CoL5H203‘, Pratt and Williams91 postulated that the pentacyano ion must also contain a water molecule and therefore, it should be formu- lated as Co(CN)5H203‘. At the same time, other investiga- tors, by means of analysis of esr and visible spectra, had ruled out the possibility of a trigonal bipyramidal, Dah structure.92'93 Trey showed that the complex had C4v sym- metry and could have a water molecule at a sixth coordina- tion site. Thus, the pentacyanocobaltate(II) ion cpuld have either of the structures of C4V symmetry as shown in Figure 1. There is no evidence for the formation of Co(CN)34‘ under equilibrium conditions << 1).91 However, (Kformation certain electron transfer reactions appear to proceed by the intermediate Co(CN)54' ion whose formation constant at 25° is estimated to be within the range of 10-1 to 10—4 l/mole.94 10 .COH AHHVoumuHonoocm>omucmm Hmcommuuwfi our 20 ll 02 fl.--.-... 20 OZ 20 map How mmnsuuzuum wanflmmom .H cusgflm Hmoflsmnxm mumsqm 2011. 20 DZ n m‘» Co‘rz‘ m we ,r... _——_——-—-—— cf the S ticlcgical cz-z :arrier Itas ; ‘3.- s .. e CEIDCH ..‘PA - .. t catlca .1,“ ‘I 11 C. The Cobalt—histidine Oxygen Carriers Of the synthetic oxygen carriers most closely resembling biological oxygen carriers, the cobalt l-histidine oxygen carrier has probably been the most extensively investigated. Histidine is an amino acid with the structure ‘lxN NH2 1/ \ -CH2 -*CH . m\/ em... .The carbon with the asterisk is asymmetric and the site of the optical activity of the compound. Since l—histidine is the optical isomer that is found biologically, this is the isomer that was used in this investigation. The histidinate anion (withoUt the carboxyl proton) is a tridentate ligand. The sites of coordination are the amine nitrogen, the protonless imidazole nitrogen and the deprotonated carboxe ylate oxygen. [All three of these coordination sites are bound to the cobalt in CoL2 (L = 1-histidinato anion) both in the solid state95 and in solution.96 In the solid state, the imidazole groups in the CoL2 are trans to each other.95'97 In the trag§_imidazole configuration, the car- boxyl groups must be gi§_to each other due to the enantio- meric conformation of the l-histidine.98 Hearon and his coworkers found that CoLz reversibly absorbed oxygen and they investigated the equilibria and stoichiometry of this oxygen absorption. They found that one mole of 02 was absorbed per two moles of CoL2.2°.99'103 The Oxygen C' asclurzcn c: cxygen carria :Etic.2°'9°': carrier is to; a:i:r. sphere rlecules c; 35 a peroxo ';_ car's-OX; la te Effier' 12C; AS 9X96: the chalt a: that the d; IE: 12 The oxygen carrier was formed very rapidly upon oxygenating a solution of the cobalt(II) histidine complex.2°v59 The oxygen carrier, L2C002CoL2, was amber colored and diamag- netic.2°I9°I1°4'1°5 The formation of the binuclear oxygen carrier is believed to occur by dissociation from the coordin- ation sphere of the carboxylate group of one of the histidine molecules on each of two CoLz molecules and the formation of a peroxo bridge at the coordination sites vacated by the carboxylate groups.59r98 The solid trihydrate of the oxygen carrier, L2C002C0L2°3H20 has been isolated.98 As expected from the two series of oxygen carriers in the cobalt ammonia and cyano systems, it was recently shown that the diamagnetic histidine oxygen carrier can be oxidized by Cer to a paramagnetic oxygen carrier.37 Even the color change during this oxidation of the histidine oxygen carrier from amber to blue-green was similar to the red to green color change in the ammonia system. The esr of the para- magnetic histidine oxygen carrier contained the 15-line hyperfine structure, once again confirming the equivalence of the two cobalt ions in the oxygen carrier.37 The bis(histidinato)cobalt(II) complex rapidly and reversibly absorbed one mole of 02 per two moles of cobalt to form the oxygen carrier.98 It then slowly irreversibly absorbed a second mole of 02 per two moles of cobalt to form cobalt(III) products.2°'1°6 These final cobalt(III) products were isoe mers of the bis(l—histidinato)cobalt(III) cation.”6 There n‘lgv_‘\ ! £8“' ”inn! 1 . are three 1 have recent Observed . 1 0 Ease a sec: r»: .. - A . . . ...; aiaLun‘ carrier 53;; 13 are three isomers of the final cobalt(III) product and they have recently been separated and their spectra have been observed.1°7 In strongly basic solutions (pH > 12), histidine can lose a second proton and can form the complex.Co(L-~H)22‘.96 .This anionic cobalt(II) complex can also absorb oxygen to form an oxygen carrier that is different from the oxygen carrier formed by the oxygenation of the neutral.CoL2.1°8 Cf h ‘ e Slee G 5. ~51 cata lurk The SUIT III. THEORETICAL A. Linear Least Squares In those cases where the kinetics of a chemical reaction are simple enough, the rate law is usually written in a linear form. It is then possible to use the linear least squares method to calculate the optimum parameters for the linear equation. -The method is as follows.1°9:11° One form of the linear equation is Y=mX+b (1) where m and b are respectively the least squares values of the slope and intercept of the straight line. The experi- mental data points are xi and yi and N is the total number of experimental data points. The residual of each data point is xim + b - yi . (2) The sum of the squares of the residuals, S. is N N N S = Z (x.m + b - y.)2 = m2 2 x.2 + 2bm Z x. . 1 1 1 1 1:1 1 1 (3) N N N .. 2 _ 2 2m § Xiyi + nb 2b é yi + § yl . 14 To 3225 be :1n1mlze- ib are 1‘; t) In (a ‘1 In J! (J I 7 En Fr .‘J‘ (D U! ( S m P1 15 To obtain the optimum values for m and b, S must be minimized. The derivatives of S with respect to m and b are set equal to zero as N N N -g— = 0 = 2m 2 x.2 + 2b 2 x. - 2 Z x.y. (4) m 1 1 1 1 1 1 1 _ as N N —— = 0 = 2m 2 x. + 2bn - 2 2 y.. (5) 5b 1 1 1 1 Equations 4 and 5 can be solved for m and b N Z xiyi - 2 xi 2 yi N Z x.2 - (Z x.)2 1 p 1 2 _ 2 xi 2 yi 2 xi 2 XiYi (7) N Z x.2 - (Z x.)2 1 p 1 It is also useful to determine the standard deviations (i.e., the 50% confidence limits) of the slope and incer— cept, Om and Ob. According to Youden,11° the values for Om and 0 respectively. b can be obtained from the following equations: ( )2 ( Exizyilz 2 y. Zx.y. - ’ Zy.2--—-J-'-—- 13' N i l N (Z x.)2 ZX-z __...3;__ 2 = 1 N (8) u L 1 fl, “i!” push H l L‘N 'i *5; 1 The va- ::r.stants t : The c:: 16 2 X12 0 = S , (10) b N Z x.2 - (Z x.)2 1 1 The values of Om and Ob can be multiplied by known constants to obtain confidence limits other than 50%. The computer program written by the author for linear least squares calculations can be found in the Appendix. B. -Non-linear Least Squares In the case of complex kinetic systems, even if one is able to integrate the differential rate expression, he is rarely able to linearize the expression. -It therefore becomes necessary to resort to a non-linear least squares procedure. Such a procedure is derived as follows.111 The generalized non-linear rate law can be written f(x, y, a, b, c, ---) = 0 (11) s where x is the concentration of one of the chemical species, y is the time and a, b, c, °-- are the kinetic parameters (the rate and equilibrium constants) which are to be optimized. By defining the residuals between experimental and calculated data points, one Obtains ~in = Xi - Xcalc <12) Ryi = y1 - ycalc ‘13) The sum of the squares of the residuals, S , now becomes One mg. kmetic par. 3 Taylor ' s F 01 M I LC H '21 I! H. K II 17 m u HMZ (R;i+ agi). (14) An obvious condition that must be met by the least squares values of the kinetic parameters, a1 s , bl s , cl.s.’ ... ls f(Xi ’ yi ’ al.s.' bl.s.’ cl.s.’ ...) = 0'(15) calc calc . One must have good enough initial estimates of the kinetic parameters, a0, b0, c0, "' to be able to truncate a Taylor's series expansion of equation 11 about the point (xi, yi, a0, b0, co, ---) after the first order terms. ‘The following terms are defined in order to simplify .following equationsa Aa = a5 - al.s. estimate ‘16) Ab = b0 - bl.s. estimate (17) AC = C0 - Cl.s. estimate’ etc. (18) Pi = f(Xidalc'yicalc’ a. b! C, ...) (19) Fi0 = f(xio, yio, a0, b0, C0, ~--) (20) F = aFi ggiaeacb t ' (21) xi 5;_- (x., Y-: a0, b0: Co: '°’) POln l 1 1 F = aFi giiaeggint i (22) 31 '5;- (x., Yit.aol b0: Car "‘) o l The 1 saint IX- . ‘r J. “arms is "J I Since 18 The Taylor's series expansion of equation 11 about point (xi, y., a0, b0, co, ...) including only first order 1 terms is F. = F. - F 7R - F R - F Aa - F Ab - F Ac - ... 1 10 xi Xi Y1 Y1 a1 bi Ci - 0 i - 1,2, ---,N. (23) Rearranging equation 23. one obtains F. = F R + F R + F Aa + F Ab + F Ac + ... 24 10 xi Xi Y1 Y1 a1 bi Ci ( ) In order to minimize the sum of the squares of the residuals, S, (see equation 14), dS is set equal to zero 2 (R dR + R dR ) x. x. y. . y d8 = 1 12 1 1 = o (25) since the change in the residuals, dRX and dR i i must also satisfy equation 24 (the right side of equation 24 must still be equal to Fi ) o F dR +F dR +F dAa+F dAb'l'F dAC'l'... X' x' Y1 Y1 a1 bi C1 = 0 i = 1,2,°--,N. (26) If M is the number of kinetic parameters, a, b, c, °° then there are N sets of equation 26 with a total of N differentials of the x residuals, de.' N differentials of the y residuals, dRyi, and M dierrentfifls of the kinetic parameters, dAa, dAb, dAc, etc. There are a total of 2N +~M differentials with only N equations. Since the N equations can be used to mathematically substitute N of the differentials, there are only 2N + M - N = N + M arbitrary differentials. M [‘7 19 Since N of the differentials are not arbitrary, one defines N Lagrange-multipliers, -A1, -A2, -A3,°'°, —AN and multi- plies each of these by equations 26 -A.F dR - A.F dR - A.F dAa - A.F dAb 1 . . y. 1 a. 1 b. -)\F dAC_....=O i=1'2’...l N. 1C 1 1 1 Xi Y1 Y1 Xi (28) + Z A.F dAa + Z A.F dAb + Z A.F dAc + °°° = 0. 1 a. 1 b. 1 C. 1 1 1 Since there are N equations with N arbitrary values for Ai in equation 28, the values of Ai are chosen to eliminate N of the differentials. This process leaves N + M differentials. However, as stated above, N + M of the differentials are arbitrary. Therefore, since the re- maining N + M differentials are arbitrary, the coeffici- ents of each differential in equation 28 must be zero RX. — Ai FX. = 0 i = 1,2,3,---,N (29a) 1. l a; R - A. F = 0 29b 2 Ai Fa. = 0 (29C) (29) l 2 Ni Pb. = 0 (29d) 1 2 Ai FC = 0 ~-- . (29e) l 1.1 '.' {831187. residuals 20 By rearranging equations 29a and 29b, one can solve for the residuals R and R X Y i = 1,2,3,---,N. (30) By rearranging equation 23, one obtains F. - F. = F R + F R + F Aa + F Ab + F Ac +°°°. 1 10 x. x. y. yi a.l bi ci (31) i = 1,2,3,°°'IN. By substituting equation 30 into 31, one obtains 2 2 . - . = , _ A + + ..., Fl Flo inAl + Fyikl + Fai a + FbiAb FciAc (32) i = 1,2,3,---.N and solving equation 32 for Ai F. - F. - F Aa — F Ab - F AC - °°° 1 lo a. b. C. _ 1 1 1 , xi - II 2 2 F + F (33) x. y. 1 1 i = 1,2,3,...IN. Substituting equation 33 into equations 29c, 29d, 29e,:-- I rearranging and dividing by the quantity (F:- + F: ) yields 1 i the following set of equations A A A --- = .- , 2 Fa Fa. a + 2 Fa Fb. b + 2 Fa FC. 0 + 2 Fa (Fl Flo) l 1 l l 1 l 1 2 F .Fa Aa + Z FbFb Ab + z Fb Fc.Ac + --- ZFb.(Fi-Fi )(34) b 0 l l l l l l l 2 F F Aa + 2 F F Ab + 2 F F Ac + °-- 2F (F -F. ) c. a. C. b. c. c. . 1 l l l 1 l 1 etc. ‘ There d fizz sclve ...l P O 8 Au v . t v.‘ ‘4‘ . ‘ 6"th -..Vu ‘Lb w. Ulla. .U 21 There are .M equations 34 and M unknowns (Aa, Ab, AC,---). Therefore, the M simultaneous linear equations can be solved for the M unknowns, Aa, Ab, AC, '°'. The easiest way to solve the system of M linear equations is to use the method of determinants. The determinental solutions are as follows: 2 Fa (Fi-Flo) 2 F Fb. 2 F FC .-- l l 1. l 1 z Fb (F1—Fio) z Fb Fb 2 Fb_Fc --- l l l 1. 2 F (F.—F ) 2 F F 2 F F ~- c. 1 10 b. c l 1. 1 l 1 A3 - (35a) 2 F F 2 F F 2 F F --- a1 a1 1 b1 ai C1 2 Fb F2. 2 Fb.Fb. Z Fb.FC °° 1 l 1. 1 1. 1 2 F .Ea 2 F .Fb. 2 FC FC °°° 1. l l 1. l .1. I F I F. I F I F Z F I F The w If .- are not c “”953 C \Ie‘YI etc Th1. The el'ical as well a» 2 Fa Fa. 2 F (Fi-Fio) 2 F FC --- l l l 1 1. 2 F F 2 F (F -F ) 2 F F -- 2 F F. 2: F (F.-—F ) >3 F F ~- 2 F F 2 F F >3 F F -- a1 a1 a1 b1 1 C1 2 Fb Fa Z Fb.Fb Z Fb.Fc ... 1 l 1 1. l 1. 2 F F 2 F F 2 F F -~ a . b. c l l 1. l 1 1. . . ' . , etc. The new values of a, b, c, --° are a = a0 + Aa new bnew = b0 + Ab (36) cnew = Co + Ac , etc. If Aa, Ab, AC, '°' are not small enough (a, b, c, -°- are not close enough to their converged values), the whole 3' a = a b - b c process can be repeated by u 1ng 0 new’ 0 new’ 0 Cnew’ etc. and calculating a new Aa, Ab, Ac, etc. This derivation is essentially that of Wentworth.111 The derivatives necessary to use this method for the chemical system which has been investigated by the author, as well as the computer subroutine, will be found in the appendix. fl) -.Ie Of S 1 ,. A ‘ m the A I“fp 23 C. Mathematical Equations for the Decomposition of Penta— cyanocobaltate(II) As will be shown later, the decomposition of penta- cyanocobaltate(II) is a simple second order reaction of the type k 2A > products (37) dA _ a - -kA2. (38) This differential equation can easily be integrated and linearized112'114 1 - 1. A. - kt + A0 . (39) By plotting 1/A versus t, one obtains a straight line of slope k and intercept of 1/Ao. The activation energy of the reaction can be obtained from the Arrhenius equationl‘lz"114 -Ea ln k = _RTI + constant. (40) By plotting the value of ln k (at various tempera- tures, T) versus 1/T, one obtains a Straight line of slope Ea/R. The optimum straight line from the experimental data points can be obtained from the linear least squares pro- cedure previously described. A computer program written by the author for the linear least squares procedure will be found in the Appendix. fl 5......» . pays -VDI t -‘ d ‘ AS ' I this 2 5.- .v 24 D. Mathematical Equations for the Formation and Decomposi: tion ofgp—Dioxygentetrakis(l—histidinato)dicobalt As will be seen,the following mechanism is proposed for this reaction (L = l—histidinato ion -- to avoid con- fusion, free histidine is shown as HL and free l—histi— dinato ion is shown as L ) _ K1 Co2+ + L < > CoL+ (41) _ K2 CoL+ + L < > CoL2 (42) - K3 _ CoL2 + L < > CoL3 (43) K4a COL2 + 02 < > COL202 (44) K41) CoL202 + CoL2 < > (CoL2)202 (45) K — 1 H+ + L < H> HL (46) HL +- H+' KZH + < > H21: (47) K 3 H2L4-+' H+' < H> H3L2+ (48) ( k5 a + _ COL2 )202 __—> COL2 + COL2 + 02 (49) I k5a + — or COL202 + CoL2 > CoL2 + CoL2 + 02 (50) k + + - CoL202 + CoL2 -§2—> 2CoL2 + 02 . (51) The e "S “lle 35 .. 25 The equilibrium expressions for equations 41 to 48 are as follows: K1 = [CoL+]/[cO2+][L'] .\ K2 = [coLzl/[coL+][L'1 15 (52) K3 = [CoL3'1/[COL2][L'] .% K4a = [COL202]/[COL2][02] K4b = [(cOL2)202]/[cOL202][CoLz] (53) KlH = [HL]/[H+][L'1 KzH = [H2L+1/[HL1[H+1 (54) K = [H3L2+1/[H2L+1[H+] . 3H The rate law including reaction 49 will be derived first and then the rate law including equation 50 will be derived. From equations 49 and 51, one obtains the following rate expression + g%92£2—l-= k5a[(CoL2)202] + k5b[CoL202][CoL2+]. (55) Substituting equations 53 into 55 + d[COL ] _ ‘ 2 T2— — k5aK4aK4b[COL2] [02] + ksbK4a[COL2][02][COL2+]. (56) Since the total cobalt ion concentration, Cot, is equal to the sum of the concentrations of all cobalt species present ecu «“atic 2.. ..St be it 26 Co t = [C02+] + [CoL+] + [CoLz] + [CoL3-1 + [CoLaoz] 4 2[(C0L2)202] + [C0L2+]. (57) By substituting equations 52 and 53 into equation 57 and rearranging, one obtains [COL 12(2K [01K ) + [C0L1( 1 - + 1 2 4a 2 4b 2 K1K2[L 12 K2[L_] + 1 + K3[L-] + K4a[02]> + [CoL2+] - Cot = O. — (58) For the purpose of simplifying equation 58, the quantity 31 is defined 1 1 B1 = K1Ké[L-]2 + E;TE=T + 1 + K3[L-] + K4a(02].(59) Equation 58 then becomes + [COL2]2(2K4aK4b[02] )+[COL2]B1+[COL2 ]-C0t = O. (60) Equation 60 is then solved for [CoLz] —B :IJB 2-4 2K K [O ] ([COL +]-C ) [CoLg] = 1 1 ( 4a 4b 2 ) 2 0t °(61) 4 K4aK4b[02] . Since [CoLz] must be zero or positive, the real root of equation 61 must be the positive root and the negative root must be extraneous and therefore, '¥ + “B1+ JB12-8K4aK4b[02] ([COLZ l-COt) 2(2K4aK4b[02]) [CoLz] = ' (62) For the purpose of integrating the rate expression, the ligand concentration is assumed to be constant. (It actu- ally varies slightly as the reaction proceeds.) Constant oxygen partial pressures are maintained in the solutions. To further simplify the writing of the mathematical expressions, some of the constant terms will be represented by single terms as shown below AIR“ by; 3 subs : ; fallowmg QC In Cr transferma “‘“aticn x z j dx dCoII Sett; tutin 9 an \- 27 (I! w I _ 8K4aK4b[02] (63) 32 = 312 + 8K4aK4b[02]COt = 312 + B3CO (64) t III will be used to represent [COL2+]- and the symbol Co By substituting equations 63 and 64 into equation 62, one obtains +31 +~/—62 - B3COIII [COL2] =. B3727 III) . (65) -‘fi'; (—Bl +JBZ " B3CO By substituting equation 65 into equation 56, one obtains the following: III k ~A 2 dCO 5 - ——-— = a -31 + J 32 - BacoIII ) dt 233 + . 2k [0 ][CoL ] ‘* + 912K451 2 2 (431 + J 132 - 33ml”) .(66) Ba In order to be able to integrate equation 66, several transformations of variables must be made. The first trans- formation is shown below x ='J_B2 — B3COIII _: III III dX = 6] B2 ‘B3CO . d (Bz ‘B3CO ) docIII ' d(B2-B3COIII) docIII _ ”B3 _ “B3 . (67) III 2x 2 JRBz ‘B3CO Setting up the integration of equation 66 and substi- tuting equations 67 in to the expression, one obtains (u ‘2 To S~' ‘efifled 28 III -— 2k51<[02]CoIII 4 - e ' —— (-B1+JB2-B3COIII)f + b 4B3 (—31+JBZ_33COIII (68) t = fdt = t 0 C0111 a ”‘32 -«x2 . —(X-B1)2 + 2k5bK4a[02] T (X -' B1) co 6”.- The second transformation of a variable is shown below u = X ""B1 (70) du = dx . By substituting equations 70 into equation 69 and rear- ranging, one Obtains CoIIIf l-(u+B1)d -2 i, n CL" -2K a[°2]k5b T+(k5a _ 41:3[021k5b31 u 2 33 OIII + (2K4alofilksb132 _ 2K4a[02]k5bB1fl 33 B3. /_) .To simplify equation 71, the following constants are defined ‘ ~ 29 2 2K4a[02]k5bB2 2K4a[02]k5bB1 a = 33 - Ba b _ k5a _ 4K4a[02]k5bB1 (72) ‘ 2 B3 . _ -2K4a[02]k5b C— B3 By substituting equations 72 into equation 71, one obtains COIII COIII COIII (u + B1)du du B1 du (73) -2 = t = -2 —2 ° u(cu2+bu+a) cu2+bu+a u(cu2+bu+a) I III III C0311 C00 C00 Both terms of equation 73 are standard forms and can be readily integrated. The standard integrations115 of these two terms is found below in equations 74 ,X = a + bu + cu2 q = 4ac - b2 fig = r du = 1 log (2cu+b- J-q) ,X qu2 +bu+a ~/ -q 2cu+b+ 4 -q _ 1 log 2cu+b — Jb5—4ac) Jb5—4ac 2cu+b+-Jb2-4ac u _ [2&1 _ 1 \fi3 b du —'- -£1°97-§: Y uX U/u(cu2+bu+a) _1_.1_ = -1—-log (J2 )_ b log 2cu+b- Jb2-4ac ux 2a cu2+bu+a 2an2—4ac 2cu+b4uJb5-4ac a c 33' introdu e Obtai. ‘4 30 By using equations 74 to integrate equation 73 and rearranging, one obtains _ bBl 2 <2cu+b-:Jb§-4ac> t - - --—— 109 axlb2 -4ac db: -4ac 2cu+b +~/b2-4ac C0111 (75) B1 uz - :;-log cu2+bu+a . III C00 Then by successively substituting equations 70 and 67 into equation 75, one obtains the following c{x-B1]+b— JET—TE) 2 t.—- (' — --—-- log a 4b” -4ac d b2 —4ac 2c[x-B1] +b +an2 -4ac ‘ III 2 .Bl [X-Bl } CO '37 log 2 ‘ (76) c{x-Bl} + b[x—B1} + a III COO (:31 2 (ZcfrJBz-B3C0‘LII—B1]+b-~/b5—4ac t = --——————— log * p - v db! —4ac 'Jbz —4ac) 2c{~/B2—B3ColII-B1}+b+~lb2—4ac (77) C0111 2 31 {J32 -B3COJ'II- B1} - Er—log 2 . cEJBz-B3COIII- B1} + b{ B2'33COIII‘31]+a III COO By introducing the limits of integration and rearranging, one obtains O. 31 r _ 2C + ————————;a <-31Wm> 3 4br 3 , III COO = t (68a) COIII #x = t (69a) 5a 2 B2_X2 ~ 2K4bKX—B1) + 2k5bK4a[02] T (X-Bl) Co},II COIII Pu + B1)du -2 . _ 2 [-4: 2k5bK4a[02]u ksa 4k5bK4a[02]B1 u -————-————————— + ———— — ———-———————-—— u B3 2K b B3 III 4 COO (71a) 2 2k5bK4a[03]Bz _ 2k5bK4a[O2]B1 B3 B3 In comparing equations 71 and 71a, one sees that the only difference is the "b" term k' 4k K [02131 _ §a _ 5b4a b - 2K4b -————§;——-—-— . (72a) Therefore, the integrated rate equation is the same as it was with equation 49. ~The only difference is in the term represented by "b". Then eluding t} Wfich was 33’ Suhsu Obtain S 33 By inspecting equation 78, one can readily see that the equation cannot be solved algebraically. It is neces- sary to use a method of numerical solution which will be described later in this section. E. Calculation of Ligand Concentration During the Forma- tion and Decomposition of u-Dioxygentetrakis(l—histi- ‘ginato)dicobalt The equation for calculating the ligand concentration is the same for either mechanism, based on inclusion of equation 49 or equation 50. By defining Lt as the total ligand present excluding the ligand from the cobalt(III) product which was present at the start of the reaction, .1. [COL2 ] I 0 Lt = [If] +[HL1 +[H2L+1 +[H3L2+HC0L+] +2 [coL21 +3 [COLa '1 +2[COL202]+4[(COLz)202]+2[COL2+]—2[COL2:]. (79) Then defining 3' as the ligand-to-metal ratio (ex— cluding the ligand and cobalt from the cobalt(III) product . . ' + which was present at the start of the reaction, CoLz ) o E'Co — 2[CoL2+] = L o t ‘80) t' By substituting equations 52 to 54 into equation 79, one obtains hp: 34 - + - + - + - Lt = [L ]+K1H[H ][L ]+K1HK2H[H ]2[L ]+K1HK2HK3H[H ]3[L ] [COLz] _ m + 2 [C0112] +3K3 [C0142] [L 1+2K4a[COL2] [02] +4K‘aK4b[COL2]2[02]+2[COL2+] —2[COL2:] o (81) Then substituting equations 58 and 81 into equation 80, collecting terms and rearranging, one obtains the following:. [CoLz] 3 (ZR—4 )K4aK4b[02] +[COL2] n ' + «111—1— +(E'—2)+(H—3)K3[L'] +(H—2)K4a[02]] K1K2[L—]2 K2[L_] (82) +(H—2 ) [Cor2 +1 -[L-] (1+K1H[H+] +K1HK2H[H+] 2+K1HK2HK3H[H+] a) ... o. The quantities AH and .E are defined to simplify the equations + + + AH ’ _(1+K1H[H 1+K1Hj<2H[H 12+K1HK2HK3H[H 13) __ (83) E = _ + 5:1? + H-2+(Yi—3)K3[L_]+(fi-2)K4a[02]. .K1K2[L ]2 K2[L ] . . By substituting equations 83 into equation 82 one ob- tains the simplified equation [CoLz] 2 (ZR-4 )K [02] +[cOL2 ] E+(fi'—2 ) [CoL2 +1 -[L-]AH=O ' (84) 4aK4b and then solving equation 84 for [CoLz], one.obtains 4:: JF-4(25-4)K4ax4b[021 {(fi-Z'HCOLgl'lLfiAH} .(8 [C0112]: 5) ’2{(2ap4)x4ax4b[ozl} n 9.1 31 k0 {€01.21 r 85 is t? as fall: {CCLz} : 35 + . III for [CoL2 ] and Since -Again using the symbol Co [CoLz] must be zero or positive, the real root of equation 85 is the positive root. Therefore equation 85 is written as follows: -E+»JE?-4Tzfi-47K4ax4b[02][(5-2)scoIII-LL']AH} [C0L2]= '(85) 2((25-4)K4aK4b[02]} Then by substituting equation 86 into equation 65 one obtains -s IJBz—4(25-4)K4aK4b[02]{(E-2)COIII-[L_]AH} (4fi-8)K4aK4b[02] = 33— 6131 +WHI )- (87) 3 . A careful examination of equation 87 and the variables within the equation, A E (equations 83), B1, B2, B3 (equa- .H' tions 59, 63, 64), reveals that the following variables are ' + present. K1: K21K31 K43. K4b’ KlHI K2HI K3HI [H ]I [02]! + _ [COLZ ], and [L ]. -The values of K1,,K2, K3, K4a’ K4b’ KIH’ KzH' and KaH are known (see Discussion section). The [H+] and [02] are fixed at known values by the experimental conditions. -There- fore, by using the experimental value for [CoL2+], it is possible to solve equation 87 for [L-]. It is necessary to use a numerical method to solve this equation. 'The numerical method used is described next. ~ -~\« 7 CCES nct 85317- :e i". equati RECESSEI"; tense.” 1‘9 equat; L‘ ‘ Since I : Q‘e F1911: Let L he wiShes ferent Va; Ohmic“ 1y ,. 3+ ‘imate « ..AEI} the E Refe )- . SinstrUth 36 F. -Numerical Method Used to Solvefigguation 87, the Newton 'Method Since it has been found that the ligand concentration does not change very much as the reaction proceeds, a good estimate can be obtained for the ligand concentration at any time during the reaction. If one has a good initial estimate for the solution.of an equation and a numerical solution of the equation is necessary, the Newton method is the best numerical technique to use.116 TheiNewton method converges on the solution to the equation very rapidly (usually to four significant figures within six iterations). Since a good initial estimate of the ligand concentra- tion is available, the Newton method is used to solve equa— tion 87 numerically. The Newton method can be best described graphically (see Figure 2). Let us assume that one has an equation f(x) = O and he wishes to find a root of the equation. ‘He can try dif- ferent values of x and plot the equation f(x) = y. Obviously, y is the residual when one substitutes his estimate of x into the expression f(x). If y is zero, then the estimate of x is a root of the equation f(x) = O. ~Referring to Figure 2, the initial estimate of a root to the equation f(x) = O is the quantity a1. Line A1P1 is constructed perpendicular to the x axis and then the 37 Y ) ¢—- tangent to y = f(x) at point P1 . a2 y = f(X) / A1 _{, -Y Figure 2. Geometric representation of the Newton method for numerical solution of equations. DJ 1 ) 38 tangent to the equation f(x) = y at point P1 is con- structed. ~The value of x. where this tangent intersects the x axis, (x = a2), is a better estimate of the root than is the original estimate, x = al. ’This process of con- structing a line perpendicular to the x axis at point ai and then constructing the tangent to f(x) y at point ai to obtain a new estimate of the root, a can be i+1' repeated until the estimate of the root is sufficiently accurate. AThe accuracy can be determined by the value of y (the residual), and the closeness of an estimate ai to the previous estimate. The initial estimate of the root must be close enough to the real root to avoid inflection points or changes in the sign of the slope of the equation y = f(x) between the point on the equation x = a1 and the point where y = 0. If there is an inflection point or a change in slope, the Newton method will fail. ~The mathematical equivalent of the geometric procedure described above and in Figure 2 is as follows. >As stated above, the initial estimate of the root to the equation f(x) = 0 is the quantity a1. Point P1 is the point on the equation f(x) = y where x = a1. Therefore, at point P1, f(al) = y (f[a1] is the value of f(x) evaluated with x = ai). The coordinates of point P1 are (x, f[a1]). Now the equation of the tangent to f(x) = y at point P1 must be obtained. The slope of the tangent at point P1 muSt be the same as the slope of the equation y = f(x) at point P1. «The slope of the equation y = f(x) at point 'r, _U—_.‘l‘ 'fliq'fim WILL v,“ “35:62 X ; By Substi' ”mix. . 39 P1 is f'(a1), (the derivative of f(x) evaluated with x = a1). The general equation for a straight line of slope m and containing point (x1,y1) is as follows: X - X1 ' Therefore, the equation of the tangent is Y ‘ f(a1) X-a1 = f'(a1)- (89) Rearranging equation 89,one Obtains Y " f(al) X = - + a1 0 (90) f'(ai) ~ The point on this tangent where y = O is the point where x = a2, the new estimate of a root of f(x) = 0. (By substituting y = 0 into equation 90, one obtains a2 f(al) f'(ai) To use the Newton method to solve equation 87, it is (91) necessary to obtain the derivative of equation 87 with respect to the unknown, [L-], and a good estimate of [L_]. The derivative of this equation can be found in the Ap- pendix. The estimate of [L-] can be obtained by using trial values of [L-] in the Newton method until a trial value is found that is sufficiently close to the true [L-] for the Newton method to work properly. The computer subroutine based upon the Newton method and written by the author will be found in the Appendix. 40 G. Numerical Method_Used to Solve Equation 78 Upon examining equation 78 and the variables within the equation, it can be seen that all the variables from k k and equation 87 are present as are K ,.K 5a' 5b 4a 4b' [CoL2+]. Byusing the value of [L-] as calculated from equation 87, choosing appropriate values for K4a and K4b (see Discussion section) and using the current estimates (either initial estimates of these variables or least squares estimates) for k a (or k' ) and k 5 5a one can solve equa- sb’ tion 87 for [CoL2+]. However, the initial estimates and in some cases the iterative computer estimates of k5a (or kéa) and ksb may not be accurate enough to use the Newton method to solve equation 87 numerically. Therefore, it becomes necessary to derive a numerical method and a computer program for the method which can be used even with poor This method initial estimates of k (or k' ) and k 5 5a 5 b. is based on the method of successive approximations. a If one has a function of the form f(x) = O and he tries two estimates of roots to the equation, x1 and x2, to get f(xl) and f(xz), he can tell from the magnitudes and signs of f(xl). and f(xz) whether there is a root between x1 and x2 and if not, whether x1 or x2 is closer to a root. If the signs of f(xl) and f(xz) are different, there must be a root between x1. and. x2. If the signs of f(xl) and f(xz) are the same, whichever has the smallest magnitude is based on a value of x which is 41 closer to a root. In this way, one can tell whether in going from x1 to x2 a root has been passed or if it is ap- proaching or leaving a root. VH. Computer Programs The computer program for the linear least squares rou- tine, which is used to determine rate constants and activa- tion energy for the decomposition of the pentacyanocobalt- ate(II) ion, is straightfoward. It is based upon equations 6, 7, 9, 10, 39 and 40° 'The computer program can be found in the Appendix. 'The computer program used for thescobalt-histidine- oxygen reaction consists of a main program, "Deriv", a ligand concentration calculation subroutine, "Aligcalc", a [CoL2+] calculation subroutine, "Co3calc", and a determinant evalu- ation subroutine, "Dterm". There are two basic versions of the main program. The preliminary version, "Kintslct", does not include any least squares calculations. -It is used to detemine order of mag- nitude estimates for k . k' and k5 It consists of 5a 5a b' reading in the experimental data, the known variables, and the estimates of k5 or kéa and k5 and then calling b subroutines "Aligcalc" and "Co3calc" to calculate the ligand a and cobalt(III) product concentrations. This computer pro- gram can be found in the Appendix. The regular version of the main program, "Deriv", includes the non-linear least squares calculations. There are, of course, two versions .; each t .- "Derivg " aquatic: (paraxete a- u 2‘0 h V. to Ed 42 of each type of main program; one is based on equation 49, "Derivg" (and therefore, the parameter "b" is defined by equation 72); the other is based on equation 50, "Derivh" (parameter "b" is defined by equation 72a). A block diagram of the main program including the least squares calculations can be seen in Figure 3. Subroutine "Aligcalc" is based on the Newton method. It consists of calculating the necessary derivative, calcu- lating a new estimate of [L-] (based upon the initial or previous iterative estimate of [L_]) by means of equation 91, checking to see whether the previous and new estimates are close enough to each other to terminate the calculation and if not, going back and calculating the derivative, a new esti- mate of [L'], etc. Subroutine "CoBcalc" is based on the method of successive approximations. ~A block diagram of this subroutine can be seen in Figure 4. ‘Subroutine "Dterm" is a standard program which was ob- tained from the Michigan State University computer program ,library. This subroutine is used to calculate the values of the determinants. -Subroutine "Cobltclc" is used to calculate [C02+]; [COL+] I [C0142] , [COL202] , and [(COLZ )202] . I. Estimation of K4a and K4b The estimation of the values of K4a and K4b is based on the observation that at 25°, K4a’K4b = 7.2 x 106.59 43 Read in the values of all constants, the experimental kinetic data, (experimental conditions, initial concen- trations of reactants, [CoL2+] and time), least squares parambters, initial estimates of the parameters (k I - 5 or ksa’ k5b and [L 1). . # ligand concentration (based on the experimental values [Call the "Aligcalc" subroutine to calculate the free I foryLCoszJ) for each experimental data point. all the "Co3calc" subroutine to calculateTthe [CoL2+] I C [(based upon the initial estimates of k a or k'a and k and thegLL'] calculated above) for each experimengal dataSBoint. L ‘T’ ’ a Calculate the derivatives necessary for the least squafes calculation (based on the current estimates of k5a or k; and ksb)’ and set up the least squares determinants. a the difference between [COL2+]exp and [CoL2+] calc 7 [Call the "Dterm" subroutine to evaluate the determinants.| +' Use the determinants to calculate new values for k5a or k5a and ksb' V Call the "CoBcalc" subroutine to calculate [CoL +], (based on the neW’choices of k5a or ksa and ka for each experimental data_point. Y? Print out the previous and new estimates of k5a or k; a + and ka, the new and old values of [CoL2 ]calc’ + - + _ + [CoL2 ]experiml the quantity ([CoL2 ]exp [CoL2 ,and the mean and standard deviations. + If the old and new estimates'of k5a or ksa and k5b are ), calc close enough to each other (indicating convergence), terminate the calculations. Otherwise repeat the least squares procedure up to a maximum number of iterations. Figure 3. A block diagram of computer program "Deriv". b hon CUUVM «MVJHNH JUNE-UN m. «3 NW aw.~\o “X0 U 200 d 44 A.mmuw m50H>me mgu s s m 50a HQ 0 m Eoum A 00v 3m 00 may me A Dov m .>m UU .mmum mom CH “cam A+nqooH u 00 “ xmA+nqoo_ u xov .:0Hmom00= wsfiuDOHQSm Housmfioo mo Emnmmflc xooHQ d .v musmflm _ msofl>wnmw I I Boo H .wssflucoo mmHBHwauo .Emumoum chE o D On Cusp low can cofluMMsono on» VCmeMMHc mum msmflm mLE__mEMm Gnu mum mcmflm NAB— mumsflEHou rumsuo zomw on 1‘ ‘7 m ‘7 nmsosm wmoHo mum moo pom LA oovm ou cmflm sou MH .usouwm . mus mummsoo cam A oovm wumasoamo IwfiU mum mcmflm may; .wEmm may mum mcmflm snag b 1‘7 m .A UUVM ou swam muH mummaoo vow Acoovw mumasoamo z\ a m m . o. 00 m s mt, c : 8E A : BEA: BE v : 8:: msofl>wumm£ m: .|T|L m A, c ‘7 H + U n o “H n no 00 m_ on _A 00vm_ mummEOUA .usmuwmwflp mum msmfim mLB .wEmm mgu mum madam one mg 4‘ , Fmoovw on swam mu“ mummEoo cam A b C UOVM wumaooamo_ a 0 HH ou swap HoHHmEm mausmflam umsm ma coo C . 00 m oumasoamo HWUU a O G a sons 00 A 00 NH HOV OH n 00 HH C 84 F] K43 total c .r- v ,1. a- be- V. :X'v.':e: ( O J “2:112 ] I absorbed By ‘J 1 .’ hally [k calCUIa‘u 45 The equations 53 can be multiplied to obtain the product K4a.K4b’ [(C0L2)202] . = 6 = ‘K4a 'K4b 7.2 x 10 (92) [COL2]2[02] ~ One can then assume that a specific percentage of the II ti after oxygenation (and before any decomposition of the total cobalt(II),-Co is in the form (CoL2)202 immediately . ‘ + oxygen carrier to form.CoL2 ). -Thencne can calculate [CoLz], [CoLzoz], and the number of moles of oxygen initially absorbed per two moles of cobalt. II t tially (CoL2)202, and rearranging equation 92, one can ‘By defining F as the fraction of Co that is ini- calculate [CoLz] as follows: [(C0L2)202] ICOII "F t .(93) . . = . 6. K4a .K4b [02] 47.2 x 10 [02] [COLz] = Before any decomposition of the binuclear oxygen carrier II Co t = [CoL2] + [CoLzoz] + 2[(COL2)202] (94) [COLQOZ] = C01: - [COLz] — 2[(COL202]o (95) Since [(Cohgkofl is assumed, [CoLz] and [CoLZOZ] can be calculated from equations 93 and 95,.K4a andK4b can be calculated by using equations 53. -The number of moles of oxygen that‘are initially ab- sorbed per two moles of cobalt(II) is equal to the quantity [(CoL2)202] + 2[COL202] OII t . (96) .20 "V 0 Cl Since, fie molar a €st+ were p 1 :39 to Its Start or en. s'CIbEmces 1, experimenta ClVelY the . 46 . + J. Correction of CoLz Absorbance Due to the Presence of II Coa ...Ji A simple linear correction on the absorbance of the quenched cobalt-histidine-oxygen solutions for the absorb- ance due to Co: : has been derived by Zompa.117 Since, at any wavelength of the spectral observations, the molar absorptivity of CoL2+ is much greater than that Of (20:31: ACOII F II = IT— (97) Co C051 . [CoL2+] A ‘III ~,Atotal-A II F + =______ =_C_9__~ COO—— (98) COL? [CoL2+;O A III A III-A II C000 C000 COO where F is the fraction of the subscripted species (rela- tive to its maximum possible concentration, at either the start or end of the reaction). The A terms are all ab- + . sorbances less any absorbance due to CoLzo. At 18 the experimental absorbance; A and A are respec~ COII COIII tively the absorbances due to C02+ and CoL2+7 A is aq II COO the initial absorbance of the solution and A III is the Co final absorbance of the solution. 00 Since the whole is equal to the sum of its parts, At-ACOII ACOII + = 1 ; - A0 -————— = 1° FCoII FC°L2+ A III'A II + A II (99) CoOO CoO Co0 The only variable in equation 99 that is not known from the .7 'fl (' experi efl‘!’ 5-7‘ 1“ yo“ be calc aid 1: d 47 experimental procedure is A II so that by rearranging this .CO 2 equation, the absorbance of the solution due to Goa; can be calculated ACOII ' At _ O .A II _ A II 1 + A _ A (100) C0 Coo COII COIII o ' a) and by difference, A III = At - A II . (101) - 3“.“ IV . 9 EXPERIMENTAL A. .Preparation of Reagents Reagent grade materials were used throughout. The l- histidine was obtained from Nutritional Biochemicals, Inc. and was used without purification. The water used to pre— pare the solutions was boiled distilled water. Throughout the boiling of the water and while cooling afterward, pre- purified nitrogen gas was bubbled through the water to remove any dissolved oxygen. (Thereafter, whenever water was pipetted out of the container, prepurified nitrogen was bubbled through the water to prevent air from entering the container. A potassium pentacyanocobaltate(II) solution of 0.17%! was prepared by mixing solutions of KCN and Co(NO3)2 in a molar ratio of 5.49 to 1.00, in a special flask which al- lowed mixing and withdrawal of samples into a spectrophotom- eter cell in an atmosphere of prepurified nitrogen. The flask, which is shown in Figure 5, is essentially "H"- shaped and contains a sidearm with a stopcock for connecting a spectrophotometer cell to the flask. rBefore use, the flask was evacuated several times and filled with prepuri- fied nitrogen. Whenever reagents were added to the flask, 48 49 2-way stopcock 1 cm spectrophotometer cell 9 24/40 Ground Hoffmann . Screw “ Glass Joint Tygon Tubing 2-way stopcock Figure 5. Special mixing cell. 50 nitrogen was passed through the flask to prevent the in- trusion of any air. The KCN solution was pipetted into one side of the “H"—shaped flask and the Co(N03)2 solution was pipetted into the other side of the flask. The flaSk was closed, tipped and shaken to thoroughly mix the re- agents and then tipped at an acute angle to allow the solution to flow through the sidearm and into the spectro- photometer cell. Hardened Tygon tubing must be used to connect the spectrophotometer cell (which must have a round top to permit the connecting of the Tygon tubing) to the "H"- shaped flask to prevent collapse of the tubing while the flask is being evacuated. When the spectrophotometer cell is about to be disconnected from the flask, a Hoffman screw is tightened about the Tygon tubing and the sidearm stop— cock is closed. Then the spectrophotometer cell (with the Tygon tubing and the closed Hoffman screw attached) can be disconnected from the "H"-shaped flask and placed in the spectrophotometer. Bis(l-histidinato)cobalt(II) solutions, buffered at pH = 7 and in a medium of lfl'KNO3, were prepared by adding the reagents shown in Table I to a 100 ml volumetric flask. For simplicity, bis(l-histidinato)cobalt(II) will be desig— nated Col.2 and bis(l-histidinato)cobalt(III) cation will be designatedCoL2+. Table I I) H y... H 2! 72 2115K It.) (3 (A) LO H I :1 ’ 51 Table I. Preparation of the CoLz solutions (2:1 histidine to cobalt ratio). I II III [CoLz] 6.08 x 10‘3 6.08 x 10‘3 12.16 x 10‘3 [CoL2+] 0.00 6.0 x 10'3 0.00 ml 1L4_KH21>04 7.00 7.00 5.00 ml 1§_K2HPO4 25.00 25.00 25.00 g KN03 10.1 10.1 10.1 g l-histidine 0.1887 0.1887 0.3774 g (CoL2+)(No3’) 0.00 0.2622 0.00 ml 0.12165 Co(NO3)2 5.00 5.00 10.00 up to the up to the up to the ml H20 100 ml mark 100 ml mark 100 ml mark _Solid (CoL2)(N03) was prepared by adding a two to one mole ratio of l-histidine and.Co(NO3)2 to water and bubbling air which was passed through a glass wool filter through the solution for three days. No buffer was added to the reaction flask. The resulting red solution was added to approximately four times its volume of acetone. The result- ing fine precipitate was filtered through a fine fritted glass funnel, washed several times with small quantities of water, washed with acetone and ether and then dried in vacuo for approximately two hours. -The yield of the non-crystal- line salmon-red powder was approximately 50%. -The powder was a mixture of the three isomers of the product.107 1.7“ I" I‘ JI“-'L"' 3, Ahathi A The c: acdificatic volume cf 5 pipetted l: .11 of cone. :0 the beak mately five :ating plat to 3.5 ‘JClt The KC :itratioml szall amour. turely Prec “(Ea drop “mint is To Che tion eCIuiva 100-5 t 0.2 In 0rd g ”line Solut; standaraizE was perfOr: 1&1003 a: :A M acetic 52 B. Analytical The cobalt nitrate solution was standardized by a modification of a standard electrochemical method.118 A volume of solution containing 150 to 200 mg of cobalt was pipetted into a beaker; 0.3 g of NaHSOa, 5 g of NH4C1, 50 ml of conc.NH4OH and approximately 20 ml of H20 was added to the beaker. ~The solution was electrolyzed for approxi- mately five hours on a Fisher electroanalyzer using a ro— tating platinum anode and a platinum gauze cathode at 3.0 to 3.5 volts, 0.5 to 1.2 amperes. The KCN solution was standardized by a silver ion titration.119 Potassium iodide was the indicator and a small amount of NH4OH was added to dissolve any AgCN prema- turely precipitated due to a locally high Ag+ concentration vhama drop of AgN03 from.the«buret enters the solution. .The endpoint is the first permanent clouding due to separation of AgCN. To check the purity of the l-histidine, a neutraliza- tion equivalent titration was performed. The result was 100.5 i 0.2% for the purity of the l-histidine. In order to determine the quantity of phOSphate buf- fer necessary to maintain a pH of 7 in the cobalt—histi— dine solutions listed in Table I, it was necessary to standardize a glass electrode for 1g_KN03. A titration was performed by using standardized dilute acetic acid in 1 _14 KN03 and standardized NaOH in la KNOa . Since the ka for acetic acid in 111 KCl is 3.071 x 10" (ref.12°), it is -.1 possible t ticn point the same i and experi :ade. The high.117 Then, gantity c 7. The te except the .zed glass (‘ . “ Experu Become A pre 53 possible to calculate the pH of the solution at all titra- tion points (by assuming that the ka for acetic acid is the same in 1!_KC1 and KNO3). By comparing the calculated and experimental values of pH, a calibration curve can be made. (The pH meter reading was found to be 0.12 pH units high.117 Then, test solutions were prepared to determine the quantity of phosphate buffer necessary to maintain a pH of 7. The test solutions were the same as listed in Table I except that no KH2P04 was added initially. Then KH2PO4 was titrated into the test solution until a Corning pH meter with a saturated calomel electrode and the 1g_KNO3 standard— ized glass electrode indicated pH 6.88. C. Experimental Procedure for the Study of the Co(CN)53‘ Decomposition A preliminary study of the decomposition of Co(CN)53‘ showed that the decomposition was affected by light. One sample of Co(CN)53‘ was kept in the light and another sample was kept in the dark. Spectra of both samples were taken periodically. Some of these spectra are shown in Figures 6 and 7. From Figure 6, one can see that the decomposition is faster in the light. From Figure 7, one can see that the products of the decomposition in the light are different from.the products in the dark. Therefore, all further kinetic experiments were performed in darkness to avoid the compli— cating effects of the photochemical decomposition. mousswa DH cam .mmosxumo as ummx mamsmn 0:» mo Esuuowmm .unmwammc CH ummx mHmEmm may no ssnuommm m d .QOAHMHmmmHm Houmm mason N How unmflammo :a can mmmsxumo a“ ummx ImmAzovou msomsvm mo muuommm >5 use: can mHnHmH> mo comflHmQEou .m musmflm Ajsv numcmam>m3 oou on com can con onv oov d m I‘ll!“ i. .c0flumnmmoum Hmumm mason we now usmfiammc ca 6cm xumo 039 CA ummx ImoAZUVOU msomsvm mo mnuommm >5 Hmmc cam manflmfl> mo somHHmQEoo .h ousmflm Ajev zumcmaw>m3 och one com com o.m onv cow |II|||| unmaq same .3 .3 The r ate(II' iC peak of t violet 5;. oxygen gas stated cel of each ex light fret: photometer ZiCH, the as sham b The m WC waYs . COT/Centrat fiére PIEpa 3"He calc: 'w‘Ere Obta; The Vaer 'i’iou51y re The earlie Error Prob All Tum for de soluticms L First! 5561 56 The rate of the decomposition of the pentacyanocobalt- ate(II) ion was followed by observing the decay of the 625 mu peak of the Co(CN)53' on the Unicam SP 800 visible-ultra- violet spectrophotometer. »The sample was kept in a stoppered oxygen gas-free 1-cm spectrophotometer cell in the thermo- stated cell compartment of the Unicam SP 800 for the duration of each experiment and thus served to prevent any stray light from reaching the sample. Since the sealed spectro- photometer cell had very little gas volume above the solu- tion, the decomposition of one of the reaction products71 as shown below was prevented > 2Co(CN)53- + Hzf .(102) < 2Co(CN)5H3" v The molar absorptivity of Co(CN)53- was calculated in two ways. First, dilute solutions of Co(CN)53- of known concentration, in which the decomposition was very slow, were prepared and the molar absorptivities of the solutions were calculated; second, the initial molar absorptivities were obtained for the solutions used in the rate studies. The value obtained was €625 = 6.15 compared with the pre- viously reported values'71I3‘?:91I121 of 10, 7, 6.3 and 7. The earlier reported spectra of Co(CN)53" 76'122 were in error probably due to the presence of some oxygen.91 All of the previous workers had used the 970 mu maxi- mum for determining the concentration of Co(CN)53— in solutions. The 625 mu peak was chosen for two reasons. -First, fairly concentrated (0.170g) solutions of the ....) pentacyanl molar abs: the other L; w '1 LQIS ka" 9 57 pentacyano complex could be used because of the much lower molar absorptivity at the 625 mu peak and second, none of the other species present have any measurable absorption at this wavelength. Neither Co(CN)5OH3_, which is one of the Co(CN)53- decomposition products, nor Co(CN)64‘, which can be produced by the Co(CN)53- catalyzed OH- - CN— exchange123 has any measurable absorbance at 625 mu. ‘The colorless Co(CN)5H3_ ion, which is the other product of the decomposi— tion of the Co(CN)53-, has no measurable absorbance anywhere in the visible region of the spectrum.84v85 Thus, the absorbance of the reacting solution at 625 mu is a direct measure of the [Co(CN)5I3- and no correction is necessary for absorbance due to the presence of other species. D. ~§xperimenta1 Procedure for the Study_of the Cobalt- ‘Histidine-Oxygen Reaction The molar absorptivity at 500 mu for solutions of CoL2+ prepared by oxygenating aqueous CoL2 for several days was 125.1, and agreed fairly well with the previously reported value of 115.117 The kinetics of the formation of CoL2+ from the oxygen carrier, L2C002C0L2, was followed by observing, on the Unicam SP 800 spectrophotometer, the growth of the absorb- ance at 500 mu due to the formation of CoL2+. The reaction was performed in a thermostated constant temperature bath at 25°. Oxygen gas mixtures were passed through a series of bubblers which were immersed in the '1 ‘kfi v :‘JU‘Ie n p , Veait‘ 58 constant temperature bath and then bubbled through the re- acting solutions. The first bubbler contained 1g_KOH and the second bubbler contained 1g_KNO3. Both bubblers satur- ated the gas mixtures with water vapor which minimized evaporation of water from the reacting vessels and brought the temperature of the gas mixtures to 25°. The 1g_KOH bubbler also removed any C02 from the gas mixtures. The gas mixtures used were prepurified oxygen, air (first passed through a glass wool filter) and a 5% 02 - 95% N2 gas mix- ture. Since the solubility of oxygen in water at various ionic strengths is known124 (and in particular, for the above experimental conditions with air as gas91), the con— centrations of 02 dissolved in the solutions were known. It was necessary to use an acid quench to destroy any oxygen carrier present as the oxygen carrier has a very large charge transfer absorbance that made it impossible to ob- tain quantitative results from the Spectrophotometric obser— vations.117 »Every 100 minutes, a 5 ml aliquot was removed from the reacting sample and the aliquot was quenched with 1 ml of 4;; HNO3. The HNOa did not affect the product,»CoL2'+, but it did convert any oxygen carrier and CoL2 to aqueous Co2+ as shown below + 2+ CoL2 + 2H > Coaq + 2HL + CoL202 + 2H > Co:; + 2HL + 02 (103) + (CoL2)202 + 4H > 2Co2; + 4HL + 02. >1 ‘. (I) 59 The Spectrophotometric readings were taken 25 minutes after quenching for reasons that will be explained. ~In the quenched solutions, the C02; had a small but measurable absorbance at 500 mu (e 2:5).117 Therefore, it was necessary to correct the experimentally measured ab- 2+ sorbance for the absorbance due to the Coaq. -This correc- tion has already been described in the Theoretical section of this work (Section III, Part J). V. RESULTS AND DISCUSSION A. The Decomposition of Co(CN)g_ The three previous investigations of the decomposition of aqueous Co(CN)§- yielded results significantly different from ours. DeVries71 calculated an activation energy of only 4 kcal/mole but did not list rate constants. Burnett and coworkers121 reported rate constants which varied un- explainably between 0.002 and 0.007 M-lsec.-1 Pratt and Williams91 did not report rate constants. All three investi— gations showed that the decomposition was second order in [Co(CN)53’]. Our investigation was carried out at 5° intervals from 25 to 50°C. Second order rate plots are shown in Figure 8. The very early part of each experimental second order rate plot deviated from linearity due to the lack of the attain— ment of thermal equilibrium. This temperature deviation is due to the high heat of reaction of 74.4 kcal/mole.125 To minimize this temperature deviation at the start of the re— action, the Co(NO3)2 and KCN solutions for the 25° kinetic run were cooled to 00 before mixing. The solutions for the 50° kinetic run were not cooled. Various degrees of cooling 'were used for the solutions that were investigated at 60 61 .QOH AHvanmuHmnoo locmhomucma ozu mo :poamomeoomc on» How muon mums Hopuo ccoowm .w seamen ACHEV mEHB cm cos cw cc .oa ca _umAzovooH H. as mm 0 can we com on an ace one 62 intermediate temperatures. Near the end of each experimental rate plot, there was a deviation from linearity due to the formation of an unidentified light brown precipitate. The precipitate was probably impure K3Co(CN)5H which, when pure, is colorless.85 Those points that did lie on a straight line were treated by the previously described linear least squares computer program by use of the Michigan State Uni- versity Control Data Corporation 3600 computer. An Arrhenius plot of the resulting rate constants yielded the straight line shown in Figure 9. A linear least squares calculation was performed on the Arrhenius equation. The deviation from linearity of the 500 point on the Arrhenius plot might be due to the decomposition of one of the products (the Co(CN)5H3' ion) according to equation 102. It is known that as the 3— O decomposes increas- temperature is increased, Co(CN)5H ingly into Co(CN)53- and H2.71 The resulting rate constants and activation energy are shown in Table II. Table II. Rate constants for the decomposition of Co(CN)§—. Temp. (0C) k(M-lsec-1) x 103 25 1.00 i 0.00 30 1.35 i 0.01 35 1.72 i 0.02 40 2.17 i 0.02 45 2.92 i 0.02 50 3.30 i 0.02 The value fOr the Arrhenius activation energy is 9.84 i 0.27 kcal/mole. 63 1 3.3 3.2 3.1 1 Temp x 103 (OK) Figure 9. Arrhenius plot for the decomposition of the pentacyanocobaltate(II) ion. 64 That the Co(CN)§— ion is oxidized by molecular oxygen much more rapidly than Co(NH3)§+ to form the peroxo bridged species L5C002C0L5 has been used as evidence to show that the cyano species is five coordinate. The rate of the up- take of oxygen by ammoniacal cobalt(II) solutions has re— cently been measured5° by the stopped—flow technique whereas an attempt to measure the rate of the oxygen absorption by Co(CN)g- by this same technique has failed because the re- action is too fast to measure by the stopped—flow method.126 The explanation being that the reaction probably proceeds by an inner sphere mechanism and the five coordinate cyano species would not have to undergo dissociation before re- acting with the oxygen, whereas the six coordinate ammine species would probably have to first undergo dissociation to react with the oxygen. However, the possibility that there is a loosely bound labile water molecule in the cyano species is not ruled out (see the Historical section).91:127 The mechanism for the decomposition need not necessarily be as previously proposed, namely 2Co(CN)§’ + H20 > (NC)5COH0HCO(CN)§‘ —5—> (104) -—o Co(CN)50H3‘ + Co(CN)5H3' but it might proceed as follows: 3- fast 3- Co(CN)5H20 < > Co(CN)5 + H20 (105) fast Co(CN)5H203‘ + Co(CN)§' ——> (NC)5COH0HCO(CN)§' (106) 1'." so: I \ 65 followed, as before,by the decomposition of the water- bridged species128 (Nc)5cOH0HcO(CN)§’ k > (NC)5COH3- + H0Co(CN)§'. (107) Therefore the decomposition or "homogeneous absorption of hydrogen" by Co(CN)§- in aqueous solutions would actually involve a disproportionation of water. If solid mononuclear paramagnetic K3[Co(CN)5] could be prepared, analyzed for the presence of water, and its spectra compared with those of solutions of K3[Co(CN)5], the question of whether Co(CN)§- is five coordinate in aqueous solutions or contains water at the sixth site might finally be answered. Any attempt to prepare solid monomeric 8K3[Co(CN)5] from aqueous solution failed as precipitation immédiately results in dimerization.72 Even an attempt to prepare solid K3[Co(CN)5] by rapid freezing of very dilute solutions of K3[Co(CN)5] sprayed from an atomizer straight into liquid nitrogen and removing the solvent by freeze drying produced a pink ice containing the dimeric diamagnetic K6[(NC)5CoCo(CN)5].91 Solid monomeric paramagnetic K3[Co(CN)5] was recently prepared by heating the solid violet diamagnetic dimer, K6[(NC)5CoCo(CN)5], to 230° under vacuum for 15 to 20 minutes.129 The product was light tan and had a magnetic moment of 2.09 to 2.22 B.M. and was probably anhydrous.129 The magnetic moment was higher than the 1.72 B.M. for aqueous solutions.62I74 However, since no visible spectra of the solid monomer are as yet available, b .... H " n to. ‘V‘. . \ Iqba- \yuc Eye: 66 the final answer to the coordination number of K3[Co(CN)5] cannot be answered. I In order to determine the nature of the electron transfer that occurs in reaction 107, it is first necessary to deter- mine the oxidation state of the cobalt and the hydrogen in the Co(CN)5H3- ion. The three possibilities are listed in Table‘III. Table III. Possible oxidation states of Co and H in Co(CN)5H3’. Co oxidation state H oxidation state Nature of the H +1 +1 Proton +2 0 Atom +3 —1 Hydride .All three of the possibilities, cobalt(I) and a pro- ton,81v13° cobalt(II) and a hydrogen atom121l131 and cobalt(III) and a hydride34:85.~132 have been proposed. How- ever, the ability of Co(CN)5H3- to hydrogenate some unsatur- ated organic compounds133 along with evaluation of the near uv Spectrum of Co(CN)5H3- and consideration of the position of hydride in the spectrochemical seriesl34 strongly suggests that the hydrogen in this ion is hydride. vSince Co(cn)§‘ is a stronger reducing agent than H2,135 one can consider the :Co(CN)g_ decomposition to be a reduction of water to give the hydride ion while itself being oxidized to CoIII. ML. .Au 7"“. ..‘n Aa,. 56.; a» B‘. ‘ a 'a'yq J‘)‘ (D .. ,l 3 [1’ f): 67 -Thus. Co(CN)5H3‘ should be formulated as [CoIII(CN)5H_]3- and should be named hydridopentacyanocobaltate(III) ion.85 We can now examine equation 107 to determine what elec- tron transfers are necessary to maintain the proper charge -The two cobalt(II) ions in the water-bridged balance. intermediate must be converted to cobalt(III). Equation 107 very probably occurs as follows: _ e' (NC)5CoIIH HOHCOII(CN)€5§- —> (NC)5CoIIH°3+_- °OHCoII(CN)5 (108) —> (NC)5COIIIH33- + 30HCOIII(CN)5. In addition to the decomposition of Co(CN)§‘ which occurs by forming a water-bridged binuclear intermediate, there are several other reactions of Co(CN)g- which occur through similar bridged binuclear intermediates. These re— actions are the reversible heterogeneous absorption of hydrogen gas bubbled into aqueous solutions of Co(CN)§_ (equation 109) 2Co(CN)§' + H2 < > 2 Co(CN)5H3' (109) and the Co(CN)g- catalyzed ortho-para hydrogen interconver- sion (equation 110) both of which presumably involve the lntermediate (NC)5CoH2cO(CN)§' 89:128'13°'131 and the CORN)? catalyzed deuterium-hydrogen exchange between H2 and H2089.13°I136 (equations 110-113) in which both H2 and I120 bridged species are probably intermediates .«nu : 68 D2 + 2Co(CN)§‘ ——e (NC)5COD2CO(CN)g- ::3_2Co(CN)5D3- (110) 2Co(CN)§' + H20 -—> (NC)5COH20CO(CN)g- (111) <— > (NC) CoHOHCo(CN)6- + Co(CN) 03' 5 5 5 < (112) (NC)5CODOHCO(CN)§‘ + Co(CN)5H DH + 2Co(CN)§’ -:3_(NC)5CODHCO(CN)g- -< > < (113) Co(CN)5H3‘ + Co(CN)5D3‘ etc. Because of the similarities of the H2 and HOH bridged species, one would expect similar activation energies for each of the above mentioned reactions. As can be seen from Table IV, the previously reported value for the activation 3.— 5 energy for the Co(CN) decomposition71 was lower than ex- pected and was the reason for the present investigation. Table IV. Activation energies for reactions similar in 3_ mechanism to the decomposition of aqueous Co(CN)5. Reaction Agfiizgyion Reference (kcal/mole) Absorption of H2 by Co(CN)§‘ 11.2 i 0.2 71 Desorption of H2 by Co(CN)§- 12 i 1 128 Catalysis of-Dz-HzO exchange by CO(CN)g_ 7.3 :-'.' 0.4 130 Co(CN)g- decomposition 4 71 Co(CN)g- decomposition 9.84 i 0.27 137 (this work) Cc Pl ,3 69 An interesting aSpect of both the homogeneous Lidi- Co(CN)§- decomposition) and the heterogeneous hydrogen ab- sorption was the large salt effect.71,84:85.91 The salts KCl and KCN were about equally effective in accelerating the heterogeneous H2 absorption and the Co(CN)?“ catalyzed Dz—HZO exchange and thus indicated that Co(CN)§— is not an intermediate in these reactions.86 Pratt and Williams showed the same salt effect in the Co(CN)g- decomposition and calculated the association constant for the Rb+, .Co(CN)§— ion pair.91 The probable reason for the large ionic strength de- pendence is the large repulsion between the two combining Co(CN)g- ions during the formation of the intermediate, (NC)5CoHOHCo(CN)g-. As the ionic strength increases, more posi— tive ions will surround the Co(CN)§- (forming M+, Co(CN):- ion pairs and M+, Co(CN)§-, M+ ion triplets) and therefore the repulsion between adjacent Co(CN)§- ions will decrease, and it should be easier to form the water-bridged inter- mediate. -The apparent activation energy for the reaction will then be lower. This means that as the activation energy decreases, the reaction for the formation of the water bridge species becomes + __ .. 2.[M, Co(CN): 1+ H20 -—> 14+, (Nc)5cOH0HCo(CN)§, M+.(114) Therefore, in performing rate studies on these systems, it is necessary to work at as low an ionic strength as pos- sible. One must also work at as low a CN:Co ratio as possible 70 and no other salt should be added. DeVries, by using a KCN:Co ratio of approximately 400 (hence, at high ionic strength), obtained an activation energy for the decompostion reaction of 4 kcal/mole.71 rWe have used a KCN2Co ratio of 5.49, which isabout as low a ratio as one can have and still have the Co(CN)g- ion. Our calculated activation energy, 9.84 i 0.27 kcal/mole, should be close to the thermodynamic activa- tion energy. We have made some qualitative observations of an inter- es ting reaction originally proposed by Piringer,13° 4Co(CN)5H3' + (NC)5C002Co(CN)g- ——-—> 3_ (115) 6Co(CN)5 + 2H20. If air is admitted to a partially "aged" Co(CN)§- solution (i\.e_., it is partially decomposed), the color changes from the green of the pentacyano ion to the orange of the 02- 1DJE‘idged species. After approximately 20 min., the solution IDeCIOmes green again and the visible spectrum returns to that of the pentacyano solution. This above mentioned phenomenon agrees with Piringer's postulated reaction (equa- tion 115). Thus, there is another advantage in using In'ZDderately concentrated solutions of the pentacyano ion to fol low the decomposition reaction; the presence of small qu aIatities of oxygen, which would produce the 02-bridged s"peczies, will not interfere with the ability to observe the eQQmposition reaction beyond the first few minutes. The Q Q (CN)5H3- already present will convert any [(NC)5C002Co(CN)5 6— 51-- y..! a. . ya“ a; s, ‘ .N‘l 71 present back to Co(CN)g- by reaction 115 as long as the stoichiometric quantity of the hydrido species is greater than the amount of oxygen present. -VVe have observed a limited amount of evidence in sup- port of the postulated monomer-dimer equilibrium of Co(CN):- in aqueous solution 2Co(CN)§- -:——> (NC)5COCO(CN)§' (116) or :2 (NC)5COC0(CN)§’+ H20. (117) Co(CN)2- + Co(CN)5H203' At the start of each experiment, the 625 mu maximum shifts to Slightly lower wavelengths. The spectrum of the solid dimer in a mineral oil mull shows the peak shifted to 535 mp. (See Figure 10). For example, at 50° (shown in Figure 11), for the first experimental observation, 1.90 minutes after mixing, the peak is at 620 mu; for the second observation, 3 -50 minutes after mixing, the peak is at 622 mu. For all The shift Subs equent observations, the peak is at 625 mu. 1ng of this peak at the start of the reaction is most evi- dent for the experiments at 50° and least evident at 25° (the shift is about 2 mu). The decreasing shift indicates t hat the equilibrium in reactions 116 or 117 shifts to the t‘ i ght with increasing temperature. B - ghe Formation of Cobalt(IIIL Products from the Oxygen i%rrier , u—Dioxygentetrakis (histidinato )dicobalt (III) Zompa's106 investigation of the decomposition of the cob a”it-histidine oxygen carrier revealed several facts. k 72 .HH52 Hohsc m an _nflzovoooomAquHoM oHHmEHc Ucm HmAzovougmx msomsvm UHumEOCOE mo muuummm >5 Hmmc.vcm manflmfl> one .OH mndmflm oflw 0mm com com I ' AdEV numcmaw>m3 E I II III‘F 1| 1 ql..‘.h umEocoz HmEflQ Dom omv 00v can b PEI Pl - ih 73 \ /D \ 600 Wavelength (mu) 650 Figure 11. Enlargement of the spectra of the first three observations during the 500 kinetic experiment of the decomposition of Co(CN)§_. (Time after the start of the reaction-- A = 1.90 min; B = 3.50 min; c = 5.00 min: D = 67.0 min.) ak VII 1AM C- a: hhc ‘1 “Us ~ ‘HH 74 After very rapid absorption of one mole of oxygen gas per two moles of CoLz (L = l-histidinate anion) to form the bi- nuclear oxygen carrier, an additional mole of oxygen was absorbed per two moles of cobalt to form cobalt(III) pro— ducts. This phenomenon of some of the absorbed 02 being reversible and some irreversible had been previously observed.20 The data could be approximately fitted for the latter part of the reaction by means ofiinon-linear least squares com- puter program which assumed the following mechanism, k k 1 > 23 and B 2 A > C. (118) The experimental conditions for this preliminary investiga- tion1°°'117 were as follows: temperature 25°, pure oxygen as gas, l-histidine to cobalt ratios of 2,3,4,6,8 and 10 to 1 andCo:I = 1.21 x 10-2g; the pH was maintained at 7.0 by a phosphate buffer and the ionic strength was kept con- stant by the presence of 1g_KN03. -As the ligand to metal ratio was increased, the rate of formation of the cobalt(III) product decreased.1°6 The data from these kinetic runs of Zompa117 are shown in-Table V. The cobalt(III) product was ftnund to be a mixture of the three isomers of [CoL2]NO3.1°6:1°7 It: “Has not possible to fit the early data points to the above PrOposed mechanism (Equation 118). It was decided to extend Zompa's investigation1°6r1°7I117 t1) Cieitermine the cobalt and oxygen dependence on the forma- ti‘Drl <>f [CoL2]N03 and to improve the least squares treatment. ‘A141 13Eite studies were performed at 25°C, pH = 7.0, 75 Table V. .Data of L.-Zompa for the formation of CoL2+ from (CoL2)202 (every other data point is shown). [Co:I] = 1.2 x IO-ZQ; pure 02 as gas; 25°c. [CoL2+] x 102 éggiigigigioto 2:1 3:1 4:1 6:1 8:1 10:1 Time (min) 0 0 0 0 0 0 0 200 0.055 0.044 0.034 0.044 0.047 0.040 400 0.167 0.130 0.103 0.115 0.118 0.101 600 0.313 0.250 0.205 0.209 0.203 0.182 800 0.475 0.388 0.323 0.318 0.302 0.277 1000 0.642 0.542 0.458 0.428 0.410 0.379 1200 0.778 0.730 0.592 0.552 0.480 0.493 1400 0.896 0.871 0.715 0.668 0.641 0.605 1600 0.979 0.970 0.826 0.773 0.740 0.707 1800 1.044 1.033 0.922 0.871 0.837 0.798 2000 1.092 1.070 0.992 0.954 0.917 0.872 2200 1.123 1.094 1.040 1.016 0.978 0.934 2400 1.128 1.079 1.074 1.063 1.025 0.980 .2600 1.063 --- 1.100 1.093 1.060 1.010 2800 --- --- 1 .100 1 .117 1 .076 1 .032 3000 --- —-- 1 .034 1 .120 1 .064 1 .036 3200 --- --- --- 1 .054 --- 0 .978 h. ‘I la.» <.=‘:.'I t.- .. .r. flk 76 histidinezcobalt = 2 and in 1gLKNO3. Rate studies of type I (see Table I) were performed with pure oxygen gas, and of type III were performed with oxygen, air and 5% 02-95% N2 . The average of the data for each type of experiment per- formed are shown in Table VI. In order to obtain the best possible least squares fits between experimental and calculated concentrations of [CoLz], it was decided to include in the proposed mechanism all equilibria which occur prior to the mechanistic steps in the formation of CoL2+. The equilibria include the step- ‘wise formation of the cobalt(II) histidine complex, the stepwise protonation of the histidinate anion and the .StepMise formation of the binuclear cobalt-histidine oxygen carrier. The first two stepwise formation constants for the formation of cobalt(II) histidine complex at 25° are well 2+ - 1> CoL+ K1 = 8.3 x 106 (41) > CoL2 K2 = 3.3 x 105.(42) » The stepwise protonation constants for the histidinate alnion at 25° are also well known133:139 + KlH — _ 9 L + H < > HL KIH — 1.5 x 10 (46) K + 23 + HL + H :——> H2L K2H = 1.2 x 106 (47) K H2L+ + H+ < 3H> H3L2+ K = 6.6 x 101. (48) 10 12 14 16 18 20 22 24 26 28 77 Table VI. [Data showing the dependence of the formation of CoL2+ from (CoL2)202 on the cobalt(II) and oxygen concentration at 2:1 l—histidine to cobalt ratio at 25°C. (Every other data point shown.) II [C0L2+] x 102 000 6 .08 x 103M 12 .16 x 10‘3g Time :7 Z ,Oagas 1 ' (min) ‘ ([CoLz ] shown - Ozgas is twice actual Ozgas Air 5%02 gas [COLz ]exp) 0 0 0 0 0 0 200 0.024 0.047 0.048 0.054 0.039 400 0.065 0.131 0.156 0.148 0.100 600 0.133 0.266 0 .307 0 .278 0.203 800 0 .230 0 .459 0 .479 i 0 .446 0 .320 1000 0 .309 0 .618 0 .640 0 .590 0 .488 1200 0.383 0.766 0.753 0.708 0.559 1400 0 .432 0 .864 0 .834 0 .802 0 .681 1600 0 .464 0 .928 0 .892 0 .890 0 .788 1800 0 .482 0 .963. 0.932 0 .937 0 .885 2000 0.492 0.983 0.932 0 .965 0 .927 2200 0.499 0.999 0.961 0.971 0.976 2400 0.502 1 .003 0.965 0.997 1 .031 2600 0 .510 1.020 0 .969 1.008 1.077 2800 -—- --- 0 .964 1 .009 1 .110 78 Several mononuclear cobalt peroxo complexes are known.5°' 132'14°’142 An investigation of the rapid reversible uptake of oxygen by bis(l-histidinato)cobalt(II) shows that the oxygen uptake is a two-step process K C0142 + 02 743—) COL202 (44) K4b CoLzoz + CoL2 T———> L2C002COL2 (45) with an overall formation constant for the binuclear oxygen carrier, .K4avK4b = 7.2 x 106 at 25°.59 A recent investiga- tion showed that the two-step formation of the oxygen carrier also occurs for the cobalt(II) complexes of diethylenetri- amine, histamine, ethylenediamine and 2—aminomethylpyridine.143 The dependence of the formation of CoL2+ on the histi- dine concentration has been described earlier and can be Seen from Table V. As the histidine to cobalt ratio increases, the ratio of fomration of CoL2+ decreases slightly. :The 315'C0L3+ on the cobalt(II) concentration is slightly less tflnan first order. As stated earlier, one mole of 02 is Iwipidly and reversibly absorbed per two moles of CoLz and 79 a second mole of 02 is slowly and irreversibly absorbed per two moles of CoL2+. Any proposed mechanism would have to include equations 41, 42 and 44-48 and would have to explain the histidine, cobalt and oxygen dependencies on the rate of formation of the CoL2+ as well as the stoichiometry and nature of the oxygen uptake. .Since there was some preliminary evidence for the de- pendence of the rate of formation of CoL2+ on [CoL2+], ex- periments of types I and II (see Table I) were performed in 'which pure oxygen was used as the gas and the results are tabulated in columns 1 to 3 of Table VII. The underlined 09309 no 885900 0 ; m N H 909552.:85900 . NORA NnHOUv MO 80909momfioom© may :9 +mqoo no 095008 U9umamumo 0:» mo HHOQQSm :9 0009. .HHH> 09909 82 increases to the rate of the solution which had 6.08 x 10-1! CoLz+ added initially (compare columns 3 and 4). The above data confirm that [CoL2+] does indeed have a catalytic ef— fect on the rate of formation of CoL2+ from the oxygen car- rier. Since the rate of formation of CoL2+ depends both on the concentration of cobalt(II) species present and on the [CoL2+], two steps are postulated; one step depends upon [CoLz] or [(CoL2)202] and the other depends upon [C0L2+] k. + _ (CoL2)202 a> CoL2 + CoL2 + 02 (49) or k. ,, + CoL202 + CoL2 a > CoL2 + CoLz + 02- (50) and + k5b + - CoL202 + CoL2 > 2C0L2 + 02 . (51) It was originally thought that the C0L202 shown above iind.in the formation of the binuclear oxygen carrier (equa- 1zions 44 and 45) might be CoIIL202 and the initial product <3f equations 49 to 51 might be COIIILZOZ- which then would taither rapidly or at a measurable rate decompose to CoL2 and 02—. However, a recent esr study of some stable mono- rluolear cobalt 02 adducts has shown that they contain only CNne unpaired electron which spends most of its time on the Cutygen atoms and therefore the adducts should be formulated 3‘3 (CoIIIXm02-).142 Thus, the mononuclear CoL202 is prob— a1>ly cobalt(III) and superoxide rather than CoIILzoz and tharefore, CoL2+ and 02- would have to be formed directly by equations 49 to 51. 83 The most likely reason for the dependence of the rate of formation of CoL2+ on histidine is the following reaction: K3 _ > CoL3 . (43) < C0142 + L- Although a species such as CoL3- would not be favored sterically, this author feels that this is more likely than a dissociation reaction such as (COL2)202 __—'> L2C003L+ + L (119) <— as the dissociation of the L_ from the oxygen carrier would involve the breakage of two strong bonds, the cobalt imidazole and cobalt amine bonds, (the cobalt carboxylate bonds having been previously broken during the formation of the oxygen carrier), whereas only one fairly weak cobalt carboxylate bond in CoL2 would have to break to allow the formation of CoL3-. Preliminary attempts to fit the experimental data of Zompa117 (see Table V) show that the equilibrium constant for the postulated formation of CoL3_ is equal to or less than 1.4 x 10‘. Considering the steric difficulty in form- ing CoL3-, a value of 1.4 x 104 for the third stepwise cobalt-histidine formation constant is a little higher than expected but it is believable. A typical set of calculated and experimental data based on K3 = 1.4 x 104 is shown in Table IX. A value for K3 of equal to or less than 1.4 x 104 will only affect the calculated data for histidine to cobalt 84 NvMuo mum.o mov.o 090.0 mbv.o wmv.o 500.0 wmv.o m9®.o Nvm.o 090.0 N0®.o OOOH mmw.o bbN.o NwN.o Nom.o mmm.o w9m.o 0mm.o mmm.o wN0.o mwm.o mmv.o 050.0 oom 009.0 Nw9.o Nw9.o mom.o ¢HN.O ooN.o HmN.o mON.o NbN.o omm.o mbN.o mHm.o ooo mmo.o 909.0 009.0 099.0 0N9.o 099.0 009.0 m0990 909.0 OMH.o mmH.o 809.0 oov wmo.o 000.0 000.0 800.0 Hmo.o 000.0 mmo.o 0mo.o moo.o 00o.o moo.o 000.0 oom 9GHEV 0899 0900. mxm 0900. mxm 0900 mxm 0900 mxm 0900. mxm 0900 mxm 9no9 9am 9am 9nw 9am. Hum 000 0000 080 09009 090900 mo9 x 9+n900H 00 0:9090m9m A.VOH N V.H H «M .mmm mm «0 QHSQ .O H 000 . IOH X HHN.H fl 000v 999 a HH .vo9 x 0.9 “.mm 03000 0030 90090500 00:00:0m00 0:9090m9z N.99m.0n.u.EON coma 0000Qv 0000 900C0E9H0mx0 0:0 0000950900 no 000 9009mm0 0 .NH 09908 85 ratios of greater than 2:1 (see Table X). This is expected since with a histidine to cobalt ratio of 221, there should be only a negligible concentration of CoL3-. After the solutions are quenched, there is a slow at- tack on the solutions by the acid quench as shown in Figure 12. A quench with HCl compared to the HN03 yielded the same rate of acid attack. Therefore the H+ is the species that is causing the attack and not the oxidizing ability of the nitrate. Since the rate of the acid attack decreases rapid- ly with time, all spectrophotometer readings were taken 25 minutes after quench when the rate of the acid attack is slow. The value used for the molar absorptivity of (C0L2)N03 synthesized by oxygenating aqueous CoLz, (e = 125.1), in- cludes a correction for the 25 minute acid attack before taking the spectrophotometer reading. The initial reversible absorption of one mole of 02 per two moles of CoL2 results from the almost quantitative initial formation of (C0L2)202 by reactions 44 and 45. The slow irreversible absorption of the additional mole of 02 per two moles of CoLz results from the shifting of the equilibrium of reactions 44 and 45 toward the CoL202 as a result of the depletion of CoL202 resulting from reactions 49 to 51. A preliminary calculation showed that if the value of K ' K is kept constant at 7.2 x 106, one can change the 4a 4b value K from 7.2 to 7.2 x 10'10 and by making aPPIOPri- 4a ate changes in k5a and k5b (see Tables XI and XII) one can obtain the identical set of calculated values for 86 000.0 050.0 000.0 050.0 050.0 950.0 500.0 950.0 090.0 050.0 090.0 000.0 0009 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 500.0 000.0 000.0 000 009.0 500.0 009.0 500.0 090.0 500.0 900.0 000.0 050.0 000.0 050.0 050.0 000 000.0 009.0 0o9.o 009.0 009.0 009.0 009.0 009.0 909.0 009.0 009.0 009.0 oo0 000.0 000.0 000.0 000.0 900.0 000.0 000.0 000.0 000.0 500.0 000.0 000.0 000 AC9EVI0E9B m < m < m 4 m < m fl m 9.09 9.0 9.0 9.0 9.m 9.m 00010000 080 09009 090900 009 x 9+a9009 00 059090090 9009 x 00.9 n 09 s o n" m 9 m N 9 O 9 o O 09 m o 9 M 09 9 00 00 0 095m 0 99900 NI09 x 990 9 HHOUV .0 9090 9000090 no 009009 90008 00 050099 900 >950 09009+0900_ 0009090 0909009095090 909 x 0.9 H.nM mo 0590> 0 0090 3090 O0 9 H mm 9093 0000950900 0000 050 NH 09909.8099 0000 0000950900 090 90 5009900800 0 .X 09909 87 100009 1000 Time (min.) 100 10a“ 1 1 1 IUZ ' 1E3 ' ° Absorbance ' Figure 12. Plot of absorbance versus time of the quenched solutions which shows the acid attack on these quenched solutions. 88 [CoL2+]. By varying K4a from 7.2 x 103 to 7.2 and making the appropriate changes in ksa and k one can obtain 5b' similar sets of calculated values for [CoL2+]. -Examples of this can be seen in Table XI for the mechanism based on reaction 49 and in Table XII for the mechanism based on equation 50. 'Therefore, it may not be possible to calculate optimum values for K4a and K4b by the least squares procedure. In this case the values for ksa or kga and ksb ob— tained by the least squares procedure would be related to the values of K4 and K4 as shown in Tables XI and XII. a b The least squares values for [CoL2+] for each of the proposed mechanisms and the experimental values for [CoL2+] for the 5% 02 rate study runs are shown in Figures 13 and ‘. 14. As can be seen from Figures 13 and 14, the agreement between calculated and experimental values of [CoL2+] is not too good. From the results shown in Figures 12 and 13, it can be seen that either the reaction mechanism must be incor— rect or there must be something additionally occurring in the reaction. Other mechanisms including the following steps were found to be far less satisfactory (C0L2)202 + 02 > C0L2+ + CoL202 + 02' (120) > (COL2)202+ . (121) < + COL202 + COL2 Equations such as (120) are unsatisfactory as they predict 89 Table XI. Values of ksa and k5b which result in almost identical sets of values of [CoLz ]calc for the mechanism including equation 49. (K1 = 8.316 x 106, K2 = 3.311 x 105, x3 = 1.40 x 104) K4a K4b k5a k5b 7.2 x 103 1.0 x 103 1.11 x 10"3 2.79 x 10"1 7.2 x 102 1.0 x 104 1.11 x 10"3 1.83 7.2 x 101 1.0 x 105 1.11 x 10'3 1.74 x 101 7.2 1.0 x 106 1.11 x 10'3 1.73 x 102 7.2 x 10"1 1.0 x 107 1.11 x 10'3 1.73 x 103 7.2 x 10"2 1.0 x 108 1.11 x 10‘3 1.73 x 104 7.2 x 10"3 1.0 x 109 1.11 x 10'3 1.73 x 105 7.2 x 10"4 1.0 x 1010 1.11 x 10"3 1.73 x 106 7.2 x 10"5 1.0 x 1011 1.11 x 10"3 1.73 x 107 7.2 x 10“6 1.0 x 1012 1.11 x 10"3 1.73 x 108 7.2 x 10'7 1.0 x 1013 1.11 x 10‘3 1.73 x 109 7.2 x 10'8 1.0 x 1014 1.11 x 10'3 1.73 x 1010 7.2 x 10'9 1.0 x 1015 1.11 x 10’3 1.73 x 1011 7.2 x 10‘10 1.0 x 1016 1.11 x 10‘3 1.73 x 1012 Table XII. Values of kga' and k 5 which result in almost identical sets of values of [CoL2+] for the mechanism including equation 50. calc (x1 = 8.316 x 106, K2 = 3.311 x 106, K3 = 1.40 x 104) K4a 4b k5b 7.2 x 103 1.0 x 103 1.45 1.13 x 10’1 7.2 x 102 1.0 104 1.45 101 2.19 x 10'1 7.2 x 101 1.0 105 1.45 102 1.30 7.2 1.0 106 1.45 103 1.21 x 101 7.2 x 10‘ 1.0 107 1.45 104 1.21 x 102 7.2 x 10"2 1.0 108 1.45 105 1.21 x 103 7.2 x 10‘3 1.0 109 1.45 106 1.21 x 104 7.2 x 10' 1.0 1010 1.45 107 1.21 x 105 7.2 x 10' 1.0 1011 1.45 108 1.21 x 106 7.2 x 10' 1.0 1012 1.45 109 1.21 x 107 7.2 x 10’ 1.0 1013 1.45 1010 1.21 x 108 7.2 x 10'8 1.0 1014 1.45 1011 1.21 x 109 7.2 x 10’ 1.0 1015 1.45 1012 1.21 x 1010 7.2 x 10'10 1.0 1016 1.45 1013 1.21 x 1011 91 .mmuoa x m n HH”woo .mmuofi x o u Hmoo .o .o n HHmoo .amuofi x o u Hmoo .m .mm@ «0 Km .vm.m n max .muoH x 8H.H n max .moH x vs.m u 9.x Hog x mm.“ u 8.x .30H x v.H u as .noH x Hm.m u «x .80H x mm.w u as. .mv cofiumsvm mcflosaocfl Emfismnomfi man How mEHu.mmmmmw oamo~+mqoua mo modam> moumsqm ummma cam H+NAOUH mo mmDHm> Hmucmeflummxm mo uoam .mH wusmflm 92 .mfi musmflm ACHEV mEHB OOOH com com oov CON IIP IP‘ IJIIPiw llPi, , L531? mxm Iw «OH x N H+ .Hoou 93 amm-oH x m u coo ammuofi x m u coo .o HHH HH .o u HHmou :fimloa x o n Hmou .m‘ .c n HHmoo ..amnofl 8 NH u Hmoo .« .mmm No em .HuoH x mo.m u aux .mH.m n mmx .mOfi x mm.H u n48 m .moH x mm.m H vs .aoH x w.H u as .moa x H«.« n as .moH x mm.w u as oamo .om soflumsvm mQHUSHocH Emflcmnomfi map How mfiflu m9mum> ~+aqoua mo mmsHm> moumsvm ummma Ucm H+uqooa mo modamv Hmucmfiflummxm no uon .vH madman 94 .VH musmflm ACHEV.mEflB oooH com com cow com «OH X _ «soul + mxm m oamo 95 a far greater oxygen dependence on the rate of formation of CoLz+ than is found experimentallyf The addition of equation 121 to the mechanism yields no change in the shape of the graph of [COL2+]calc versus time. There are several unexpected results which are probably related to the influence of the oxygen on the decomposition of the binuclear cobalt-histidine oxygen carrier. These results can be used to explain the lack of agreement between the calculated and experimental curves in Figures 12 and 13. These unexpected results as described below are evidence for the presence of an additional oxygen oxidation reaction. Since the additional oxidation was suspected, only the data from the experiments performed with 5% 02 were used in the least squares procedure. As the reaction proceeds, there is a small downward shift of the spectral peak at 500 mu to about 485 mu. vThis downward shift occurs at different rates for the oxygen, air and 5% 02 gases. The molar absorptivity at 500 mu of a mixture of the three isomers of (CoL2)N03 (prepared and purified as de- scribed in the Experimental section) is 84; the separated isomers have molar absorptivities at 500 mu of approximately 100, 40 and 34.107 However, the molar absorptivity of a solution of (CoL2)NO3, produced by bubbling air for several days through a solution containing a known number of moles of CoLz and then diluting with water to a known total volume, is reported to be 115.1117 and 125.1 by this author. The 96 absorbance of oxygenated solutions of CoLz is always greater than the absorbance of pure (CoL2)NO3. Studies of the oxygen uptake of CoLz solutions show that initially more than one mole of 02 per two moles of CoLz is absorbed (about 1.14 to 1.32 moles of 02 per two moles of CoLzloa). In addition, Csaszar, Kiss and Beck144 found the presence of traces of unidentifiable organic residues after the oxygenation of CoLz is complete and they suggest the most probable cause as the oxidation of histidine by oxygen. To determine if the oxygen could attack the final product, (CoL2)NO3, a solution of 6.08 x 10-3§_(C0L2)N03 was oxygenated for 900 minutes. The absorbance of this solution varied irregularly (within experimental error) from 0.501 to 0.509 (initial absorbance = 0.508, final absorbance = 0.505) and indicated that the oxygen does not attack the final product. Since it is also possible for the initial oxygen up- take in excess of one mole of 02 per two moles of Cosz to be due to the formation of CoL202, a calculation (as described in the Theoretical section, Part H) was performed to estimate K43, K4b and moles of 02 absorbed per two moles of CoL2+. -The calculation is based on the knowledge that K4a - K4 = 7.2 x 106 and on the assumption of various b values for the percentage of total cobalt that is (CoL2)202 (before any decomposition of the oxygen carrier). The re- sults of this calculation are shown in Table XIII. .Since it is not possible to confirm spectrophotometrically 0f chemically the presence of CoL20259 and since, in the 97 .Rm.vm usonm ma «Oaflnqoov mm uHono mo wmmucmonmm manflmmom ESEAme one um.H «OH x mv.m «OH x H©.b Hv.m mwm.o oo.m on mN.H non x mm.H moH x vm.m ®H.v mv®.o om.m om wH.H «OH x mo.m «OH x o¢.m Hm.N vmm.o om.v on wo.H noH x om.m moH x mw.H m®.H «$5.0 ow.¢ ow sm.o voH x vo.fi «as x ov.v Hv.o smu.o ow.m‘ om no.0 noH x H HOH x w no.o mow.o #m.m vm WHoom Av ma 8 a - a - a a .- «OaAuqoov mm Hmm Umnuomnm K x H 0 nova qooa 0 A00 H saamfluflcu No r, H ,. H A v_c 00 mo & cmssmmm nu/\ EMOHX v v moflxm.sugx.mx .AUomN umv mmm NO musm Ucm.flnloH x N.H n WHOU How AHMflUflCHV Hmumwoom mom Umnuomnm madmauflcfi NO mo mmHOE mo Hogans mo coaumasoamo .HHHN magma 98 kinetics of the formation of (CoL2)202, the steady state approximation for CoLzoz appears to be valid,59 it is highly unlikely that more than 10% of the total cobalt is in the form of CoL202 immediately after oxygenation. By looking at Table XIII, one can see that the maximum 02 absorbed per II t is about 1.07. Therefore, the presence of CoL202 cannot 2 Co that can be accounted for by the presence of CoL202 be used to explain the unexpectedly high experimental value for the initial 02 absorption. The shape of the graph of the apparent rate of forma- tion of CoL2+ (assuming 6500 = 125.1) changes markedly as the gas bubbled into the solution is varied from oxygen to air to 5% 02—95% N2 (see Figure 15). When pure oxygen is the gas, the apparent [Cosz] begins to decrease after ap- proximately 2500 minutes from the start of the reaction. With air as the gas, the apparent [CoL2+] appears to decrease after about 3000 minutes whereas with 5% 02, the apparent [CoL2+] continues to increase. The above phenomena strongly suggest that there is an oxygen attack on some species in the reacting solutions. The absorbance of the solutions are initially increased by the oxygen attack which causes the increase in the 6500 from 87 to 125. Whereas oxygen rapidly attacks solutions of lycine and 2+ Co , as evidenced by C02 evolution, oxygen does not attack 2 145 . . . . lycine without the Co +. This suggests that histidine is not attacked by 02 unless Co2+ is present. Therefore, Absorbance at 500 mu Figure 15. 99 1.04 B 0.8-l 0.2 I ' fl 5'0 1000 1500 2000 2500 Time (min) Absorbance versus time of cobalt—histidine solu— tions oxygenated with various gases, CogI = 1.2 x 10_2g, A = pure 02 gas, B = air, 0 = 95% N2 — 5% 02. 100 the oxygen must attack one or more of the following: éoL+, CoLz, CoL3_, CoL202, (CoL2)202. ~The product of the oxygen attack was originally thought to be a cobalt amine complex. .However, this was not likely since over 90% of the cobalt at the end of the reaction is recoverable as CoL2N03.117 Upon separation of the three isomers of CoL2N03 by ion exchange, there is only a small quantity of yellow to brown residue which remains on the ion exchange column‘.117 Since only a small quantity of the oxidation product is formed, it must have an absorptivity, 6500, of several hundred to be able to raise the net molar absorptivity of the solution from 84 to 125. There are no known simple cobalt(II) or cobalt(III) complexes which have a large enough molar absorptivity in the visible region to cause the increase in the absorbance of the solution. ~There is some evidence for the formation of traces of the superoxo cobalt ammine complex upon oxygenation of aqueous ammoniacal cobalt(II) solutions.146 From the esr and visible spectra of oxygenated aqueous solutions of Coz+ and excess cyanide, it has been shown that the superoxo co- balt cyanide oxygen carrier is formed in one to two percent yield.36v68 The recently isolated superoxo cobalt histidine complex has been shown to be stable even in strongly acidic solutions.37 This superoxo complex has a broad peak at 477 mu (€477 = 502, €500_= 498) and another broad peak at 677 mu (6 = 601).147 101 A solution containing 1.2 x 10-2§LC0L2 was oxygenated with a 5% 02 - 95% N2 gas mixture for several days. -Spectra of the solutions (see Figures 16 to 19) show that with in- creasing time, there is an increase in the absorption in the region of 477 and 677 mu and the peak at 500 mu gradu- ally shifts to 482 mu. This is strong evidence for the presence of the superoxo complex. The solutions were quenched with both HCl and HNO3. The spectra of both quenched solu- tions were identical which proves that the HN03 is not causing the oxidation. The absorbance due to the superoxo complex is greater with water rather than acid quench (see Figure 19) and indicates that the acid does slowly decompose the superoxo complex. »This explains the slow rate of de- crease in the absorbance after the solutions are quenched (see Figure 12). An experiment to attempt to observe the known esr spec- trum of the superoxo complex did not succeed due to the low concentration of the superoxo complex and the presence of trace paramagnetic impurities in the quartz and Pyrex tubing used for the sample tubes. ~There did appear to be a small signal from the sample in the quartz tube. »At the high gain necessary to observe this signal, the noise level is high and the signal from the impurities in the quartz is high which makes it impossible to ascertain if the signal is from the superoxo complex. -Therefore, the additional reac- tion which causes the poor correlation between the least squares calculation and the experiment is 102 89.2308 omflflsm 3.3 x «A .n .Hom.fiv mo HE H.3uH3 omnocmsv asp m mm 06mm .0 .mCHQUcmsv Hmumm . N .I o .l C an I: mmuscHE mm Ammo O Rm SuIOH x N H I H 00v 023 2v mo HE H nuHB Umzocmsw Ucm CHE oow How pmumcm mxo mHmEmm HE m .m .msHHmmmm .4 .mozANHOUV mo mcoHusHom mo muuommm 0HQHmH> .mH musmHm 103 00h onm 000 (P k 7 (P ABEV Sumcwam>m3 omm iblw oom .mH wusmflm omv ”I; U .m J. v.0 aoueqxosqv 104 $021.88 8333.1 at: x «A .o .rowsv Hmumm muscHE H .Ammm NO Rm xfinloH x N.H n HWOUV .mozm.mv «0 HS H zqu Umnocmsv cam CHE mmmH How pmumammwxo mHmEmm mo HE m .m .mGHHmmmm .< .mozAuqouv mo mCOHuSHOm mo muuommm mHQHmH> 1;? , “wi‘ .bH musmHm 105 con i FTF omw Ajav numcmHm>m3 cow can .I D com .hH musmHm onv rlu eoueqxosqv w.o N.H 106 .socwsv Hmumm muscHE H .Ammm No Rm aflnloH x N.H u Hwoov .mozm.fiv mo HE H nuH3 omnocmsv pom CHE comm Mom omumcmmwxo mHmEmm mo HE m .0 . moi 303 B09393 w. ~-oH x N.H .m .wcHHmmmm .4 .mozAuqouv mo mGOHusHOm mo muuommm mHQHmH> .wH wusmHm 107 CON com I cow b Afiev numcmHm>mz can b) com. I .mH mHDmHm omv D F ”I O r 00 o uN.H eoueqxosqv 108 .UHum mo HE H mo ommumcH coopm umum3 no He H .pmnocmdwss pan 0 mm 080m. .m .HUm.m« mo HE H nuHB Umnocmsv usn 0 mm 080m .9 .Socmsv Hmuwm muscHE H .Ammm NO Rm zfiulOH x N.H u Hmoov .mozm.fl¢ mo HE H nuH3 Umnocmsv cam :HE comm Hem Umumcmmmxo mHmEmm mo H8 0 .U .mozxuqouv @3339 $8-3 x «J .m .mcHHmmmm .< .mozfiaqouv Mo mCOHusHOm mo muuowmm mHQHmH> 1.... . 0...! .mH mHDmHm 109 Ajev numstm>03 com in) own # Com .mH mHSmHm ~ eoquIosqv 110 (COL2)202 + 02 > (COL2)202+ + 02-. (122) At long reaction times, especially with pure 02 as gas, there probably is a further oxidation which fragments the histidine. .This would explain the decrease in the absorbance, after about 2400 minutes,of the solutions oxygenated by pure oxygen, the presence of unidentifiable organic residues as found by Csaszar, Kiss and Beck,144 and the traces of yellow to brown residue as found by Zompa.117 Both proposed mechanisms (including either equation 49 or 50) appeafi‘to be about equally as good at predicting + calculated values for [CoLz ]. (The values for K , K4 4a b' I 5a resulting from the least squares pro- b cedure are probably order of magnitude values. Additional experiments must be performed in which the solutions are quenched for several days to destroy any superoxo cobalt-histidine complex and also experiments which include measuring of the absorbance at 677 mu ( by using 5 cm cells) to estimate the concentration of the superoxo complex so that corrections can be made for the presence and the absorbance at 500 mu of the superoxo complex. There is the possibility that the apparent catalytic . + . . . . actiV1ty of CoLz (as shown in equation 51) is due instead to the following reaction: + + COL202 + COL2 > (COL2)202 . (123) 111 If equation 123 rather than equation 122 is the major source of fOrmation of the superoxo complex, (CoL2)202+, then an increase in [CoL2+] will result in an increase in the rate of formation of (CoL2)202+ which will increase the absorbance of the solution at 500 mu. 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By defining the following terms: E1 = 2/7753 - 4ac (124) E2 = :PBl (125) a'Jb2 - 4ac T1n = Zeb/B2 - B3 CogII - B1) + b -'J‘b2 - 4ac(126) Tld = 2c(~/ 132 - B3 c6311 - B1) + b +~/_b2 - 4ac (127) Tzn = ((8; - B3 Co},II - B1)2 (128) 12d = c(~/Bz-83CC(I,II - B1)2+ b(J;2-B3CC§II - B1)+a (129) Tan = 2c(~/;2-B3 CoIII -Bl)+b- W (130) Tad = Zoo/82-83 CoIII -Bl)+b+uf5;:Z§E (131) '1'4n = (f8. - B3 COIII - 131)2 -- (132) 2 T4d = Cde‘BaCOIII “B1) +b(JB2‘BaCOIII -B1) ‘1“ 3(133) E3 = Bl/a ' (134) and substituting these terms into equation 78, one obtains: 120 121 t = (E1 + Ea)log (g?) + E3log T—7—— E‘J—Z—T—fi). (135) - 3n 3d) - For simplicity, the following terms are defined: f(z r ) = f(cCIII K K K K K k or k' k ) (136) i I 1: 2! 3! 4a! 4b, 5a 53 1 5b ‘ and Bri is the derivative with reSpect to one of the vari- ables of equation 135. By substituting equation 135 into equation 136, T1nT3d) Tan: f(Zri) = (E1+E2)log T T )+ E3 log . (137) 16. an TTzd 4n - The generalized partial derivative of equation 137 is in 3d 315(31‘1)§[loga(T—_M1d:+3n]]m:(__f_1n'r3dar>16(EfiE2) 5 n = (E1+Ez) r.'I'T1d3 1 Blog(:r:: :ij+ Eaaal: T 10925“ T4d 5E3 at . Tsz4n r1 5?‘ -.—- (...) For all r., i %§7-= 0. (139) 1 5 lo _ 11. Since 5___9_X. - y 3x , one obtains T T a( 1n 3d) af(2ri) (81+32)T1dT3n Tld'r3 n 3d:1nT 332 5r. = T T Bri + log 1 1n 3d 5(12n1:i) + E3T2dT4n Tsz + lo T2nT4d 5E3 (140) T2 nT4d 3r 9 T Sri ° ‘ i Tad 4n 122 Two of the above terms can be expanded as follows: TinTad) 8T3d aTin aTan all‘1d B T T T1dT3n Tin 5r. +T3d .Br. -T1nT3d T1d 5r. I3n 5r. 1d_§n _ - 1 1 1 1 Br. — 2 2 1 T1d T3n (141) T T BT BT BT BT ._££_1Q 4d 2n _ 4n 2d B T T Tsz4n(T2n Br. +T4d Br. TznT4d (Tzd Br. J:4n Br. 2d 4n = 1 . 1 1 1 ' 2 2 ari Tzd T4n (142) The generalized derivatives of the variables from equations 124 to 134 are as follows: Bc Ba §b_ B81 4a Br. + 4C Br. 2b Br. _ 1 1 1 3?.- - 4 3) (143) 1 (b2 - 4ac) 2 ' 4210—35 -4a—§f: -..—3;) bB1 1 1 1 +m55 ——-§: BEZ b2 - 4ac i Eri a2(b2 - 4ac) (144) b 381 + B 5b Br. 1 Br. _ 1 1 anY*- 4ac BT BB. BB 1 1 2 1 BC Bb 3le = 2°(ar— 3? ‘ Br.>+ “432 ‘ Bi) 5* a? ’B2 1 1 1 1 1 Bb Bc Ba _ 2b 5——-— 4a 5- - 4C'_—— (145) Nb2 - 4ac ri J:1 Brl) BT BB BB 1d 1 2 1 5c 8b - 20 3— "” 2(‘JB '3 ) + ri (2J3; 5r; ri‘ 2 1 5r; 5r; B B B (146) 1 b c a - + (2b -— -4a -4c ) b -4ac 6ri arl arl B BB BB 5?;— " 29’32 - 31>(2fi32 Bri Br— (14") BT BB BB 2d 1 2 1 5c BF:=2°(2,-—BZB?1‘BT; + “Ba-BIVBT; + (148) ri (149) - m; 20 3: 3: -—§: b‘ -4ac i 1 1. Brad = 2C 1 B32 ‘33 acOIII -CoIII B33) - B31 5Ii ZJBz—33COIII 5r1 5r1 Bri Bri III Bc Bb 1 Bb Bc + 2( Bz-B3CO -B1)——— + + 2b -4a . ar- ari m M .5ri ‘BT4n B?’=2° 1 BT i For the non-linear least squares calculation, (JBz-BscOIII-Bl) fid— =2C(JBz 'B3COIII-Bl) derivatives with respect to can be obtained from the folldwing derivatives: B31 = o 5K4b BB1 B(k BB1 5k 1 = O or k' ) 5a 5a 5b ~ 1 BB2 _ B 8C0III _COIIIBB3 Sri 3 Eri Sri 531 2r—---III ' r. L B2 ‘B3CO 1J (151) P 1 BB2 _B 5C0III -c IIIBB3 Bri 35ri Sri 5B1 BIE;:§;EBIII sriJ ' a a 32 _B BcOIII _COIII B3 5r. 35r. 5r. BB1 +b 1 i 1 _ I ZJBz-BchIII ri +'§%I (152) .1. (153) the 1 III K4b' k5a or k5a , ksb and Co (154) (155) (156) 125 l O BCoIII g1 NH (157) (158) (159) (160) (161) (162) (163) (164) (165) (166) (167) (168) (169) (170) 126 Bb _ 1 BT61"— ' 2K (171) 5a“ 4b . Bb 1 ( 1 1 - = - -—————1r1r'+ + 1 + K [L ] 5ksb 2K4b KleiL 1 Kth 1 3 (172) + K4a[02]) - iii—III = o (173) Co . k 51‘: = 5b 2 (174) 4b 4K4b . 8c _ B(k5a or k;‘ ) - 0 (175) 176) 5k5b 4K4b ‘ 8c _ —BCBIII — o (177) III g%°— = o (178) 4b . III 5C0 51k or k' ) = O (179) . 5a 5a . Bc'oIII = o (180) Skfib ‘ III §C_Oi_fi_ = 1 . (181) 5C0 7 For the mechanism including equation 49 k %E___= 5b 1 _ + 1 :_ + 1 +K3fL-1 + K4a[02{) (182) 4b 21(4):)2 K1K3[L] K2[L] ~ and for the mechanism including equation 50 instead of equation 49 127 y 1 1 - k5b(l(.1K"2—[L"]2+ K2[L-] + 1+K3[L ]+K4a[02]) -k5a V 5§_—'= »2 4b 2K4b (183) By substituting equations 154 to 183 into equations 143 to 153, then substituting the results into equations 141 and 142 and finally substituting the results into equation 140, one obtains all the necessary derivatives of the type df(2 ri) 3r. ° 1 To obtain the final derivatives required for the least squares calculation, the term qi is defined as ri except that CoIII is not included (see equation 136). Q The final derivatives are 3f(2ri) III Sq. 3C0 . (184) a i qu BfTZri) 8C0III Thus, the final derivatives are obtained by substi- tuting equations 140 into equation 184. B. Derivative for thefigigand Concentration Calculations By substituting equation 65 into 84, one obtains III -Bl+~JBz-Baco 2 I _ 1 2E + (-B1+ V BZ "B3COIII) n 2 f(L—) = Ba -B3 + (n-2)COIII - [L-IAH’z o. (185) To be able to calculate the [L-] by the Newton method, it is necessary to obtain bf[L-]/d[L-] which is as follows: 128 Bf[L'] ‘31“ B2 ‘BaCOIH 2n n-1 BIL‘] = 33 (2) (“'3)K3'__‘ K1K2[L-]3 K2[L-]é I 2_._ + __1._ - _ 2 _ _1_ KK1K2IL‘13 Kalli]2 K") B‘ K3 K1K2IL‘13 I<2[L‘]2 + E + 4K4aK4b[02] 4K4aK4b[02]~/WIII r——III 2 F— 2 1 - - - -- +—-—:— - - AH . 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