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J ) >)a.:.)VI.J?r 3. blxrfl: ,. f. 2 2b).. 13)!) >5..&)> 9.; 1.3.25. )1. 13.12:? .aim‘mmISfifi 4?. .u rsoiirlu..vncr. . uh ,1... an...“ . . wbximfgfi ..)>..Isu\>).u..\ . 3...»: $55753: . 35...) 13.2.1. 1.)) ~u§v¢AL.L.. . ‘ ; u I..|\¢l4 . ‘ . Cwnruuwfi‘..fifi.uuh. «rue... r..¢.<..~hr..;.LL... ., a . w: 1 5. .. c.‘ . v .11.. I Ltel?..7fi.0& M . Ln... fivflnflmhumr. ‘ . 3:45....) 3 [1E3qu' 0.2» ataxia; mun-- er 1* "fl- . as: “r e 3‘- - OV‘J WA .1 ’ h «v ' .a‘ -f \V “ L ' : Iv, V-‘n My". , I". j. l\.4). . -|. . :1... ‘ ~ -.~ . a'.‘ ‘J yi¥':'u:'\;‘l."l'll‘" r1113: '2 97:17: '2 .2:V=.-.RS!TY DEPAHI‘ ..,.. :14"? (3;: SHEiw’liSTRY MICHIGAN D ABSTRACT THE ACCELERATION OF THE URANIUM(IV) — URANIUM(VI) ELECTRON EXCHANGE REACTION BY TARTARIC ACID By E. Phillip Benson, Jr. The effect of several organic acids on the exchange reaction be— tween uranium(IV) and uranium(VI) in aqueous perchloric acid was studied. The catalytic effect of these acids was found to increase in the order malonic acid < maleic acid < malic acid << tartaric acid. More detailed studies of the reaction in the presence of tartaric acid revealed that the order of the reaction is 1.3 with respect to uranium(IV) and Ooh? with respect to uranium(VI)o The exchange is 0.90 order with respect to tartaric acid and hydrogen ion has an order of ~2o9. The predominant uranium species in solution are U4.4 and UOZ++. The following three paths for exchange U+4 + H20 <———> U0}?3 + H+ (fast) UOH+3 + U02+2 <2:> Y” + 2H+ (fast) Y+3 + UOH+3 <+——? 2+6 (rate-determining) and U+4 + H20 <2) UOH+3 + H+ (fast) HZTar <:> Hrar‘ + H+ (fast) +3 _ +2 . . UOH + HTar ———‘> (AOC.) (rate-determining) +2 ++ (A.C.) + U02 > products (fast) and IIIIIIIIII________________________________________________“Fj_‘;;_“_——_III E. Phillip BensonJ Jr. U+4 + H20 UOH+3 + H+ (fast) HZTar éZZ?’ HTar_ + H+ (fast) UOH+3 + HTar‘ ‘éZZ?’ [(U0H)-(Hrar)]+2 (fast) [(UOH).(HTar)]+2 + U02++ ———A> (A.C.)+4 (rate—determining) > products (fast) (A.c.)+4 combine to give an expression for the overall rate = 567 x 10‘4[U+4]2[U02++] + 7.3 x 10'5[U+4][H2Tar] R [HJ']4 [W12 192 x 10‘5[U+4][H2Tar][Uoz++] [HHZ Rates calculated using this expression agree well with rates obtained experimentally. The rate of the reaction increased with increasing ionic strength and was markedly accelerated by temperature increases. Irradiation with an ultraviolet lamp caused a very large increase in the rate of the reaction. THE ACCELERATION OF THE URANIUM (IV) - URANIUM (VI) ELECTRON EXCHANGE REACTION BY TARTARIC ACID By E. Phillip Benson, Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1963 ACKNOWLEDGMENTS The author wishes to acknowledge the advice and encouragement of Professor Carl H4 Brubaker, the patience and understanding of his wife, Beverley, and the financial aid of the Atomic Energy Commission. ii TABLE OF CONTENTS PAGE INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . l THEORETICAL . . . . . . . . . . . . . . . . . . . . . . . . . . 1h EXPERIMENTAL . . . . . . . . . . . . . . . . . . . . . . . . . . 19 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . Al [HSCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . . . 68 APPENDICES A. Preparation of Exchange Solutions using a pH Meter . . 72 B. Computer Program . . . . . . . . . . . . . . . . . . . 75 c. Original Kinetic Data . . . . . . . . . . . . . . . . . 80 TABLE II III IV VII VIII IX LIST OF‘TABLES PAGE Isotopic composition of tracer . . . . . . . . . . . . . 20 Melting points of organic acids . . . . . . . . . . . . . 29 Oxidation of uranium(IV) stock solutions . . . . . . . . 32 Effect of various organic acids on the exchange rate . . b5 Dependence of exchange rate on the concentration of ’ uranium(IV) and uranium(VI) . . . . . . . . . . . . . . . h8 Dependence of exchange rate on the concentration of ' hydrogen ion . . . . . . . . . . . . . . . . . . . . . . b8 Dependence of exchange rate on the concentration of tartaric acid . . . . . . . . . . . . . . . . . . . . . . SO Dependence of exchange rate on ionic strength . . . . . . Sl Dependence of exchange rate on temperature . . . . . . . 51 iv FIGURE LIST OF FIGURES Uranium(IV) preparation and storage flasks .Nitrogen purification train . Adaptor for volumetric flask Typical rate data for different organic acids . Log R vs log of concentration of uranium(IV) and uranillHVI) O O O C C C O C C O O O O O O O C 0 Log R vs log of concentration of hydrogen ion and tartaric acid . Known hydrogen ion concentration as a function of measured pH . . . . . . . . A function of R XE uranium(VI) concentration PAGE 21; 26 3b ALL A7 A9 53 58 INTRODUCTION In the last fifteen years, many papers have appeared which are con- cerned with the kinetics of inorganic oxidation-reduction reactions. The increase came partly as a result of the development of many new techniques of kinetic observation, and partly because of the increased availability of radioactive nuclides. As a result of the increased activity in experimental work in this area, interest grew in the nature of the mechanisms by which such re- actions occurred. Shafferl,2 and Michaelis3 were the first to attempt to explain the observed rates of reactions as dependent on some factors other than thermodynamic considerations. Michaelis' principle of "compulsory univalent oxidation steps" in- vokes the limitation that all oxidation-reduction reactions involving stable oxidation states that differ by two electrons (e.g. Tl+ - Tl+§ Sn+2 - Sn+4) occur by successive one electron steps. It evolved from consideration of a limited number of oxidation—reduction reactions and is now believed to be without universal validity. Shaffer's rule of "equivalence change" states that reactions be— tweenCXe-equivalent oxidizing agents and two-equivalent reducing agents (or vice-versa) are often slow, compared with those between one-equiva— lent reducing agents and one-equivalent oxidizing agents or between two—equivalent oxidizing and two-equivalent reducing agents. Examples are the slow reduction of Tl+3 by Pe++, or of Ce+4 by Tl+ compared with the rapid reduction of Tl+3 by Sn+2 or of Ce+4 by Fe+2. The slowness of the former types of reactions is explained by mechanisms which in- volve either a termolecular step or the formation of unstable inter- mediate oxidation states. 2 Although there is still no complete compilation of data for ex— tensive comparison, Halpern4 has compared three systems involving combin- ations of one and two electron equivalent oxidizing and reducing agents. While he concludes that one cannot draw any detailed results from the +3 and comparison, the rates for two of the systems studied (Fe+2 - Tl Tl+ - Co+3) are not lower than those of the corresponding exchange re- actions, as would be predicted, but are intermediate between them. This would indicate that the principle of equivalence change is not a uniquely applicable rule. Halpern considers the principle further in a recent review article.5 Accompanying the increase of experimental work on the kinetics of aqueous oxidation-reduction reactions has been an increase of interest in the theoretical aspect of electron transfer, since it is only recent— ly that systems have been investigated in which clear—cut interpretation of results is possible. In an electron transfer reaction, it is not known if the electron lost by the reducing agent is the same one that is gained by the oxidizing agent and how this electron moves from the reducing agent to the oxidizing agent. Most of the systems studied have come to be explained by two important forms of the activated complex in electron transfer. These are usually denoted as the ”outer sphere" acti-v vated complex and the ”inner sphere" or "bridged" activated complex.6 The distinction between the two is not always sharp and many reactions at this stage cannot be assigned with certainty to either class.7 In the "outer sphere" activated complex, the number and identity of the groups comprising the first coordination sphere remains unaltered by electron transfer. This means that substitution is a much less rapid process than transfer. In this case the readjustments which 3 accompany electron transfer take place largely in the solvent, and there is little change in the dimensiomsof the molecules on electron transfer. Wahl8 has summarized results for some reactions of this type. The other general class of electron—transfer mechanisms involves the ”bridged” activated complex. The first clear demonstration was by Taubeg in the reaction of [(NH3)5COCl]+2 with Cr+2 to give NH4+, Co+2, and CrCl+2. Since both the'Co+3 complex and the Cr+3 product are sub- stitutionally inert, electron transfer must occur through a bridged intermediate of the type [(H3N)5 Co+3 - c1 - Cr+2 (0H2)5]+4 in which Cl is simultaneously coordinated to both metal ions. It should be noted that although the bridging ligand is generally transferred from the oxidant to the reductant, this is not a necessary requirement for electron transfer. Also, catalysis by anions or incorporation of anions into the coordination sphere of the oxidized metal ion does not indicate the participation of the anion as a bridging ligand.10 Pumar- ate and p-phthalate are of special interest as bridging ligands in the oxidation of Cr+2 bleH3N)5 Col.T2, since the rates are much higher than for other carboxylic acids.11 This has been interpreted in terms of a bridged intermediate in which the two metal ions are coordinated through the "remote” carboxylate groups 4 [(H3N)5 Co - o o — Cr(OH2)5]+ c - CH = CH - c H I 0 OR where R = H, CH3, or C2H5, with the electron being transferred between them by ”conduction” through the conjugated n-electron system. This 1; attack is sterically favored over attack at the adjacent carboxyl group. The use of such conjugated bridging groups for distinguishing between the two types of mechanisms and for the systematic variation of struc- tural parameters makes these systems extremely valuable. A possible mechanism of electron transfer between metal aquo-ions, first suggested by Dodson and Davidsonlz, is through transfer of a hydrogen atom between hydration shells. There is some evidence in sup- port of such a mechanism. For example, the rates of the Fe+2 - F‘e+3 and the Fe+2 - FeOH+2 reactions are lowered by a factor of two in passing from H20 to D20 as the solvent.13 In addition, the activation ener- gies of a large number of diverse redox reactions involving metal aquo- ions are close to 10 kcal/mole, and their activation entropies close to -25 eu, suggesting that they proceed by a common mechanism involving water. A modified view14 of the role of water in thesezeections is that the coupling of the hydration shells of the two ions by hydrogen bond— ing lowers the energy of the activated complex and, by increasing the overlap between the exchanging orbitals, provides a more effective con- ducting path for electron transfer. In this context transfer of hydro- gen is incidental to its bridging role, and whether or not it occurs depends on the relative proton affinities of the two hydration shells after electron transfer. In some cases redox processes proceed through mechanisms which do not involve direct reaction between the oxidizing and reducing agents. Such indirect mechanisms are frequently responsible for catalytic ef- fects in redox systems. 5 One possible alternative is the release of an electron by the re— ducing agent to the solvent and its subsequent capture by the oxidizing agent. Also oxidizable or reducible ligands can act as electron car- riers between metal ions. Intermediate oxidation of the bridging ligand without release from the bridged complex is another mechanism of elec- tron transfer. In addition, ions which can exhibit two or more stable oxidation states may also serve to transport electrons in redox reac- tions through a chain mechanism. various theoretical aSpects of electron transfer processes in solu- tion have been considered by W. F. Libby,15;16 R. A. Marcus,173¥8 N. S.. Hush,19 R. J. Marcus, B. Zwolinski, and H. Eyring,20 and K. J. Laidlerini22 Nearly all these treatments have emphasized the dependence of the rate on the following factors: electrostatic interactions between the over— all charges of the reactants, the reorganization energy of the ligands and of the surrounding medium prior to andduring electron transfer, as- sociated with the Franck—Condon restriction, and the rate of the electron- transfer process itself in the activated complex. Libbyl5 discussed the formation of the activated complex and empha- sized the restrictions of the FrandeCondon principle in its application to electron transfer in aqueous solution. The Franck—Condon principle states that transfer should be inhibited by the relatively long times required for movement of the heavy water molecules constituting the hydration spheres compared to the transit time for the electron. The differences in rates of movement of the electron and the extra energy .of hydration due to the electron exchange process mean that the electron must make the transition against a barrier comparable in magnitude to the amount of energy involved in the subsequent slow orientation of the 6 water molecules to the new charge situation. This gives rise to the principle that electron exchange can be catalyzed by complexing the ex- changing ions in such a way that the complexes are symmetrical. In a later article, Libby16 applied the principle to oxidation-reduction re- actions of the transition elements in which a bridged activated complex is Operative. R. A. Marcusl7 has attemptedEiqwmfifitative treatment, incorporating the restriction of the Franck—Condom principle, to describe a mechanism for electron transfer. In the reaction between two reactants, A and B, the following steps may take place (1) A + B X'y (2) X( X (3) X > products where X% is the activated complex. The overall rate is given by (h) v = kc c where c's denote concentration and k is the observed rate constant. If the forward step is at least as probable as the reverse step in reaction (1), then (S) zkl Using the restriction that only slight overlap of the electronic orbitals of the two reacting species in the activated complex is neces- sary, he obtains a value for the overall rate constant that is given by 7 (6) k gkl = Z exp (— Alfie/ET) where Z*= collision number in solution y AP = free energy of formation of X” in excess of that for two neutral, nonreactive particles in solution .5 = Boltzmann constant T = absolute temperature AP* is obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction. In a second article18 he applied the model to some previously reported homogeneous isotopic exchange reactions and obtained impressive agreement with the experimental data. N. S. Hush19 has also proposed a theory of electron transfer for processes in which the coordination shells about the ions are not dis— rupted on electron transfer. The central concept is that the probability density for electron transfer in each step can readily be found and the equations for the calculation of the free energy, enthalpy, and entropy of activation are then easily derived. Reasonably good agreement with experiment is found for isotopic exchange reactions. This method of ap- proach is similar to that of R. A. Marcus and the general conclusions obtained by either method are similar. R. J. Marcus, B. Zwolinski, and H. EyringzO have classified avail- able data pertaining to electron—exchange reactions on the basis of the entropy of reaction: one group with negative entropies of activation and another with positive entropies of activation. In the oxidation-reduc- tion reactions considered, the ions modify their structures in such a way that transfer of the electron leaves the total energy unchanged. During the approach of the reactive ionic species leading to the transi- tion, ionic repulsion forces are overcome and the coordination and 8 hydration shells of both ions are rearranged until their electronic states are symmetrical, thus permitting a rapid transition to take' place. Those configurations which give the fastest reaction will be the ones measured. Since these will not have too high a free energy of activation, any measurable rate for an oxidation-reduction reaction involves a transmission coefficient (probability of transition) less than unity. Its magnitude will be determined by the height and thick- ness of the electronic barrier for this transition. For convenience the electronic transmission coefficient (K'e) can be represented in the following form: Ti -8 = _ 1/2 (7) K8 8X13 _ rab(2m(V W)) 3h i where V = height of the electron barrier W = kinetic energy of tunnelling electron r = tunnelling distance ab m = electron mass h = Planck's constant. The class of reactions with positive entropies of activation have an electronic barrier that is quite thin at the transition point with the transmission coefficient near unity. The reactions characterized by apparent negative entropies of activation are those with appreciable electron barrier widths at the activated state, consistent with smaller energies of activation at larger critical distances of ion approach. Laidler“:22 has also given a theoretical treatment of electron— transfer reactions involving quantum-mechanical tunnelling. His more complete calculation also includes terms which account for repulsive 9 free energy and the energy of solvent reorganization. His calculation for the reaction > +3 %+2 (8) Fe+2 + Fe*+3 < Fe + Fe predicts a minimum weighted value of 15.9 kcal/mole for free energy of activation at an interionic separation of h.2 A. This compares well with the experimental value of 16.8 kcal/mole. Newton and Rabideau23 have reviewed many of the aqueous oxidation— reduction reactions of uranium, neptunium, and plutonium. They summarized all of the kinetic information in terms of the equations for the net activation processes and the associated thermodynamic quantities of acti- vation. Using the assumption that all of the reactions were one—electron oxidation—reduction reactions, the equations for the net activation processes were obtained from the rate laws. The equations were formu— lated in terms of any rapid equilibrium reactions which may have occur- red prior to the rate-determining step. The result described the form- ation of the activated complex without regard to the detailed mechanism. The thermodynamic quantities of activation, AE*, AH*, AS%, were calculated from the equations of the absolute reaction rate theory.24 The quantity called S* is the formal ionic entropy of the acti- complex vated complex calculated from AS* using the standard entropies of the ordinary Species present or: (9) S* = AS% + .§:§0 complex reactants The values for these standard entropies are calculated on the convention -0 = that SH+ O. It was observed that the data reviewed did not fall into distinct classes as suggested by R. J. Marcus, B. Zwolinski, and H. Eying20 but 10 instead exhibited a range of values. This wide range is reduced when allowance is made for the hydrolysis equilibria involved. A relation between AH% and the heat of reaction, AHO, was found to hold for a large number of oxidation-reduction reactions of the actinide elements. Within this correlation, AH),c for purely "electron- transfer” reactions such as > (10) Pu+3 + Pqu+2 < Pu+4 + Pqu+ appeared to be somewhat lower than for reactions involving hydrolytic or structural changes such as (11) Np+4 + NpOz+2 + 2H20 <:ZZ:> 2Npoz+ + hH+ which presumably reflects an additional contribution to AH* from bond rearrangement in the latter cases. A series of formally identical reactions exhibited varying values of AS% but had approximate agreement among the §*complex values. This indicates that an important source of the difference in the AS* values lies in the differences in the entropies of the reactant ions. The most important single factor which determines the entropy of the activated complex appears to be its charge. It was found that all reactions with an activated complex having a given charge type exhibited the same values of S* It was noted that the activated complexes complex° of simple electron exchange reactions exhibited values of S* complex similar to those of other reactions. Electron exchange reactions between uranium(IV)andtxanium(VI) have been studied in sulfate solutions by Betts,25 in chloride solutions by Rona,26 and in perchlorate solutions by King,27 and by Masters and Schwartz.28 11 King reported only that the exchange reaction was slow and suggested that this was due to the formation and breaking of metal—oxygen bonds. Betts reported the exchange in sulfate medium in the presence of constant external illumination. Although he presented no detailed mechanism for the exchange, it has been suggested that the active intermediate in the exchange is uranium (V). It has been shown by Heal29 that illumination causes a considerable increase in the concentration of uranium (V). Rona has studied the exchange reaction in chloride solutions and found that it is second order in uranium (IV), first order in uranium (VI) and negative third order in hydrogen ion concentration. She also 9 noted no effect due to added ions or due to illumination of the solu- tions. The reaction was found to have an apparent activation energy, (33), of 33.i1 kcal per mole. She eXplained her results by means of the following mechanism. While uranium (VI) is present as UOZ++ in these solutions, uranium (IV) is present according to the following rapid equilibrium 4. (12) U+4 + H20 <"""> UOH+3 + H The value of the equilibrium constant, Kh’ had previously been evalu- ated by Kraus and Nelson.30 Rona suggests that UOH+3 will react more readily with U02++ to form an intermediate ion, Y+3, containing an oxygen bridge according to the following equation: (13) UOH+3 + U02++ + ZHZO <——f> Y+3 + 2H+ The equilibrium constant for this reaction is K1. This intermediate ion now reacts further with uranium (IV) in the rate determining step to form the activated complex, 2+6 12 +6 (1h) Y+3 + UOH+3 > 2 which breaks down into the final products +6 (15) Z -———+> products. This mechanism gives a calculated reaction rate, v, that agrees well with the experimental results. (16) v k[Y+3] [UOH+3] and substituting [U(IV)]2 [U02++] [[H+] + l 2 [H+]2 (17) v = kKl _K;_ More recently Masters and Schwartz have investigated the uranium (IV)-uranium (VI) system in perchlorate solutions. They confirmed Rona's work in perchlorate solutions and identified another path which predomin— ates at conditions of low uranium (IV) ion concentrations and at tempera— tures above 25°C. This path was found to be first order in uranium (IV), first order in uranium (VI) and negative third order in hydrogen ion. The energy of activation, (Ea), was found to be 38.1 kcal per mole. The strong effect due to ultraviolet irradiation suggested that the reaction path involved uranium (V) as an intermediate. The forma- tion of U(V) can be given by the expression (18) g. [UOZ+] = 2k [U+4] [U02++] [HIT3 which is twice the experimentally measured rate. The disproportionation of U(V) is given by (19) — 5% [U02+] = kD[U02+]2[H+] 13 By equating the above equations, the equilibrium constant, K , may be determined (20) KB = kD/2k Masters and.Schwartz obtained a value of 1.02 x 109 for K.B which agrees well with the value of 1.05 x 109 observed by Kraus and Nelson31 in polarographic studies of the U(IV)-U(V)—U(VI) equilibrium. This result meant that the activated complex formed in the ex- change reaction was identical with that formed in the disproportionation reaction. The mechanism may be described schematically as + 23H + UOZ++ + ZHZO <:-3—}—{q:> (HO-U-O-UOZ)+3 (21) U+4 and —H+ ——> (22) (HO—U-O—UOZ)+3 <:fi*' 21102+ This reaction sequence is formally identical with that encountered in reactions of other members of the actinide series.23 THEORETICAL In an exchange reaction (23) AX + 13x"? = A)?" + BX where X* designates the isotopically labeled compound, let R be the rate of exchange.32 If the concentrations are designated as follows, (211) [AX] + [118"] = a (25) [BX] + [an] — b (26) [118"] = x, [1x] = a -x (27) [BXT‘] = y, [BX] = b -y then the net rate is given by dx _ d _ (a — x) x (b - ) _ R (ay - bx) ‘28) _——l—R%—a—__Ra—bx__§5 dt dt But since (29) Y'Ym=x‘xm and (30) Xm/ch = a/b therefore (31) 3-15- = 2% [(x.. -x>1 On integration one obtains (32) In [xm /(xa,- x)] = :7. (a + b)t The more familiar form of the equation is 11. 15 (33) In [1 - x/xm} = - aa; b Rt The quantity x/xa, is the fraction of exchange and is often merely designated as F. An exchange system conforms to this rate expression if a graph of 1n (l-F)'ys t is rectilinear. If a straight line is ob- tained, then R may be determined directly from the slope of the line. The fraction of exchange can be conveniently determined in a variety of ways. If the separation is not quantitative or reproducible, it is often convenient to use the specific activity (counts per unit time per unit weight) of one of the exchanging species. Prestwood and Wahl33 have shown that S — S0 (311) F = gm—j'S—O where S is the specific activity of AX at time t, SO the specific activ- ity at zero time, and Sa, the specific activity when complete exchange has occurred. The rate of the exchange reaction, R,is equal to some function of the various concentrations involved and one or more rate and equilibrium constants. For example, for a simple bimolecular reaction (35) R = k[a][b] where k is the specific reaction rate constant. The order with respect to each species in solution may be determined by systematically vary- ing its concentration while all others are kept constant. This dependence of reaction rate on temperature34 has been quanti- tatively formulated by Arrhenius as (36) ln k = ln A—Ea/RT or k = A exp(—Ea/RT) 16 Ba is the activation energy for the reaction and A is known as the pre— exponential (or Arrhenius) factor. Experimentally a graph of 1n k'ys the reciprocal of the absolute temperature gives Ea from the slope and ln A as the intercept. It should be pointed out that the above discussion applies only to individual specific reaction rate constants. A complex reaction may appear to follow a simple kinetic order over a limited range of exper- imental conditions. The apparent rate constant for such a reaction is not a rate constant for a single process but may be a complicated func- tion of many rate constants. If this rate constant is plotted against temperature it may be expected that the Arrhenius equation will not be obeyed. This lack of agreement is often useful in indicating the com— plexity of the reacting system. In the theory of absolute reaction rates,24 the equilibrium between reactants and the activated complex can be represented as (37) all + bB + ....... 4—3 11* where M* represents the activated complex and the equilibrium constant can be represented as (38) K = C where CW is the concentration of the activated complex. The rate of reaction of the activated complex formed is given by a b (39) rate = kr CA CB ....... where kr is the rate constant. From the theory of reaction rates a pseudo equilibrium constant, K*, can be defined that is related to the 17 rate constant for the reaction by kT H (110) k,. = (71-) K where k is the Boltzmann constant, T is the absolute temperature, and h is Planck's constant. Thus, the definition of quantities analogous to the thermodynamic functions associated with equilibrium constants is possible. (1.1) AF”e = - RT in K H d ln KI (h2) AH = RT2 -—afiF—-' or (113) AH)" = RTZ d 1“ kr - RT dT and H H (1.1.) 15* = ———AH " AF It follows that (1.5) 11* = exp(-AF*/HT) = eXp(As*/H) eXp(-AH*/RT) or in terms of the rate constant (16) k, = (tr/h) exp<1s""/R> exp<-AH’"/RT> The relations derived from the theory of absolute reaction rates can be compared with the Arrenhius equation to calculate thermodynamic quantities. The differential form of the Arrhenius equation is d 1n k _ 2 If this equation is compared with equation (AB) it can be seen that (18) 111* = Ea - RT By substituting the above equation H1(N6)the entropy of activation, 18 AS*, can be determined from the result (1.9) k, = 2371/11 exr 1102++ + 2Fe++ + 11H+ with one equivalent of iron (II) produced for each equivalent of uranium (IV) oxidized, the iron (II) released in the reaction can then be ti— trated with the standard cerium (IV). 31 The procedure used was as follows. Samples of uranium (IV) rang- ing from 0.5 ml to 2.0 ml, depending on the concentration of the stock solution, were treated with 1.0 or 2.0 ml of a 2% solution of iron (III) chloride (depending on the concentration of the uranium (IV)). To this was added 2 ml of a solution made by diluting 25 m1 of concentrated sulfuric acid with 100 m1 of deionized water. This step is taken to make certain the cerium (IV) will remain in a sulfate solution since the potential for the reduction of cerium (IV) to cerium (III) depends on the medium.46 The solution was next diluted with 20 ml of water and two drops of the iron (II)—o—phenathroline complex (Ferroin) added. The solution was now titrated at room temperature with the standard cerium (IV), the endpoint being indicated by the color change from red- orange to pale blue which occurs when the Ferroin is oxidized to a complex containing iron (III). An indicator blank was run. Uranium (VI) was the only other oxidation state present in the uranium (IV) stock solutions. Any uranium (III) formed was removed immediately after the electrolysis and any uranium (V) disproportion- ated49 under these conditions. The total uranium content was determined by pouring the same size sample through a Jones reductor50 with 5 ml of a 1:9 concentrated sul- furic acid-water solution and washing with two 10 ml portions of deion- ized water. Air was bubbled through this solution for two minutes to oxidize any uranium (III) formed to uranium (IV). The reduced solution was then titrated as before except no dilution was necessary. The uranium (VI) concentration in the stock can be found by difference. The total hydrogen ion content, (Ht+), of the stock solutions was determined by passing an aliquot (usually 0.5 to 1.0 ml) through a 32 column of Dowex 50W-X12 ion exchange resin (Baker's Analyzed Reagent, 100-200 mesh, hydrogen form). Uranium (IV) attaches itself to the col— umn, releasing four moles of hydrogen ion for each mole of uranium (IV).38 The column is eluted with fifteen milliliters of deionized water and the eluant titrated with standard base. The free hydrogen ion concen- tration, (HO+) in the stock solution can be calculated by the equation: ) + . (51) Ho+ = Ht - UC4 - 2C6 where C4 is the concentration of uranium (IV) and C6 is the concentration of uranium (VI) in moles per liter. It should be noted here that although all of the uranium (VI) was reduced in the electrolysis to produce uranium (IV) and the uranium (IV) was stored in a closed flask under an inert atmosphere, small amounts of the uranium (IV) appeared to be oxidized over a period of time, as illustrated in Table III. Table III. Oxidation of uranium stock solutions Date Elapsed Time [H*l A u(1v) u(v1) 5/2h/63 ——————— 0 8A2.N 0.3686 g 0.000 .8 6/3/63 10 days ------- 0.36112 11 0.0025 11 6/27/63 1 3h days 0.892 N 0.3533 N 0.016035 7/11/63 h8 days 0.910 g 0.31.12 A 0.0278 A 8/25/63 93 days 1.123 M 0.2334 131 0.1356 .111 Since the half-reaction for the oxidation of uranium (IV) is *> (52) U+4 + 2H20 U02++ + 111* + 2 e“ 33 it can be seen that the hydrogen ion concentration will increase more rapidly than the uranium (VI) concentration. Because of these changes in titer all uranium (IV) solutions were restandardized before a series of runs was made, if more than four days had elapsed since the last restandardization. Stock solutions of uranium (VI) were analyzed for uranium in the same manner as the total uranium content of the uranium (IV) stocks was determined. The free hydrogen ion content was also determined in the same manner. Kinetic Studies This section describes the steps involved in following an exchange reaction using the normal procedure. Earlier work utilizing another method is presented in Appendix A. The exchange experiments were carried out at a molar ionic strength of 2.00 in 100 ml flasks which had been blackened by dipping them first in X-I-M bonding material (H. Forsberg Company) and then in black enamel paint. The flasks were cleaned by allowing aqua regia to stand in them overnight after which they were thoroughly rinsed and dried. The rins- ing process included a minimum of six washings with distilled water followed by a minimum of six more with deionized water. Since the re- actions are very slow, the solutions were protected from the atmosphere by nitrogen. A 1h/35 standard taper joint was fitted with 6 mm inlet and outlet tubes as shown in Figure 3. The vertical tubing served as the nitrogen inlet and the horizontal tubing acted as the outlet to the next inlet 3h 1%); 1.1 '. --. tube. Eleven flasks were mounted in a constant temperature bath with these special adapters in series as tops. The flasks were flushed before use by maintaining a rapid nitrogen flow overnight. Experiments carried out with a positive nitrogen pressure above the solutions were studied for a period of four weeks without detect- Figure 3 able loss of uranium (IV). The exchange solutions were prepared by combining the required amounts of water, sodium perchlorate, perchloric acid, tartaric acid and uranium (VI) perchlorate in that order in a 150 ml beaker. Then the proper amount of uranium (IV) perchlorate stock was added, the re- sulting solution mixed with a stirring rod, and then poured into one of the previously flushed flasks while a slow flow of nitrogen was maintained. Earlier results indicated that the experiments would have to be car— ried out at conditions where the hydrogen ion concentration would be 1.0 M. Although the amount of hydrolysis of both uranium species is low at these conditions, stock solutions of uranium (IV) and uranium (VI) were made up with free hydrogen ion concentrations near 1.0 M. This minimized any change from the calculated hydrogen ion concentration by hydrolysis changes which might occur when the stock solutions were mixed. The total mixing process required a maximum of fifteen minutes. Of this time the uranium (IV) was exposed to the atmosphere for a maximum of two minutes although Lundell and Knowles51 note that solutions of uranium (IV) undergo no change in titer on exposure to the atmosphere 35 for one half hour. For reactions carried out above room temperature the procedure was altered in the following manner. The uranium (IV) was withdrawn and added directly to the reaction flask. The solution made up of the other reagents was stored in a clean flask in another part of the bath. After a lapse of four hours to allow the contents of each flask to attain the bath temperature, the contents of the flask containing the uranium (VI) were poured into the reaction flask, the protective top replaced, and the flask agitated vigorously to complete mixing. Separation Procedure The separation procedure used was adapted from that described by Masters and Schwartz.28 Five milliliter aliquots of the reaction solu— tion were withdrawn from the reaction flask and delivered into five milliliters of a 0.1 M solution of h,h,h—trifluoro—l, (2 thienyl) -l,3- butanedione (hereafter called thenoyltrifluoroacetone) in benzene con— tained in a 25 ml separatory funnel. The separatory funnel was shaken vigorously for one and one half minutes and the lower layer drawn off. The uranium (IV) was extracted into the benzene layer as a complex con— taining four moles of the thenoyltrifluoroacetonate anion. + —> (53) U+4 + h HTTA < U(TTA)4 + hH Five milliliters of a 0.5 M perchloric acid solution was added and the funnel shaken vigorously for another one half minute. The lower layer was drawn off again and discarded. The uranium (IV) was then re-ex— tracted into the aqueous phase by shaking it vigorously with 5 ml of 3.0 M hydrochloric acid for one and a half minutes. The uranium (IV) 36 is extracted as a chloro complex into the acid solution. The five mil- liliters of aqueous solution was drawn off into a twenty milliliter beaker for sampling. The thenoyltrifluoroacetone (Columbia Southern Chemical Company) was purified by sublimation in a vacuum of approximately one milli- meter at room temperature. The purified product was dissolved in ben- zene (C.P. grade) to prepare the solution used for the extraction. One molar perchloric acid, 0.5 M perchloric acid, and 3.0 M hydrochloric acid were prepared by adding the calculated amount of the concentrated reagent (perchloric acid — Baker's Analyzed Reagent and G. Frederick .Smith Chemical Company Reagent; hydrochloric acid — Baker's Analyzed Reagent and E.I. Du Pont de Nemours Reagent) to deionized water. The time of each separation was taken as the time when the sample was delivered into the separatory funnel. Since the reactions were slow, the time was read to the nearest minute from an electric clock. For convenience, zero time for a reaction was taken as the time when the first sample was removed. Handling of the Sample Three 0.5 ml aliquots of the uranium (IV) in 3.0 M hydrochloric acid were withdrawn and were placed on three separate 25 mm watch— glasses. Since this was near the capacity of the watch glasses, the edge of each watchglass was ringed with a line drawn with a grease pen- cil that prevented the solution from creeping over the edge of the watch— glass. Each set of three samples was heated to dryness under an infrared 37 lamp and transferred to a muffle furnace. When the samples had been heated to a temperature of 500 to 5500C, they were cooled and removed from the oven. This treatment converted the samples to orange uran- ium (VI) oxide . The above preparation of the triplicate counting samples gave a uniform deposit of uranium (VI) oxide over the surface of the watch— glass since evaporation was rapid. This prevented a large build—up of sample in the center of the watchglass and thus helped to lower the amount of self absorption of the o—rays emitted. The triplicate samples were always very similar in appearance. Since there were only small variations in the amount of uranium (IV) extracted for each separation during a run, the difference in self—absorption from separation to separation was negligible. The samples were counted for alpha activity in the pr0portional region using a windowless preflush flow counter (Radiation Instrument Development Laboratory - Model 2-7) with external pre—amplifier and a glow tube scaler (Baird—Atomic, Inc. — Model 131A). A 90% argon and 10% methane gas mixture (The Matheson Company) was used. If U18 obser- is short compared to the half-life of the isotOpe,52 vation time, t, then the standard deviation is given by (51.) s = W 'where M is the average number of atoms disintegrating in the time, t. If a reasonably large number, m, of counts has been obtained, that: number, m, may be used in the place of M for the purpose of evaluat- ing s. The counting rate R is given by (55) R = m/t 38 and the standard deviation of the rate is given by (56) SR = (m) 1/2/1: Five or ten minute intervals were usually sufficient to reduce SR to about 2% of the rate, R. The uranium (IV) in hydrochloric acid solution that remained after the counting samples were withdrawn was used to determine the concen- tration of the solution. The sample was placed in a one centimeter quartz cell and the absorbance measured at a wavelength of 650 mu, using a Beckmann DU spectrophotometer. Solutions of uranium (IV) in hydrochloric acid obey Beer's law and have a molar absorptivity of about 58 M_lcm—l. Therefore, the concentration of the solution can be determined from the following relationship: (57) C = 11/61 Where A is the measured absorbance, (i is the molar absorptivity, C is the concentration of the solution in moles per liter, and 1 is the path length of the cell used. Infinite time or complete exchange samples were prepared by taking advantage of the fact that the specific activity is the same in both ox- idation states when the exchange is complete.53 An ”H" cell was pre- pared by connecting two six inch test tubes by a length of ten millimeter tubing that contained a coarse frit. Into one side of the cell was placed an appropriate amount of concentrated perchloric acid and deion— ized water to make 6 or 7 m1 of a solution that was 2.5 to 3.0 M in hydrogen ion. One milliliter of concentrated perchloric acid was placed in the other side of the cell and to this was added a 5.0 ml aliquot of 39 the exchange solution. Electrolyses were carried out at one half ampere for 60-75 minutes using a platinum square for the anode and a carbon rod for the cathode. The solution produced, which contained all of the uranium as uranium (IV), was separated and treated as above. Miscellaneous Experiments Initially the attempt was made to study the exchange reaction us— ing a separation technique described by Rona.26 This technique separ— ated uranium (IV) from uranium (VI) by precipitating it as uranium (IV) fluoride. It was soon discovered that a separation by this means gave erratic and unreproducible results. Attempts were made to improve the results using thorium (IV) as a carrier in the precipitation since the solutions were not very concentrated in uranium (IV). This gave no increase in the efficiency of the separation and still gave erratic results as well. In addition the hydrofluoric acid used attacked the volumetric ware and thus required the use of constant calibrations. The extraction method of separation was successful. The geometry of the flow counter was determined by doing a standard separation on a known sample which contained only natural uranium (IV) and counting aliquots from this separation. Calculations indicated that the geometry was 85.6%. This high value is probably due to a large amount of back—scattering. The spectra of the uranium (IV) and uranium (VI) stocks were deter— mined on the Beckmann DK—2 spectrophotometer and were found to agree with those reported in the literature.54 Samples from several kinetic ho runs where the tartaric acid concentration was varied were also measured, but no evidence for any complex formation could be observed. It was observed that solutions made up for kinetic studies would often form a white to pale gray precipitate if tartaric acid was pres- ent. The stability of such solutions depended on the relative concen- trations of the uranium (IV), free acid, and tartaric acid present. For example, when [U+4] = 0.025 M, [U02++] = 0.027h M, [HZTar] = 0.260 M, [H+] = 1.00 M, and I = 2.00, a stable solution results. If the concen- tration of uranium (IV) or tartaric acid is increased or the amount of free acid decreased, precipitation occurs immediately. The precipitate slowly dissolves on the addition of perchloric acid to give a stable solution. With maleic, malonic, or malic acids, it is found that when other conditions are as above the [H+] can be lowered to 0.27 M without any precipitation occurring. Two experiments were carried out in which solutions in clear flasks at 25°C were subjected to the light emitted from a 250 W ultraviolet lamp (Kenmore; Sears, Roebuck, and Company). It was found that a solu- tion containing [U+4] = 0.025 M, [U02++] = 0.027h M, and [H+] = 1.00 M with I = 2.00 exhibited a half—time for exchange of only 750 minutes while a similar solution without light would be expected to have a half- time of exchange of 7.8 x 105 min. A similar solution 0.130 M in tar- taric acid was found to have a shorter half-time of 100 minutes compared to 2.h x 104 minutes without the influence of light. RESULTS From the triplicate counting samples and their corresponding absorb- ance values, specific activity values (hereafter designated by the sym- bol S) were obtained. These were corrected for the radioactive 238U present by subtracting the specific activity of a sample made up with— out any added 233U. This simple correction was valid since the maximum amount of 233U present was 2% of the total uranium and the half—life of 238U is 28,000 times that of 233U. Calculations were carried out by means of a program written for and executed by a Control Data Corporation l60-A computer. A print-out of the program, including the input for an experiment, is shown in Appendix B. In addition a reproduction of the results from the calculations performed on the data is duplicated on the next page of Appendix B. The fraction of exchange (F) was calculated from the following relation S — SO (3A) F = gagfffigg For convenience the first sample was taken as the zero time sample and its activity was used for So. The specific activity of a sample that had been electrolyzed for an hour was taken as S0,,which is possible because the specific activity of either oxidation state is the same at infinite time. The samples which determine S are taken as a func— tion of time. The McKay equation is written in the form of the equation of a straight line t1 A2 (58) Y = K' x + P where K', the slope, has the value —R/ab (a+b), P, the intercept, is given by 1n 100, y is the value of 1n (lOO-lOOF) and x is the elapsed time, t. Since the most probable slope of such a straight line is given by a least squares treatment,57 this calculation was performed on all data using the equations (59) K' = EEEEQL;;£E££§LZ an2 - (2x)2 (60) P = EPXZEPY ‘ Eixii§l n§§X2 - (EEX)2 where n is the number of values of x and y. The standard deviations of the results were then calculated by the treatment in Youden.58 In this treatment it has been assumed that the values of x are known with negligible error compared with the values of y, a valid assumption, because the reactions are slow, and thus there is relatively little error in measuring time. If this treatment is used, an estimate of the standard deviation of a single y measurement (s) is given by (61> We >12 - $313 - % Lie—fiat}: The quantity (n—2) is used instead of (n-l) since the data were used to estimate K’ as well as least squared values of y. The data were tested for the rejection of points in the following manner. Least squared values of y (labelled Y) were calculated for each value of x. The absolute value of the difference between this value and the experimental value (y) was then determined. Any A3 experimental value which did not fit the following test (62) |Y-y| éas was rejected. The standard deviations of the slope (sK,) and the intercept (SP) were then calculated by means of the following equations: 2 (63) 82 “S K' nExz - (2oz and (61) s; = 82-sz anz - (2)02 The standard deviation of the intercept showed that there was no evidence of induced exchange by the separation method, since all values for the intercept from the least squares treatment were within i 2% of the theor~ etical value. The standard deviation in the slope is used in determin— ing the standard deviation of the rate. Since ab (65) R " (‘K') 5:3 then ab (66) SR = SK' 5:5 A survey of the effects of several organic acids on the exchange reaction was carried out. Figure A shows some typical graphs of ln(lOO—lOOF) against t for different acids. Since the rate of the reaction at these conditions without any added organic acid was too slow to measure conveniently, it was estimated by extrapolation of Rona's data. It can be seen that tartaric acid has the greatest ac- celerative effect on the reaction. Maleic and malic acids have a similar Ah pmom owomoome owom owconz ofiom owfimz poor olefin: a.o has ooo.mm .oo.m u H .+: m os.a .AH>V: a samo.o .A>HV: a ommo.o .mpflom oficmmoo boooommwp now Home oboe Hmowaxw .1 onsmwm «OH x mosses: m m H 0 III N.Q a II Mid I? x m n O Ilam q 0.: (H001-001)UI 115 effect on the rate while malonic acid has little effect on the re— action. Table IV shows the calculated half—times for these reactions. The stability of the solutions containing the organic acids was studied further. It was found that s01utions that were 0.0250 M in U(IV), 0.027h M in U(VI), and 0.013 M in organic acid were stable down to hydrogen ion concentrations of 0.708 M for tartaric acid and to 0.270 M for the others. At these limits the effect due to tartaric acid was still greater than the others. Therefore, a more detailed study of the reaction in the presence of tartaric acid was carried out. These studies were conducted at a hydrogen ion concentration of 1.00 M so that the tartaric acid concentration could be studied over a moder— ate range. Table IV. Effect of various organic acids on the exchange rate. Uranium (IV) perchlorate = 0.0250 M, Uranium (VI) perchlorate = 0.027h M, Perchloric acid = 1.76 M, Organic acid = 0.130 M, Ionic strEngth = 2.00, Temperature = 25.00C. Organic Ac1d M iagel :,42 None* 1.93 x 10—9 h.68 x 106 malonic 8.h6 x 10_9 1.07 x 106 maleic 2.2h x 10‘8 h.05 x 105 malic 3.32 x 10'8 2.72 x 105 tartaric 1.29 x 10‘7 7.01 x 104 %Estimated value. A6 A log-log plot of the gross rate of exchange, from independent var- iation of uranium (IV) and uranium (VI) concentrations, exhibits the ex- pected linear relationship in Figure 5. When the uranium (IV) concentra- tion was varied while the uranium (VI) concentration was held constant, it was found that the order with respect to uranium (IV) was 1.3 i 0.1. The maximum concentration of uranium (IV) that could be used in these studies was 0.0A0 M; above that concentration precipitation occurred in a short time. The lower limit was governed by the slowness of the re- action at reduced uranium (IV) concentrations. Constant values of uranium (IV) concentration and variation of uranium (VI) concentration resulted in an order with respect to uranium (VI) of 0.A7 i 0.07. These data are summarized in Table V. The effect of hydrogen ion on the exchange was evaluated over the range from 0.80.M to 1.25 M. These data, summarized in Table VI and graphed in Figure 6, show that the order with respect to hydrogen ion is -2.9 i 0.2. Here again, the narrow range of the investigation was dictated by the precipitation that occurred in solutions with hydrogen ion concentrations less than 0.80 M. Because of the higher order de— pendence on hydrogen ion concentration, the rate becomes too slow to measure conveniently above 1.25 M. Two different investigations of the effect of varying the concen- tration of tartaric acid on the rate were carried out. One investiga- tion was carried out using solutions made up in the normal manner as described in the experimental section. These data gave an order with respect to tartaric acid concentration of 0.89 i 0.11. They are re- ported in Table VII. Another series of experiments carried out with postage/V: SE: a ommoo E 3:: a fimoohooaoos SC: AS ooo.mm ... a. .oo.m n H .68.. confines a 63.6 fimlz 664 .AH>VD pom A>HVD Mo cowbmobcoocoo mo moH m> m mob .m mermmm powwom> mo combmobcoocoo mom! Nd on a; c; I: m; 6; Bo co é- _ _ _ _ _ . A7 A8 Table V. Dependence of exchange rate on concentration of uranium (IV) and uranium (VI). Perchloric acid = 1.00 M, Tartaric acid = 0.130 M, Ionic strength = 2.00, Temperature = 25.00C. [U(IV)] [U(VI)] R x 107 (calc) R x 107(obs) M M M min-1 M min“1 0.0120 0.027A 1.68 1.51 0.0178 0.027A 2.51 2.13 0.0250 0.027A 3.55 3.82 0.0A00 0.027A 5.77 6.68 0.0250 0.027A 3.55 3.82 0.0250 0.0A00 A.08 A.07 0.0250 0.0750 5.58 5.93 0.0250 0.100 6.65 5.90 0.0250 0.150 8.80 8.79 Table VI. Dependence of exchange rate on the concentration of hydrogen ion. Uranium (IV) = 0.0250 M, Uranium (VI) = 0.027A M, Tartaric acid = 0.130 M, Ionic strength = 2.00, Temperature = 25.00C. + [H ] aH+ R x 107(calc) R x 107(0bs) ‘M M M min-l M min—l 0.800 0.8A6 5.62 8.22 0.900 0.961. 11.110 11.911 1.00 1.08 3.55 3.82 1.12 1.23 2.79 2.8A 1.25 1.38 2.25 2.19 A9 coHon> oHom oHnoonnH m+z a oo.H A00 coo Amv . cHon anoonHH s QmH.o accuse» +: Aav ooo.mm u H oo.m ” H AH>02 2 Ammo.o .AsHv: a ommo.o .pwom oHHmHHmH 0cm cow comoeozb Ho coHHmHHCoocoo mo 00H MN m 004 .0 oHsmHm HcmHnm> cpomHHcoocoo moql mm; 0m.H mm.H 004 ms.0 0m.W v2.0 00.0 070:. _ cm. H 501 0.01 50 solutions made up in the manner described in Appendix A gave an order of 0.90. Graphs of these data are also Shown in Figure 6. Table VII. Dependence of the exchange rate on the concentration of tartaric acid. Uranium (IV) = 0.0250 M, Uranium (VI) = 0.027A M, Perchloric acid = 1.00 M, Ionic strength = 2.00, Temperature = 25.00C. Tartaric Acid R x 107 _(calc) R X 107(obs) M M min 1 M nin‘l 0.0130 0.AA2 0.36A 0.0750 2.09 1.86 0.130 3.55 3.82 0.260 6.99 A.AA The effect of varying the ionic strength, I, is seen in the data reported in Table VIII. The data could not be extended to lower values of ionic strength at the conditions used. Experiments were also carried out to measure the effect of tem- perature on the rate of the reaction. The data in Table IX indicate the marked increase of the rate with increasing temperature. Analysis of these data to determine activation energies could not be carried out due to the complexity of the reaction. 51 Table VIII. Dependence of exchange rate on the ionic strength. Uranium (IV) = 0.0250 M, Uranium (VI) = 0.027A M, PerchloriC‘ acid = 1.00 M, Tartaric acid = 0.130 M, Temperature = 25.00C. . 7 Ionic Strength R x lo_(obs) M min 1 1.33 2.87 1.67 3°19 2.00 3°82 Table IX. Dependence of the exchange rate on temperature. Uranium (IV) = 0.0250 M, Uranium (VI) = 0.027A M, Perchloric acid = 1.00 M, Tartaric acid = 0.130 M, Ionic strength = 2.00 R x 107(0bs) Temperature . -1 M min 25.00C 3.82 32.000 8.A0 39.80C 25.7 DISCUSSION Several experiments were firSt carried out on the uncatalyzed sys- tem in order to repeat some of the work of Ronax":6 In experiments where hydrogen ion was varied, the order was found to be —3.5 compared with Rona's value of —3.0. This difference may be reconciled partially by briefly examining the mechanism she reports. One of the important pre- liminary steps is the hydrolysis of uranium (IV). As equations (12) to (15) show, incorporation of this step in the mechanism predicts a nega- tive second order dependence on hydrogen ion at low acidities and a negative fourth order at conditions of high acidity. Since the acid concentrations used in this work extended beyond the high acid end of the range used by Rona, a larger negative order might be expected. In addition it should be noted that experiments carried out at con- ditions that were supposedly identical with Rona's gave rates higher than those she found. This increase in rate can be attributed to a difference between the hydrogen ion concentrations calculated from her pH measurements and the true hydrogen ion concentrations of her solutions. Rona reported that pH measurements were made at the beginning and the end of each of her experiments. However, the pH measured probably varied from experiment to experiment since no attempt was made to con- trol ionic strength during her studies. A calibration described in Appendix A and illustrated in Figure 7 shows the linear relation be- tween true hydrogen ion concentration and measured pH at a high ionic 52 53 RH .30 venomous Ho coHHocsm H mm coHHmHHcoocoo coH comoprfi ozocx .m oHSQHm ma noHSmmoz 39H mma 0.H ®.0 0.0 q.0 m.0 0.0 . __ _ _ _ _ _ _ a . 1L D 2.6 J Moo; uotieaiuaouog H umouy + 5A strength. The correction factor thus obtained will be a function of ionic strength. The results of the two series of experiments, in which the tartaric acid concentration was varied, show the same disagreement in the value of the estimated hydrogen ion concentration. Line C of Figure 6 shows a log—log plot for exchange solutions made up by the method described in Appendix A. Graph B exhibits a similar result for a series of solu— tions made up in the standard manner. It can be seen that, although the order of the reaction with respect to tartaric acid concentration is the same, the absolute values of the slopes (K') and therefore the 9 rates, for reactions supposedly made up to the same conditions differ by a constant amount. This difference is undoubtedly due to the method used in making up the solutions. The method used in Appendix A is sus- pect since it involves a large increase in the hydrogen ion concentra— tion after the pH measurement has been made. Dissociation of the tar- taric acid which had occurred prior to this measurement would now be repressed. However, the primary effect is probably a decrease in the amount of hydrolysis of U+4. These discrepancies support the idea that the solutions made up as described in the experimental section are close to the desired hydrogen ion concentration. From the experimental results, the following rate law is estab— lished k' [U(IV)]l‘3 [U(VI)]°°47[H2Tar]°'9° [H+]2«9 (67) R = The appearance of fractional orders in the expression suggests that more than one principal path is contributing to the overall observed rate. 55 The large, negative order for hydrogen ion concentration may be inter— preted as a result of hydrolysis or ionization reactions. A knowledge of the principal species in solution is necessary before a mechanism can be proposed. Since perchlorate is a very weak complex— ing anion,59 its use as the anion in solution reduces the possibilities for complex species. Therefore, the main species in the solutions would be U+4 U02++ and undissociated tartaric acid. 9 ) There have been several studies on the hydrolysis of U02++ ion.5°: 51362553 Calculations from equilibria presented in these studies in— dicate that the main species found in the present experiments is U02++ with no more than 0.03% of the uranium(VI) present as the dimer, (U02)2(0H)2+2. Studies have also been made on the hydrolysis of U(IV).30:64:55 Consideration of the equilibria presented show that U+4 is the principal Species in the present studies. Less than 3% of the uranium(IV) is pres— ent as the hydrolyzed species, U0H+3. The other species present in the experimental rate law is tartaric acid. Consideration of its stepwise ionization constants show that unionized tartaric acid was the main species present in the exchange solutions with an upper limit of 0.3% of the tartaric acid present as the bitartrate ion. A rate law which will fit the data obtained for this reaction will probably contain at least two terms since thereiare fractional orders observed. It seems quite likely that some c0ntributi0n due to the un- catalyzed path postulated by Rona26 will be present although the high acidity of the solutions relegate it to a minor contribution to the + rate, since the concentration of the intermediate UOH 3 is minimal. 56 Extrapolation of Rona's data allows evaluation of the rate at [H+] = 1.00 M. Calculations based on her rate law at conditions of high acidity k1[U+4]2[U02++J (68) R = [H+]4 give a value of 5.7 x 10‘4 molesZ/l2 — min. for k1. If a two term rate law such as k1[U+4]2[U02++] + h2[U+4][H2Tar] (69) R = [11*14 111*]?— is fitted using the data from the experiments in which the concentra— tion of tartaric acid is varied, then the rate law can be written as (70) R = F + kZC and values of the constant k2 determined. When k2 is substituted in this equation, using the rest of the data, a poor fit is obtained when the data involving the variation of U02++ is tested. This indicated there is a path that is operative which involves both uranium(VI) and tartaric acid. If this third path is taken into account, the rate law then be— COMICS kl[U+4]2[U02++] + H2[U+4][H2Tar] + k3[U+4][H2Tar][U02++] (71) R = + + + [H 14 [H 12 [H ]2 which can be written (72) R = F + H20 + k3C [U02++] where 57 [U+4] [H ZTar] [11*]?— (73) C = This can be rearranged to the form (7A) 5%: = k2 + k3 [U02++] A graph of (R-F)/C XE [UOZ++] for the experiments where the U02++ con- centration was varied should give a straight line if this equation is followed. The result is shown in Figure 8. From the graph k2 is esti- mated to be 7.3 x 10-5 and k3 to be 1.21 x 10-3. Rates calculated from this rate law show good agreement except for the one obtained at the lowest hydrogen ion concentration. The second term of the proposed rate law is consistent with the mechanism (75) U"4 + HZTar + 2H20 <221> (A.C.)21+2 + 2H+ with a rate constant kg, for the forward step. The quantity (A.C.)21+2 represents the activated complex in the theory of absolute reaction rates24 for the first mechanism pr0posed for the second term of the rate law. This step is followed by a rapid reaction with U02++ (7o) (A.C.)21+2 + U02++ > products In this case the rate is given by 1:21 [UM] [HzTar] (77) R" = [11*]2 Identical results are obtained by considering the following mechan- ism for the second term. The two equilibria 58 .coHHmHHcoocoo AH>VESHCHHS MN m Mo ooHHocsw d .® oosmwm as Nos x Hiwoa 04 n0 3 _ rd X m4 m .v ) __w m. U . on _( mum 0.m 59 (i2) U+4 + H20 éZZf> U0H+3 + H+ (78) HzTar é:::> HTar— + H+ with equilibrium constants Kh and K1 respectively would be present in the exchange solutions. The species formed in these equilibria would then react to form the actiVated complex (79) : UOH+3 + HTar‘ -——> (A.c.),_2+2 in the rate determining step with a rate constant kzz followed by a rapid reaction with U02++ (80) (A.C.)22+2 + U02++ -——+> products Here the rate is given by = kZZKhKl[U+4][HZTar] (81) R" [Hi]-2 where the group of constants, kzthKl, is identical with k2 of the equa— tion (71) A path also can be envisioned in which tartaric acid dissociates completely to form the tartrate ion (82) HZTar <221> HTar‘ + H+ (83) HTar— <2) Tar= + H+ with an equilibrium constant K2 for reaction (83). The tartrate sub— sequently reacts with U+4 in a rate determining step (8A) U+4 + Tar= -——> (A.C.)23+2 with a rate constant k23, followed by a rapid reaction with U02++ to give products 60 (85) (A.C.)23+2 + U02++ .——e> products For this series of steps the rate would be given by (86) R” = kzs [U+4][Tar=] which on inclusion of the two equilibria (78) and (83) gives for the rate eXpression _ k23K1K2[U+4][H2Tar] (87) 8" [11*12 The third term could consist of the following sequence of reactions: First would be the formation of a uranium(IV) — tartaric acid (HZTar) complex (88) U+4 + HZTar éiif> (UonTar)+4 with an equilibrium constant K31, followed by a rate determining step which forms the activated complex (89) (U-Hziar)+4 + U02++ + 2H20 a::> (A.C.)31+4 + 2H+ which has a rate constant k3, for the forward reaction. The activated complex formed then rapidly breaks down into products +4 (90) (A.C.)31 ———H> products The rate for this mechanism is given by = k31[(U°HzTar)+4][U02++] (91) em [11‘le If the equilibrium (88) is included, the expression becomes = k31K31[U+4][Hzlar][U02++] [11+]"- (92) R'" 61 Alternatively the third term could be formulated by the consideration of the equilibria shown in equations (12) and (78) followed by the re- action ——> (93) UOH+3 + HTar‘ non.” with a rate constant k32 to give the activated complex which would rapidly break up into products. The overall rate law given hy this sequence of reactions would be = ksszthKl[U+4][H2Tar][U02++] [11"]2 (95) R"' Here again a third path which involves the tartrate anion is pos- sible. An equilibrium forming an uranium(IV) — tartrate complex (96) U+4 + Tar= é:::> [U-Tar]+2 with an equilibrium constant K33 can occur. This complex reacts with U02++ in a rate determining step (97) [U-Tar]+2 + 1102++ ——H> (11.033;4 with a rate constant k33. This activated complex then breaks down to form products. Incorporating the preliminary steps gives as a rate expression for this path + ++ = k33K1K2K33[U 4][HZTar][U02 ] (98) R1" [11*]?- 62 The overall rate is then given by the sum of the rate for the un- catalyzed path (F) and the rates calculated from the mechanism chosen for the two separate paths which involve tartaric acid (99) R = F + R” + Rm The three alternative mechanisms presented for each path are kinetically indistinguishable and thus it is difficult to choose one over the others. There is some qualitative evidence that the first mechanism for both paths is favored from the data on dependence of the rate on ionic strength. The Bronsted equation68 (100) log k = c + 1.018 zAzB 11/2 with G a constant, ZA and ZB the ionic charges of the species forming the activated complex, and I the ionic strength, predicts the rate constant, k, will increase with increasing ionic strength, if the species A and B combining to form the activated complex have a charge of the same sign. Although each rate constant postulated was not determined at different ionic strengths, the increase of the overall rate of exchange with increasing ionic strength as shown in Table VIII does suggest a positive primary salt effect. However, at the high ionic strengths employed, it is also doubtful'UxHLOOCU applies. There is an objection to the first mechanism presented for both steps involving tartaric acid. Rather than a slow, rate determining step followed by fast breakup into products, the mechanism must account for the inverse hydrogen ion dependence by use of an equilibrium in the rate determining step for formation of the activated complex. For the reverse of this step to occur requires a termolecular step. Since no 63 prior equilibria occur, this reverse step must be of some importance since a low rate is observed.‘ Such a reaction in solution is not too likely. The mechanism involving the tartrate anion is less likely than one involving only bitartrate because of the strongly acidic solutions used. While only a small amount of bitartrate may be present, there will be.even less tartrate since formation of the bitartrate must occur first. The small quantities of these reactive species could lead to the overall slowness of the rate. Even so, a path involving tartrate could still be kinetically important. The mechanism involving a hydrolysis step seems most likely. Al- though the equilibria shown in equations (12) and (78) are suppressed to some extent by the acidity of the solutions, the other steps lead— ing to the activated complexes occur readily. The calculated rates of exchange fit well with the observed rates in all but a few cases. It should be noted that the three values which fit the least closely are for the three points where the data was ob- tained near the limit of the experimental range. These are the points obtained with high tartaric acid concentration, high uranium(IV) concen- tration, and low hydrogen ion concentration. In all experiments where attempts were made to extend the range studied, some precipitation occurred. There is, then, the possibility that the solutions at these conditions were not truly stable but were slowly transforming to some other metastable condition prior to precipitation. Because the rate law did not fit the experimental rate exactly, for the experiment where the hydrogen ion concentration was the lowest, 6A an attempt was made to calculate the rate using estimated hydrogen ion activities since the activity coefficient for perchloric acid could vary even though the ionic strength is kept constant. Activity coefficients for perchloric acid in sodium perchlorate were estimated using Harned's rule68whichsflates the logarithm of the activity coefficient of one elec- trolyte in a mixture of constant total molality is directly proportional to the molality of the other component. This estimation was made using Guggenheim's treatment,69 and variationsin activity coefficients were seen to be small. It was found that rate constants calculated using those "activities" fit no better than those determined from concentra- tions. It is probable that the calculated ”activities” are no better a measure of the actual activities than are the concentrations. In addition to the mechanism proposed one might expect a path in- volving U02+ as an intermediate species. In the absence of light this is not likely, since solutions having a moderate concentration of U02+ are only obtained near pH 2.0-2.5. The rate constant, k3, for dispro- portionation of U02+ has been measured by Kern and Orleman7O at 3H = 1.0 and I = 0.A R3 (101) 2U02+ + AH+ efiifi> U+4 + 002++ + 2H20 k3 was found to be 7.3 x 103 1 mole—1 min_1 indicating little U02+ would be found. The tremendous effect of light on the system is difficult to ex- plain. Rona observed no effect due to light and one would expect the same result in perchlorate solutions. At the present one can only ex- plain this observation in terms of a more favored path involving U02+ even though acid conditions are used. When solutions containing tartaric 65 acid are irradiated the rate is even higher, indicating that some acti— vated species containing U02++ and tartaric acid may be formed which greatly accelerates the reaction. Uranium(VI) is known to be photo— chemically active in the presence of many organic acids.71 SUMMARY The effect of several organic acids on the exchange reaction be- tween uranium(IV) and uranium(VI) in aqueous perchloric acid was studied. The catalytic effect of these acids was found to increase in the order malonic acid < maleic acid< malic acid << tartaric acid. More detailed studies of the reaction in the presence of tartaric acid revealed that the order of the reaction is 1.3 with respect to uranium (IV) and 0.A7 with respect to uranium(VI). The exchange is 0.90 order with respect to tartaric acid and hydrogen ion has an order of —2.9. The predominant uranium species in solution are U+4 and U02++. The following three paths for exchange +4 ——+> +3 + U + H20 <+——r UOH + H (fast) UOH+3 + 1102” <:> Y+3 + 2H+ (fast) Y+3 + UOH+3 4:::> 2+6 (rate—determining) and 0+4 + H20 <:> U0H+3 + H+ (fast) HzTar <::::> HTar- + H+ (fast) UOH+3 + HTar_ > (A.C.)22+2 (rate-determining) (A.C.)2?_+2 + U02++ > products (fast) and 66 67 U+4 + H20 <:> U0H+3 + H+ —> —. + HzTar .<____ HTar + H UOH+3 + HTar" a:::> [(U0H)°(HTar)]+2 [(UOH)°(HTar)]+2 + 110.,++ ——>i (1.0)..” (A.C.)32+4 > products combine to give an expression for the overall rate R (fast) (fast) (fast) (rate-determining) (fast) = 5.7 x 10_4[U+4]2[U02++] + 7.3 x 10'5[U*4][H2Tar] [11"]4 . [11“]2 1.2 x 10‘3[U+4][H21ar][U02++] [11*]2 Rates calculated using this expression agree well with rates obtained experimentally. The rate of the reaction increased with increasing ionic strength and was markedly accelerated by temperature increases. Irradiation with an ultraviolet lamp caused a veny large increase in the rate of the reaction. 10. ll. 12. 13. 1A. 15. l6. l7. l8. 19. 20. 21. LITERATURE CITED Shaffer, P. A., J. Am. Chem. Soc., 55, 2169(1933). Shaffer, P. A., J. Phys. Chem., LEA 1021(1936). Michaelis, L., Trans. Electrochem. Soc., ll, 107(1937). Halpern, J., Can. J. Chem., 51, 1A8(1959). Halpern, J., Quart. Rev. (London), 25, 207(1961). Taube, H., Can. J. Chem., 51, 129(1959). Taube, H., in H. J. Emeleus and A. G. Sharpe, Advances in Inorganic Chemistry and Radiochemistry, New York, Academic Press, (1960), Vol. I. Wahl, A. 0., Z. Electrochem., 55, 90(1960). Taube, H., R. K. Murmann and F. J. Posey, J. Am. Chem. Soc., 29, 262(1957)- Ogard, A. E., and H. Taube, J. Am. Chem. Soc., 80, 108A(l958). Taube, H., J. Am. Chem. Soc., 11, AA81(1955). Dodson, R. W., and N. Davidson,. J. Phys. Chem., 56, 866(1952). Hudis, J., and R. W. Dodson , J. Am. Chem. Soc., 18, 911(1956). Stranks, D. R., in J. Lewis and R. G. Wilkins, Modern Coordination Chemistry, New York, Interscience Publishers, Inc., (1960), Chap. 2. Libby, w. E., J. Phys. Chem., 55, 863(1952). Libby, w. F., J. Chem. Phys., 5g, A20(l963). Marcus, R. A., J. Chem. Phys., 25, 966(1956). Marcus, R. A., J. Chem. Phys., 25, 867(1957). Hush, N. 8., Trans. Faraday Soc., 51, 557(1961). Marcus, R. J., B. J. Zwolinski, and H. Eyring, J. Phys. Chem., 5_8, A32(195A). Laidler, K. J., Can. J. Chem., 21, 138(1959). 68 22. 23. 2A. 25. 26. 27. 28. 29. 30. 31. 32. 33. 3A. 35. 36. 37. 38. 39. 1.0. A1. A2. A3. AA. 69 Sacher, E., and K. J. Laidler, Trans. Faraday Soc., 52, 396(1963). Newton, T. W., and S. W. Rabideau, J. Phys. Chem., Q5, 365(1959). Glasstone, S., K. J. Laidler and H. Eyring, The Theory of Rate Processes, New York, McGraw—Hill Book Co., Inc., (19Al), pp. 195—199. Betts, R. H., Can. J. Research, 255, 702(19A8). Rona, E. R. J. Am. Chem. Soc., 12) A339(l950). ) King, E. L., MDDC-813(19A7). Masters, B. J. and L. L. Schwartz, J. Am. Chem. Soc., 85, 2620(1961). Heal, H. 0., Nature, l5Z, 225(19A6). Kraus, K. A. and F. Nelson, J. Am. Chem. Soc., IE: 3901(1950). Nelson, F. and K. A. Kraus, J. Am. Chem. Soc., 15, 2157(1951). Frost, A. A., and R. G. Pearson, Kinetics and Mechanisms, New York, John Wiley and Sons, Inc., (1962), pp. 192—193, Prestwood, R., and A. C. Wahl, J. Am. Chems Soc., 1;, 3137(19A9). Benson, S. W., The Foundations of Chemical Kinetics, New York, Mc Graw—Hill Book Co., (1960), pp. 66—73. Love, C. M., unpublished results. Friedlander, G. and J. W. Kennedy, Nuclear and Radiochemistry, New York, John Wiley and Sons, Inc., (1955), pp. 132-13A. Meyer, R. J. and E. Pietsch, Gmelin's Handbuch der Anorganischen Chemie, Berlin, Verlag Chemie, G.M.B.H., (1936), p. 136. Arhland, S. and R. Larsson, Acta. Chem. Scand., 8, 137(195A). : Quinn, L. P., PhD Thesis, Michigan State University, (1961). Meyer, F. R., and G. T. Ronge, Angew. Chem., 52, 637(1939). Stone, H. W. and C. Beeson, Ind. Chem., Anal. Ed., 8, 188(1936). Gordon G. and H. Taube, J. Inorg. Nuclear Chem., 15, 272(1961). Lange, N. A., Handbook of Chemistry, Handbook Publishers, Inc., Sandusky, Ohio, (1952). Kolthoff, I. M. and E. B. Sandell, Textbook of Quantitative Inor- ganic Analysis, The Macmillan Company, New York, (1952), p. 521. A5. A6. A7. A8. A9. 50. 51. 52. 53. 5A. 55. 56. S7. 58. 59. 60. 61. 62. 63. 6A. 65. 66. 67. 70 Leininger, E. and K. G. Stone, Elementary Quantitative Analysis, Michigan State College Press, East Lansing, Michigan, (1950), p. 109. Willard, H. H. and P. Young, J. Am. Chem. Soc., 5;, 3260(1933). See reference AA, p. 580. Young, P. Anal. Chem., 2A, 152(1952). ) Katz, J. J. and G. T. Seaborg, The Chemistry of Actinide Elements, Methuen and Company, Ltd., London (1957), p. 176. See reference AA, pp. 569—570. Lundell, G. E. F. and H. B. Knowles, J. Am. Chem. Soc., AZ, 2637(1925). See reference 36, p. 258. See reference 36, p. 316. See reference A9, pp. 173—17A. McKay, H. A. C., Nature, 1A8, 997(1938). Duffield, R. B. and M. Calvin, J. Am. Chem. Soc., 68, 557(19A6). Daniels, F., C.D. Cornwell, J. W. Williams, P. Bender, and R. A. Alberty, Experimental Physical Chemistry, New York, McGraw—Hill Book Co., Inc., (1962), p. A13. Youden, W. J., Statistical Methods for Chemists, New York, John Wiley and Sons, Inc., (1951), pp. A2-A3. Klanberg, F J. P. Hunt, and H. W. Dodgen, Inorg. Chem., 2, 139(1963). .3 Crandall, H. W., J. Chem. Phys., l2, 602(19A9). Hearne, J. A. and A. G. White, J. Chem. Soc., 1957, p. 2168. Hietanen, S., and L. G. Sillen, Acta. Chem. Scand., 13, 1828(1959). Baes, C. F., Jr. and N. J. Meyer, Inorg. Chem., 1, 780(1962). ) Hietanen, S., Acta. Chem. Scand., 10, 1531(1956). Hearne, J. A. and A. G. White, J. Chem. Soc., 1957, p. 2081. Comyns, A. E., Chem. Rev., 60, 115(1960). Moore, W. J., Physical Chemistry, Englwood Cliffs, N. J., Prentice— Hall, Inc., (1962), pp. 368-373. 68. 69. 70. 71. 71 Robinson, R. A. and R. H. Stokes, Electrolyte Solutions, London, Butterworths Scientific Publications, (1955), pp. A27-A28. Harned, H. S. and B. S. Owen, The Physical Chemistry of Electrolytic Solutions, New York, Reinhold Publishing Corporation, (1958), pp 0 602—607 a Kern, D. M. H. and E. F. 0rlemann, J. Am. Chem. Soc., 11, 2102(19A9). Heckler, G. E., A. E. Taylor, C. Jensen, D. Percival, R. Jensen, and P. Fung, J. Phys. Chem., 61, 1(1963). APPENDIX A PREPARATION OF EXCHANGE SOLUTIONS USING A pH_METER 72 When work was first begun on the system, attempts were made to duplicate the work of Rona.26 Because hydrolysis was important at these conditions, the pH of the solutions was determined as the stock solutions were mixed. pH measurements were carried out with a Beckman Model G pH Meter using a glass electrode and a calomel reference electrode. Since er- ratic readings were obtained using a standard calomel reference elec- trode with a saturated potassium chloride electrolyte in the perchlorate solutions due to precipitation of potassium perchlorate at the fiber junction, a saturated sodium chloride solution was substituted as the electrolyte. It was also noted that there is an error in the hydrogen ion concentration of the solution calculated from the pH measurements made at high ionic strength. The pH's of a series of solutions of known hydrogen ion concentration at I = 2.00 were measured to be 0.39 pH units lower than the true pH. This correction factor was added to all measure- ments made. All solutions for this series of runs were combined in a 150 ml beaker in which was fitted the electrodes for the pH meter and a glass tip drawn to a small opening through which passed a stream of nitrogen. Uranyl perchlorate and sodium perchlorate were first added to the beaker. The pH of this solution was checked. The uranium(IV) was next added while the nitrogen flow continued. The pH was measured and recorded. The pH reading was corrected and the hydrogen ion concentra- tion determined. The number of moles of hydrogen ion needed to give the required acidity was then calculated and the prOper amount of stock 73 7A solution added. The solution was next diluted to the desired volume and the tartaric acid added. Upon completion of this final step the solu- tion was poured into a darkened flask. The chief disadvantages of this method are that solutions with a pH lower than 0.A cannot be directly measured and the system is sub- ject to error because of the great changes in hydrogen ion concentra- tion it undergoes after the pH measurement is recorded. Once experi- ments were begun at 1.00 M in hydrogen ion this method was abandoned for the one described in the body of the thesis. APPENDIX B COMPUTER PROGRAM 75 PHILLIP BENSON PROBLEM NUMBER 21-946T 214 KEDZIE CHEM LAB. MAIN PROGRAM ' COMMON NQTOSQT[MEGABSORBOCOUNTSOBKGNOQBKGRATOCORATOCAVRATOCONCO ICRSPAQACTNETQENFACTOFQFIOOOFINVALOSLOPEOAOTHALFORATEQUOUOZO ZACIDQORGQTEMPOCODQSAOSBOSR DIMENSION TIME(25)oAbSORB(25)QCOUNTS(2593)QBKGND(3)OBKGRATI3IO ICOURAT(3925)QCORATIBOZS)9CR$PA(25)QFINVALIZS)0C(3025)OD(3025) 10 READ llQPGRQNQTQSQ(BKGND(J)OJ=193) II FORMATIIZQBXQ1293X9F30093XoF3oOQ3X93‘F50093X)I 12 FORMAT(1H1024HTHIS IS KINETIC RUN PGR-o I2 I I3 FORMAT(F804o3X0F80403X9F80493X9F80493X9F602 I 14 FORMAT(IHOQ2HU=9 F864¢3X94HU02=6 F80403X95HACID=9 F80403X9 I 4HORG=Q F80403X95HTEMP=9F602 ) PRINT IZOPGR READ IBQUoUOZoACIDvORGoTEMP PRINT I49U9U029ACIDOORGQTEMP DO 15 J=103 ‘ BKGRATIJ)=BKGND(J)/T 15 CONTINUE CALL REFINE CALL SLSTSQ RATE=((“SLOPE)*U*UOZI/(U+UOZ) THALF300693I5/(‘SLOPE) PRINT 160 THALFQ RATE l6 FORMAT(IH096HTHALF=O E120694X05HRATE=¢ E1206 ) SR=(SB*U*U02)/(U+U02) PRINT 179 SR 17 FORMATCIHOQZZHSTD DEVIATION IN RATE=0 E1408 ) GO TO 10 STOP END SUBROUTINE FOR REFINING DATA SUBROUTINE REFINE COMMON N9T959TIME.ABSORBoCOUNTSoBKGNDvBKGRAToCORAToCAVRAToCONCo ICRSPAQACTNETQENFACTQFQFIOOQFINVALQSLOPEQAQTHALFORATEOUQU020 ZACIDQORGOTEMPQCODOSAOSBOSR DIMENSION TIME(25)QABSORB(25)QCOUNTS(2593)QBKGND(3)QBKGRAT(3)9 ICOURAT(3925)OCORAT(3925)QCRSPA(25)9FINVAL(25)OC(3925)90(3925) PRINT 21 21 FORMAT(1HO¢4OHVALUES OF CORRECTED SPECIFIC ACTIVITY ) READ 220 (TIME(I)9 ABSORB(I)¢ COUNT5(I91)0 COUNTS(I92)9 1coust.I=1.N) ' 22 FORMAT(F80093XQF60393XQ3(F80093x)I DO 25 I=IQN SUM=OO DO 23 J=lo3 COURAT(I9J)=COUNTS(IOJ)/S CORAT‘IOJ)=COURAT(IQJI-BKGRAT(J) 23 SUM=SUM+CORAT(IOJ) MSU 2 4 25 200 26 27 28 CAVRAT=SUM/30 CONC=ABSORB(I)*20520 SRECAC=CAVRAT/CONC CRSPA(I)=SPECAC-00623 PRINT 24. CRSPA(I) FORMAT(IH2911XQEI206 I CONTINUE M=N ENFACT=CRSRAIM>—CRSRA F-16 0°0250.M U(IV) -0.092 -— 0 0.0271 M USVI) 0.163 1.590 1055 1.76 .1 H ~0.091 1.605 1362 0.0262 M. maleic acid“ 0.111 1.591 11516 I = 2.00 0.119 1.593 19672 T = 25.0°C 0.176 1.588 27253 _ _ _ 0.213 1.580 35517 R = 6.2 t 2.9 x 10 9 moles 1 1min 1 1.930 —- G> 83 Table XI (C0nt.) S ln(100—100F) 't(min.) F-17 0.0250 M U(IV) 0.139 -- 0 0.0217 M U(VI) 0.112 1.601 1060 1.76 M H+ 0.091 1.619 1378 0 0262 M malic acid 0.227 1.579 11571 I = 2.00 0.269 1.567 19731 T = 25.000 0.165 1.598 27265 _ _1 _ 0.211 1.583 35610 R = 1.01 i 0.78 x 10 8 moles 1 min 1 3.608 -- F-51 0.0250 M 0(1v) 0.322 —— 0 0.0271 M U(VI) 0.517 1.557 2150 1.76 .1 H+ 0.781 1.187 11076 0.130 M tartaric acid 0.861 1.166 17105 1 Z 2. 00 1.138 1.387 21600 T = 25. 0°C 1. 590 1.211 33083 R = 1. 29$ 0. 19 x 10 7 moles l 1min 1 1.177 —— a) F-69 0.0250 M U(IV) -0.012 —— 0 ‘ 0.089 1.582 130 0.0271 M U(VI) 0.083 1.581 577 + 0.078 1.585 869 0.708 M H 0.179 1.562 1169 0.119 1.569 1565 0.013 M tartaric acid 0.277 1.539 2208 0.281 1.537 2153 I = 2.00 0.221 1.551 2703 T = 25.000 0.331 1.526 3692- _7 -1 -1 0.231 1.519 1290 R = 2.02 i 0.21 x 10 moles 1 min 0.215 1.553 5516 0.159 1.191 6801 0.680 1.138 8216 0.711 1.129 9621 1.169 —— m 85 Table XII. Study of the effect of variations in U(IV) 0n the rate of exchange. 3 ln(100-100F) t(min.) G-19 0.0100 M U(IV) 0.079 -- 0 ‘ 0.278 1.528 282 0.0271 M U(VI) 0.228 1 518 599 + 0.118 1.170 1377 1.00 .1 H 0.167 1.572 1837 0.371 1.189 2091 0.130 M tartaric acid 0.228 1.518 2191 0.191 1.137 3195 I = 2.00 0.605 1.387 1159 T = 25.00C 0.579 1.399 1561 _7 _l -1 0.702 1 311 1931 6.68 i 1.0 x 10 moles 1 min 0.661 1.359 5590 0.717 1.319 6006 2.763 -- 03 0—27 0.0250 M U(IV) 0.166 —— 0 0.278 1.575 133 0.0271 M U(VI) 0.390 1.511 1222 + 0.581 1.190 1956 1.00 M H 0.519 1.199 3217 0.801 1.122 1218 0.130 M tartaric acid 0.719 1.139 1891 0.996 1.359 5608 I = 2.00 0.698 1.155 6969 T = 25.000 0.961 1.371 7657 -1 -1 1.110 1.310 8217 3.82 t 0.15 x 10‘7 moles 1 min 1.182 1.295 9132 1.229 1.278 9821 3.976 -- w 86 Table XII (Cont.). s ln(100-100F) t(min.) 0-33 0.0120 M U(IV) 0.157 -- 0 0.811 1.568 565 0.0271 M U(VI) 0.898 1.563 983 + 0.957 1.557 1311 1.00 M H 1.159 1.537 2072 1.125 1.510 2861 0.130 M tartaric acid 1.635 1.188 1317 2.013 1.117 5110 I = 2.00 2.251 1.120 6553 T = 25.000 2.196 1.393 7911 _7 _ —1 2.638 1.376 11513' 1.51 1 0.10 x 10 moles 1 1min 2.910 1 310 12665 2.928 1.311 13566 1.113 -— 00 0—67 0.0178 M U(IV) 0.266 —— 0 ‘ 0.886 1.530 1211 0.0271 M U(VI) 1.329 1.173 2869 + 1.151 1.156 1271 1.00 M H 1.382 1.166 5857 0.130 ‘M tartaric acid 2.052 1.371 7801 I = 2.00 2.038 1.373 8865 T = 25.000 2.088 1.366 9929 2.592 1.288 11392 2.13 1 0.20 x 10’7 moles 1‘lmin‘l 2.375 1.322 12987 2.806 1.253 11333 8.828 —- CD 8? Table XIII. Study of the effect of variations in U(VI) on the rate of exchange. 5 ln(100-100F) t(min.) 0-23 0.0250 M U(IV) 0.282 -- 0 ‘ 0.281 1.605 219 0.0750 M U(VI) 0.371 1.587 538 + 0.167 1 568 1308 1.00 M H 0.722 1.511 1836 " 0.669 1.526 2051 0.130 M tartaric acid 0.709 1.517 2566 0.716 1.516 3203 I = 2.00 0.868 1.182 1217 T = 25.000 1.019 1.118 1622 _7 _ _ 1.039 1 113 1989 R = 5.93 1 0.38 x 10 moles 1 1min 1 1.096 1.130 5618 1.209 1.103 6061 5.317 -- 0° 0-25 0.0250 M U(IV) 0.608 —~ 0 0.392 1.611 59 0.150 M U(VI) 0.315 1.658 219 + 0.175 1.630 311 1.00 M H 0.556 1.615 538 0.101 1.612 658 0 130 M tartaric acid 0.631 1.600 1308 0.727 1.583 1136 1 = 2.00 0.853 1.559 1836 T = 25.000 0.778 1.573 2051 _ _ -1 0.876 1.555 2566 R = 8.79 i 0.67 x 10 7 moles 1 1min 0.877 1.551 3203 1.129 1 501 1291 1.379 1.152 1573 1.525 1.121 1951 6.018 —— m 88 Table XIII (Cont.) ln(100—100F) ~t(min.) 8 0-17 0.0250 M U(IV) 0.780 —- 0 1 113 1 567 756 0.0500 M U(VI) 1.163 1.531 1576 + 1 127 1.536 2291 1.00 M H 1.706 1 501 2501 1.926 1.178 2996 0.130 M tartaric acid 1.732 1.501 3536 2.323 1 130 5711 1 = 2.00 2.302 1.133 6816 T = 25.000 2.135 1.116 8005 _7 -1 _ 2.376 1.121 9317 R = 2.69 1 0.27 x 10 moles 1 min 1 2.633 1.391 10038 2.600 1.395 10692 10.390 -— 0 0—57 0.0250 M U(IV) 0.122 —— 0 0.817 1.551 1223 0.0100 M U(VI) 1.212 1.507 2616 + 1.681 1 111 1331 1.00 M H 1.801 1 127 5680 ‘ 1 926 1 110 7262 0.130 M tartaric acid 2.121 1.336 9205 ‘ 2.652 1.300 10270 I = 2.00 2.873 1.261 11315 T = 25.000 3.097 1.226 12797 _7 _1 _1 3.161 1.215 11395 R = 1.07 i 0.17 X 10 moles 1 min 8.908 —- (D 0—59 0 0250 M U(IV) 0.891 -— 0 0.980 1.597 1000 0 100 M U(VI) 1.697 1.530 2371 + 1.978 1.502 1013 1.00 M H 2.220 1.177 5133 2.832 1.112 7033 0.130 M tartaric acid 2.819 1.110 8972 3.917 1.285 10031 I = 2.00 3.712 1.310 11097 T = 25.000 3.680 1.311 12555 _7 -1 _1 1.130 1.219 11158 R = 5.90 i 0.50 x 10 moles l min 5.227 1.107 15199 CD 89 Table XIV. Study of the effect of variations in tartaric acid concen- trations on the rate of exchange. _4. s ln(100-100F) t(min.) F—71 0.0250 M U(IV) 0.069 -- 0 " 0.168 1.583 201- 0.0271 M U(VI) 0.151 1.587 770 + 0.369 1.538 1320 1.00 M. H 0.287 1.556 1785 0.291 1.556 2369 0.0650 M tartaric acid 0.288 1. 556 3161 0.376 1.536 3907 I = 2.00 0.622 1.177 5322 T = 25.0°C 0.773 1.139 8533 _7 _ _ 1.308 1.292 13921 R = 2.60 1 0.13 x 10 moles 1 1min 1 1.511 1.229 18891 1.673 -- 0° F-75 0.0250 M U(IV) 0.096 .—;_. 0 ' 0.161 1.592 201 0.0271 M U(VI) 0.160 1.592 792 + 0.181 1.588 1370 1.00 M H 0.171 1.590 1806 ‘ 0.098 1.605 2390 0.0130 M tartaric acid 0.252 1.571 3185 ‘ 0.215 1.581 3928 I = 2.00 0.232 1.578 5313 T = 25.000 0.250 1.571 8551 _8 _1 _1 0.191 1.521 13912 R = 5.16 1 0.68 x 10 moles 1 min 0.189 1.521 18912 5.135 -- 1" 90 Table XIV (Cont.) S ln(lOO-IOOF)‘ t(min.) 0—2 0.0250 M U(IV) 0.203 —- 0 ' 0.167 1.611 166 0.0271 M U(VI) 0.277 1.588 618 + 0.316 1.578 920 1.00 M H 0.717 1.169 1515 0.936 1.117 3876 0.130 M tartaric acid 1.277 1.316 6180 1.798 1.139 8729 = 2.00 1.857 1.116 10212 = 25.000 2.018 1.011 12287 1.909 1.096 11063 R = 1.88 1 0.11 x 10‘7 moles 1'1min‘ 1.957 1.077 15931 2.290 3.936 17283 1.181 -- m G—3 0.0250 M U(IV) 0.229 —— 0 0.329 1.583 166 0.0271 M U(VI) 0.185 1.518 618 + 0.591 1.523 920 1.00 M H 1.168 1.376 1515 1.358 1.323 3876 0.260 M tartaric acid 2.191 1.018 6180 2.677 3.811 8729 I = 2.00 2.628 3.867 10212 T = 25.000 3.002 3.680 12287 _ 2.933 33717 11063 R = 8.62 1 0.18 x 10‘7 moles 1 1min‘1 3.118 3.597 15931 3.510 3.351 17283 1.825 -— ‘11 91 Table )CIV (Cont . ) _‘ s. ln(100-100F) t(min.) 0-39 0.0250 M U(IV) 0.091 —- 0 0.300 1.578 571 0.0271 M U(VI) 0.170 1.555 1013 + 0.610 1.536 1316 1.00 M H 0.620 1.531 2011 0.761 1.511 2808 0.0750 M tartaric acid 1.031 1.175 5716 I = 2.00 1.189 1.152 7671 T = 25.000 1.352 1 127 10765 , _7 -1 —1 1.701 1.371 13119 R = 1.86 1 0.12 x 10 moles 1 min 7.792 —— 91 Table XVI. Study of the effect of varying ionic strength on the rate of exchange. 8 ln(100-100F) t(min.) 0-29 0.0250 M U(IV) 0.211 —- 0 0.261 1.591 131 0.0271 M U(VI) 0.263 1.591 1222 + 0.101 1.553 1956 1.00 M H 0.389 1.558 3217 0.565 1.507 1218 0.130 M tartaric acid 0.197 1.527 1891 ‘ 0.692 1.171 5608 I = 1.33 0.602 1.197 6969 T = 25.000 0.713 1.161 7657 0.827 1.129 8217 R = 2.87 1 0.26 x 10'7 moles 1‘1min‘1 0.967 1.385 9132 0.967 1.385 9820 1.036 -- GD 0—19 0.0250 M U(Iv) 0.511 —- 0 0.810 1.566 763 0.0271 M U(VI) 1.339 1.195 2321 1.00 M H1 1.628 1 152 3555 0.130 M tartaric acid 1.521 1 169 6290 I 3 1.67 2.192 1.362 8111 T = 25.0°c_7 -1 _ 2.117 1.321 9397 R = 3.19 1 0.58 x 10 moles 1 min 1 8.192 -— CD G—51 0.0250 M U(Iv) 0.101 -- 0 0.0271 M U$VI) 0.531 1.588 763 1.00 .1 H 0.917 1.538 2321 0.130 M tartaric acid 1.108 1.512 3555 I = 1.33 1.386 1 172 6290 T = 25.000 1.908 1 391 8111 _7 _l _1 1.881 1.398 9397 R = 2.91 i 0.27 x 10 moles l min 8.305 —- (D 9S Table XVII. »Study of the effect of variation of temperature on the exchange reaction. 5 ln(100-100F) t(min.) H-1 0.0250 M U(IV) 0.519 -- 0 ‘ 1.091 1.523 258 0.0271 M U(VI) 1.659 1.128 1073 - + 2.313 1.307 1171 1.00 M H 2.578 1.251 1835 2.723 1.223 2510 0.130 M tartaric acid 3.677 3.991 3110 1.322 3.801 1038 I = 2.00 1.109 3.775 1618 T = 39.800 5.011 3.536 5180 -6 _1 . _1 5.377 3.383 6007 2.58 i 0.11 x 10 moles 1 mm 7.391 -— ‘79 H—5 0.0250 M U(IV) 0.850 —— 0 1.011 1.581 258 0.0750 M U(VI) 2.291 1.136 1073 + 2.790 1.370 1171 1.00 M H 3.369 1.228 1835 ‘ 1.171 1.161 2510 0.130 M tartaric acid 1.593 1.088 3115 6.161 3.755 1038 I = 2.00 7.233 3.139 1618 T = 39.800 7.790 3.225 5180 _6 _1 —1 8.361 2.912 6007 R = 5.31 i 0.36 x 10 moles l min 10.121 -- m H-7 0.0250 M U(IV) 0.193 -- 0 0.636 1 581 215 0.0271 M U(VI) 1.117 1.509 1056 + 1.510 1.113 1163 1.25 .1 H 1.913 1.365 1811 2.391 1.277 2198 0.130 M tartaric acid 2.123 1.271 3130 I E 2.00 2.520 1.251 1601 T = 39.800 3.711 3.956 5166 ; _6 _1.. _1 3.700 3.967 6010 1,35 1-1.5 x 10 ' mofles 1 ml“ 7.292 -- a; 96 Table XVII (Cont.) S ln(IOO-lOOF) t(min.) H—9 0.0250 M U(IV) 0.261 —- 0 0.508 1.570 215 0.0271 M U(VI) 0.937 1.505 1056 + 1.015 1.193 1163 1.00 M H 1.327 1.112 1811 1.735 1.372 2198 0.0650 M tartaric acid 1.871 1.316 3130 ' 3.026 1.109 1025 I = 2.00 1.517 1.110 1601 T = 39.800 2.895 1.139 5166 _6 _ _ 3.053 1.103 6010 R = 1.02 1 0.20 x 10 moles 1 1min 1 7.328 —— 0 H-11 0.0120 M U(IV) 0.795 —— 0 1.695 1.179 391 0.0271 M U(VI) 1.999 1.132 738 + 2.390 1.369 1133 1.00 M H 3.281 1.207 1923 3.071 1.128 2919 0.130 M tartaric acid 5.033 3.787 1101 I = 2.00 5.039 3.785 1877 T = 39.80c 5.190 3.610 5692 _6 _1 _1 5.711 3.519 6183 R = 1.36 t 0.05 x 10 moles l min 8.379 —— m H—l3 0.0250 M U(Iv) 0.250 —- 0 ‘ 0.350 1 588 290 0.0271 M U(VI) 1 207 1 121 1073 . + 1.232 1.119 1119 1.00 M H 1 395 1.385 1717 1.187 1.365 2158 0.130 M tartaric acid 1.817 1.283 2836 ' 1.790 1.296 3162 I = 2.00 2.098 1.221 3917 T = 32.000 2.026 1.239 1190 2.178 1.120 5385 R = 8.37 1 1.2 3110'7 moles 1'1min‘1 2.032 1.237 5988 6.012 0 97 Table XVII (Cont.) s ln(100-100F) t(min.) H—11 0.0250 M U(IV) 0.111 -- 0 0.619 1.588 290 0.0750 M U(VI) 1.503 1.197 1073 + 1.350 1.511 1119 1.00 M H 0.923 1.558 1717 2.028 1.139 2158 0.130 M tartaric acid 1.991 1.113 2836 2.751 1.353 3162 I = 2.00 2.861 1.339 3917 T = 32.0000 3.061 1.311 1190 _6 -1 _1 3.358 1.275 5177 R = 1.19 i 0.13 x 10 moles l min 10.816 -- a) H-15 0.0250 M U(IV) 0.317 —- 0 0.525 1.582 290 0.0271.1 U(VI) 0.935 1.525 1081 + 0.901 1.529 1138 1.250 M H 0.989 1.517 1755 l 059 1 507 2183 0.130 M tartaric acid 1.090 1.503 2853 1.258 1.178 3162 I = 2.00 1.162 1.117 3863 T = 32.0000 1.623 1.122 1101 _ _ 1.630 1.121 5105 R = 3.81 i 0.32 x 10.7 moles 1 1min 1 1.660 1.116 5885 70972 "' CD H—l6 0.0250 M U(IV) 0.196 -— 0 0.265 1 591 290 0.0271 M U(VI) 0.652 1.530 1081 + 0.713 1.520 1138 1.00 [M H 0.511 1.519 1755 0.831 1.199 2183 0.0650 M tartaric acid 0.751 1.512 2853 0 811 1.197 3162 I = 2.00 0.922 1.183 3516 T = 32.0000 1.092 1.152 1101 _7 -1 -1 0.872 1.192 5105 R = 2.30 1 0.51 x 10 moles 1 min 0.910 1.179 5885 6.193 -- m 98 Table XVII (Cont.) ln(100-100F) t(min.) s H-17 0.0120 M U(IV) 0.128 —— 0 0.887 1.552 289 0.0271 M U(VI) 1.526 1.173 1093 + 1.598 1.161. 1155 1.00 .1 H 1.526 1.173 1761 1.831 1.133 2529 0.130 .1 tartaric acid 1.972 1.111 2868 2.238 1.377 3167 I = 2.00 2.520 1.336 3928 T = 32.0000 2.128 1.319 1155 _7 _1 _1 2.522 1.336 5297 R = 3.26 1 0.35 x 10 moles 1 min 2.653 1.330 5900 9.290 -- 0 H-18 0.0250 M U(IV) 0.663 —- 0 _ 1.032 1.551 217 0.0750 M U(VI) 1.606 1.168 392 + 1.118 1.197 595 1.00 .1 H 1.810 1.136 721 2.173 1.376 1199 0.130 .1 tartatic acid 2.110 1.335 1383 3.051 1.213 1617 I = 2.00 3.281 1.166 2022 T = 39.80c 1.511 3.866 2753 _ - 11001 11001 3179 R = 1.21 1 0.23 x 10‘6 moles 1 1min 1 5.025 3.709 3665 1.991 3.721 1229 5.566 3.511 1675 8.031 -- <0 99 Table XVII (Cont.) s ln(100-1008) t(min.) H—20 0.0250 M u(IV) 0.322 -- ~ 0 0.562 1.519 217 0.0271 M U(VI) 0.727 1.508 392 .+ 0.770 1.197 595 1.00 M H 0.792 1.191 721 . 1.118 1.101 *1199 0.130 M tartaric acid 0.938 1.153 1383 1.376 1.329 1617 I = 2.00 1.278 1.358 2022 T = 39.800 1.811 1.177 2753 _ _ 1.818 1.176 3179 R = 1.78 1 0.11 x 10‘6 moles 1 1min 1 2.269 1.016 3665 2.111 3.951 1229 2.258 1.021 1675 1.695 -- ‘11 Table XVIII. Study of the effect of irradiation on the exchange reaction. 100 S 1n( 100-1001‘) t (min. ) H—21 0-9250.M U(IV) 0.100 -— 0 0.010, .1.627 '5 0.0271 1. U(VI) 0.110 1.603 10 + 0.059 1.615. 16 1.00 .1 H 0.097 1.606 22 . 0.001 1.629 28 0.00 M tartaric acid ... 0.130 1.598 31 0.152 1.592 12 I = 2.00 0.251 1.566 51 T = 25.000 0.191 1.582 59 0.277 1.560 67 R = 1.21 1 0.08 x 10‘5 moles 1‘1min‘1 0.210 1.570 71 0.539 1.189 113 0 711 1.139 196 1.31 1.231 317 1.77 1.068 196 1.75 1.075 .706 1.11 -- a1 H-22 0 0250.1 U(IV) 0.178 —- 0 0.153 1.531 6 0-9271.1 U(VI) 0.672 1.171 10 + 0.528 1.511 16 1.00 M H 1.11 1.332 22 1.21 1.301 29 0.130 M -tartaric acid 1.11 1.230 39 ' 1.61 1.167 50 I = 2.00 2.05 3.979 60 T = 25.000 2.30 3.860 72 _ 2.37 3.822 81 R = 9.16 1 0.77 x 10'5 moles 1 1min‘1 2.10 3.958 98 2.31 3.852 112 2.17 3.926 129 3.18 3.237 112 2.99 3.109 151 3.09 3.322 168 3.10 3.318 181 1.21 <9 31mm! LIBRARY . as! é...) .. 110.141.3111 . Hut...1.vs1\..uitlhp)..v)\iotiih all . I . .2. P311541. .Xiianflasn... inniniarlfinwuu Eurasfluduuim}? m. 131M125. .23173636116 . 1 92:11.. at. a. .Ikntttfifiilkc. Iiigzallfie ‘ ‘fl‘IC-A: \‘Dsndxllt‘ “tin-5‘3 . 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