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A kinetic study of the catalytic activation of molecular hydrogen by silver amine complexes Milne, John Buchanan 1960

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A KINETIC STUDY GF THE CATALYTIC ACTIVATION OF MOLECULAR HYDROGEN BY SILVER AMINE COMPLEXES by JOHN BUCHANAN MILNE B. A., University of British Columbia, 1956 A THESIS SUBMITTED IN PfiRTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, I960 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 3 , Canada. ABSTRACT (i i ) The kinetics of the reduction of silver amine complexes in aqueous solutions were investigated and found to be second order overall, the rate being proportional to silver complex and hydrogen concentrations. These systems were studied under conditions of essentially complete complexing and therefore the rates were independent of amine concentration. The rates were also shown to be independent of amine perchlorate concentration and thus of pH within a limited range. Enthalpies and entropies of activation were determined for each system and an attempt was made to correlate kinetic data with information on complex stability constants and amine basicities. The most prominent trend in the results was the inverse dependence of rate on complex stability constant. Two mechanisms are proposed both involving heterolytic cleavage of the hydrogen molecule. In the f i r s t mechanism, the proton released in the rate determining step is taken up by the basic ligand directly. In the second mechanism, a water molecule replaces the amine ligand and acts as the proton acceptor. The strength of the silver-ligand bond and the difficulty of ligand replacement by water account for the inverse dependence of rate on complex stability for each mechanism respec-tively. Arguments are presented to support both mechanisms. In general dibasic amine complexes activated hydrogen more readily and displayed a more negative entropy of activation than do the monoamine complexes. These observations are attributed to the presence of a free basic group in the ligand aiding the cleavage of the hydrogen molecule in the rate determining step. The proximity of the second basic group to the central silver atom also appears to be important. These effects and the possible role of the free basic group in the ligand are discussed,, ACKNOWLEDGEMENTS The author wishes to express his gratitude for the advice, help and encouragement given by Dr. J. Halpern for his inspiring direction of the research reported in this thesis. The author also wishes to express his appreciation to Dr. W. A. Bryce for his constructive criticism of the manuscript during its preparation. (iv) TABLE OF CONTENTS Page INTRODUCTION 1 Heterogeneous Catalysis 1 Homogeneous Catalysis 3 EXPERIMENTAL 10 Materials 10 Analysis 10 Procedure 11 RESULTS AND DISCUSSION H CONCLUSION 38 REFERENCES 41 (v) TABLES Table No. Title Page I EFFECT OF COMPLEXING ON ACTIVITY 9 II RATES OF REACTION WITH SILVER -TERTIARY DIAMINE COMPLEXES 20 III RATES OF REACTION WITH SILVER - DIAMINE COMPLEXES 21 IV RATES OF REACTION WITH SILVER - SIMPLE MONOAMINE COMPLEXES 22 V RATES OF REACTION WITH SILVER - AMINOACID COMPLEXES 24 VI RATES OF REACTION WITH MISCELLANEOUS SILVER COMPLEXES 25 VII SUMMARY OF KINETIC DATA, STABILITY CONSTANTS AND BASICITIES 31 VIII RELATIONSHIP BETWEEN RATE OF ACTIVATION AND A FUNCTION OF AMINE BASICITY JND COMPLEX STABILITY 33 (vi) FIGURES Figure No. Title 1 Apparatus for Experiments from 50° C, to 85° C. at Atmospheric Pressure 13 2 Typical Rate Plots for the Reduction of Silver Complexes of Methyl-, Ethyl-, Propylamine, Ethylenediamine and 1,3-Diaminopropane 15 3 Typical Rate Plots for the Reduction of Silver Complexes of N,N-Dimethylethylenediamine, N,N'-Dimethylpiperazine, Piperazine, Triethylenediamine and N,N,N«,N'-Tetra-methylethylenediamine 16 U Typical Rate Plots for the Reduction of Silver Complexes of Triethylamine, Triethanolamine and Diethylamine 17 5 Typical Rate Plots for the Reduction ofSilver Complexes of Pyridine and Ammonia 18 6 Typical Rate Plots for the Reduction of Silver Complexes of Aminoacids 19 7 Dependence of Rate on Hydrogen Partial Pressure at 65° C. for N,N-Dimethylethylenediamine Complex 27 8 Dependence of Rate on Hydrogen Partial Pressure at 70° C. for Ethylenediamine Complex 28 1 INTRODUCTION Molecular hydrogen is a relatively inert substance as indicated by the high endothermicity of i t s uncatalysed reactions. The chain ini t -iating step for the hydrogenation of ethylene; H 2 + C 2H 4 >- H + C 2H 5 has an activation energy of 60-70 ke&U/nole (l), (2) # The unreactive nature of this molecule has been attributed to the high bond energy of 103 kcal./mole and closed shell electronic configuration. However, on the sur-face of a catalyst an alternative reaction path requiring less energy i s provided. Thus, while the apparent activation energy for the homogeneous hydrogenation of ethylene i s 43 kcal./mole, the reaction takes place on a nickel surface with an apparent activation energy of only 11 kcal./mole (3). The catalytic activation of hydrogen may be conveniently divided into two types; activation taking place on the surface of a solid and activation occurring homogeneously in solution. HETEROGENEOUS CATALYSIS Heterogeneous catalytic processes are widely known and extensively used. However, the mechanism by which hydrogen reacts on a surface with a lower energy requirement than in the gas phase remains to be adequately 2 explained. The activation of hydrogen i s considered to occur through homo» lytic cleavage of the H-H bond with simultaneous formation of covalent bonds with the catalysts Both crystal dimensions and electronic character of the metal have been employed in attempts to explain the heterogeneous activation of hydrogen but with only limited success. Some experimental support for the relationship between activity and crystal dimensions and geometry has been provided by studies on the hydrogenation of ethylene (3) and benzene (4)* (5) on surfaces of transition metals. A semiquantitative treatment of the variation of activation energy for chemisorption of hydrogen on carbon with lattice parameters by Sherman and Eyring (6) has lent theoretical support to this approach. However, several objections to this point of view have been raised; (a) metals such as Cu and Zn have optimum lattice spacing, yet show no catalytic activity and (b) catalysis on alloy surfaces bears no relationship to geometric factors (7), (8), (9)* At present crystal dimensions appear to be of secondary significance and of greater importance in catalytic activation is the electronic character of the solid (10). The ability of metals to catalyse hydrogen reactions has been related to incomplete f i l l i n g of the metal d-bands (9). This i s demonstrated by the catalytic activity of the transition metals and the reduction in activity caused by alloying with strong electron-donating metals such as those of group IB where electrons are donated into the d-bands of the trans-ition metal (9). Similarly these metal catalysts are poisoned by electron-donating compounds such as the sulfides. The paramagnetic susceptibility of palladium decreases upon absorption of hydrogen indicating f i l l i n g of metal d-bands (11). This indicates that hydrogen i s activated through the 3 formation of an actual bond involving donation of electrons from the hydrogen into the metal d-bands. Dowden has given a theoretical treatment to the electronic approach (12). He points out the proportionality between catalytic activity and the energy density of electron levels at the Fermi surface and the electronic work function of the transition metals. Some experimental evidence has been presented to support these ideas but at present quantitative application of the theory is difficult. HOMOGENEOUS CATALYSIS Calvin in 1938 was the f i r s t to demonstrate that hydrogen could be activated homogeneously (13) and since that time numerous similar systems have been discovered and studied (14), (15), (16). These systems are of particular interest in the study of the catalytic process because of their simplicity compared with the heterogeneous systems. Calvin showed that cupric acetate and benzoquinone could be reduced homogeneously in the presence of cuprous acetate in quinoline at temperatures of about 100° C. He reported the process to be between f i r s t and second order dependent in Cu(I) concentration and i t was proposed that the active species was a dimer of Gu(l) (13), (17). However, further study of this system has shown the Cu(l) dependence to be exactly second order (18), (19) and this along with other evidence (20) indicates that a single termolecular step involving homolytic splitting of hydrogen i s rate determining: 2Gu(l) + Hg ^- 2CuH 4 Cuprous acetate has also been shown to activate hydrogen at moderate tempera-tures in dodecylamine and pyridine (21) but in these solvents f i r s t order dependence on Cu(I) concentration was observed. The reason for the difference in order of dependence on Cu(l) concentration remains to be adequately explained. While cupric acetate was not noted to activate hydrogen in these solvents, this salt was reduced to Cu^ O in aqueous solution (22). Similarly cupric perchlorate was observed to catalyse reduction of substrates such as dichromate and iodate in aqueous solution (23). However cuprous salts were found to be inactive in aqueous medium (24). Both Cu(l) and Cu(II) heptanoates were found to activate hydrogen in heptanoic acid, biphenyl and octadecane (20) at 125° C. In a l l solvents except quinoline the kinetics were f i r s t order in the active copper species and the mechanisms proposed involve the formation of hydride intermediates with heterolytic splitting of hydrogen? Cu(ll) + H 2 CuH+ + H + Cu(l) + H 2 >- GuH + H + The nature of the copper salt and i t s state of complexing affect the rate of hydrogen activation. This has been attributed to the difference in basicity of the ligand or anion but other evidence (16) and the results of the present work indicate that the stability of the activating species as defined by the degree to which the d-orbitals are f i l l e d by electrons from the ligand i s of prime importance. Thus ethylenediaminetetra-acetic acid and ethylenediamlne inhibit the rate of reaction in quinoline (25) and cuprion (2j2'-bisquinoline) appears to have the same effect on the catalytic activity of Cu(l) in heptanoic acid (20). A summary of previous work on 5 the effect of complexing Cu(Il) in aqueous solution and information on com-plex stability are given in Table I. The activation of hydrogen by Ag(I) salts has been studied in aqueous solution (26), pyridine and dodecylamine (21) and heptanoic acid (27). First order dependence on Ag(I) concentration was observed in a l l four sol-vents suggesting a mechanism similar to that for Cu(l) in pyridine and heptanoic acid involving heterolytic splitting of the hydrogen molecule: Ag + * H AgH + H + In aqueous solution a second activation path kinetically second order in Ag(I) concentration was also observed for which a mechanism similar to that for cuprous acetate in quinoline has been proposed. In this mechanism the hydrogen is split homolytically: 2Ag+ + Hg ^ 2AgH+ Where the silver i s activating hydrogen in a basic ligand environment the bimolecular mechanism is preferred. Both Hg(l) and Hg(Il) activate hydrogen in aqueous solution (28), (29) and Hg(ll) undergoes reduction by hydrogen in both heptanoic acid and biphenyl (27). These reactions were a l l kinetically f i r s t order in the mer-cury salt and the mechanisms proposed are similar to those for Cu(Il) and Ag(I) although thermodynamic considerations indicate that the formation of an hydride intermediate i s unfavourable (30): Eg*+ + Hg + 2H + Hgg* + Hg 2Hg + 2H+ 6 The effects of completing Cu(ll) (31), Hg(ll) (32), (23) and Ag(l) (33) have been studied in aqueous solution and varying rates noted* This work is summarised in Table I with data on complex stability. The presence of a proton-accepting ligand in the heterolytic mechanism would tend to accelerate the rate of activation but in several instances marked slowing of the rate i s observed even with strong basic ligands. These ef-fects may be explained on the basis of an activated complex of the typer n * " 1 r : ~ M z + - X s- H « H S+" where X = ligand, M = metal cation, n = total no. of ligands and Z = total cation charge. In a complex of this type i t is apparent that the rate will depend directly on the strength of the M-H and X-H bonds and inversely on the strength of the M-X bond. The strengths of a l l these bonds will depend on the character of the ligand, X. Donation of electrons from the ligand into the d-orbitals of the metal will reduce its ability to form the M-H bond, a process analogous to poisoning in heterogeneous catalysis, while increasing the basicity of the ligand should accelerate the reaction by strengthening the X-H bond. This explains the results of complexing with Ag(I), Cu(Il), and Hg(II)) where increasing complex stability reduces the rate of reaction while with the weak complexes, increasing ligand basicity ac-celerates the rate. Several other systems have been noted to activate hydrogen homo-geneously or cause deuterium exchange with the solvent* Chloropalladate (II) (34) and chlororhodate (II) (35) complexes both activate hydrogen as shown by the reduction of Fe(III) substrate in their presence. The kinetics are f i r s t order in each complex. Dicobaltoctacarbonyl has also been demonstrated 7 to activate hydrogen homogeneously (36). Hydrogen i s apparently split homolytically through the mechanism: Cog(GO)8 + Hg - *~ 2HCo(G0)4 Similarly cobaltous cyanide solutions catalyse the reduction of substrates such as cinnamic acid homogeneously (37). The species (GN)^Co-GN-Co(CN)^ has been proposed as the catalyst by Winfield (38). Ethylene platinous chloride has been observed to catalyse addition of hydrogen to thee ethylene double bond homogeneously at high ethylene concentrations and temperatures below 0° C. (39). It has been suggested that the reduction takes place through the sequence of steps: (PtGl 2C 2H^) 2 + C2H^ < > 2PtCl 2(C 2H 4) 2 2EtCl 2(C 2H^) 2 * 2H2 ^ (PtCljjCgH^g + 2CgH6 The oxyenion MnO£ has also been shown to cause hydrogen oxidation (4O) involving a bimolecular rate determining step of the type: MhO£ + Hg >- HMnO~ + H + However, a solution of Ag(I) and MnO^  obeys kinetics of the form: rate = k [H2] [Ag +] [mil] : <a) B n d V^ 0 ( 4 2 ) » ^ 3>» exchange reactions have been observed in basic medium and the reaction was found to be f i r s t order in NHg and OH" concentrations respectively. However, no reduction of dissolved substrate, CrO^, was observed in the aqueous solution. The homogeneous activation process discussed above i s unique in that i t occurs at temperatures far below that required for uncatalysed hydrogenations. •. ^4. ++ 4+ ++ Severs! other metal cations including C a , Mg » Zn , Mn , Ni , Gd , 8 Pb , Al , Cr , TI , Ce and CrG^ have been studied up to tempera-tures of 150° G. and found to be inactive. The purpose of the work on which this thesis i s based was to study further the effect of completing on the rate of hydrogen activation by Ag(l). A series of silver-amine complexes was chosen for study since information about the stability of these complexes i s readily available. It was hoped that such a study would provide more information about the configuration of the activated complex and reveal the effects of ligand basicity and cony plex stability on the rate of catalytic activation. TABLE I 9 Effect of Completing on Activity  Complex (a) Stability Constant (to) Relative Activity HgS04 22 1.8 Hg~ 1.0 HgAc2 2.7 x 108 4 x 10"2 HgPr2 4 x 1G"2 HgCl2 1.7 x l© 1 3 2.5 x 1G"3 HgBr2 1.2 x 10 1 5 1.7 x l G " 3 Hgten)^ 2.6 x 10 2 3 1.G x 1G"3 AgAc 4.4 80 Ag(en)2 5 x 1G7 25 Ag + — 1 Ag(CN)J 6 x 10 2 0 inactive CuBag — 150 GuPi^ — 150 CuAe2 4 x 1G2 120 CUSO4 2.2 x 102 6.5 GuCl£ 1G5 2.5 _ ++ Gu MO 1 CuGlg 4 x 1G 1 5 < 0.5 Cu(en )2 1 x 10 0.1 (a) Ligand designations: Bo* = butyrate, Pr~ = propionate, Ac" = acetate, Gl" = glycinate, en = ethylenediamine. (b) Kn = [MXn] / [M] [xf (44). 10 EXPERIMENTAL MATERIALS Silver perchlorate used in this investigation was a G. F. Smith Reagent grade product. NjNjNSN'-tetramethylethylenediamine, N,N'-dimethyl-piperazine, N,N-dimethylethylenediamine and 1,3-diaminopropane were products of K&K Laboratories. Distillation of these products had no effect on reaction rate and hence they were a l l used without further purification. Triethyl-amine, BDH Reagent grade, was redistilled before use. The Houdry Process Corporation triethylenediamine was used directly, since the rate of Ag(I) reduction was unaffected by using recrystalllzed amine. Al l other amines were Eastman Kodak White Label and except for methyl-, ethyl- and propylamine, were redistilled before use. A l l other chemicals were Baker and Adamson Reagent grade. Hydrogen and nitrogen gases were supplied by the Canadian Liquid Air Go. Distilled water was used in the preparation of a l l solutions. In the D20 experiment, recovered D20 (88.855) was employed, ANALYSIS The normality of a l l the liquid amines was determined by direct titration using 0.1N HGIO^ or by back titration using 0.1N NaOH and HCIO^ solutions. These amines were used directly in making up the reaction mix-tures. Aqueous solutions of the amino-acids of known normality were made up gravimetrically and were used to prepare reaction mixtures. Other solid amines were made up in aqueous solution and employed to prepare reaction 11 mixtures in this form. The silver analysis was done by thiocyanate titration using ferric indicator. To avoid interference due to silver metal and insoluble amine salts the sample was filtered while warm, then diluted and acidified. PROCEDURE For rates that could be determined at atmospheric pressure and in the temperature range 50° G. to 85° C,, the glass apparatus depicted in Figure I. was used. A presaturator f i l l e d with aqueous solution of the same ionic strength as the reaction mixture was employed to prevent volume changes in the mixture. The whole apparatus was immersed in a constant temperature bath thermoatated to within - 0.03° G. A 250 ml reaction mixture was made up? from stock solutions and placed in the reaction vessel. Nitrogen was run into the mixture, entering the reaction vessel through a glass sinter at the bottom, for periods of up to an hour. Samples were taken during this time to establish the stability of the mixture. Hydrogen was then introduced and, when the mixture became saturated with hydrogen, samples were taken at appropriate intervals and analysed for silver content. The uncertainty of the reaction starting time was of the order of a minute during which time the solution was becoming saturated with hydrogen. A high rate of hydrogen flow was used to insure complete saturation of the reaction mixture and to provide adequate mixing. For rates of reaction requiring more severe conditions an autoclave was used. The apparatus used was of Parr manufacture (series 4500) with a stainless steel reaction vessel provided with a stirrer, gas inlet, sampling 12 tube, pressure gauge and thermowell, surrounded by a 250 watt electric heating mantle controlled by a rheostat. A glass liner was used In a l l the present work. Fine temperature control was achieved by use of an auxiliary 5 watt heater placed directly in the reaction mixture through the thermowell. It was controlled by a Thermistemp Temperature Controller (model 71) and probe placed in the reaction mixture through as opening originally provided for a cooling coil. This arrangement gave temperature control of * 0.3° C. A 500 ml reaction mixture was made up from stock solutions and placed in the reaction vessel. Nitrogen gas was run into the mixture at atmospheric pressure, the vessel was sealed and brought to temperature. Samples were taken over a one hour period to establish the stability of the solution. One of two procedures was then used to introduce the hydrogen. With the less volatile amines the solution was flushed with hydrogen and then brought to the desired pressure. With the volatile amines the desired hydrogen partial pressure was established directly and was determined by correcting the total gauge pressure for the contribution made by the nitrogen. Samples were then taken at appropriate times and analysed for silver content* The stirrer was rotated at 600 rpm. It has previously been established that these reactions are independent of stirring rate,, A. Gas Outlet B. Reaction Mixture C. Sintered Glass Plate D. Presaturator Solution E. Gas Inlet Fig. 1. Apparatus for Experiments from 50° at Atmospheric Pressure. u RESULTS AND DISCUSSION The stoichiometry of the reduction of silver amine complexes by hydrogen reported in this thesis is probably the same as that reported by Webster (26) in the absence of substrate such as Gr^O^t 2Ag+ + H2 >- 2kg + 2H + It was not possible to follow the reaction using CrgO^ in the basic medium in which the reactions reported here were studied due to the preferential reduction of Ag+». Webster observed that at high temperatures and in basic + solutions the reaction was predominantly f i r s t order in Ag concentration and in the perchlorate system f i r s t order dependence on was observed (26), (33 )w Similar results are reported in this work, The disappearance of Ag + at constant pressure for a l l the silver amine complexes studied in the present investigation obeyed f i r s t order kinetics as i s shown by the linear plots given in Figures 2 - 6 inclusive. This dependence was verified by the fact that the same rate constant was obtained for two different silver concentrations in the study of each of several complexes. Results are given in Tables II - VI inclusive. In several instances, notably diethylamine, triethylamine, ammonia, ethyl-enediamine, 1,3-diaminopropane, ^ -alanine, methyl-, ethyl- and propylamine, an increase to higher order of Ag dependence was observed as the reaction proceeded. This was attributed to autocatalysis an the surface of the precipitated silver metal. The onset of autocatalysis could normally be delayed by buffering the reaction mixture at a lower pH, In those instances 15 0 1200 2400 3600:' Time-Seconds Figure 2 Typical Rate Plots for the Reduction of Silver Complexes of Methyl-, Ethyl-, Propylamine, Ethylenediamine and 1,3-Diaminepropane 16 -2.2 -2.4 -2.6 -2.8 LOG Ag + -3.0 -3.2 A Amine Run No. N,N-Dimethylethylenediamine 4f • N, N'-Dimethylpiperazine 2f o Piperazine 5e V Triethylenedi amine lg o N,N,N«,N»-Tetramethyl-ethylenediamine 3a 1200 2400 Time-seconds Figure 3 Typical Rate Plots for the Reduction of Silver Complexes of N,N-Dimethyl-ethylenediamine, N,N1-Dimethylpiperazine, Piperazine, Triethylene-diamine and N,N,N1,N'-Tetramethylethylenediamine Typical Rate Plots for the Reduction of Silver Complexes of Triethylamine, Triethanol amine and Diethylamine 18 Amine Run No. O Pyridine 18d • Ammonia 8d 900 1800 2700 3000 Time-seconds Figure 5 Typical Rate Plots for the Reduction of Silver Complexes of Pyridine and Ammonia Typical Rate Plots for theReduction of Silver Complexes of Aminoacids 20 Table II Rates of Reaction with Silver-Tertiary Diamine Complexes Initial AgC104 3 Amine Name M.xl0 Eg Pressure atm. Amine M, Amine Per-chlorate M. T°C h sec No. Triethylene- 2.7 0.803 0.18 0.060 60 0.83 l a di amine 5.5 0.803 0.18 0.060 60 0.87 lb 5.5 0.803 0.13 0.022 60 0.81 lc 5.5 0.803 0.13 0.135 60 0.82 Id 5.5 0.803 0.09 0.030 60 0.87 le 5.5 0.755 0.09 0.030 65 1.22 If 5.5 0.691 0.09 0.030 70 1.86 lg 5.5 0.879 0.09 0.030 50 0.42 lh 5.5 0.848 0.09 0.030 55 0,62 l i N,N«-Dimethyl- 2.7 0.803 0.09 0.030 60 0.40 2a piperazine 5.5 0.803 0.09 0.030 60 0.40 2b 5.5 Gv803 0.13 0.045 60 0.43 2c 5.5 0.803 0.13 0.022 60 0.43 2d 5.5 0.755 0.09 0.030 65 0.57 2e 5.5 0.691 0.09 0.030 70 0.81 2f 5.5 0;879 0.09 0.030 50 0.17 2g 5.5 0.848 0.09 0.030 55 0.27 2h N,N,Nf,Nf-Tetra- 5.5 0.691 0.13 0.045 70 1.48 3a methylethylene- 5.5 0.691 0.18 0.060 70 1.44 3b di amine 5.5 0.691 0.13 0.022 70 1.48 3c 5.5 0.755 0.13 0.045 65 1.02 3d 5.5 0.803 0.13 0.045 60 0.72 3e 5.5 0.848 0.13 0.045 55 0.50 3f 5.5 0.879 0.13 0.045 50 0.34 3g N,N-Dimethyl- 5.5 0.532 0.18 0.060 80 0.72 4a e thylenedi amine 5.5 0.532 0.24 0.080 80 0.71 4b 5.5 0.532 0il8 0.030 80 0.70 4c 5.5 0.429 0.18 0.060 85 0.95 4d 5.5 0i620 0.18 0.060 75 0.47 4e 5.5 0.691 0.18 0.060 70 0.30 4f 5.5 0.755 0.18 0.060 65 0.22 4g 5.5 1.74 0.18 0.060 65 0.18 4h 5.5 2.75 0.18 0.060 65 0.21 4 i 5.5 3.75 0.18 0.060 65 0.18 21 Table III Rates of Reaction with Silver-Pi amine Complexes Amine Name Initial AgClO^ M.xlQ3 Pressure atnu Amine Amine Per-chlorate Hi T°C M ; - i sec -1 No. Piperazine Ethylenediamine 1,3-diamino-propane 5.5 9.53 0.075 0.150 80 0.097 5a 5.5 9.53 0.150 0.300 80 0.093 5b 5.5 9.53 0.075 0.300 80 0.100 5c 5.5 9.75 0.075 0.150 65 0.031 5d 5.5 9.69 0.075 0.150 70 0.051 5e 5.5 9.62 0.075 0.150 75 0,069 5f 5.5 9.43 0.075 0.150 85 0.135 5g 5.5 10.69 0.180 0.060 70 0.017 6a 5.5 10.69 0.270 0.090 70 0.017 6b 5.5 10.69 0.180 0.180 70 0.016 6c 5.5 7.69 0.180 0.180 70 0.016 6d 5.5 5.09 0.180 0.180 70 0.015 6e 5.5 10.75 0.180 0.180 65 0.010 6f 5.5 10.62 0.180 0.180 75 0.024 6g 5.5 10.53 0.180 0.180 80 0.039 6h 5.5 10.43 0.180 0.180 85 0.059 6i 5^ 5 10.69 0.180 0.180 70 0.0082 7a 5.5 10.69 0.270 0.270 70 0.0090 7b 5.5 10.69 0.180 0.360 70 0.0088 7c 5.5 10.62 0.180 0.360 75 0.014 7d 5.5 10.53 0.180 0.360 80 0.020 7e 5.5 10.43 0.180 0.360 85 0.029 7f 5.5 10.31 0.180 0.360 90 0.045 7g 22 Table 17 Rates of Reaction with Silver-Simple Monoamine Complexes Amine Name Ammonia Methylamine Ethylamine Propylamine Diethylamine Initial AgClO^ M.X103 H2 Pressure atau Amine Amine Per-ehlorate M. T°C sec Mo. 5.5 31.31 0.045 0.360 90 0.0034 8a 5.5 31.31 0.090 0.720 90 0.0035 8b 5.5 31.31 0.045 0.720 90 0.0034 8c 5.5 31.43 0.045 0.360 85 0.0021 8d 5.5 31.17 0.045 0.360 95 0.0061 8e 5.5 31.00 0.045 0.360 100 0.0096 8f 5.5 30.85 0.045 0.360 104 0.0174 8g 5.5 16.43 0.045 0.360 85 0.054 9a 5.5 16.43 0.090 0.720 85 0.051 9b 5.5 16.43 0.045 0.720 85 0.051 9c 5.5 16.62 0.045 0.360 75 0.022 9d 5.5 16.53 0.045 0.360 80 0.041 9e 5.5 16.31 0.045 0.360 90 0.086 9f 5.5 16.17 0.045 0.360 95 0.121 9g 5.5 16.43 0.090 0.360 85 0.015 10a 5.5 16.43 0.180 0.720 85 0.016 10b 5.5 16.43 0.090 0.720 85 0.016 10c 5.5 16.69 0.090 0.720 70 0.0040 lOd 5.5 16.62 0.090 0.720 75 0.0059 lOe 5.5 16.53 0.090 0.720 80 0.0095 lOf 5.5 16.31 0.090 0.720 90 0.022 lOg 5.5 16.62 0.045 0.360 75 0.0085 11a 5.5 16.62 0.090 0.720 75 0.0084 l i b 5.5 16.62 0.045 0.720 75 0.0085 11c 5.5 16.80 0.045 0.360 60 0.0020 l i d 5.5 16.75 0.045 0.360 65 0.0032 l i e 5.5 16.69 0.045 0.360 70 0.0048 l l f 5.5 16.53 0.045 0.360 80 0.0154 Hg 11.0 10.69 0.180 0.180 70 0.044 12a 11.0 10.69 0.270 0.270 70 0.044 12b 11.0 10.69 0.180 0.360 70 0.041 12c 11.0 10.80 0.180 0.180 60 0.019 12d 11.0 10.75 0.180 0.180 65 0.027 12e 11.0 10.62 0.180 0.180 75 0.067 12f 11.0 10.53 0.180 0.180 80 0.114 12g 23 Table IV (continued) Amine Heme Triethylamine Initial AgClO^ M.xl03 Pressure atm. Amine M, Amine Per-chlorate M. T°C k i r - i sec No. 11.0 7.92 0.180 0.360 40 0.053 13a 11.0 7.92 0.270 0.540 40 0.049 13b 11.0 7.92 0.270 0.270 40 0.053 13c 11.0 7.96 0.270 0.540 30 0.017 13d 11.0. 7.94 0.270 0.540 35 0.028 13e 11.0 7.90 0.270 0.540 45 0.079 13f 11. G- 7.88 0.270 0.540 50 0.130 13g 11.0* 7.90 0.270 0.540 45 0.079 13h t - rate determined in 88.8$ D20 24 Table V Rates of Reaction with Silver-Aminoacid Complexes Initial Amino-Acid Name Glycine o<-Alanine ^3 -Alanine AgClO^ M.X103 Pressure atnu Amine -acid Mi NaOH M, k - l M - l sec No, 5.5 9.53 0.107 0.107 80 0.104 14a 5.5 9.53 0.214 0.214 80 0.106 14b 5.5 9.80 0.107 0.107 60 0.0176 14c 5.5 9.75 0.107 0.107 65 0.030 14d 5.5 9.69 0.107 0.107 70 0.048 14e 5.5 9.62 0.107 0.107 75 0.076 14f 11.0 9.80 0.107 0.107 60 0.0178 14g 11.0 9.80 0.107 0.240 60 0.161 l4h 11.0 9.80 0.107 0.190 60 0.127 14i 5.5 9.80 0.107 0.130 60 0.050 143 5.5 - '9.8G0 0.107 0.090 60 0.0084 14k 5.5 19.80 0.107 0.090 60 0.0086 141 5.5 19;80 0.107 0.065 60 0.0055 14m 5.5 19.80 0.107 0.050 60 0.0051 14n 5.5 9.62 0.120 0.120 75 0.0305 15a 5.5 9.62 0.240 0.240 75 0.0309 15b 5.5 9.75 0il20 0.120 65 0.0173 15c 5.5 9.69 0.120 0.120 70 0.0250 15d 5.5 9.53 0.120 0.120 80 0.0491 15e 5.5 9.43 0.120 0.120 85 0.0699 15f 5.5 9.62 0.120 0.120 75 0.040 16a 5.5 9.62 0.240 0.240 75 0.039 16b 5.5 9.75 0.120 0.120 65 0.015 16c 5.5 9.69 0.120 0.120 70 0.029 I6d 5.5 9.53 0.120 0.120 80 0.051 I6e 5.5 9.43 0.120 0.120 85 0.075 I6f 25 Table VI Rates of Reaction with Miscellaneous Silver Complexes Amine Name Initial AgC104 M.xlG3 *2 Pressure atm. Amine Amine Per-chlorate T°G sec k i No. Triethanolamine Pyridine 5.5 0.691 0.180 0.720 70 0.47 17a 5.5 0.691 0.225 0.900 70 0.45 17b 5.5 0.691 0.180 0.360 70 0.49 17c 5.5 0.803 0.180 0.720 60 0.19 17d 5.5 0.755 0.180 0.720 65 0.30 17e 5.5 0.620 0.180 0.720 75 0.68 17f 5.5 0.532 0.180 0.720 80 0.96 17g 5.5 9.53 0.270 0.270 30 0.019 18a 5.5 9.53 0.540 0.540 80 0.018 18b 5.5 9.53 0.270 0.135 80 0.020 18c 5.5 9.43 0.270 0.135 85 0.029 18d 5.5 9.31 0.270 0.135 90 0.043 18e 5.5 9.17 0.270 0.135 95 0.060 18f 5.5 9.00 0.270 0.135 100 0.093 18g 26 in which antocatalysis interfered to a large extent, reproducible rates could be determined from the f i r s t 5% of reaction. As in the acid perchlorate medium, the rate was directly dependent on hydrogen concentration as i s shown in Figures 7 and 8. At different hydrogen pressures a constant k' was also obtained for glycine complexes (Table V), Thus, the overall rate law may be expressed ast dfe! = -£ iL&g!3 = "k'fAg+JpgOC = kJAg+^E,] dt dt ^ where p ^ i s the hydrogen pressure and <X i s Henry's constant. In the region of pressures investigated, Henry's law i s obeyed. The values taken for hydrogen solubility at different temperatures were those of Weibe and Gaddy (46), It was assumed that the hydrogen solubilities in the solutions used in the present study were, within the limits of experimental error, the same as for pure water. These kinetics suggest a mechanism of the types A g+ + ^ S l 0 w > AgH + H + . « . . + fast „+ AgH + Ag >- H + 2Ag which has been justified on thermodynamic grounds (30). Except for triethylamine, a l l experiments were made under conditions in which the silver was completely complexed by the amine. Limitations due to the insolubility of triethylamine in water allowed only 95% complexLng in this case but, since the rate with this amine is 1000 times that for uncom-plexed silver, the error in true rate for triethylamine complex is small. Figure 7 Dependence of Rate on Hydrogen Partial Pressure at 65° C. for N,N-Dimethylethylenediamine Complex H 2 Pressure-ATM. Figure 8 Dependence of Rate on Hydrogen Partial Pressure at 70° C. for Ethylenediamine Complex 29 That the rate i s independent of amine concentration is shown in Tables II-VI. A l l the reaction mixtures were buffered with an amine-amine per-chlorate system to prevent large changes in pH. The rate was shown to be independent of amine perchlorate concentration in a limited range. This is shown in Tables II-VI. It is consequently independent of pH within the fiH change caused by the protons liberated in the complete reduction of the Ag+. The agreement between rates obtained in the glass apparatus and those determined in the autoclave i s shown In the results for N,N-dimethyl-ethylenediamine (Table II). The activity of the silver-glycinate complex was studied in solutions containing excess base (NaOH) and excess glycine (Table V, runs 14g-14n inclusive). The reaction mixtures containing excess base were unstable, silver being reduced in the absence of hydrogen. However, by sub-tracting this background rate from the observed rate with hydrogen, semi-quantitative rate constants could be determined. The large increase in rate with increasing OH concentration has been observed before for silver ethyl-enediamine and mercury (II) ethylenediamine complexes (26), (32) and may be explained in one of two ways. The OH" may participate directly in the rate determining step: +Ag(H2NCH2C00~)2 + OH" + Eg AgH + HgO + 2H2NCH2G00" or an equilibrium of the type observed with Co amine complexes by Pearson and Basolo (47) may be responsible: + +" 00GCH2IH2AgNH2CH2C00 + OH *- OOCCHjNEjAgNNHCBgCOO + H20 30 where "NHCHgCOO" is a much stronger base than EjNCBgCOO". The decrease in rate in the region of constant total glycine plus glycinate concentration with decreasing glycinate concentration is anomalous in as much as sufficient glycinate is present to complex fully the silver in a l l cases and the rate has been shown to be independent of glycinate concentration in this region. This effect remains to be explained. A 10,000-fold variation in rate for the silver complexes studied —Z. —1 _ i + was observed, ranging from 3.3 x 10 l.moles sec. for Ag(NH3)£ to 1.8A Lmoles'^sec."^- for the triethylenediamine complex; at 70°C. A complete resume' of thermodynamic values, complex stability constants, amine basici-ties and rates i s given in Table VII. In general the differences in rates are reflected primarily in the activation energies. The activation entropies are normal for the simple bimolecular mechanism suggested, although with the exception of triethanolamine, pyridine and glycine, those for the dibasic ligands are somewhat more negative (-7 to -19 eu.) than those for the mono-amines (7 to -6 eu.). These differences suggest differences in the rate determining step for the dibasic amines and the monobasic amines. Table VII contains evidence of two different trends: (a) a decrease in catalytic activity with increasing complex stability and decreasing amine basicity and (b) a generally greater activity for the dibasic amines than the monobasic. These two trends will be discussed separately in this order. On the basis of the rate determining step: + + HjNAgNR-j + Eg ^ AgH + R^ NH + R^ N 31 Table VII Stnnmary of Kinetle Data Stability Constants and Basicities Amine , » B a s i c i t y u ; Stability Constants^ 4H* kcal. AS* Amine Name P Ka log Kx log K2 mole eu. log k(70 ) Ammonia 9.25 3.37 3.78 7.15 28.3 +7.6 -3.48 Methylamine 10.72 3.15 3.53 6.68 22.3 -2.8 -1.91 Ethylamine 10.61 3.37 3.93 7.30 21.6 -7.1 -2.42 Propylamine 10.58 - - 7.39 23.3 -1.5 -2.26 Diethylamine 10.98 - - 6.36 20.5 -5.4 -1.33 Triethylamine 10.77 - - 4.76 18.8 -4.8 -0.13 Ethylenediamine 10.18 4.62 2.92 7.54 20.8 -6.7 -1.80 1,3-Diamino-propane 10.72 5.77 - - 18.9 -13 -2.00 Piperazine 9.81 3.32 - - 16.8 -16 -1.32 N,N-Dimethyl-ethylenedi amine 9.53 - - - 17.1 -11 -0.49 N,N,N',N'-Tetra-methylethylene-di amine 9.30 - - - 15.1 -14 0.17 N,N'-Dimethyl-piperazine 8.30 - - 17.9 -7.2. -0.07 Triethylenedi amine 8.19 1.57 - 17.1 -8.1 0.26 Glycine 9.78 3.51 3.38 6.89 21.5 -2.5 -1.33 ex -Alanine 9.87 3.64 3.54 7.18 16.2 -19 -1.61 /? -Alanine 10.19 - - - 18.3 -13 -1.63 Triethanolamine 7.90 2.30 1.34 3.64 17.5 -9.7 -0.36 Pyridine 5.45 2.04 2.18 4.22 19.3 -12 -2.09 (a) K = [ AIH*) , Values taken from (45) a [AH+] (b) Kx = [AgNR^] , K2 = [Ag(NR3)2'] , /32 = K1 K2 Values taken from [Ag+][NR3"] [Ag+NR3][NR3] ^ corrected where necessary to 25° G., using temperature coefficient for Ag(NH2C2H5)2 = d log % / d t = d log Kg/dt = -0.016 (48) 32: an activated complex of the type: + R3N - Ag - NR3 %- H - H£+ may be postulated for the monoamines (R may represent an alkyl group or H). On the basis of such a configuration the rate of hydrogen activation by the complex should depend directly on the strength of the Ag-H and H-NR^  bonds and inversely on the strength of the Ag-NR^  bond. Therefore, since the pKa is a measure of the strength of the H-NR3 bond and log Kg a measure of the strength of the Ag-NR^  bond being cleaved, one might expect a correlation between the rate of activation of hydrogen and a function involving these parameters of the type: log k CX (pKa - log Kg) A comparison of log k at 70° C. and the function (pKa - log Kg) for simple monoamines is given in Table VIII and the dependence is clearly shown. Pyridine and triethanolamine are monoamines but their characters are dif-ferent from that of the simple monoamine and they should be considered in their own homologous series. The diamines follow a similar pattern (Table VIII) but because for most of these amines only information on the f i r s t stability constant is known, log K^  is used. The relative correlation between the f i r s t stability constant and the overall stability constant is good and the use of log K^  should not detract from the relationship drawn. For the dibasic amines i t was felt appropriate to use the logarithm of the f i r s t basicity Table T i l l Relationship between Rate of Activation and a Function of Amine Basicity and Complex Stability Monoamine Name Function (pKft - log Kg) log k Ammonia 5.47 -3.48 Ethylamine 6.68 -2.42 Methylamine 7.19 -1.91 Diethylamine 7.68 -1.33 Triethylamine 8.61 -0.13 Diamine Name Function (pKa - log K-^ ) log k 1,3-Diaminopropane 4.95 -2.00 Ethylenediamine 5.56 -1.80 Piperazine 6.49 -1.32 Triethylenediamine 7.41 0.26 34 constant in as much as the ligand accepts one proton in the rate deter-mining step. Table VIII shows the relationship between log k and (pKa - Log K x). In the dibasic amines (including amino-acid anions) the presence of the second basic group may increase the rate. A comparison of the rates of ethylamine and ethylenediamine complexes and of diethylamine and piper-azine complexes shows that the rate for the diamines is greater. * Whether this is due to ligand basicity and complex stability effects or the presence of the second basic group i s not clear. The proximity of the second basic group appears to be important. The logarithm of the stability constant for the Gu(II) glycine complex is greater than that for the Cu(Il) -alanine complex. This relationship is likely to hold for the Ag(l) complexes as well and i f this is the case the faster rate with the glycine complex may be attributed to the proximity of the carboxy 1 group. The tendency for chelation in silver complexes is small. In the solutions studied the silver complex would carry two monocoordinated dibasic + ligands e.g. HgNCHgCHgNHgAgHgNCHgCHgNHg. A rate determining step involving direct acceptance of the proton by the non-bonded basic group in the ligand suggests an activated complex of the form: + HgNCRgC^NHgAgBgNCEj The greater negative entropy change noted above for the diamine complexes may be indicative of an activated complex different from that suggested for the monoamine complexes. The acceptance of the released proton at a different site in the activated complex for the diamine mechanism may require a greater 35 degree of solvation for these complexes than for the monoamine complexes. This greater degree of 'freezing out' of solvent molecules for the diamine complexes may be the cause of the greater negative entropy change. A second configuration deserving consideration i s : C H g C H g m , NEg - Ag - HgNCHgGHgNHg S- H - H S+ However, i f the formation of the Ag-H bond is dependent upon vacant d-orbitals in the silver as has been suggested earlier (16), coordination with the second amino group of one ligand would be expected to hinder this process and this type of activated complex would be unlikely. All previous discussion has depended upon a mechanism in which the ligand accepts the proton in the rate determining step directly. How-ever, certain general considerations and evidence would suggest a mechanism in which water acts as the proton acceptor or as a bridge between the pro-ton and the ligand. This would give rise to an activated complex of the type: + R3N - Ag S-H A similar configuration may be postulated for the dibasic complexes. In as much as the electrons responsible for the basicity of an amine would be donated to the silver in the formation of the covalent bond in the complex H 1 0-H - H£ + 36 i t would appear difficult for the ligand amine to accept a proton in the rate determining step. If this were true, i t seems reasonable that water as a ligand may act more readily as the proton acceptor in that i t has two coordinative positions. Evidence which would favour such a mechanism is the possible proton accepting role of OH", CO", acetate and propionate suggested by Korinek to explain the acceleration of hydrogen activation noted with Hg(II)-ethylenediamine complexes when these anions were added (32). Support for this point of view i s found in the measurement of rates of proton transfer for methylamines and ammonia by NMR techniques. Meiboom and co-workers by observing the broadening of the water and amine proton signals have been able to distinguish and measure the rates of the two separate paths of proton transfer; one employing an intervening water molecule end one by direct transfers + k l + R-jNH + NRj =>- R^ N + H NR^  R3NH+ + 0-H + NR3 — ^ R^ N + H-0 + H+NR3 H H They have observed that the second path is preferred by the methylamines (kj/k^ = 1.4, 14 and >10 for methylamine, dimethylamine and trimethyl-amine respectively) but not by ammonia (^/^ * 0^085) (49). The above considerations explain the observed variation in rates with different complexes. A water mediated mechanism seems plausible for the alky!amine complexes at least and the observed inverse variation of rate with complex stability constant may be due to the difficulty of replace-37 merit of the ligand by a water molecule in the activated complex. The abnormally low rate constant for ammonia complex may be the result of direct proton transfer to the ligand in preference to the water mediated mechanism. Such a direct transfer would account for the anomalously high activation energy and positive entropy change for this complex in that the ligand removal would not be compensated for by replacement with a water molecule. In order to determine whether the direct transfer mechanism was in operation for a l l the complexes or whether a water mediated mechanism was used, an experiment was made in DgO with the triethylamine complex which should activate hydrogen by the water mediated mechanism i f these ideas are correct. It would be expected that i f a water mediated mechanism were in operation the difference in basicity of water and DgO would be reflected in the rate. No such difference in rate was observed (Table IV) which would appear to substantiate the mechanism suggested earlier of direct proton transfer to the ligand. However, in as much as i t i s not clear whether the difference in basicity of the solvents i s the only effect, this evidence i s not conclusive. CONCLUSION 38 The rate of activation of hydrogen by silver amine complexes was observed to be fi r s t order dependent on both complex and hydrogen concen-tration. This is in agreement with Webster's observations on the silver system at high temperatures and in the presence of basic ligands. Hetero-lytic splitting of the hydrogen molecule is suggested in the rate determining step (26), (33). The rate of activation was seen to vary inversely with complex stability in a manner similar to that reported for Cu(II), Hg(ll) and some silver complexes (31), (32), (33). Two possible mechanisms can be used to explain these results; the f i r s t involves direct transfer of the proton released in the rate determining steps Hj + Ag(R 3N) 2—*-R 3N - Ag - NR^ —=>- AgH + R3NH+ + R^ f - H - Es-In the other water acts as the main proton acceptor in a l l cases except that of the ammonia eomplexs ' + ? • Hj + Ag(R3N)2 + B^O-^RjN - Ag - 0-H NR 3^R 3N + AgH + R3NH + IL^ O g-E - Hg + The f i r s t mechanism finds support in the reasonable correlation drawn between the rate of reaction and the function (pKft - logK^) for the simple monoamines. Since amine basicity should be a measure of the strength of the incipient H - NR3 bond and the complex stability a measure of the strength of the Ag - NR3 bond, the reaction rate should increase with in-creasing magnitude of this function. In addition the rate of activation by silver - triethylamine complex in D20 and HjO i s the same suggesting that 39 solvent molecules are not involved in the rate determining step and that the proton is accepted directly by the ligand amine. However, this evidence is not conclusive since i t is not clear whether the use of Dg0 ^ Place of HgO would introduce only a solvent basicity difference, A water mediated mechanism appears plausible in that the ability of a ligand such as an amine with its one coordinative position bonding to silver would be hindered from accepting a proton, A water ligand having one free coordinative position would be able to accept the proton in the rate determining step. The inverse dependence of rate on complex stability would reflect the difficulty of replacing the amine ligand by a water molecule, A recent study of proton transfer between amines in aqueous medium indicates two mechanismsi the f i r s t , preferred by the alkylamlnes, involves proton transfer through an intervening water molecule. The second, used by ammonia, involves transfer of the proton directly between ammonia molecules. The anomalously low rate observed for the silver-ammonia complex (slower than for the water complexed species) compared to those rates observed for the other monoamines may be explained by the difficulty in effecting a direct proton transfer to the ammonia ligand in the rate determining step. The abnormally high activation energy and positive entropy change for the ammonia complex appears reasonable in that, unlike the alkylamine complexes, release of the proton accepting ligand would be uncompensated by coordi-nation of a water molecule. The dibasic complexes displayed a greater activity and were ob-served to have a greater negative entropy change than the monoamine com-plexes. This suggests an accelerating effect due to the presence of the 40 second basic group possibly by accepting the proton released or by coordinating with the silver in the position vacated by the proton-accepting ligand in the rate determining step. The participation of the free basic group in the activation is further substantiated by the fact that the rate decreases as the second basic group becomes more distant from the silver atom in the complex. A water mediated mechanism may occur with these com-plexes as well. It would appear reasonable that the presence of a basic ligand i s responsible for the generally faster rates observed with silver amine com-plexes than the water coordinated silver species. Unlike similar Cu(Il) and Hg(ll) complexes, donation of electrons from the ligand into the silver d-orbitals does not have a great effect on the formation of a bond between hydrogen and the activating species. 41 REFERENCES 1. Rice, F. 0. and Herzfeld, K.F., J. Am,Chem. Soc., j>6, 284 (1934). 2. Varnerin, R. E. and Dooling, J. S., J. Am. Chem. Soc. 28, 1119 (1956). 3. Beeck, 0., Rev. Mod. Phys., 12, 61 (1945). 4. Balandin, A. A., Zeit.fur physik. Chem., 2B, 289 (1929), ibid.3B. 167 (1929). 5. Beeck, G. and Ritchie, A. W., Disc. Farad. Soc, 8, 159 (1950). 6. Sherman, A. and Eyring, H., J.Am.Chem.Soc., 5Jt» 2661 (1932). 7. Reynolds, P. W., J.Chem.Soc, 265 (1950). 8. Dowden, D. A. and Reynolds, P. W., Disc.Farad.Soc., 8, 184 (1950). 9. Couper, A. and Eley, D. D., Disc.Farad.Soc., 8, 172 (1950). 10. Beeck, 0., Disc.Farad.Soc., 8, 118 (1950). 11. Mott, N. F. and Jones, H., 'The Theory of the Properties of Metals and Alloys', Oxford University Press, London (1936). 12. Dowden, D. 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