ll I 1 ‘ IW'MIHWTII’M \ i g LIIH‘HMWI”NH THE CATALYTEC EF FECT OF SSE/ME QRGANE C ACES QN THE OXQAT'ECR {3F URANIUM (EV) 3“! THALLELEM {Hi} i“\ FERCHL‘C REC éCiD Thesis {or flue Deqtee of pin D. ffiiflf1 an; i 5V «LE-31‘ é D‘A'im El {39‘ 2:4-1 1 fi“::Ti’ Lawrence F’. Quinn 1961 LIIHIWWI WW1 WWW WWI * 3 1293 00994 9631 ‘ at“ ‘9 -‘r / zqzcmzw: 9 l_!:’-3!\.’ERSH'Y -.. ‘ .. ,' 4" V bwfl ~f "i. ;‘-\A:‘i»lll."|/L\L {'3‘“ r‘H FLU,” :Jkrlt'i'tzt EAST LANSENG, MICHIGAN .- 3‘, 'r ,', H, '..-‘ I .- ~ 6 ‘ “W“. k s) 1-x: «n ‘ 5.5,, ~ , THE CATALYTIC EFFECT OF SOME ORGANIC ACIDS ON THE OXIDATION OF URANIUM (Iv) BY THALLIUM (III) IN PERCHLORIC ACID by Lawrence P. Quinn A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1961 ACKNOWLEDGEMENTS Grateful acknowledgement is hereby accorded to the author's parents for their guidance during the first years of his life; to Professor Carl H. Brubaker, Jr. for his counsel and advice during the most recent years; to the Atomic Energy Commission for financial aid and to those friends who endured the days of disappointment as well as those of success. iii THE CATALYTIC EFFECT OF SOME ORGANIC ACIDS ON THE OXIDATION OF URANIUM (IV) BY THALLIUM (III) IN PERCHLORIC ACID by Lawrence P. Quinn AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Year 1961 Approved iv ABSTRACT THE CATALYTIC EFFECT OF SOME ORGANIC ACIDs ON THE OXIDATION OF URANIUM (Iv) BY THALLIUM (III) IN PERCHLORIC ACID The reaction between uranium (IV) and thallium (III) in the presence of various organic acids was studied. Dibasic saturated acids studied were oxalic acid, malonic acid, and succinic acid. Oxalic acid and succinic were found to inhibit the reaction. Oxalic acid has only a slight effect on the system compared to succinic acid. Malonic acid has no effect on the rate of the system. The unsaturated dibasic acids, fumaric acid and maleic acid, were investigated along with the hydroxy dibasic acids, malic acid and tartaric acid. Under the appropriate conditions these acids all catalyze the reaction. At low concentrations of fumaric or maleic acid, the reaction between uranium (IV) and thallium (III) is catalyzed, but as the concentration of the organic acid is in- creased, the effect is to inhibit the reaction. This is attributed to the formation of a one to one complex that catalyzes the reaction, followed successively by a one to two (uranium to organic acid) complex which inhibits the reaction. Tartaric acid appears to ex- hibit the same behavior, and although the evidence is scanty malic acid is believed to catalyze the reaction. Most of the graphs of the rate equation - ifig—é—Ifl = k [MN] [THIN] were found to be linear over a large part of the reaction studied. Almost all curves, however, exhibited a peculiar deviation. The extrapolation of the linear curve to zero time did not pass V through log TlO/Uo, which is required by theory. Rather, initial experimental points formed a curve which became linear only after several hundred seconds. Experiments at low temperatures showed that this curvature was due to two separate reactions, one occurring with a fast rate, and ending rather rapidly as it uses all of one reactant, and the other occurring simultaneously but with a slower rate. The energy of activation was determined for this fast re- action and found to be 27.4 kilocalories when maleic acid was present as the catalyzing substance. The energies of activation were also determined for the reaction that occurred more slowly. The values obtained were 31.8 kilocalories and 22.1 kilocalories for concentrationsof maleic acid that inhibit and that accelerate the reaction, respectively. Partial rate laws were determined. The reaction is first order in uranium (IV) and thallium (III), and in the accelerated area the order of the maleic acid is 0.07, while in the inhibited area the maleic acid has an order of ~O.84. The hydrogen ion was found to have an order of -l.l7 in the inhibited area. vi l. 2. 3. 5. TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . . HISTORICAL . . . . . . . . . . . . . . . A. OXIDATION-REDUCTION MECHANISMS . . . B. URANIUM CHEMISTRY . . . . . . . . . . C. URANIUM OXIDATION-REDUCTION MECHANISMS THEORETICAL . . . . . . . . . . . . . . . EXPERIMENTAL . . . . . . . . . . . . . . A. PREPARATION OF REAGENTS . . . . . . . B. SPECIAL APPARATUS . .... . . . . . . C. ANALYTICAL DETERMINATIONS . . . . . . D. THE OXIDATION-REDUCTION REACTION . . E. MISCELLANEOUS EXPERIMENTS . . . . . . RESULTS . . . . . . . . . . . . . . . . A. SUCCINIC ACID . . . . . . . . . . . . B. OXALIC ACID . . . . . . . . . . . . . C. MALONIC ACID . . . . . . . . . , . . D. MALIC ACID . . . . . . . . . . . . . E. FUMARIC ACID . . . . . . . . . . . . F. SODIUM PERCHLORATE . . . . . . . . . G. TARTARIC ACID . . . . . . . . . . . H. MALEIC ACID . . . . . . . . . . . . DISCUSSION . . . . . . . . . . . . . . . SUMMARY . . . . . . . . . . . . . . . . LITERATURE CITED . . . . . . . . . . . . APPENDICES - ORIGINAL KINETIC DATA . . . METHOD OF LEAST SQUARES . . vii lO 13 18 23 23 33 37 48 52 59 59 61 63 65 67 7O 7O 77 90 96 98 101 133 LIST OF TABLES I Uranium Ions In Aqueous Solution . . . . . . . . . . . 11 II Oxidation Potentials Of Uranium Ions . . . . . . . . . 13 III Oxidation-Reduction Reactions of Uranium . . . . . . . 14 IV Thermodynamic Data For Uranium Oxidation-Reduction ReaCtionscoco-09000900000000.0015 V Initial Absorbance of Uranium Solutions . . . . . . . 44 VI Initial Absorbance of Uranium Solutions . . . . . . . 4# VII Molar Extinction Coefficient of Uranium (IV) - Organic ACid SOlutionB o o o o o o o o o o o o o o o o 45 VIII Uranium (IV) Standards 0 o o o o o o o o o o o o o o #6 IX Concentration of Reactants for a Typical Oxidation- RedUCtion ReaCtion o o o o o o o o o o o o o o o o o o 49 X Absorption Peaks of Uranium (IV) Perchlorate . . . . . 53 XI Absorption Peaks of Maleic and Fumaric Acids . . . . . 58 XII Rate Constants for Reactions Containing Succinic ch-d O O O O O C C O O O Q 0 O O O O I O O O O O O O O 61 XIII Rate Constants for Reactions Containing Oxalic ACid o o o o o o o o o o o o o o o o o o o o o o o o o 62 XIV Rate Constants for Reaction Containing Malonic ACid o o o o o o o o o o o o o o o o o o o o o o o o o 6} XV Rate Constants for Reactions Containing Malic Acid . . 67 XVI Rate Constants for Reactions Containing Fumaric ACid o o o o o o o o o O o o O o o o o o o o o o o o o 68 XVII Rate Constants for Reactions Containing Sodium PerChlorate o o o o o o o o o o o o o o o o o o o o o 71 XVIII Rate Constants for Reactions Containing Tartaric ACid O O O O O 0 O O O O O O O O O O O O O O O O O O O 7" XIX The Rate Constant as a Function of Hydrogen Ion . . . 77 XX The Rate Constant as a Function of Maleic Acid . . . . 79 XXI Variation of the Rate Constant with Temperature . . . 85 XXII Thermodynamic Quantities for the Maleic Acid Catalyzed ReaCtion o o o o o o o o o o o o o o o o o o 89 XXIII Typical Data supplied to MISTIC o o o o o o o o o e o 140 XXIV Output or Program 7 o o o o o o o o o o o o o o o o o IHA viii 3. 4. 5. 6. 7. 8. 9. 10. ll. 12. 13. l#. 15. l6. 17. 18. 19. 20. 21. 22. 23. LIST OF FIGURES Inverse of the Uranium Concentration As a Function of Time for a Normal Reaction . . . . . . . . . . . . . The Inverse of the Uranium Concentration As a Function of Time for A Catalyzed Reaction . . . . . . . Uranium (IV) Preparation Flask . . . . . . . . . . . . . Direct Current Supply . . . . . . . . . . . . . . . . . Nitrogen Purification Train . . . . . . . . . . . . . . Uranium (IV) Storage Flask . . . . . . . . . . . . . . . Uranium (IV) Concentration As A Function of Time . . . . Spectrum of Uranium (IV) Perchlorate . . . . . . . . . . Spectrum of Maleic Acid . . . . . . . . . . . . . . . . Spectrum of Fumaric Acid . . . . . . . . . . . . . . . . The Rate Equation for a Reaction Containing SUCCiniCACid0.0000000000000009... The Rate Equation for a Reaction Containing MaloniCACidoooooooooooooooooooooo The Rate Equation for a Reaction Containing M3110 ACid O O O O O O O O 0 O O O O I O O O O O O O 0 O The Rate Constant as a Function of Fumaric Acid . . . . The Rate Constant as a Function of Sodium Perchlorate...................... The Rate Equation for a Reaction Containing TartariCACidcoo-0.000000000009009 The Variation of Initial Rate With Initial Hydrogen Ion.......................... The Apparent Rate Constant As a Function of MaleiCACid00000000000000.0000... The Initial Rate as a Function of Maleic Acid . . . . . The Initial Rate As a Function of Initial HaleiCACid00000000000000.0000... Variation of the Apparent Rate Constant with Temperature The Rate Equation for a Reaction Containing HaleiCACidcocoon-000000000000... Variation of the Apparent Rate Constant with Temperature for Maleic Acid . . . . . . . . . . . . . . ix 21 22 28 35 36 38 #2 54 56 57 60 61+ 66 69 72 76 78 81 82 83 86 87 88 1. INTRODUCTION The question of the simultaneous transfer of two electrons as against two single electron transfers is still receiving much attentionl’a. Various systems, all having in common the fact that at least one of the reactants changes its oxidation state by two, have been studied. The oxidation of uranium (IV) to uranium (VI) is one such system. Several investigations have been made using oxygen gas}, iron (III)#, and thallium (III)5 as the oxidizing agent: The thallium (III) - uranium (IV) system is particularly interesting since both the oxidizing and reducing agents undergo an oxidation state change of two. A system such as this might then provide some information on the question of one or multi- electron transfers. Taube6’7 has shown that certain organic acids will catalyze the reaction between chromimm (II) and cobalt (III). According to Taube the unsaturated acids act as a bridge between the two reacting species and provide a path for the transfer of the single electron. Brubaker and Andrade8 have studied the effect of several organic acids on the thallium (I) - thallium (III) exchange. Acetic and succinic acids retard the exchange while the other acids studied all reduce the thallium (III) at a rate comparable to the exchange rate. This study was undertaken with the following purpose in mind: to discover the nature and sequence, if more than one, of the elementary steps which comprise the overall reaction, to ’ For a more complete list see table III. 1 determine the composition and configuration of the activated complex in the electron transfer step, to elucidate the atomic rearrangements accompaning the electron transfer process, and to discover whether multi-electron redox reaction occur in a single step or more than one successive electron steps. It was decided, therefore, to study the oxidation of uranium (IV) by thallium (III) in the presence of various organic acids. Perchloric acid was chosen as the medium in order to reduce the possibilities of complexing by the acid anion. A general study of several acids was to be made and a detailed study of one of these, maleic acid, was also to be carried out. 2. HISTORICAL A. OXIDATION — REDUCTION MECHANISMS Introduction Oxidation is defined many times as the loss of electrons. In elementary teaching of chemistry this definition serves a val- uable purpose and is an efficient tool. It allows half cells of the form -2 + - +3 =_. 1 Cr207 + 14H + 6e 20r + 7HZO ) to be written. With the use of such half cells, oxidation-reduction equations may be balanced and electrode processes may be written, both with some view towards what is actually occuring in solution. In reality these half cells, while very useful, do not represent accurately what is occuring. They simply represent the reactants and products of an oxidation reduction equation. The mechanisms may be quite different. This field of inorganic mechanisms (or inorganic chemical kinetics) has received little attention until recently. Enough work had been reported prior to 1959 to be reviewed by Basolo and 9 Pearson in their textbook. This book, while certainly a pioneer work in the field, allocates only one relatively short chapter to oxidation-reduction mechanismslo. There are three generally accepted mechanisms by which oxidation-reduction may occur. They are atom transfer, electron transfer and the tunneling process. The Tunneling Process The tunneling hypothesis was first introduced by Marcus, Zwolinski and Eyringll. This simply amounts to an extension of electronic orbitals to that point where transfer occurs at distances larger than one would suspect, and greater than corresponds to act- ual collision. This is merely saying that there is a possibility for an electron to leak through the potential barrier to a given reaction. Atom Transfer The second method of oxidation-reduction is atom transfer. Taube12 has demonstrated several cases of atom transfer. 2 +2 Co(NH3)5C1+ + Cr = Co(NH3)5+2 + CrCI+2 2) This reaction requires that a chlorine atom, not an ion, be transferred. Since the chromium (III) is not labile, the chlorine must have transferred during the oxidative process. While this does not necessarily prove that chlorine atom transfer caused the oxidation, this certainly seems likely, although chloride ion transfer could have accompanied electron transfer. Taube has also shown atom or group transfer for several other ligands, among them thiocyanate, azide, phosphate, acetate, oxalate, and bromide. Oxygen atom transfer has been demonstrateéjin the oxidation of nitrite with hypochlorous acid and in the oxidation of sulfite with hypochlorite, chlorite, chlorate, and bromate ions. Hydrogen Atom Transfer Hydrogen atom transfer is a special case of atom transfer. There is good reason for this, although the fact that it is merely atom transfer should be remembered. Several facts all point to the importance of the hydrogen atom transferlu. 1) There are a surprising number of redox reactions between metal ions which have activation energies close to 10 kilocalories per mole and entrOpies close to ~25 calories per mole degree suggesting that they proceed by a common.mechanism. 2) In a number of redox reactions of metal complexes there seems to be the requirement that one of the inner shell ligands be a water molecule. 3) The rates of several exchange reactions are reduced by a factor of two on changing from water to deuterium oxide as a solvent. This is consistent with the isotOpe effect expected for breaking an oxygen to hydrogen bond. There are, however, reactions which give larger water to deuterium oxide isotope effects than this. These facts, of course, suggest that the reactions all proceed by a common mechanism, which probably involves water. 15, 16 Dodson and coworkers have made the suggestion that these facts point to the transfer of a hydrogen atom between hydration shells. The classic example which they studied is the iron (II) - (III) isotope exchange reaction. 4+ 1: V _ O *-OH + Ho‘-Fe 3* = FeZ‘IO-H-O-Fe3+ = Fe3*OH + H20Fe l l I H H H 3) At this point in the discussion it might be pertinent to 2 2+ Fe point out that only in the case of the hydrogen atom can it be determined whether the atom transfers in one direction or the electron transfers in that direction followed by a negative ion transfering in the Opposite direction, since these two processes are formally equivalent. Electron Transfer The third method, electron transfer, is known to exist in the gas phase where the collision of an atom and an ion can bring about the transfer of an electron. However, in the liquid state a more complicated situation exists. The transfer of the electron here is hindered. For example, one cannot merely consider an ion but must also consider the hydration shells and the distortion of the electronic orbitals by the solvent. How close these entities can approach, and the influence of other substances also dissolved in solution must also be considered. Calculations must consider a much larger number of particles than in the gas phase. The pos- sibility of an activated complex forming must be examined, and it must be remembered that since there are more configurations possible than in the gas phase there are now more energy levels available for the electron. No longer is a simple collision possible. Rearrangement of coordinated groups must occur before the movement of electrons. This is due to the Franck-Condon principle. The Franck-Condon principle, in its simplest form, states that the motion of nuclei is so slow compared to that of electrons that an electron transfer occurs without any appreciable movement of nuclei. The situation can be made clear by considering a specific case, the electron exchange of iron (II) - iron (III). +3 +2 - .‘ +2 ‘ +3 4) Fe(H20)6 + Fe(H20)6 _ Fe(H20)6 + Fe(H20)6 F;(HZO)6+2 + F;(H20)6+3 = Fe(H20)6+2 + Fe(H20)6+3 + heat 5) The asterisk with the products of reaction 4) indicates that these iron atoms are in an energy rich state. It would, of course, be possible for them to deactivate giving up their excess energy to the solvent, and returning to the unexcited state that they were in as reactants. But this whole process is a violation of the law of conservation of energy in that heat energy is created. Thusfibecomes necessary to rearrange the hydrations shells of the ions to some intermediate position before the electron transfer can occur. This rearrangement to form an activated complex will require energy from the solution, but when the products revert to their average state an equivalent amount of energy will be released. However, this enables the electron transfer to take place without the creation of products in an excited state. The least amount of energy will be required to form an activated complex consisting of identical configurations for both iron ions so that electron transfer probably involves a symmetrical transition state, intermediate between the iron (II) and the iron (III) arrangements. If one considers electron transfer taking place between two ions not the same, then exothermic reactions are favored. Since heat is to be evolved, the lack of energy conservation shown in the iron (II) - iron (III) reaction is no longer necessarily a factor. Nonetheless rearrangement of the ligands of the two re» acting species is still necessary so that the actual transfer of the electron is not hindered. The reactants must assume a con- figuration which will allow the electron to transfer without chang- ing its energy state. For the electron transfer will occur many times before the activated complex breaks up. One other important restriction is that during the transfer of one electron from one atom to another no overall change of electron spin should occur. The spins of the other electrons in the system should be undisturbed by the electron that transfers. This can be important for a metal ion in a complexing environment. Two Equivalent Redox Reactions There are certain reactions in inorganic chemistry which require the transfer of two electrons. Transition metals generally exhibit oxidation state differing by one electron and consequently react with each other by one equivalent steps. Several of the post- transition elements have oxidation state differing by tWO electrons: thallium (I) - thallium (III). tin (II) - tin (IV), etc. Naturally the question arises as to whether the electrons transfer in one electron 17 steps or whether they transfer simultaneously. Michaelis has prod- uced the principle of compulsory univalent oxidation steps. This has evolved from the consideration of a restricted field of redox re- actions, and is generally considered no longer vaild. Shaffer'sl8 principle of equivalence change statesthat complimentary reactions are fast compared to noncomplimentary ones. A complimentary re- action is one in which the oxidant and reductant undergo the same 9 19 amount of change. Higgenson has suggested three rules. 1) Species derived from the transition elements will react with each other by a series of univalent changes. 2) Species derived from the nontransition elements will react with each other in a series of bivalent changes unless at least one of the reactants is a free radical, in which case univalent change occurs. 3) Species derived from a transition and a nontransition element will react with each other by either univalent or bivalent changes, univalent changes being more common. Thus while it is impossible to predict accurately what will occur in a given situation, the preceeding rules make it possible for reasonable predictions to be made. The Effect of Anions The anions present during an oxidation-reduction reaction can vastly change the rate of that reaction. There are several reasons for this. Most oxidation-reduction reactions occur between ions bearing a positive charge. It is easier for these ions to approach each other, and less energy is required if a negative ion interposes itself between the positive ions in an activated complex. Anions can also stabilize one of the reacting ions or product ions by complexing. Cobalt (III) for example is not stable in aqueous solution unless it is complexed by some ligand. It is also possible for the anions to form a bridge between the reacting species thus making the electron transfer more likely, and secondly this bridge may be an easier pathway for electron transfer than other pathways 10 available to the electron. Finally sharing one ligand may symmetrize the transition state, again making the transfer of an electron more probable. Thus the anion which has many times in the past been rel- egated to the position of a spectator ion is assuming more and more importance in oxidation-reduction reactions. Consequently the effect of the anion on the rate of oxidation-reduCtion reactions is being examined more closely. B. URANIUM CHEMISTRY Uranium was discovered in a pitchblende sample from Czechoslovakia in 1789 by M. H. Klaproth, who named it after the then recently discovered planet Uranus. It was over one hundred years later that Becquerel discovered that uranium undergoes radio- avtive decay. It was an additional forty years before the crucial importance of uranium was discovered. Hahn and Strassman showed in 1938 that uranium undergoes fission.Shortly thereafter a crash program was instituted in the United State to produce a bomb based on the fissionability of uranium. It was during this program that uranium chemistry underwent a more careful scrutiny than any element had ever been subjected to before. Of major interest to the bomb program were the gaseous compounds of uranium, and consequently the aqueous chemistry was somewhat neglected. A rather complete record of binary compounds and the chemistry of uranium is found in Katz and Rabinowitch2 , while Seaborg and Katz21 provide a general record of uranium chem- istry. There are four common oxidation states of uranium. Each is listed along with its color and formula in table I. 11 Table I . ' . 22 Uranium Ions In Aqueous Solution Oxidation State Formula Color +3 If.“3 Red +A n+4 Green +1 +5 U02 --- +6 U02+2 Yellow Two outstanding prOperties that uranium ions possess are their ease of hydrolysis and with the exception of uranyl ion, their instability. Considerable hydrolysis is expected because of the relatively high charge that the ions possess, and in order to main- tain monomeric species in solution a high hydrogen ion concentration is necessary. With decreasing hydrogen ion concentration, hydrolysis occurs, then polymerization of the hydrolysis products and finally precipitation of hydroxides. The order of increasing hydrolysis is U(IV) < U(VI) < U(III).. As has been mentioned uranyl ion is the only stable Species in solution. All other species react with water, oxygen or them- selves to produce a more stable species. Consequently special techniques are necessary to produce and preserve these ions. The order of stability of the uranium ions is U(VI) :> U(IV) )> U(III) .> u(v). All uranium species can be produced by electrolysis or by dissolving the appropriate chloride in water. 12 Uranium in the plus three oxidation state can be produced by dissolving uranium trichloride in water or by electrolysis. It is unstable, reacting readily with air, and reducing water to pro- duce hydrOgen. The uranium in the plus four oxidation state is most easily produced by electrolysis or solution of uranium tetrachloride in water. It is unstable and reacts slowly with the oxygen in the air, consequently it must be protected with some form of inert gas. If this is done, the uranium (IV) solution can be maintained in the laboratory indefinately. Uranium (V) is very unstable and disprOportionates according to the equation that follows. +1 + _ +4 +2 2 UO2 + 4 H - U + UO2 + 2 H20 6) The equilibrium constant for this reaction is reported by Nelson and Krause23 to be 1.7 X 106. Thus in any solution con- taining uranium in the oxidation states of four and six, there will be a small amount of uranium (V). In a recent paper Gordon and TaubeeI report several methods of producing uranium (V). Chromium (II), europium (II), and uranium (III) all reacting with uranium (VI) will produce uranium (V) in 25 solution. Krause and Nelson report that the dissolution of uranium pentachloride in water first forms a solution of uranium (IV) and (VI) which then reacts to form uranium (V). Uranium (VI) is the familiar stable oxidation state of uranium. It is easily prepared and is completely stable under all normal conditions. 13 The oxidatiqp potentials for the various oxidation states of uranium are shown in table II. Table ‘II Oxidation Potentials of Uranium Ions26 U 1.80 > U” 0.637,,1-9’ -O.32 -0.58 -0.063 ‘ +a + UO . UO2 Formal potential in 1 M Perchloric Acid at 25°C. C. URANIUM OXIDATION-REDUCTION MECHANISMS Even though uranium has received much careful attention recently, there is a dearth of quantitative data. The oxidation reduction reactions which have been studied are tabulated in table III. The thermodynamic information that is available is listed in table IV. The isotopic exchange betweefi uranium (IV) and uranium (VI) was studied by Rona27 in 1950. The reaction is second order in uranium (IV) and first order in uranium (VI). The activated complex postulated contains UOH+3 and U0 +2 ions. It is very 2 interesting to note that added chloride had no effect on the rate of the reaction. 28 Moore studied some aspects of the reduction of uranium (VI) with tin (II) determining that the rate was first order in both uranium (VI) and tin (II). Qualitative effects of hydro- chloric acid, chloride ion and hydrogen ion were noted. Increas- ing the hydrochloric acid concentration, increases the rate 11+ a Fire} . as . «ray Amman NM :M + A+mv .M mommNU an All .u 0mm aHavs A>Hvs on soaom aH>Voa AaHvs Inn m m”— \ m+moafl “SE1.— sm n S \ m+oafl e S3% 35% CE; m Am- m3 me + T mummy WEQ meta u »s\ WES”— s I58m 3339 25s mm Somme AHHHVoa A>Hvs mm @Hvow manta”— R u Sam Ga 25: 335. m FAQ \ Wow 25$ a u as \ madam a Sodom N.o can a am m2: mm + w \ m+moamm WEE ass a Sam 8m 35s 25s I. . Wicca“. 65$ muss \ Am+o5 a 1.03m “Edna QED usom< psmmm mononomom 3mg ovum Suave: msflufivfixo mnfiosuem EDHz¢mD ho monBo¢mm ZOHHUDnmmIZOHadnHNO HHH oanne 15 mm nun s.sa AHavs AHHVnm mm m.m m.na swoon AsHvoo A>Hvs am m.mm w.mm mososo AH>V= A>Hvs on H.ma ¢.Hm oomomopom on :.m m.ua oomomosomm Awsvom A>Hvs Hm :.n m.wa AH>vaz A>Hvs m a s.am Haos n ma m.sm demos AHHHVHB AsHvs mm .: nun m.nm one: mm .s u.. m.mm names xHHHvoa A>Hvs Noamsoo 38mm pded oononomom .m d. .m < conning meanaawxo mnaoasmm >H monBoSmm ZOHBUDQmmIZOHadnHNO ZDHE mom 48 This, upon integration, yields 1 ln AOB _ kt 9) B -A B A - O 0 O This may be plotted several ways. The first is simply to plot the quantities on the left hand side of the equation as a function of time. Then the slope of the line is equal to the constant, k. An easier procedure, however, is to rearrange the equation into the following form. B B -A A = - i log K §%36% kt log Bo 10) Here log B/A, a quantity more easily determined, may be plotted as a function of time. The slope of this line will equal (Bo-A0) k / 2.305 and so k may be determined by solving the equation for k. _ 2.303 X Slope k — B -A 11) o o In equation 9) the intercept at time equals zero is zero since the logarithm term is equal to zero. In equation 10) this is no longer true. The intercept will be equal to kg Bo/Ao when time is equal to zero. 18 19 Two other significant situations need to be discussed. It is obvious that at equal concentrations both of the previous equations give no solution due to the term Bo-Ao which appears in each equation. Using equal concentrations of two reactants is equivalent to the case of a second order reaction with one reactant. This condition of exactly equal concentrations is difficult to achieve experimentally, thus an equation for the case of very nearly equal concentrations is necessary. This method is discussed in both of the kinetic texts pre- viously liSted. Essentially the desired equation is (—IdI-L-x -%=kt 12) where d is the mean initial concentration. When the quantity 1 / (d - x) is plotted as a function of time, the graph will be a straight line with a lepe equal to the constant k. The second situation arises as a result of mathematical rearrangement of the equation. Assume that over the first part of the reaction, the concentration of 3.13 a constant and that B is in excess over A. Then rearrange equation M3) ;__kB-At Bg log A. — 2.303 + log AoB 13) and substitute kSB-Q-AQ) K = 2.303 14) and write the resulting equation in the exponential form. l a -n—B ext 15) A AOB 20 Kt . Now expand e as a series. 2 2 3 3 eKt = 1 + Kt + K t K t 16) and substitute into equation + .0.) l7) In the early part of the reaction, eKt may be approximated by (l +- Kt) to give the following equation. 1 _ B (1 +A Kt) K. _.o 18) l-§_§2§ .120 A ‘ AOB t * BAo 19) Now a graph of the quantity l/A as a function time should be linear, at least for the early part of the reaction. Figure 1 shows a graph of l/U as a function of time for a typical reaction. It can be seen that the graph is linear for approximately the first sixteen hundred seconds. In many reactions where catalysis was observed, the l/U graphs do not yield a straight line. This is illustrated in figure 2. Here, as later discussion will show, there are two paths, both second order, occuring simultaneously, and resulting in curvature of the l/U graph. 21 L Tm u .m on; n :38 .m. so; u 5sz .m muoaxooa n SHSE as. mnoawmsfi n 9.3: .doapodmm Hmahoz w pom mafia mo soapossm m m¢ dowumhpcmosoo SSflsmuD ms» mo mmhm>sH .H mmwah muss x mazoomm mm om ma 3 m o _ _ _ i O O O O E. ‘1 H O O mm. mm. mm. mm. 2. 22 N mu.m u vflom OfiAMphmB a all ' I. Tm u l 22.; u :oaomémoé u soaomz .2 uoaxooa u 3H3? . muoaxsma u SS: .sowuomom nouhHMpmo 4 how vsfle mo soaposzh m md soprHQQooqoo Edflsmab map mo mmuo>sH oge .m mmeHm NIOH_N mazoomm mm om ma oa m o _ _ _ _ mm. 0 I1 on. O o E D II . H l} O 0 IL mm. 0 O a om. 4. EXPERIMENTAL A. PREPARATION OF REAGENTS All reagents used were analytical grade or were purified by recrystallization before use. Perchloric Acid The perchloric acid used was Baker's Analyzed Reagent or Mallinckrodt 70% Analytical Reagent, both of which were used with- out further purification. No noticeable difference appeared in the kinetic runs as a result of using different brands of acid. Thallium (III) Perchlorate The thallium source was a thallium (I) sulphate stock solution previously prepared by Mickelas. The original material was purchased from E. H. Sargent and Company. The thallium (I) sulphate was oxidized with l‘fl potassium hexacyanoferrate (III) solution which was 3.fl in sodium hydroxide. The oxidation went smoothly and a rich cocoa brown precipitate was produced. The precipitate and supernatant liquid were transferred to a large beaker. After standing, the supernatant liquid was removed with a fine fritted glass filter stick. The thallium (III) oxide was washed with boiling demineralized water until the supernatant liquid gave no detectable test for sulfate ion with barium nitrate, or for hexacyanoferrate (III) ion with ferrous ammonium sulfate, or for hexacyanoferrate (II) with ferric nitrate. The precipitate was then dissolved in hydrochloric acid. The thallium was repreu cipitated with solid sodium hydroxide. Twenty-five milliliters 23 2A of the oxidizing solution were added to assure complete oxidation. The precipitate was washed with boiling water until it gave no test with silver nitrate.‘ The precipitate was then dissolved in a slight excess of perchloric acid, and diluted to one liter with demineralized water. The solution produced was about 2.5 N in hydrogen ion and O.#6 g in thallium (III) ion. Uranium (IV) Perchlorate Baker's C. P. Analyzed Reagent was used to prepare uranium (VI) perchlorate by a method modified from that found in Gmelin39. About seventy-five grams of uranium (VI) nitrate hex- ahydrate was dissolved in water. Thirty per cent hydrogen peroxide was diluted to three per cent, and added with stirring to the uranium (VI) nitrate which had been heated to a temperature higher than seventy degrees centigrade on a steam bath. A coarse lemon yellow precipitate was formed. This was filtered and washed with conductance water. Here again the importance of using a hot solution is seen. The precipitate formed under room temperature conditions is characterized by small particle size, poor filterability, etc. If the precipitation is carried out at 80°C., the precipitate is coarse, easy to filter, settles out rapidly, and generally has more desirable characteristics. * It is essential that very hot water be used, otherwise the pre- cipitate changes characteristics and becomes almost impossible to filter. The use of cold water also causes peptization. The use of boiling water was found to eliminate both problems. 25 The uranium (VI) peroxide thus prepared was mixed with four hundred milliliters of conductance water and sixty-four milliliters of concentrated perchloric acid, and heated on a steam bath. Solution generally took some hours depending on the hydrogen ion concentration, the higher concentration being the one in which solution took place more rapidly. When complete solution was attained, the solution was filtered through a fine grade fritted glass filter and the pro- cess of precipitation repeated. After three precipitations had been made the solution of uranium (VI) perchlorate was kept hot for twenty-four hours and then boiled for one-half hour to remove any remaining traces of peroxide. Then the solution was poured into an electrolysis flask. The preparation of uranium (IV) perchlorate was carried out in a manner similiar to that described by Ahrland#o. The electrolysis flask was a modified one liter one neck flask. A small "L"'shaped piece of tubing was added to the bottom of the flask to provide an external electrical connection to the mercury cathode. On the side of the flask was attached a fifteen millimeter "L" shaped tube containing a coarse fritted disk about three centimeters from the flask prOper. The closure consisted of a bent tube with stopcock pass- ing through a 2#/#O standard taper joint and reaching to the bottom of the flask. Two additional inlets to the joint were provided. The finished apparatus is shown in figure 3. In Operation the solution of uranium (VI) perchlorate was placed in the flask over a pool of mercury six centimeters in diameter. The side arm was filled with 0.5 N perchloric acid. A 26 platinum electrode was inserted in the side arm and a platinum wire in the mercury leveling bulb. Dry oxygen-free nitrogen was bubbled through the inlet (A) and then through the solution. It exited via (I), when the electrolysis was complete (I) was closed off by clamp- ing the attached rubber tube, and nitrogen was admitted through (B). The pressure then forced the liquid out of the flask via (M), assuming appropriate adjustment of the st0pcock at (M). The pumping time had to be short so that the pressure would not force the solution out of tube (B). When the electrolysis of the uranium (VI) perchlorate was begun the solution was about 0.5 g in perchloric acid and 0.13 E in uranium (VI) ion. As the electrolysis began the solution was yellow. A current of 0.7 amperes at 7 volts was passed into the solution and very rapidly a green coloration was produced above the mercury. Agitation of the solution was provided by a stream of dry nitrogen which was bubbled through the flask. The electrolysis was continued for several hours until the solution turned quite dark due to the production of uranium (III). When the uranium (III) appeared to be fairly well distributed through the flask, the electrolysis was discontinued. The excess uranium (III) was des- troyedly bubbling oxygen through the flask. Oxygen reacts rapidly with uranium (III) but only slowly with uranium (IV). The electrolysis was carried out at room temperature. Gordonl+1 notes that the electrolysis proceeds to completion if the solution is cooled to 0°C. No attempt was made to cool the solution, consequently the uranium (IV) solution always contained some uranium (VI), generally on the order of a few per cent. 27 This preparation was carried out at first in a different manner from the above. The wire dipping into the mercury was ordinary tinned copper, the hydrogen peroxide used was three per cent not diluted thirty per cent, and demineralized water was used. In these cases a small amount of unidentified very finely divided solid was found. This would make the solution appear cloudy, although it settled out after a day. The first preparation was transferred immediately after electrolysis to the storage flask and thus the precipitate settled out in the storage flask. The second solution was allowed to stand in the electrolysis flask for two days until settling had occured. Then the solution was carefully transferred. Additional preparations were carried out in the nammer first noted and no precipitates were produced. The precipitate was isolated but never identified. A suggestion was made that the precipitate might be U304 since this is suspected to be formed in certain electrolyses42. No evidence could be found that this precipitate inter- fered with the oxidation reaction as long as the precipitate was removed before the use of the uranium. Two different materials were used for the anode in the electrolysis procedure. One was a platinum wire with a one centimeter platinum square attached to the end. This electrode produced no side reactions. The other was a gold wire coiled into a spring. This was used in two electrolyses and both times a black deposit appeared on the gold which could be removed by nitric acid but only with difficulty. Use of the gold was discontinued. 28 .xmdah doapmnmmonm A>HV Badman: on madman smaseo coaseflom pass sesamema ovonuso humoumz muoano hunches on and: asGHpMHm pmapso flowchpflz la. la Lt} Azzmav sew seam muons szsflpwam xmwe nephews mmumoo masses nowhu Ham: h>dmm soapSHom adasmns f/lll usfiOn henna unmasm»m o:\:m .IIII sodas nomoesaz (Cu peasfi ammonufiz 29 Finally it should be noted that the D. C. source was such that approximately a one volt ripple was imposed on the direct current. This was determined by viewing the current on a calibrated oscillosc0pe. The effect of this on the electrolysis is unknown. Water For the first part of the program demineralized water was used. The demineralized water was produced by passing distilled water through a mixed bed of anion and cation ion exchange resins. This water contained less than 0.5 parts per million impurities. It is possible that this water contained some organic impurity introduced by the resin. However difficulty was experienced in preparing the uranium (IV) perchlorate solution and in reproducing the same rate cpnstant values as reported by Harkness and Halperns. In an effort to improve this situation conductance water was substituted for the demineralized water. This water was prepared by taking demineralized water and distilling it out of alkaline potassium permanganate solution. Conductance water was used exclusively from February 9, 1961. In the appendix all reactions using conductance water are noted by an asterisk after the uranium concentration. Nitrogen Prepurified nitrogen which had been further treated to remove the last traces of oxygen was used to protect the uranium (IV) perchlorate from atmospheric oxidation, and to remove the uranium solution from the storage flask. For a description of the 30 nitrogen purification train see the special apparatus section below. Sodium Perchlorate Anhydrous sodium perchlorate was obtained from the G. Frederick Smith Chemical Company. This was dissolved in demineral- ized water, filtered and placed on a hot plate to reduce the solution volume. As the solution was heated a pale reddish gelatinous material precipitated out of solution. The solution was filtered and the precipitate tested for ferric ion by adding thiocyanate ion in a solution made acidic with hydrochloric acid. The test was positive. The evaporation procedure was continued until no further precipitate was produced. The solution was filtered and put back on the hot plate. It was cooled after further reduction of the volume. When the production of crystals had ceased the solution was filtered and the crystals so obtained were washed and redis- solved, and the process repeated to produce a new cr0p of crystals. After filtration the crystals were washed, dried, and stored in a vacuum desiccator. Maleic Acid Maleic acid was obtained from Eastman Kodak Company. This was dissolved in ninety-five per cent ethanol until a saturated solution was formed at room temperature. The solution was cooled with stirring in an isopropanol-dry ice bath. Cry» stallization occured as the solution cooled. When crystallization was complete the crystals were filtered in a Buchner funnel which had been cooled with dry ice and then the crystals were washed with 31 ethanol which had also been cooled with dry ice. The crystals, when dry, were stored in a vacuum desiccator. The melting point of the crystals was determined as 129-13200. The literature value is given as 130-130.5°C.43 Tartaric Acid Mallinckrodt Analytical Reagent was used without further purification. Succinic Acid Baker's C. P. Analyzed crystals were used without further purification. Oxalic Acid Baker Analyzed Reagent was used without further purifi- cation. Fumaric Acid Fumaric acid used was obtained as the practical grade from the Eastman Kodak Company. It was recrystallized from boiling water 0 Malonic Acid The malonic acid was the practical grade from Dis- tillation Products Industries. An unsuccessful attempt was made to recrystallize the acid from water. A sample was then purified two times via sublimation at 130°C. under a pressure of less than 32 ten milliliters of mercury. A sample melted at 134—135.5°C. The melting point found in the literature is 135.6°C.43 Malic Acid Practical dl-malic acid from Eastman Kodak Company was recrystallized from a mixture of absolute ethyl alcohol and trichloroethane. A three to two mixture of alcohol to trichloroe- thane was used and a saturated solution at the boiling point was formed. An additional four parts of trichloroethane was then added and the solution allowed to cool. Crystallization occurs slowly as the cooling proceeds. It was found necessary to cool the solution with dry ice-isoprOpanol mixture 1x>initiate crystallization on occasion. The malic acid was recrystallized three times in the above manner. Monomethyl Ester of Maleic Acid Several attempts were made to produce the methyl half (ester of maleic acid, but all were unsuccessful.‘ In one preparation maleic anhydride was reacted with methyl alcohol in ethyl ether. The maleic anhydride was recovered unreacted. Maleic anhydride was also reacted with sodium methoxide in ethyl ether. 0n removal of the ether a thick syrup was obtained. This crystallized after a day and much stirring. Maleic acid was recovered after filtering and recrystallizing from ethyl ether. ' The author would like to thank Mr. James D. Hoeschele and Mr. Calvin M. Love for their work in attempting these preparations. 33 Finally maleic anhydride was reacted with sodium methoxide in methyl alcohol. A crystalline product proved to be maleic acid under analysis. Siegel and Moran44 claim to have produced the methyl half ester in acetone by reacting equimolar amounts of maleic anhydride and methyl alcohol. The ester was never isolated. Their proof of its existance rests mainly on the value of the neutralization equivalent determined by titrating the acetone solution with standard hydroxide solution. When these solutions of the ester in acetone are titrated with aqueous sodium hydroxide, the neutralization equivalent so determined is that of maleic acid. Any attempt to isolate a solid by removal of the acetone results in the production of a white solid with a neutralization equivalent equal to that of maleic acid. Solutions of the recrystallized ester in methyl alcohol were titrated with standard alcoholic sodium hydroxide. The neutralization equivalent obtained was again that of maleic acid. Therefore it must be concluded that while the methyl half ester apparently exists under anhydrous conditions, any attempt to isolate or purify the substance introduces enough water to hydrolyze it. B. SPECIAL APPARATUS The several pieces of special apparatus used in this research are illustrated in the figures that follow. A short des- cription of each appears below. Circles are used to designate the stopcocks, the solid line (8) in the circles showing the holes bored in the stopcock. All joints are either 24/40 standard taper if they are connected to 34 flasks or ball and socket joints if they appear in transfer lines. No joints or stopcocks that contacted the solution were greased. Direct Current Supply Figure 4 illustrates the direct current supply. The diagram is self-explanatory. The component parts for the supply were mounted on a piece of plywood. A one volt alternating current ripple was shown to be present by means of an oscillosc0pe. Nitrogen Purification Train The nitrogen purification train is shown in figure 5. The method followed was that of Gordon45. Prepurified nitrogen from the Matheson Company was passed over copper turnings kept at 450°C. in a tube furnace (A). Then the gas passed over copper deposited on Kieselguhr also heated to 450°C. (B). From there it passed successively through four gas washing bottles equipped with glass frits. The first two towers (C,D) contain alkaline pyrogallol (fifty grams of sodium hydroxide and thirty grams of pyrogallol in three hundred milliliters of water). The final two towers (E,F) contain water and aqueous perchloric acid, respectively. The perchloric acid is adjusted to the same acidity as that present in the uranium storage flask. The purified nitrogen was then bubbled through the uranium solution. A hydrogen outlet, (0), is used when the cepper is regenerated. This also serves to remove the water formed during the process. 35 OUTPUT - + ______Q h—_m 110 VAC .aJ (:A;> O-l amperes ; :.a 0-50 volts t i F variable transformer 50 ohms 500 microfarads 14 ohms ’WW‘W 500 microfarads IL ' ll ..——__.. Figure 4. Direct Current Supply 36 Uranium Storage Flask This is a three neck flask shown in figure 6, two necks of which (B,C) are fitted with tubes that lead to the bottom of the flask. The third neck (A) has a bent tube with stopcock fitted into it. This serves as an exit tube for the nitrogen. The center tube (B) serves not only as a delivery tube for the uranium solution but also as a gas inlet tube for the nitrogen. The remaining tube (C) serves also as an inlet for nitrogen as well as an outlet for the uranium solution. During storage a slow stream of nitrogen is admitted through tube (C). StOpcock (F) is turned to allow nitrogen to flow through the "tygon" tube (E). To provide for an exit for the nitrogen, tube (A) is Open. To allow for removal of uranium solution exit (A) is closed and nitrogen inlet (B) is used to admit nitrogen. This requires adjusting stOpcocks (F) and (H) to allow nitrogen to flow through tube (I). Finally stOpcock (D) is turned so that the uranium solution will flow out the lower of the two connections. In normal removal the tube (C) is filled with uranium solution twice (allowinga.1ittle to flow out exit (J) ) before re- moving a sample. C. ANALYTICAL DETERMINATIONS Sodium Hydroxide A sodium hydroxide solution that was 0.5 N was prepared as described by Kolthoff and Sandelll+6 and stored in polyethylene bottles, protected from the atmOSphere by "Ascarite" carbon dioxide absorbent. It was standardized against potassium acid phthalate (Mallinckrodt Analytical Reagent - primary standard) Which had been 37 sundae soapsoflmwndm ammonpwz .m ondmflm U a m a o filv 51V Rflv my D OxO i. v.2: , has 3:: i h H O... on. __ J1. _ Mme BMW/Jo: J OW“ fiIII owe . a C (.1 N Z l D 38 me o Hedges o mayo M mm pm A>Hv . b .m was a him fi‘ 39 dried at 125°C. and stored in a desiccator. Perchloric Acid The 5 N perchloric acid was standardized against the standard sodium hydroxide in the normal way using phenolphthalein as the indicator. Potassium Permanganate Standard 0.1 N potassium Permanganate was prepared ac- cording to Kolthoff and Sandell47. It was standardized against sodium oxalate (Mallinckrodt Analytical Reagent - primary standard) which had been dried at 110°C. Uranium Solutions of uranium perchlorate were analyzed for both uranium (IV) and uranium (VI), as well as for hydrogen ion. To determine the uranium (IV) content, (Op), the solution was simply diluted with conductance water and titrated with stand- ard potassium permanganate to the first pink coloration.l+8 The total uranium, (Ct) was determined by reduction of a sample in a Jones reductor thus reducing any uranium (VI) to uranium (IV). The solution was then titrated to a pink color with standard potassium permanganate. If the same size sample was used in both analyses, the uranium (VI) concentration, (C6), can be calculated from the difference in the two titrations. 06:0 .04 20) 40 The total hydrogen ion was determined by replacing the uranium ions on a column of Dowex 50x X 12 (Bio-Rad Analytical Grade - 100-200 mesh - hydrogen form). The resulting solution was titrated with standard sodium hydroxide to a phenolphthalein end- point. The free hydrogen ion then can be calculated from the equation below Ho = Ht - 4c1+ - 206 21) In this equation H equals the total amount of hydrogen ion in t the titrated solution, and H0 equals the amount of free hydrogen ion in the original solution. Concentrations were in units of molarity. It was found that a pH titration did not give accurate results in the determination of H+ ion. Difficulty was caused in these titrations by the precipitation of the uranium hydroxides, so the ion exchange method, which was much simpler and more accurate was adopted. The fact was soon discovered that the uranium solutions change titer with time. This is really to be expected but it was h0ped that this could be cut to a minimum by the precautions taken to keep oxygen out of the flask. However, the titer did change and so the uranium (IV) analysis was repeated every few days and the points graphed. The uranium concentrationany given day was determined to the nearest quarter day. After each uranium (IV) determination the method of least squares was applied to obtain the best line through the points. Figure 7 shows a typical graph that was 41 obtained in this way. Uranium (IV) perchlorate solutions were prepared four times during the course of the project. For the final solution several changes were made to minimize any time depend- ent change of uranium concentration. First, extreme precautions were taken to prepare and keep the uranium solution pure. And secondly the solution storage flask was wrapped with aluminum foil to bring to a minimum the amount of light entering. It was impossible to cut off the light completely since tubings lead from the flask and these cannot be completely wrapped. The protection from light did not provide any reduction in rate of change of titer. For example, the uranium solution molarity changed by 0.0140 moles per liter in one hundred and twenty-five days in the third uranium (IV) perchlorate preparation. The fourth preparation changed its molarity by 0.0123 moles per liter in one hundred and twenty days. Thus even with the utmost precautions it was impossible to stOp the uranium (IV) solution from changing titer. In order to know the uranium (IV) concentration at any time, it was necessary to constantly analyze the uranium (IV) solution. In addition to this it appeared from several reactions that the amount of uranium (IV) supplied to the reaction flask, was not equal to the amount of uranium (IV) present when the re- action is initiated. Since some of the uranium (IV) had reacted in the interval between preparation of the solution and initiation of the reaction, it was important that a method of determining the concentration of the uranium (IV) at the beginning of the reaction be developed. 42 OOH mwdn ow mafia mo moapoqam ¢ md soapmapsmoqoo A>Hv assess: Om cs .5 mASMfih owmo. |.Oomo. 0:00. Vowwo. ommo. (AI) wnIuean fi' 43 In the section on theory, the reasons were given why a graph of the reciprocal uranium concentration as a function of time should be linear. Such a graph can then be used to determine the uranium concentration by extrapolating the line time to zero and determining the value of l/U at that point. This method gives the uranium concentration most consistent with the reaction data. By the use of this method, the initial concentration of uranium could be determined rather accurately from the reaction data. At this point a rather interesting discrepancy was noted. In reactions where the amount of maleic acid present was varied, it was noticed that the initial concentration of the uranium (IV) varied also. Table VI shows the variation of the absorbance of maleic acid as a function of the temperature and concentration of maleic acid. The variation could be caused by several factors. One possible source of error is the normal Operative and instrumental errors associated with quantitative analysis. A second cause might be reaction of the uranium (IV) with the oxygen of the air. A complex with a different molar absorption coefficient might slowly form causing a third source of error. Fourth the uranium could react with the organic acid present reducing it. The first error can be eliuninated by considering the data listed in table VI. The changes with temperature and cone centration are too regular to be due to random error. In order to determine whether complexing of the organic acid by the uranium might cause any change in the absorbance, the molar extinction coefficient was determined for several acids using the Beckman Model DK-2 spectrophotometer. The results are shown in 44 Table VI Initial Absorbance of Uranium Solutions, Sodium perchlorate - 1.06 M, Pgrchloric Acid - 1.76 M, Thallium (III) Perchlorate - 9.00 x 10- M, Uranium (IV) Perchlorate - The starting concentration of the uranium varied. All solutions contained 0.70 milliliters of stock solution. Temperature Maleic Agid Total Volume Initial Absorbance °C M x 10 Added ml. at 100 Sec.‘ 35 900. 7.69 0.156 35 90.0 7.69 0.162 35 9.00 7.69 0.166 25 900. 7.69 0.172 25 90.0 7.69 0.183 25 9.00 7.69 0.181 15 900. 7.69 0.192 15 90.0 7.69 0.195 15 9.00 7.69 0.198 ‘ Absorbance determined at 650 mpk. table VII. The data indicate that within the limits of error there is no change in color due to complexing. There might be some questw ions in the case of tartaric, but in a later study by Job's method in an attempt to show complexing of the tartaric acid with the uranium, all solutions prepared were within 0.02 absorbance units of the standard. This is well within the limits of error in using 4S the Beckman spectrOphotometer. It can be concluded that the change in absorbance is not due to the organic acid complexing with the uranium (IV) ion. Table VII Molar Extinction Coefficient of Uranium (IV)-0rganic Acid Solutions Organic Concentration Uranium Molar extinction Acid of Org. Acid M Concentra- Coefficient‘ ion M None ------ 0.0155 55.8 Succinic 0.0170 0.0154 56.6 Malic 0.0170 0.0154 56.1 Tartaric 0.0170 0.0154 54.5 Fumaric 0.0170 0.0154 55.9 * Determined at 650 m/J. Thus while it certainly is possible that the uranium could be reducing the organic acid, it seems more likely that it is reacting with the oxygen of the air. The carboxyl group is rather resistant to reduction either by chemical or catalytic meansEO. It would appear that the change in initial absorbance is due to reaction of the U(IV) with the air, the reaction being catalyzed by the organic acid present. 46 Uranium Standards To interpret the data from the kinetic reactions a relationship was needed between the concentration of a uranium (IV) solution and the absorbance of that solution. All absorbance read- ings were made at 6500 angstroms. The necessary data were pro- vided by making up a series of solutions varying in uranium con- centration but constant in hydrogen ion and ionic strength. When the absorbance for the solutions was plotted against the concentra- tion a straight line was obtained. The method of least squares was applied to the data and the equation obtained was used to calculate concentrations corresponding to any absorbance reading. The equation is reproduced below. Y = 17.6 x +r 0.0176 22) In this equation X = the absorbance of the U(IV) solution and Y = the concentration of uranium (IV) x 103. Table VIII lists the absorbance and the concentration of the uranium standard solution. Table VIII Uranium (IV) Standards Sodium Perchlorate = 1.06 M, Perchloric Acid = 1.76 M, r] = 2.9 ,M x 103 Absorbance 1.06 0.059 2.12 0.119 3.18 0.180 4.24 0.242 5.30 0.297 t+7 While no study was carried out to determine the effect of hydrogen ion concentration on the molar absorption coefficient, in- formation from two reactions indicates that this can be neglected. In these two reactions the hydrogen ion concentration varied from 0.88 M to 2.50 M. The same volume of uranium was added to each solution and the initial concentration was determined experimentally to be 3.50 x 10-3 M. If the hydrogen ion affects the molar absorption coefficient, then the initial concentration should be different. The initial concentrations were determined by the l/U method. 51 Krause and Nelson also report that the variation of molar absorption coefficient with hydrogen ion is negligfible at this high acidity. Thallium Both oxidation states as well as total hydrogen ion were determined for solutions of thallium (III) perchlorate. Total thallium, (Ct)’ was obtained by reducing a sample of the thallium (III) perchlorate solution with sulfur dioxide to the thallium (I) state. The thallium was then precipitated as the 52 chromate , dried and weighed. Thallium (III), (03), was determined by making the solution basic, thus precipitating thallium (III) oxidesa. This was filtered in Gooch crucibles, dried and weighed. Thallium (I), (Cl)’ can then be calculated from the following equation, if the sample volumes are identical. c-_-c-c 23) 48 Total hydrogen ion, (Ht)’ was determined as in the uranium solution. The thallium ions were exchanged for hydrogen ions on Dowex 50 ion exchange resin, and the resulting solution was titrated with standard sodium hydroxide. Potentiometric titrations were attempted, but thallium oxide precipitates as sodium hydroxide is added, and the results cannot be reproduced. The free hydrogen ion could be determined more easily and accurately using the ion ex- change technique. The free hydrogen ion was calculated from the equation that follows. H = H — 3c - c 24) Again the concentrations are expressed as molarity. D. THE OXIDATION-REDUCTION REACTION A reaction was initiated by mixing equal amounts of two solutions, one containing the thallium and the other containing the uranium. Both solutions were as similiar as possible to minimize dilution effects, slow hydrolyses, etc. Obviously the thallium and uranium were kept separated, but in all other aspects the solutions were identical. Normally the organic acid was added only to one solution, usually the uranium solution, but reactions were examined out where both the thallium and the uranium solutions contained equal amounts of the organic acid. Reactions were also studied in which the organic acid was added to the thallium. Table IX gives the normal concentrations of substances used in a reaction. In most reactions only the organic acid was varied. It was necessary to vary other substituents, in a few cases. 49 The preparation of the solutions was usually divided into two sections, the dividing point being the removal of the uranium from the storage flask. Up to this point the initiation of reactions could be delayed any length of time, but once the solution of uranium is removed from the storage flask the reaction had to be carried out in the next few hours. To minimize errors the time, from removal of the uranium solution from the storage flask until the reaction was initiated, was kept constant. No precautions were taken to protect the uranium solution after it was removed from the storage flask, thus the reaction had to be completed before deterioration of the uranium solution had taken place. Table IX Concentration of Reactants for a Typical Oxidation-Reduction Reaction Uranium Solution Thallium solution .15. 14. U (Iv) 3.50 x 10‘3 ........... T1 (III) ----------- 9.00 x 10‘3 3010, 1.76 1.76 NaClOu 1.06 1.06 Maleic Acid 4.50 x 10"3 ........... Reactions were executed in one of three different ways. The catalyzing substance was added either to the uranium, the thallium or to both solutions. Normally the reaction was carried 50 out with the catalyzing substance mixed in with the uranium. Therefore this procedure will be discussed in detail and only the difference between this and the other procedures noted. Reactions were carried out in sets of three. Two of these would be catalyzing reactions and the third a standard reaction containing no catalyzing substance. Solutions with the exception of the uranium stock were stored in a water bath maintained at 25.00C. The necessary amounts of sodium perchlorate and perchloric acid were pipetted into one ten milliliter volumetric flask, while thallium perchlorate, sodium perchlorate and perchloric acid were pipetted into a second flask. Pipettes were given a two second drain time. Various types of pipettes were used at different times and no difference was noted in the results. All pipettes were cleaned in the same manner. After an immersion in aqua regia they were rinsed several times with distilled water and then ten times with deionized water. The pipettes were dried in an oven. Extreme care was taken to keep the glass equipment clean and free from possible contamination. The volumetric flasks were also cleaned in aqua regia and rinsed several times with both dis- tilled and demineralized water. Once the flasks had received all the reactants except the uranium and the catalyzing solution, they could be stored until needed, providing they were sealed against dust, etc. To complete the experiment the organic acid along with the uranium solution was added to the partially filled flask. Then the liquid level in the flasks was adjusted to the mark on the neck of the flask with 51 conductance water. If the runs were carried out at a temperature different from 25°C., the liquid level was not adjusted until the solution had equilibrated in a1appropriate bath for one hour. The amount of reaction was followed by noting the dis- appearance of the uranium (IV) peak at 6500 angstoms. A Beckman model DU spectrophotometer was used. This was kept at constant temperature by means of the bath in which the reactant solutions were stored. When the solution were put into the bath the spec- tophotometer was turned on and allowed to warm up. Also at this time a cell holder containing four cells, one of which was filled with demineralized water, was inserted in the spectrophotometer. Demineralized water was used as the reference solution for all reactions. After the solutions had been stored in the constant temperature bath for the prescribed time, four milliliters of the thallium solution was measured into a thirty milliliter Erlenmeyer flask. Immediately thereafter four milliliters of uranium solution was added and the timing was begun. The uranium and the thallium were both measured with class A pipettes so there would be no drain time. Timing commenced when the pipette containing the uranium was half drained. After the addition of the uranium the contents of the flask were mixed well, a cell filled and the first measure- ment made when one hundred seconds had elapsed. Additional reactions to a total of three were started at two hundred second intervals. This has the result of staggering the reading time of the solutions. If the absorbancy of each solution is read every three hundred seconds, then staggering AV v F- 5‘ in :4 ~\~ he . . «\H 52 of the times allows the reading of one solution every one hundred seconds. Unless there was a specific reason, reactions were concluded at 2500 seconds. Some of the slower reactions were studied for as long as 10.000 seconds. When as much data as desired were gathered, the cells were rinsed with water and stored in 3 M hydrochloric acid. The 3 M acid served two purposes. It kept growths from forming in the water and also removed any thallium (III) oxide deposited on the cell walls during the rinsing process. The reaction residues were saved so that they might be reclaimed for uranium and thallium later. E. MISCELLANEOUS EXPERIMENTS Spectra The spectrum of uranium (IV) perchlorate was determined and found to agree with that reported in the 1iterature5l’53. The spectrum is shown in figure 8 and the absorption peaks are noted in table X. Growths In Acids One unusual problem occurred in connection with the organic acids. several of the acids repeatedly developed growths that appeared to fungi on long standing. Because of this all organic acid solutions used in this project were freshly prepared. Job's Method Attempts were made in two cases to determine the compo- sition Of several complexes by Job's method of continous variations. 53 onshoaaonom A>Hv EdfiamnD mo Esnpoomm .w ouomwh LE. 2H mawzmgmbis com com com 00m 00m 00: I - n _. .Il ma II.NM IL w: :m 4UGIOIJJ900 u0140UI4xa Jvtow 54 Table X Absorption Peaks of Uranium (IV) Perchlorate Uranium (IV) Perchlorate - 0.0154 M, Perchloric Acid - 1.76 M, Sodigm Perchlorate - 1.06 M, Ionic Strength - 2.9, Temperature 24.9 C. Principle Absorption Bands Molar Extinction Coefficients 680 20.3 655 55.8 555 18.1 498 26.0 488 i 21.9 .431 16.0 The first attempt, that of tartaric acid and uranium, has already been mentioned. A slight difference was noted between the molar extinction coefficient of a tartaric acid-uranium solution and a uranium standard. To check this, several solutions containing varying amounts of uranium (IV) perchlorate and tartaric acid were compared with uranium (IV) standards. In all cases the difference in absorbance between the mixtures and the standards was less than or equal to 0.002 absorbance units. This is well within the limits of error of determining the uranium concentration. Thus it must be concluded that if differences in absorbance do exist, they are too small to detect with existing equipment. An attempt was also made to carry out Job's method to determine uranium-tartaric acid complexes by the change in rotation that the tartaric acid under- goes On complexing. This method has been successfully used to 55 54 determine thorium complexes . Unfortunately no rotation could be detected with the existing equipment and solutions. This method may be practical with this system, but it will require a more concentrated uranium solution as well as a very sensitive polarimeter. Extraction Experiments Several extractions were carried out on the reaction products of the uranium-thallium system as catalyzed by maleic acid. The extraction was carried out in a liquid-liquid extractor designed for use with an extracting liquid lighter than water. The extracting liquid was ethyl ether. This was removed by evaporation. Due to the slight solubility of water in ether, a small amount of water solution was obtained from the ether. This solution was initially purple but over a period of days the color changes to light brown. The extracted species were not identified. Infra-Red Spectra In connection with this study the infra-red Spectra of maleic acid and fumaric acid were determined. The spectra are shown in graphical form in figures 9 and 10. The main absorption peaks are listed in table XI. 56 Tk 2H mawzmqm><3 ea NH OH Has: Honsz n anaemz ofiom owoamz mo adnpoomm .m mhsmfih _ _ _Jd' :.0 m.o LONVHHOSHV /) 57 Has: Hoesz n suave: cHod owhmadh mo asuuoomm .OH on:MHh fix zH mawzmqm><3 :H NH OH w w a _ q _ A I _ N.O ¢.o w.o AONVHHOSHV 58 Table XI Absorption Peaks of Maleic and Fumaric Acids Maleic Acid __M Fumaric Acid Wavelength Intensity wavelength Intensity M H 2.57 6.2 2.59 1.6 4.65 Sh 6.01 10.0 4.92 Sh 7.61 2.50 5.33 4.1 7.88 7.50 5.88 9.41 8.18 5.0 6.14 5.2 8.27 Sh 6.51 5.0 9.91 2.50 6.42 5.5 10.85-11.15 2.2 7.97 4.7 12.89 4 1 8.28 2.6 15.90 1.6 10.26 <1 10.6.-10.89 5.2 11.44 Sh 11.61 10.0 12.76 7.6 13.84 4.4 5. RESULTS All rate constants reported in this section are the apparent second order rate constants from the equation 9% = k [U(IVE] [TMIIIE] 25) A. SUCCINIC ACID Several reactions were carried out with various amounts of added succinic acid. The range of succinic acid concentrations 2 M to 1.12 x 10.3 M. The rate constants for covered was 4.5 x 10- these reactions are listed in table XII. The graph of the rate equation for the first reaction listed in the table appears in figure 11. The other rate plots are similar to this one. It should be noted that the first few points do not fit the straight line. This is quite common and occurs in almost all reactions studied. If the straight line is extrapolated to zero time, for the second order plot it should pass through the point, log Tlo/Uo. However, the extrapolated line does not pass through this point. This will be discussed fully below. The results of this series of reactions can be seen best by examining table XII. When the succinic acid concentration is low enough, then the system has a rate constant equal to the rate constant of the system in the absence of succinic acid. As the succinic acid concentration increases, the rate constant for the reaction decreases to a minimum. From that point on additional succinic acid has no effect. The last two reactions, where the succinic acid concentration increase by a factor of two caused no 59 60 6000.:NHH endpmhmmame m.N "K‘s .fl.mb.H u 6H0¢ OHHOHnohOm .m.mO.H u OQMMOHnoHem SSHwom .2 muoa x oo.m u 38038.8 3H: 53ch .m macs x slim u 31.8288 95 e322: vaom OHaHoozm wsH:H8psoo sowpomom a Mom SOHpmswm mpmm 839 .HH oHsmHh OH N mnzoomm m mm om ma 3 m o _ _ H _ 3.0 nv 1 +3.0 nu \\\ up 0 3 m3 I 3.0 \\\\\\\\\AU nu . I mm.o O C) ,wm.o 61 Table XII Rate Constants for Reactions Containing Succinic Acid Thallium (III) perchlorate = 9.00 x 10'.3 M, Perchloric Acid = 1.76 g, Sodium perchlorate = 1.06 M, Ionic strength = 2.9 Temperature = 24.9OC. Succinic cid Uranium (gv) 1.51.. 10.2.1 M x 10 M x 10 M sec 1.12 5.46 24.7 3038 3046 1073 6.75 3.46 1.23 1305 301+? 8.2 22.5 5.47 7.4 1+5'0 3047 504 corresponding decrease in the rate constant. For all succinic acid reactions, the first few points deviated from the straight line. Most reactions had only the first 13°th deviating, thus the reaction illustrated is worse than usual in this respect. Bo OXALIC ACID The results of several reactions carried out with varying amounts of oxalic acid present are listed in table XIII. The C>Xe'tlic acid concentration was varied from 2.25 x 10-4 M to 2.25 x 10""3 M. When attempts were made to increase the oxalic acid Concentration above this level, a pale green-white SOlid precipitated in the reaction flask. Presumably the precipitate is a I‘eaCHZELon product between oxalic acid and uranium (IV)° 62 The graphs of the rate equations all yield excellent straight lines for reactions containing oxalic acid. In all re- actions the first point deviated from the straight line provided by the: 128st of the points. In addition the straight line failed to paxas through the log Tlo/Uo point. In the higher concentrations of oxalic acid, the plotted lines approach the zero time intercept (16g Tlo/Uo). The relation between oxalic acid and the rate constant is aan..inverse one. As oxalic acid increases, the rate constant decreases. The change in rate constant is not very large and no minimum is reached; due, perhaps, to the fact that the oxalic acid concentration cannot be very large or precipitation occurs. Table XIII Rate Constants for Reactions Containing Oxalic Acid Thallium (III) perchlorate 9.00 x 10.3 M, Perchloric Acid = 1.753 £1, Sodium perchlorate — 1.06 M, Iona; strength = 2.9, Temperature = 24.9 C. Oxalic Acid Uranium (N) k x 102 I! x 103 g x 103 5’1 sec"1 _________ 2.25 3.48 2.23 4.50 5.48 2.21 1102 301+? 1092 22.5 3.48 1.87 22.5 3.47 1.69 63 c, MALONIC ACID The reactions containing malonic acid are tabulated in table XIV. The malonic acid concentration range covered is 9 x 10-8 M to 9.00 x 10.3 M. When the data from these reactions is graphed two facts are noted. One is that all experimental points occur on a line, and secondly this line includes the point log Tlo/Uo. In the two acids discussed previously neither of these two facts was true. The first reaction in table XIV is plotted as a second order reaction in figure 12. There is no catalysis of the uranium-thallium reaction by malonic acid. The table shows that there is only scatter in the rate constant, k, and no relationship between malonic acid and the rate constant is seen when the malonic acid varies by a factor of ten. Table XIV Rate Constants for Reactions Containing Malonic Acid Thallium (III) perchlorate 9.00 x 10"3 g, Perchloric Acid = 1°76 M, Sodium perchlorate = 1.06 M, Ionic Strength = 2.9, Temperature = 24.900. \ \ Malonic Acid Uranium (IV) ' k x 102 1‘. x 104 14. x lo3 g'l aec‘l 9.00 3.53 2.13 22.5 3.26 2.19 45.0 3.26 2.30 67.5 5.62 2.29 90.0 5.62 2.58 64 z euoa x oo.m u cacc carcac: ..oom.sm n manumamQSoe .m.m n summonpm OHOOH cm mu.H n uHod OHAOHsonmm .m.mo.H n OOMHOHAOHOQ Bassom .2 nnoa x oo.m u cacacaacaca xHHHV aaaaacae cm muoa x mm.m u cacaoascacm ASHV scarce: uwo< OHmOHmz mchHMpnoo sOHpomom m pom newnessm spam one .NH ousmHh muoa x mnzoomm mm om ma OH m c flH MWOH I4 w:. 65 D. MALIC ACID Four reactions were carried out with malic acid included as the catalyzing agent. The range of malic acid concentrations studied was from 2.25 x 10.3 M to 9.00 x 10"3 M. The graphs of the rate equations for two of the reactions are pictured in figure thirteen. All reactions gave a curve when plotted as a second order reaction. A gradation can be noticed in the curves with the final half of one of the reactions assuming a straight line. This reaction, the only one that gave any semblance of linearity on the rate plots was the one with the lowest malic acid con- centration, 2.25 x 10'”3 M. The sIOpe of this line was determined as noted in table XV. While it is dangerous to use one reaction to decide, it appears that malic acid catalyzes the reactions. First the rate constant is fifty per cent higher than the standard rate constant," and secondly this curvature occurs in all cases where catalysis occurs. The features of the rate plots to be noted are the linearity occuring only with low concentration and the non-linearity occurring in the range where the ratio of organic acid to uranium (IV) is one. i The rate constant in reactions containing no catalyzing agent i S referred to as the standard rate constant. 66 .Amv m muoH x oo.m .nav m_n-oa x mm.m u cacc caacz ..oom.em u cacccaamEca .m.m mumsonpm OH:OH .m.wm.H u cHom oHaOHsonmm .m.mo.H u opSHOHnoumm 85Hsom : m OH N oo.m cacacaacace aHHHV aaaaacse .Amc m_mnoa x mm.m .ACD CDC) C)C) mpmnOHnohem ESHvom ..oom.¢m u manpmhomaoe .sH oasmwh H o — :0 .1 m4 I1 o.m mu II w.N min x ZOI M 70 F. SODIUM PERCHLORATE Harkness and Halpern5 studied the effect of ionic strength on the oxidation of uranium by thallium. These data were checked in the present study and since small differences appear this work is presented here. The data gathered are reported in table XVII, and presented graphically in figure 15. All of the points determined by both authors fall in the same region of the graph, but the present study gave a line with a higher slope than the data gathered by Harkness and Hal- pern. G. TARTARIC ACID Over twenty-five reactions were studied in an attempt to elucidate information on the effect of tartaric acid on the uranium-thallium oxidation reaction. The range of tartaric acid studied was from 9.00 x 10-3 to 2.25 x 10-3. The apparent rate constants for these reactions are listed in table XVIII. In the first group of reactions shown, the tartaric acid was varied while the uranium concentration was held as constant as possible. The results, at best, are poor. In the range of tartaric acid studied there appears to be a strong catalysis, with the catalysis de- creasing with decreasing acid concentration. Great difficulty was encountered in this range of tartaric acid concentration. Graphs of the second order rate equation in this range of tartaric acid are very frequently not linear or linear only after a certain amount of reaction has occurred. Figure 14 illustrates this same property for malic acid. In the first set of reactions only three produced 71 Table XVII Rate Constants for Reactions Containing Sodium Perchlorate Uranium (IV) perchlorate = 3.48 x 10.3 M, Thallium (III) per- chlorate : 9.00 x 10'"3 M, Perchloric Acid = 1.76 M, Temper- ature = 24.900. . 2 2 Sodium perchlorate k x 10 k x 10 M M51 sec-l M.1 sec-l Harkness & Halpern This work 0.000 1.08 ---- 00821} -""- 1'78 0.84 1.55 -_-- 00949 """"- 2000 1.06 ---- 2.21 1.29 2.00 ---- 1048 --"'" 2.1+? 2.12 ---- 3.00 2.58 5.24 —--- 2.96 5.85 -_-_ 72 O 0 In all 0 II oom em I eunuchomsoa Emu H I UHom oHaOHnoaom .2 nuoa x 00.0 n cocaoaaoaoa xHHHc eaaaanma .2 muoa x ma.m OQMLOHzoaom ESHUOm mo soHposdm m we pampmsoo oumm was. com N HI HIS NIOH M a n .ma .naaaa memAOHsopom A>Hv Hafisms: H _ _—l x aOI X 73 straight lines based on all points. Three reactions produced non- linear graphs. Three more yield six or fewer straight lines based on points. One reaction is very interesting in that when the data are plotted the points group themselves into two distinct lines. The graph of the rate law for this reaction is reproduced in figure 16. The first two reactions of the second set show again the effect of varying tartaric acid. These were run at a different uranium (IV) concentration than those above. With the lower uranium concentration the graph of the rate equation had very little curv- ature. In the final three reactions of this set the effect of de- creasing uranium while keeping tartaric acid constant is seen in the increasing rate constant. In the reaction previously discussed the tartaric acid was mixed with the uranium solution. In the third set of reactions the tartaric acid was mixed with the thallium solution, and in the last set the tartaric acid was split equally between the uranium and thallium solutions. In both of these cases, the apparent second order rate constant increases as the concentration of the uranium decreases. Thallium (III) perchlorate Table 74 XVIII Rate Constants for Reactions Containing Tartaric Acid 9.00 x 10.3 M, Perchloric acid 1.76 g, Sodium perchlorate = 1.06 M, Ionic strength = 2.9. Temperature = 24.9°c. Tartaric Acid Uranium (IV) k x 102 g x 103 g x 103 3? sec"1 9.00 5.41 4.95 9.00 5.50 4.48‘ 8.75 3.64 5.42 6.75 5.50 Curve 6.75 5.64 2.27 4.50 5.41 Curve 4.50 5.50 Curve 5.50 5.64 5.55‘ 2.25 5.41 2 lines 2.25 5.62 1.14 9.00 1.96 5.89 4.50 1.96 4.59 6.75 2.60 5.24 6.75 1.82 6.70 6.75 1.04 6.85 . Not treated by the method of least squares. 75 Table XVIII (Continued) -M‘ .w— —_.—‘ Tartaric Acid Uranium (1v) k x 102 M x 103 M x 103 Mfl sec'”1 6.75' 5.64 2.56 6.75* 5.64 1.94 6.75‘ 2.60 4.84 6.75* 1.82 4.79 6.75‘ 1.04 5.60 6.75"”I 3.62 3.95 6.75“ 2.60 4.02 6.75“ 1-79 5.52 6.75** 1.02 6.54 35-0 “ 3.48 3.96 17.5 .. 5.48 Curve ’ In this group of reactions the tartaric acid was added to the thallium solution, not the uranium solution as usual. ## In these reactions the uranium was divided equally between and mixed with both the uranium and the thallium solution. 76 .oom.:m n eyepmuomsOB .m.m u summonum oHOOH am mm.H u vHom OHHOHnoaom .m mO.H u ouMHOHsoaom Edeom .m mnoa a. oo.m u 31.8238 3H3 asaficsa :2. muoa 0. din u cocaoasoaoa 25 cameras vHod Owampame msHsHMpcoo nOHpomom 8 90m :OHpmsvm comm one .mH oaSMHh NIOH N mazoomm mm om mH OH m 0V — a _ A r N+No I .3. l o... .1 we. om. 77 Maleic Acid Maleic acid was investigated rather completely and in more detail than the preceeding acids. Consequently the data concerning it is presented in several tables. The first of these, table XIX skuows the variation of the rate constant with the hydrogen ion. Table XIX Rate Constant as a Function of Hydrogen Ion Trisilfilium perchlorate = 9.00 x 10.3 M, Maleic acid = 4.50 x 10-3 M: Ionic strength = 2.9, Temperature = 24.9°C. Hydrogen ion Sodium perchlorate Uranium (IV) k x 102 M M M x 103 M'1 sec'1 2.50 0.52 5.55 1.88 1.76 1.06 3.29 2.66 0.88 1.94 3.14 6.37 . The maleic acid was divided equally between the uranium and thallium solutions . One of the most common ways of determining the order of a substitutent is to carry out a series of reactions where only the concentration of the substitutent under consideration is varied. This has been done in the case of the hydrogen ion for the maleic aiCd catalyzed reaction. To determine the order of the sub- stitutent then, a graph is made of the logarithm of the initial concentration for the varied substance as a function of the logarithm of the initial rate for the reaction. The slope of this line is equal to the order of the substitutent. Figure 17 shows 78 .Oom.:m u endpmhomswa .m.m n someonen cacoH em muoa x om.e u caoc oaoac2 em muoa x oo.m u caceoamoaca AHHHV aeaaamme 20H sameness . anaaacH sea: comm HoaaanH mo noaecaaca one .sa oaamam seem aaHeHzH sea m.m- a.m- a.n- a.e- m.e- m.e- _ _ _ _ m.o- fi' +3 TVIIINI 901 The Rate Constant Thallium (III) perchlorate 1.76 M, Sodium perchlorate Temperature 79 Table XX as a Function of Maleic Acid 9.00 1.06 x 10'3 M, Perchloric Acid = M, Ionic strength = 2.9, = 24.9°c. w 5““ Maleic Acid Uranium (IV) k x 10 M'x 103 M x 103 Mfl eec'1 55.0 5.48 0.425 9.00 3.53 0.998 6.75 5.62 0.684 4.50 5.62 1.85 4.50 5.40 1.51 3.50 3.48 2.28 2.25 5.60 5.76 0.900 5.60 2.94 0.550 5.51 2.64 0.0550 5.51 2.12 4.50 5.40 1.79‘ 4.50 5.47 0.905*f 4.50 3.52 1.05" solution. #0 mixed with both the uranium and the thallium solution. In this reaction the malic acid was added to the thallium In the reactions the uranium was divided equally between and 80 such a graph for the variation of hydrogen ion in maleic acid catalyzed reactions. The Slope of the line is -1.l7. Table XX shows the rates as a variation of maleic acid concentration. Since there is large variations in the data this has also been presented in graphical form in figure 18. There is Egreat similarity between this curve and the one already seen in the tsection on fumaric acid. Beginning with low concentrations of maleic acid, the system reacts as though no organic acid were gxresent. As the concentration of the maleic acid increases, the rate of the reaction increases, with a maximum occurring at 9.00 x ZLHw.ssHsmaD vampmnoo mumm.paonmmm< one .wH oASMHh a. 33. 82.22 . MIOH :nOH MIOH NIOH HIOH _ _ H _ o 0 AV II. H O 0 II N .lllllllllllllIAU O O/ o n IIIIIIIIII J 82 .Oom.¢m u oedemaoQSoB .m.m n camconan canoH .m.ms.a u caoo oaaoaaonom .m.mo.a u connoamoaoa HHHHV season .m macs x oo.m n ouMhOHnonom HHHHV ESHHHmna .nOHpsHom Hooch mo whovHHHHHHe 5.0 u opmAOHnouom H>Hv 82Hsmnb mace oaoacz eo aoaooeea n no chem HoaoacH one .ma enemas E OHOc OHMH<£ HaHEHZH OOH- m.m e.m m.m o.m w.H m.a ¢.H i _ I4, _ H _ m.m nu ll Oo+~ nv AU //// AV ll :.¢ //////AU II w.: mu 1 e. /! EIVH TVIIINI 901' 83 .Oom.:m u oasumaoQSme .mom n someonon cacoH .m.0s.a A caoc caeoamoaom .m_00.a u cecaoacohoa aHHHc season as msoa x 00.0 n OpmaOHnonom AHHHV adHHHmna .sOHpsHom MOOpm mo muouHHHHHHS 5.0 u ovaOHnonom A>Hv ESHGmAD cane oaoac2 HoaoaeH 0o ooaaocam c n. comm acaoaaH one .0m enemas Z QHOd OHMH<2 HdHBHzH OOHI 0.m 0.: m.s m.m ¢.m 0.m _ _ _ H m.0 w.0 O.H N.H HIVH TVIIINI 001’ 84 Table XXI presents the variation in the apparent rate constant with temperature for three different concentrations of maleic acid. These data are presented graphically in figures 21 and 23. Represented in figure 21 are the data from two of the con- centrations. Excellent lines are obtained in each case and the lepe is the same for each line within experimental error. The (data for these curves was treated by the method of least squares 230 that the best slope and intercept might be Obtained. The data calatained in this manner are listed in table XXII. The data presented in figure 21 are from concentrations of maleic acid where the relation between k and maleic acid is cizirect. The graphs Obtained in this area are distinctly different :ffirom the graph obtained at other concentrations. The points (Dietained deviate only a little from a straight line, and the inter- cept is much closer to the theoretical than has been found to be normal for these systems. Also presented in table XVII is a set of data gathered Eit a maleic acid concentration where the relation between k and ‘the maleic acid concentration is an inverse one. Data collected in.this area are similar to the data collected on the other acids. The first few points taken deviate greatly from a straight line, and the intercepts for these reactions deviate from the theoretical by a large magnitude. However, a very interesting pheonomenon was noted as these reactions were subjected to a decrease in temperature. The graph of the rate equation for the reaction at five degrees centigrade and a maleic acid concentration of 9.00 x 10"3 $.15 shown in figure 22. Here it is Obvious that the points are related 85 Table XXI Variation of the Rate Constant with Temperature Maleic Acid 9.00 x 10“ Thallium(III) perchlorate = 9.00 x 10"3 M, Sodium perchlorate = 1.06 M, Perchloric acid = 1.76 M, Ionic strength = 2.9. Temperature Uranium (IV) k x 102 ka x 102 °c. M_x 103 M71 eec'l M71 sec'1 35.0 2.81 1.74 ---- 24.9 5.09 1.11 1.77 15.0 5.55 0.240 5.86 5.0 4.24 0.0261 0.645 Maleic Acid = 9.00 x 10‘3 55.0 3.17 8.61 24.9 3.33 2.98 15.0 5.45 0.821 5.0 5.78 0.225 Maleic Acid = 9.00 x 10' 55.0 5.14 6.80 24.9 5.51 2.57 15.0 5.49 0.685 15.0 5.72 0.651 5.0 5.52 0.175 86 n summohpm 0H20H .m wu.H u u camhoamonoa AHHHveaaHHcca .coaoaaon Mooou mo unoeaaaaaaa s.0 u Omom oocnoHsonca season .2 muoa x 00.0 opMMOHnouom H>HvadflsMAD cane cancamvom .n 00.H u 2 enoa x 00.m u m m muoa x 00.m u a 2H0< OHmHmz Mom eunuchomaoe apHs pampmnoo comm usohmmm< on» we :OHpMHAm> .HN onsth MOH N Hlmmmmomn mm.m nm.m m¢.m mm.n mm.m mH.m HI _ _ _ .mv\\\\ no mo no .Av no no \0 OO.HI OmoHI om.NI 87 .Ooo.m n eunuchomsoa .m.N n someohpm OHsOH .m.mh.H a vHom OHHOHnohom .m.mO.H u epmHOHnohom adHoom .2 MIOH N oo.m n opmaOHnoaom HHHHvasHHHona .2 MIOH x sm.: n oomaOHnoaom A>Hvssfismap 0H0< OHOHmz mquHMpnoo sOHpomom w you nOHpmsvm comm one .NN oasth uoa x mozoomm N OOH Ow om OJ ON O _ H _ _ Hm. \Q R. O \ \O \O flaw WOH Ill mm. II mm. mm. 88 emoN fluvmdwhvm OHGOH 0”: QBoH H “34.06 OHMOHQOHOQ 0”. mOoH H wwwHOHSOHmnH season .2 0.02 x 00.0 n oocnoacoaoo xHHHvaaaHamse .coaoaaoc acorn 0o uncoaaaaaae s.0 u oomHOHnonom H>HvsquonD .m.MI0H H 00.0 n 0Hom OHonz .20Huomom 30Hm u m .nOHuomom HspHsH n d 0Ho< oHonz Mom eunuchomaoa nqu unmpmnoo OpMm unopened 02» mo OOH20H20> .MN ohsmwh N MOH Hummmmomn mm.m mm.m 02.0 mm.m mm.m mH.m _ \- — — ONOHI. mu < O I 8.7 no no Ill OJON' no a I a..- \J c oo.mu 3 DOT 89 to one of two lines with a few points falling in a curved area between the two lines. A similiar situation occured with all runs at this concentration. Rather than a curve which became linear, there were two linear sections with a curve between them. The deviation from linearity of the first line increased with a increase in temperature until it was impossible to tell that a straight line existed in the first portion of the rate plot. Graphs of the Arrhenius equation hawabeen prepared and are pre- sented in figure 23. Table XXII Thermodynamic Quantities for the Maleic Acid Catalyzed Reaction Maleic Acid A H A S 'M kilocalories calories/degree C. 9.00 x 10"3 M (A) 27.40 55.42 9.00 x 10"3 M (B) 51.8 44.98 9.00 x 10'“ 22.52 14.87 9.00 x 10"5 21.9 12.77 6. DISCUSSION The temperature dependence studies show rather well that the curvature often appearing in maleic acid catalyzed reactions is due to two second order reactions. The first one is fast at 25°C. One of two situations could exist here. The first reaction could go to completion so that the first reaction stops, allowing the second to be seen. Another possibility, and perhaps the more likely one, is that one of the reactants is slowly formed, and this reactant is used up rapidly until the concentration is reduced to a level determined by the equilibrium constant of the reaction. At this point the speed of the reaction depends on the rate of pro— duction of that reactant. If at certain concentrations, the rate of production of the desired reactant, and the rate at which uranium is used up in the second reaction are comparable, then the graph of the rate equation could be curved for the major part of the reaction. These reactions whose graphs of the second order rate equation are n0n~ linear, have been recalculated and graphed according to all common rate laws. NO linear relationship was discovered. The energy of activation for this reaction has been determined. Unfortunately, these data, as all data regarding this reaction are subject to great error. The energy and entropy of activation have been determined from a line which is dependent on only two points. It should be noted that information on this reaction is subject to more error, than other reactions considered. Finally it should be noted that all information gathered on this fast reaction, was gathered from reactions where the cone 90 91 3 centration of maleic acid was 9.00 x 10' M, that range where an increase in maleic acid concentration results in a reduction of rate. No curvature resulted in the other two reactions, also ob— served at 5°C. Both of these reactions with concentrations of 9.00 x 10.,+ M and 9.00 x 10.5 M maleic acid occur in that range where the catalysis is positive, that is where an increase in maleic acid results in an increase in the rate. It is unfortunate that a single rate equation cannot be written for the system uranium (IV) perchlorate, thallium (III) perchlorate and maleic acid. It should be evident from the evidence presented in the results that this system is complicated. However, this is not to say that the system is undefineable. It does mean that there are areas where more research is necessary if the system is to be defined in detail at all. If one considers the uranium-thallium reaction alone, an expression can be written for the disappeanance of uranium (IV). M = k [U(Ifi] En (III-D 26) dt Here all other variables such as temperature, hydrogen ion con- centration, etc. are kept constant, and the U(IV) and T1(III) expressions are used so that exact species need not be Specified. Likewise, it is possible to write a similiar equation for the system uranium, thallium, maleic acid. Before this can be done, it is necessary to make some definition so that the area of validity for the equation is known. The first equation that is presented covers the area of maleic acid concentration where the reaction is catalyzed by maleic acid. 92 That is the region between 5.5 x 10'5 M and 2.25 x 10"3 M. The expression that can be written for this area is: - d U(Ifil _ E j E . 0.075 at -.. k Dav—)3 T1(III) Maleic 27) The second expression covers the area of maleic acid con- centrations from 2.25 x 10.3 M to 3.5 x 10.2 M. Here the maleic acid retards the reaction. Consequently the maleic acid term now appears in the denominator. -M a k EJ(IV—)J [THIN—fl Edaleic Aci‘g '1°16 28) dt It should be noted at this point that the equations presented are valid only over the linear region of graph of the rate equation for any reaction. The effect of hydrogen ion was determined in the region where the first equation is valid. The graph of initial rate versus initial concentration for hydrogen ion had a slope of -l.l7 in- dicating a hydrogen order of the same value. The essential point is that the previously important second order path in hydrogen ion found by Harkness and Halpern is now almost non-existent. It would appear that only a slight amount of reaction occurs by this path. Energies and entrOpies of activation have been determined. These are for the overall reaction and do not account for the fact that there may be two paths present, as has been suggested for the uranium-thallium system. The energy of activation for that part of the curve where positive catalysis occurs is slightly lower, 22.1 kilocalories, than the energy of activation found in the uranium-thallium 93 reaction for the path that is first order in hydrogen ion, 24.6 kilocalories. The energy of activation for the reaction taking place in the region of negative catalysis is much larger, 31.8 kilocalories, presumably indicating an intermediate that is more difficult to form. Thus it appears that there are two paths initially, the normal hydrolysis path and a path that may be the one to one complex of uranium and maleic acid. The latter reacts slightly faster with the thallium than the hydrolysis product, thus causing a slight amount of catalysis. As the amount of one to one complex increases so does the catalysis. However, as the amount of maleic acid increases, larger and larger portions of the two to one complex of maleic acid and uranium, respectively, form, and this does not react with thallium at any significant rate, thus rapidly slowing the reaction. It appears from all available evidence that all acids studied can be placed in one of three classes: those which in- crease the rate of the reaction, those which slow down the reaction, and those which do not affect the system at all. In this latter case there is one acid, malonic. It has been suggested that this might be due to the reaction in acid to produce carbon dioxide and acetic acid. The acetic acid would not be eXpected to affect the system much at all. The addition of catalytic amounts of the acid was found to have no effect on the rate. This may also indi- cate that no strong complex is formed between malonic acid and the thallium or uranium, and thus no effect on the reaction. In the second group there appear two acids, succinic and oxalic acids, which reduce the rate of the reaction. The most likely explanation for this behavior is that both oxalic and 94 succinic acids form complexes that are less reactive than the hydrolyzed species that normally react. But if one considers the series, oxalic, malonic, and succinic, it is immediately noticed that the three carbon dibasic acid has no effect on the rate, while the two and the four carbon dibasic acids inhibit the rate. This may be due to the fact that succinic and oxalic acids form strong com- plexes while malonic acid does not, perhaps due to steric con- siderations. The simple act of complex formation should destroy the ability of the uranium and thallium to react unless the ligand provides a lower energy path for the electron than is normally available. Three acids catalyze the reaction between uranium and thallium, and there is strong indication that the same is true for a fourth acid. The fourth acid is malic acid, the one acid on which almost no data could be gathered because of the non-linearity of most of the graphs of the rate equation. One of the graphs was linear and indicated catalysis. The fact that the graphs were non- linear is in itself suggestive of positive catalysis for these acids, since nonlinearity occurred only in cases of positive catalysis and never with cases where the reaction was slowed down. The other three acids, tartaric, fumaric, and maleic acid, all de- finately catalyze the reaction. Their graphs of rate versus con- centration of catalyzing acid have similar shape. That is they first catalyze the reaction and with increasing acid concentration, the acids then inhibit it. The case of maleic acid has already been discussed in some detail. Rather great difficulty was experienced with tartaric 95 acid. The similarity between malic and tartaric should be noted. It was impossible to obtain linear graphs of the rate equation for many reactions. All orders of reaction were checked and none were found to be linear whether considering uranium, thallium, or some appropriate combination of these. It would seem logical therefore, on the basis of the information gained from maleic acid, that in these reactions there are at least two reactions occuring with different rates. These rates are such that they do not produce a linear graph when plotted according to any common rate equation. In order to elucidate completely any one of these re- actions more detailed research is necessary. Malic, fumaric, and tartaric should all be studied in more depth. Certainly the work on maleic acid indicated in which direction the future work should proceed. A whole series of reaction should be carried out at 5°C. so that the initial reaction taking place can be studied in detail. It is quite possible that the information gained here will aid greatly in explaining the slower reaction that is occurring. Quantitative information should be determined on the complexes of the acid being considered. Ion exchange might be used for this since the colorless acid do not present the normal means. Then too, this method is more adaptable to low concentrations than many of the other methods. 7. SUMMARY The reaction between uranium (IV) and thallium (III) in the presence of various organic acids was studied. Dibasic saturated acids studied were oxalic acid, malonic acid, and succinic acid. Oxalic acid and succinic acid were found to inhibit the re- action. Oxalic acid has only a slight effect on the system com- pared to succinic acid. Malonic acid has no effect on the rate of the system. The unsaturated dibasic acids, fumaric acid and maleic acid, were investigated along with the hydroxy dibasic acids, malic acid and tartaric acids. Under the appr0priate conditions these acids all catalyze the reaction. At low concentrations of fumaric or maleic acid, the reaction between uranium (IV) and thallium (III) is catalyzed, but as the concentration of the organic acid is in- creased, the effect is to inhibit the reaction. This is attributed to the formation first of a one to one complex that catalyzes the reaction, followed by the formation of a one to two (uranium to maleic or fumaric acid) complex which inhibits the reaction. Tartaric acid appears to exhibit the same behavior, and although the evidence is scanty, malic acid is believed to catalyze the reaction. Most of the graphs of the rate equation _ M a 484115] [THIN—fl 29) dt were found to be linear over a large part of the reaction studied. Almost all curves exhibited a particular deviation from the eXpected. The extrapolation of the linear curve to zero time did not pass 96 97 through log Tlo/Uo, which is required by theory. Rather, initial experimental points formed a curve which became linear only after several hundred seconds. Experiments at low temperatures showed that this curvature was due to two separate reactions, one occurring with a fast rate, and ending rather rapidly as it uses all of one reactant, and the other occurring simultaneously but with a slower rate. The energy of activation was determined for this fast re- action and found to be 27.4 kilocalories when maleic acid was present as the catalyzing substance. The energies of activation were also determined for the reaction that occurred more slowly. The values obtained were 31.8 kilocalories and 22.1 kilocalories for concentrationsof maleic acid that inhibit and that accelerate the reaction, respectively. Partial rate laws were determined. The reaction is first order in uranium (IV) and thallium (III), and in the accelerated area the order of the maleic acid is 0.07, while in the inhibited area the maleic acid has an order of -0.84. The hydrogen ion was found to have an order of —1.17 in the inhibited area. l. 2. 3. 4. 5. 7. 8. 9. 10. ll. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 98 8. LITERATURE CITED W. C. E. Higginson and J. W. Marshall, J. Chem. Soc., 447 (1957)- J. Halpern, Can. J. Chem., 31, 148 (1959). J. Halpern and J. 0. Smith, ibid., 53, 1419 (1956). R. H. Betts, ibid., 55, 1780 (1955). A. C. Harkness and J. Halpern, J. Am. Chem. Soc., 8;, 5526 (1959). D. K. Sebera and H. Taube, ibid., 83, 1785 (1961). R. T. M. Fraser and H. Taube, ibid., §5, 2259 (1961). C. H. Brubaker, Jr. and C. Andrade, ibid., 8;, 5282 (1959). F. Basolo and R. 0. Pearson "Mechanisms of Inorganic Reactions", John Wiley and Sons, Inc., (1958). See reference 9, pp 303 - 331. R. J. Marcus, B. J. Zwolinski and H. Eysing, J. Phys. Chem., 8, 452 (1954). H. Taube, J. Am. Chem. Soc., 21, 4481 (1955). H. Taube, Record Chem. Progr. Kresge-Hooker Sci. Lib., ll, 25 (1956). J. Halpern and L. E. Orgel, Diss. Faraday Soc., 22, 7 (1960). Dodson and Davidson,J. Phy. Chem., 26,‘§éé (1952). J. Hudis and R. w. Dodson J. Am. Chem. Soc., zg, 911 (1956). L. Michaelis, Trans. Electrochem Soc., 2;, 107 (1937). J. Shaffer, J. Am. Chem, Soc., 52, 2169 (1955); J. Phys. Chem. 59, 1021 (1956). W. C. E. Higginson and J. W. Marshall, J. Chem. Soc., 1952 447. J. J. Katz and E. Rabinowitch "The Chemistry of Uranium, The Element Its Binary and Related Compounds," Dover Publications, New York, (1961). J. J. Katz & G. T. Seaborg "The Chemistry of the Actinide Elements," Methuen and Co. Ltd., London, (1957). PP 94 ' 2030 See reference 21, p. 172. 23. 24. 250 26. 27. 28. 29. 30. 31. 32. 33. 34. 35- 56. 37. 38. 39. 40. 41. 99 F. Nelson and K. A. Krause J. Am. Chem. Soc., 23, 2157 (1951). G. Gordon and H. Taube, J. Inorg. Nucl. Chem., ;é, 272 0961). K. A. Krause and F. Nelson, J. Am. Chem. Soc., 2;, 2517 (1949). See reference 21, p. 180. E. Rona, J. Am. Chem. Soc., 22, 4339 (1950). R. L. Moore, ibid, 22, 1504 (1955). C. F. Baes, Jr. " The Reduction of Uranium (VI) by Iron (II) in Phospharic Acid Solutiod'Preprint No. 224, Nuclear Engineering and Science Congress, Cleveland, Ohio (1955). T. W. Newton, J. Phys. Chem., £2, 943 (1958). D. M. Mathews, J. D. Hefley and E. S. Amis, ibid, Q2, 1236 (1959). S. L. Melton, J. 0. wear, and E. S. Amis, J. Inorg. Nucl. Chem., $2, 517 (1961). S. L. Melton, A. Indelli and E. S. Amis, ibid, ;2, 325 (1961). J. C. Sullivan, A. J. Zielen and J. C. Hindman, J. Am. Chem. Soc. 82, 5288 (1960). T. W. Newton and Rabidean, J. Phys. Chem., Q}. 365 (1959) A. A. Frost and B. G. Pearson, "Kinetics and Mechanism", John Wiley and Sons, Inc., New York, (1953), p. 15. S. W. Benson, "The Foundation of Chemical Kinetics", McGraw-Hill Book Company, Inc., (1960), p. 18. C. H. Brubaker, Jr. and J. P. Mickel, J, Inorg. Nucl. Chem., 2, 55 (1957); See also J. P. Mickel, PhD. Thesis, Michigan State University, (1957). Gmelins Handbuch der Anorganishen Chemie, 25, 136 (1936). S” Ahrland and R. Larsson, Acta. Chem. Scand., M, 137 (1954). G. Gordon and H. Taube, J. Inorg. and Nucl. Chem., ;§, 272 (1961). 100 #25 R. C. Young, ibid, z, 418 (1958). 1&5. J. Heilbron, Dictionary of Organic Compounds, Oxford University Press, New York (1953). 41.. E. F. Siegel and M. K. Moran, J. Am. Chem. Soc., £2. 1457 (1947). 45. G. Gordon and C. H. Brubaker, Jr., ibid, 82, 4448 (1960). See also G. Gordon, Ph. D. Thesis, Michigan State University (1959). 46. J. M. Kolthoff and E. B. Sandell, "Textbook of Quantitative Inorganic Analysis", The MacMillan Company, New York, (1952), Page 526. 47. See reference 46, Page 564. 48. W. F. Hildebrand, G. E. F. Windell, H. A. Bright and James I. Hoffman, "Applied Inorganic Analysis," 2nd ed., John Wiley and Sons, Inc., New York, (1953), Page 471. 49. See reference 48, p. 108. 50. E. E. Royals, "Advanced Organic Chemistry", Prentice-Hall, Inc., Englewood Cliffs, N. J., (1954), P. 571. 51. K. A. Krause and F. Nelson, J. Am. Chem. Soc., 22, 3901 (1950). 52. See reference 48, Page 478. 53. D. Cohen and w. T. Carnell, J. Phys. Chem., g3, 1933 (1960). 54. L. J. Katzin and E. Gulyas, ibid, 62, 1347 (1960). 55. J. F. Randolph, "Primer of College Mathematics", The MacMellan Company, New York, (1950), p. 336. 56. "MISTIC Programming Manual", Michigan State University, East Lansing, Michigan, (1959). 101 APPENDIX ORIGINAL KINETIC DATA These data are organized in the same manner as they appear in the results section. To locate the original data it is only necessary to note the position of the desired reaction in its table. For example, if in the table discussing succinic acid, the original data are desired for the fourth reaction listed; this will be the fourth set of data in the group containing succinic acid in this appendix. 102 ORIGINAL DATA FROM TABLE XII (Page 61) Time A log Tl/U 5.46 x 10"3 g, U(IV) 100 .188 .4255 9.00 x 10"3 g T1(III) 400 .169 .4555 1.76 g 3* 700 .156 .4781 1.06 g NaClO# 1000 .145 .4991 2.9 1500 .138 .5134 1.125 x 10"3 g Succinic Acid 1600 .151 .5299 1900 .125 .5434 2200 .119 .5594 2500 .113 .5747 5.46 x 10"3 g, U(IV) 100 .189 .4247 9.00 x 10"3 g T1(III) 400 .170 .4555 1.76 g, 3* 700 .165 .4649 1.06 g. NaClO,‘L 1000 .155 .4795 2.9 1500 .150 .4890 5.58 x 10‘3 g_ Succinic Acid 1600 .140 .5097 1900 .142 .5049 2200 .131 .5299 2500 .152 .5274 3.46 x 10"3 g U(IV) 100 .186 .4288 9.00 x 10"3 g T1(III) 400 ---- ..... 1.76 g 3* 700 .167 .4582 1.06 g NaClOk 1000 .165 .4649 2.9 1300 .159 .4720 6.75 x 10"3 g Succinic Acid 1600 .154 .4815 1900 .150 .4890 2200 .147 .4957 2500 .145 .5058 Original Data from Table XII - Continued Time A log Tl/U 5.47 x 10'3 g U(IV) 100 .190 .4226 9.00 x 10"3 g T1(III) 400 .181 .4558 1.76 g H+ 700 .177 .4420 1.06 g NaClO# 1000 .175 .4482 2.9 1300 .169 .4547 1.35 x 10'2 g Succinic Acid 1600 .167 .4576 1900 .164 .4654 2200 .161 .4684 2500 .158 .4735 3.47 x 10"3 g U(IV) 115 .192 .4195 9.00 x 10"3 g T1(III) 400 .185 .4299 1.76 g 11+ 700 ,180 .4568 1.06 g NaClO# 1000 .177 .4420 2-9 1300 .175 .4447 2.25 x 10‘3 g Succinic Acid 1600 .171 .4510 1900 .168 .4567 2200 .166 .4595 2500 .165 .4645 3.47 x 10"3 g U(IV) 100 .193 .4226 9.00 x 10"3 g_ T1(III) 400 .185 .4299 1.76 g, H*‘ 705 .181 .4558 1.06 g, NaClo4 1015 .178 .4405 2.9 1500 .175 .4447 4.50 x 10-2 g Succinic Acid 1615 .174 .4464 1910 .170 .4529 2200 .168 .4567 2505 .171 .4510 104 ORIGINAL DATA FROM TABLE XIII (Page 62) Time A log Tl/U 3.48 x 10"3 g U(IV) 110 .188 .4245 9.00 x 10"3 g T1(III) 400 .175 .4478 1.76 g, H+ 700 .165 .4659 1.06 g NaClOA 1000 .154 .4805 2.9 1500 .146 .4957 2.25 x 10'“ g Oxalic Acid 1600 .140 .5087 1900 .152 .5262 2200 .125 .5423 2500 .120 .5553 3.48 x 10"3 g_ U(IV) 100 .179 .4379 9.00 x 10"3 g T1(III) 410 .165 .4609 1.76 g H+ 700 .155 .4781 1.06 g NaClO# 1000 .146 .4957 2.9 1500 .140 .5087 450 x 10'4 g Oxalic Acid 1610 .152 .5262 1900 .125 .5423 2200 .121 .5523 2515 .115 .5689 5.47 x 10"3 g U(Iv) 100 .190 .4475 9.52 x 10"3 y T1(III) 400 .177 .4675 1.76 g, H+ 700 .167 .4834 1.06 g NmC10,+ 1000 .159 .4976 2.9 1500 .150 .5151 1.12 x 10'3 g Oxalic Acid 1600 .144 .5280 1900 .138 .5402 2200 .131 .5573 2500 .125 .5711 Original Data from Table XIII - Continued Time A. log Tl/U 5.48 x 10"3 g U(Iv) 100 .192 .4454 9.52 x 10"3 g T1(III) 400 .177 .4669 1.76 g 3* 700 .167 .4850 1.06 g NaCio4 1000 .160 .4961 2.9 1500 .152 .5112 2.25 x 10"3 g Oxalic Acid 1600 .145 .5250 1900 .140 .5359 2200 .133 .5513 2500 .127 .5669 3.47 x 10"3 g_ U(IV) 100 .195 .4400 9.52 x 10"3 g T1(III) 400 .185 .4574 1.76 g 3* 700 .174 .4719 1.06 g, NaClO# 1000 .167 .4854 2.9 1500 .160 .4966 2.25 x 10"3 g Oxalic Acid 1600 .152 .4854 1900 .145 .5256 2200 .141 .5340 2500 .154 .5492 ORIGINAL DATA FROM TABLE XIV 53) Time A log Tl/U 3.53 x 10"3 g, U(IV)* 100 .197 .4105 9.00 x 10"3 g T1(III) 400 .185 .4270 1.76 g 3* 700 .175 .4417 1.06 g 14.51010,+ 1000 .165 .4585 2.9 1500 .156 .4745 9.00 x 10'“ g, Malonic Acid 1600 .148 .4897 1900 .141 .5035 2200 .154 .5182 2500 .127 .5354 Original Data from Table XIV - Continued 106 Time A log T1/U 5.26 x 10"3 g U(Iv)*‘ 100 .181 .4462 9.00 x 10"3 g T1(III) 400 .169 .4654 1.76 g, 3* 700 .160 .4812 1.06 g, 11.10101* 1000 .150 .4994 2.9 1500 .144 .5120 2.25 x 10"3 g_ Malonic Acid 1600 .157 .5266 1900 .129 .5449 2200 .125 .5605 2500 .117 .5752 3.26 x 10‘3 g U(IV) ‘ 100 .182 .4445 9.00 x 10"3 g T1(III) 400 .168 .4675 1.76 g H+ . 700 .160 .4812 1.06 g NaClo4 1000 .150 .4994 2.9 1500 .145 .5144 4.5 x 10'"3 2’ Malonic Acid 1600 .135 .5317 1900 .128 .5476 2210 .121 .5647 2500 .115 .5814 5.62 x 10"3 g u(1v)' 100 .200 .4014 9.00 x 10'3‘5, T1(III) 400 .185 .4224 1.76 g 3* 700 .175 .4570 1.06 g Na01o4 1000 .166 .4518 2.9 1500 .157 .4676 6.75 x 10"3 g, Malonic Acid 1600 .148 .4847 1900 .141 .4986 2200 .133 .5159 2500 .125 .5344 5600 .104 .5920 107 Original Data from Table XIV - Continued Time A log Tl/U 3.62 x 10'3 g U(IV)‘ 100 .197 .4059 9.00 x 10'85, T1(III) 400 .184 .4252 1.76 N. 3* 700 .175 .4406 1.06 g, NaClOu 1000 .164 .4556 2.9 1500 .155 .4707 9.00 x 10’3 g, Malonic Acid 1600 .145 .4904 1930 .136 .5095 2200 .129 .5249 2500 .125 .5401 5200 .107 .5834 ORIGINAL DATA FROM TABLE ( Page 67) Time A log Tl/U 3.50 x 10"3 g. U(IV) ‘ 100 .165 .4628 9.00 x 10'} g. T1(III) 400 .154 .5200 1.76 g 3* 700 .120 .5541 1.06 g NaC104 1000 .107 .5905 2.9 1500 .098 .6192 2.25 x 10'3 g Malic Acid 1610 .091 .6450 1900 .086 .6625 2200 .080 .6854 2500 .075 .7079 3.50 x 10-3.! U(IV)‘ 100 .155 .4814 9.00 x 10"3 g, T1(III) 405 .125 .5412 1.76 g 3* 700 .108 .5870 1.06 g NaClO# 1000 .098 .6192 2.9 1300 .089 .6514 4.50 x 10‘3 g_ Malic Acid 1600 .081 .6850 1900 .076 .7028 2200 .072 .7240 2500 .066 .7529 Original Data from Table XV - Continued Time A log Tl/U 5.58 x 10‘”3 g U(IV)* 100 0.185 .4244 9.00 x 10"3 g T1(III) 400 0.160 .4646 1.76 3 3* 700 .143 .4972 1.06 g, NaC104 1000 .150 .5245 2.9 1515 .121 .5467 6.75 x 10"3 M Malic Acid 1600 .116 .5600 1900 .110 .5774 2200 .105 .5908 2500 .100 .6069 5.58 x 10‘3 g U(IV) ‘ 100 0.185 .4270 9.00 x 10"3 g T1(III) 400 0.156 .4719 1.76 g, 3* 700 0.140 .5051 1.06 g NaClOn 1000 0.128 .5299 2.9 1500 0.121 .5467 9.00 x 10"3 g Malic Acid 1600 0.115 .5651 1900 0.110 .5774 2200 0.107 .5858 2500 0.104 .5944 ORIGINAL DATA FROM TABLE XVI 68) Time A log Tl/U 3.45 x 10'3 g. U(IV) 100 .182 .4595 9.00 x 10"3 fl. T1(III) 405 .160 .4765 1.76 M 3* 700 .146 .5051 1.06 g NaCIO4 1000 .140 .5164 2.9 1500 .155 .5517 5 x 10'3 g Fumaric Acid 1600 .128 .5441 1900 .125 .5570 2200 .118 .5705 2500 .113 .5834 109 Original Data from Table XVI - Continued Time A log Tl/U 5.45 x 10‘3 g U(Iv) 100 .181 .4422 9.00 x 10'3 gl T1(III) 400 .159 .4797 1.76 g 3* 700 .145 .5077 1.06 g, NaC104 1000 .138 .5224 2.9 1300 .132 .5369 4.58 x 10‘3 M Fumaric Acid 1600 .125 .5558 2200 .112 .5895 2500 .107 .6050 3.45 x 10"3 U(IV) 100 .185 .4587 9.00 x 10‘3 T1(III) 400 .158 .4819 1 . 76 M 3* 700 .144 .5001 1.06 E. NaCth 1000 .132 .5369 2.9 1500 .128 .5465 5.75 x 10'3 M Fumaric Acid 1600 .122 .5625 1900 .115 .5815 2200 .108 .6015 2500 .102 .6215 3.45 x 10'3 g U(Iv) 100 .184 .4579 9.00 x 10"3 g T1(III) 400 .165 .4685 “1.76 M 3* 700 .150 .4972 1.06 g NaClO 1000 .158 .5224 2.9 1500 .128 .5465 5.12 x 10'3 g Fumaric Acid 1600 .121 .5641 1900 .115 .5815 2200 .105 .6122 2500 .100 .6272 Original Data from Table XVI - Continued Time A log Tl/U 5.41 x 10"3 g U(IV) 100 .170 .4616 9.00 x 10"3 g T1(III) 400 .146 .5064 1.76 3 3* 700 .133 .5353 1.06 g, NaCIO4 1000 .126 .5505 2.9 1500 .119 .5714 5.12 x 10'3,3 Fumaric Acie 1600 .111 .5941 1900 .105 .6115 2200 .100 .6284 2500 .094 .6505 3.41 x 10‘3 g U(Iv) 125 .180 .4450 9.00 x 10‘3 g T1(III) 400 .163 .4735 1.76 g 3* 700 .148 .5050 1.06 g NeCIO,+ 1000 .158 .5256 2.9 1500 .127 .5491 5.12 x 10"”3 M Fumaric Acid 1600 .120 .5682 1900 .112 .5906 2200 .105 .6115 2500 .100 .6284 5.45 x 10'3,§ U(IV) 100 .182 .4595 9.00 x 10’3 g T1(III) 400 .165 .4704 1.76 g 3* 700 .148 .4984 1.06 E. NaCIO4 1000 .158 .5201 2.9 1500 .127 .5469 2.50 x 10‘3 3' Fumaric Acid 1600 .120 .5644 1900 .112 .5867 2200 .106 .6058 2500 .100 .6260 111 Original Data from Table XVI - Continued Time A log Tl/U 5.41 x 10"3 g U(IV) 110 .171 .4597 9.00 x 10"3 g T1(III) 400 .150 .4985 1.76 M. 3* 700 .138 .5236 1.06 g NeLCIO,+ 1000 .127 .5491 2.9 1500 .119 .5714 2.50 x 10'3 M Fumaric Acid 1600 .111 .5941 1900 .105 .6115 2200 .099 .6522 2500 .093 .6526 3.41 x 10'3 ! U(IV) 100 .180 .4450 9.00 x 10'3,§, T1(III) 400 .165 .4755 1 .76 M 3* 700 .148 . 5050 1.06 g, NeC10,+ 1000 .158 .5256 2.9 1500 .128 .5476 1.88 x 10‘3 M Fumaric Acid 1600 .119 .5714 1900 .109 .5991 2200 .105 .6189 2500 . 095 .6463 3.41 x 10'3 M U(Iv) 100 .185 .4596 9.00 x 10"3 M. T1(III) 400 .165 .4695 1.76 3 3* 700 .151 .4961 1-05.H NeCIO,+ 1000 .140 .5198 2.9 1500 .129 .5449 1.88 x 10"3 M Fumaric Acid 1900 .111 .5941 2200 .105 .6189 2500 .095 .6463 Original Data from Table XVI - Continued 3.45 x 10"3 g U(IV) 110 .185 .4578 9.00 x 10"3 g T1(III) 400 .162 .4725 1.76 N. 3* 705 .147 .5008 1.06 g NaCIO4 1000 .156 .5279 2.9 1500 .127 .5469 ' 1.25 x 10"3 M Fumaric Acid 1600 .122 .5585 1905 .115 .5785 2200 .110 .5934 2500 .103 .6147 3.45 x 10'3 E U(IV) 100 .185 .4542 9.00 x 10"3 g T1(III) 700 .155 .4852 1.76 E, 3* 1000 .145 .5060 1.06 E. NaCIO4 1500 .156 .5255 2.9 1600 .128 .5441 1.25 x 10"3 M Fumaric Acid 1900 .120 .5644 2215 .112 .5867 2500 .106 .6056 3.45 x 10-3.2 U(IV) 100 .187 .4517 9.00 x 10-3.3 T1(III) 400 .169 .4606 1.76 M 3* 700 .158 .4797 1.06 g NaClOu 1000 .148 .4984 2.9 1500 .140 .5164 6.25 x lO-LIL M Fumaric Acid 1600 .132 .5345 1900 .125 .5512 2200 .118 .5705 2500 .112 .5867 113 Original Data from Table XVI - Continued Time A log Tl/U 3.45 x 10"3 M U(Iv) 100 .186 .4554 9.00 x 10-3.! T1(III) 400 .170 .4586 1.76 M 3* 700 .160 .4765 1.06 E. NeCIO,+ 1000 .150 .4962 2.9 1500 .145 .5091 2.50 x 10'* M_ Fumaric Acid 1600 .155 .5266 2200 .122 .5585 2500 .116 .5753 ORIGINAL DATA FROM TABLE XVII 71) Time A . log Tl/U 3.52 x 10-3.3. U(IV) 100 .189 .4515 9.00 x 10-3.3 T1(III) 400 .175 .4521 1.76 M 3* 700 .166 .4672 0-424.fl NaClO 1000 .159 .4791 1500 .151 .4940 1600 .145 .5065 1900 .140 .5172 2200 .134 .5298 2500 .128 .5443 5.41 x 10"3 E. U(IV) 100 .192 .4225 9.00 x 10-3.! T1(III) 400 .177 .4450 1.76 M 3* 710 .166 .4626 0.848 M NaClOM 1000 .158 .4765 1310 .150 .4916 1600 .145 .5064 1900 .156 .5211 2200 .130 .5340 2500 .124 .5491 114 Original Data from Table XVII - Continued Time A log Tl/U 3.33 x 10"3 !. U(IV) 100 .184 .4576 9.00 x 10-3.! T1(III) 400 .169 .4618 1.76 M_ 3* 700 .160 .4770 1.06 E. NeLCIOLF 1000 .149 .4980 1500 .143 .5107 1600 .135 .5279 1900 .128 .5438 2200 .122 .5593 2500 .116 .5743 3.42 x 10'3.! U(Iv) 100 .192 .4218 9.00 x 10-3.fl T1(III) 400 .175 .4472 1-75.! 3* 700 .164 .4660 1.484 !. NaCIO4 1000 .153 .4856 1500 .145 .5012 1600 .157 .5180 1900 .129 .5362 2200 .122 .5542 2500 .115 .5723 5.58 x 10'3.M U(IV) 100 .185 .4544 9.00 x 10-3.! T1(III) 400 .169 .4594 1.76 M 3* 700 .154 .4856 2.12 M NeC101+ 1000 .144 .5070 1300 .135 .5252 1600 .125 .5480 1900 .117 .5684 2200 .109 .5907 2500 .105 .6097 115 ORIGINAL DATA FROM TABLE XVIII (Page 74) Time A 10g Tl/U 5.41 x 10"3 !. U(IV) 100 .165 .4288 9.00 x 10'3.fl T1(III) 400 .155 .4850 1.76 M 3* 700 .118 .5249 1.06 M NaClOQ 1000 .104 .5655 2.9 1300 .093 .6007 9.00 x 10"3 fl Tartaric Acid 1600 .085 .6505 1900 .078 .6612 2200 .073 .6839 2500 .070 .6984 3.46 x 10"3 M U(Iv) 100 .164 .4741 9.00 x 10‘3 fl T1(III) 400 .158 .5252 1-75.§ 3* 700 .122 .5610 1.06 E. NaClO 1000 .108 .6005 2.9 1500 .099 .6291 9.00 x 10"3 M Tartaric Acid 1600 .091 .6550 1900 .082 .6906 2200 .078 .7077 2500 .074 .7258 3.46 x 10"3 U(IV)‘ 100 .155 .4697 9.00 x 10"3 T1(III) 400 .126 .5506 1.76 M 3* 700 .110 .5739 1.06 M NaClOn 1000 .099 .6069 2.9 1500 .088 .6448 8.75 x 10‘3 M Tartaric Acid 1605 .077 .6915 1900 .070 .7233 2200 .064 .7560 2505 .057 .7962 116 Original Data from Table XIII - Continued Time A log Tl/U 5.62 x 10-3.fl U(IV)‘ 100 .173 .4406 9.00 x 10'3.§ T1(III) 400 .147 .4804 1.76 M 3* 700 .134 .5132 1.06 M Na010# 1010 .125 .5401 2.9 1500 .115 .5607 6.75 x 10"3 E Tartaric Acid 1600 .109 .5767 1900 .103 .5955 2200 .100 .6044 2500 .095 .6215 2800 .092 .6514 3125 .090 .6397 5400 .088 .6461 5720 .085 .6660 4000 .082 .6707 4500 .081 .6754 5010 .080 .6778 6200 .081 .6754 5.64 x 10'3 E U(IV) * 115 .175 .4864 9.00 x 10'3.fl T1(III) 400 .149 .5507 1.76 M 3* 700 .155 .5616 1.06 M NaC10# 1010 .125 .5851 2.9 1500 .116 .6094 6.75 x 10"3 fl. Tartaric Acid 1600 .110 .6275 1920 .105 .6415 2200 .100 .6580 2500 .097 .6697 Original Data from Table 117 XIII - Continued Time A log Tl/U 3.41 x 10'“3 H. U(IV) 105 .169 .4225 9.00 x 10"3 E T1(III) 400 .144 .4666 1.76 E. 3* 700 .129 .4985 1-05.§ NaClOQ 1000 .119 .5225 2.9 1500 .110 .5465 4.50 x 10‘3 M Tartaric Acid 1600 .105 .5622 1900 .100 .5792 2200 .096 .5906 2500 .094 .5975 3.50 x 10"3 E. U(IV) 100 .168 .4672 9.00 x 10'3 E. T1(III) 700 .132 .5373 1.76 M 3* 1000 .125 .5581 1.06 M_ NaCIO4 1500 .115 .5791 2.9 1600 .108 .6005 4.50 x 10"3 M Tartaric Acie 1900 .105 .6091 2200 .101 .6216 2500 .098 .6310 3.64 x 10-3.N 3(Iv)‘ 100 .165 .4527 9.00 x 10'3 M_ T1(III) 400 .157 .5060 1.76 M 3* 710 .120 .5460 1.06 M NaC104 1000 .109 .5755 2.9 1506 .100 .6052 3.50 x 10"3 E Tartaric Acid 1600 .095 .6205 1900 .087 .6491 2200 .082 .6694 2511 .076 .6938 Original Data from Table 118 XIII - Continued Time A log Tl/U 5.41 x 10'3 E. U(Iv) 100 .174 9.00 x 10"3 M. T1(III) 400 .160 .4571 1.76 M 3* 700 .153 .4495 1.06 M_ NaC104 1000 .146 .4626 2.9 1500 .145 .4685 2.25 x 10-3.! Tartaric Acid 1600 .159 .4765 1900 .156 .4829 2200 .132 .4916 2500 .129 .4983 5.62 x 10'3 M U(IV)‘ 110 .180 .4295 9.00 x 10-3.! T1(III) 400 .167 .4499 1.76 M 3* 700 .162 .4586 1.05.! NaCIO4 1000 .156 .4697 2.9 1550 .152 .4771 2.25 x 10-3.! Tartaric Acid 1600 .149 .4826 1900 .145 .4904 2200 .143 .4950 2500 .140 .5009 2800 .137 .5070 5100 .155 .5120 5400 .151 .5210 3700 .130 .5223 4000 .128 .5276 4500 .126 .5317 5000 .125 .5544 119 Original Data from Table XIII - Continued Time A 10g Tl/U 1.58 x 10-3.3 3(Iv)‘ 100 .082 .7840 9.00 x 10'3 E. T1(III) 415 .065 .8691 1.76 E. 3* 700 .055 .9307 1.06 !. NaC104 1000 .048 .9826 2.9 1515 .040 1.0425 9.00 x 10'3 M. Tartaric Acid 1600 .055 1.1058 1930 .031 1.1517 2200 .027 1.2055 2500 .024 1.2519 2805 .021 1.3047 5100 .020 1.3252 5400 .018 1.3659 5700 .016 1.4120 4000 .014 1.4640 4500 .012 1.5258 1.52 x 10-3.! U(IV)‘ 400 .068 .8562 9.00 x 10'3 M T1(III) 700 .059 .9062 1.76 M 3* 1000 .055 .9481 1.06 M NaClOu 1525 .048 .9857 2.9 1625 .045 1.0278 4.50 x 10-3.fl Tartaric Acid 1900 .059 1.0652 2200 .056 1.0966 2555 .033 1.1307 2805 .050 1.1675 5125 .028 1.1951 5410 .026 1.2240 5710 .024 1.2555 4005 .0225 1.2815 4500 .021 1.5081 120 Original Data from Table XIII - Continued Time A 10g Tl/U 1.91 x 10’3 E U(Iv)‘ 100 .120 .6026 9.00 x 10"3 fl. T1(III) 400 .098 .6701 1.76 M. 3* 750 .085 .7192 1.06 M NaClOQ 1000 .076 .7565 2.9 1500 .070 .7868 6.75 x 10"3 M Tartaric Acid 1600 .065 .8140 1910 .061 .8571 2200 .055 .8745 2500 .055 .8886 1.60 x 10"3 M. U(IV)‘ 100 .082 .7722 9.00 x 10"3 M T1(III) 400 .065 .8567 1-75.! 3* 700 .055 .9181 1.06 E, NaClOu 1000 .048 .9698 2.9 1500 .040 1.059 6.75 x 10"3 M Tartaric Acid 1600 .055 1.091 1900 .052 1.126 2200 .028 1.178 2500 .024 1.239 .901 x 10"3 ! U(IV)* 100 .044 1.045 9.00 x 10"3 !. T1(III) 400 .055 1.156 1.76 E. 3* 700 .025 1.264 1.06 M_ NeCIO,+ 1000 .022 1.515 2.9 1500 .020 1.352 6.75 x 10’3 M Tartaric Acid 1600 .016 1.441 1900 .013 1.523 2200 .011 1.588 2500 .010 1.624 Original Data from Table XIII - Continued Time A log Tl/U 5.62 x 10-3.H U(Iv)‘ 100 .172 .4425 9.00 x 10'3.! T1(III) 400 .146 .4881 1.76 M_ 3* 700 .151 .5210 1.06 M NeCIO4 1000 .120 .5475 2.9 1500 .110 .5751 6.75 x 10'3 M Tartaric Acid 1600 .101 .6009 1900 .095 .6285 2200 .090 .6397 2500 .088 .6461 2.60 x 10"3 E. U(IV)‘ 100 .120 .6026 9.00 x 10"3 M. T1(III) 400 .099 .6661 1.76 M. 3* 700 .086 .7146 1.06 M Na010# 1000 .075 .7616 2.9 1500 .068 .7986 6.75 x 10'3 M Tartaric Acid 1600 .061 .8571 1900 .056 .8692 2200 .051 .9028 2500 .047 .9332 1.79 x 10‘3 fl U(IV)‘ 100 .082 .7736 9.00 x 10"3 M. T1(III) 400 .065 .8585 1.76 E, 3* 700 .055 .9197 1.06 M NaC10# 1000 .047 .9533 2.9 1500 .040 1.0410 6.75 x 10‘3 M_ Tartaric Acid 1600 .055 1.0924 1900 .052 1.1274 2200 .028 1.1801 2500 .025 1.2258 Original Data from Table XIII - Continued Time A log Tl/U 1.02 x 10'3 M U(IV)‘ 115 .045 1.0555 9.00 x 10'3 M T1(III) 405 .055 1.1566 1.76 M 3* 710 .027 1.2555 1.06 M NaClOu 1000 .025 1.2991 2.9 1505 .019 1.3742 6.75 x 10"3 M Tartaric Acid 1600 .016 1.4423 1900 .014 1.4946 2200 .012 1.5545 2500 .010 1.6246 5.48 x 10‘3 ! U(IV)‘ 100 .165 .4609 9.00 x 10'3 M T1(III) 400 .140 .5087 1.76 M. 3* 700 .125 .5425 1.06 E, NeC10,+ 1000 .115 .5689 2.9 1500 .106 .5951 3.50 x 10.2 M Tartaric Acid 1600 .095 .6300 1900 .090 .6484 2208 .081 .6842 2500 .079 .6915 3.48 x 10-3.! U(IV)* 100 .147 .4946 9.00 x 10'3 M T1(III) 407 .118 .5592 1.76 M 3* 700 .105 .6058 1.06 M NaCth 1000 .090 .6484 2.9 1510 .080 .6866 1.75 x 10.2 M Tartaric Acid 1650 .071 .7280 1900 .068 .7452 2200 .063 .7698 2500 .060 .7895 123 ORIGINAL DATA FROM TABLE XIX (Page 77) Time A log Tl/U 3.55 x 10‘3 E. U(IV)‘ 100 .185 .4568 9.00 x 10‘3 M T1(III) 400 .174 .4535 2.50 E. 3* 700 .165 .4686 0.52 M NaClO# 1000 .157 .4829 2.9 1500 .150 .4958 4.50 x 10'* M_ Maleic Acid 1600 .144 .5084 1900 .157 .5228 2200 .130 .5384 2500 .125 .5507 5.29 x 10"3 M_ U(IV)‘ 100 .180 .4456 9.00 x 10-3.fl T1(III) 400 .165 .4706 1.76 M 3* 715 .155 .4880 1.06 M Na0104 1000 .145 .5081 2.9 1300 .135 .5301 4.50 x 10’* M_ Maleic Acid 1600 .127 .5488 1900 .120 .5660 2200 .112 .5876 2500 .105 .6078 3.14 x 10"3 fl. U(IV)‘ 100 .165 .4781 9.00 x 10-3.! T1(III) 400 .139 .5292 0.88 M 3* 700 .119 .5772 1.94 E NaCth 1000 .105 .6255 2.9 1500 .089 .6729 4.50 x 10'* E. Maleic Acid 1600 .077 .7224 1900 .067 .7696 2200 .059 .8148 2500 .051 .8695 ORIGINAL DATA FROM TABLE XX 124 (Page 79) Time A 10g Tl/U 3.48 x 10'3 M U(IV)’ 100 .184 .4502 9.00 x 10"3 !. T1(III) 450 .182 .4556 1.76 M 3* 700 .180 .4562 1.06 M NaC10# 1000 .178 .4397 2.9 1500 .176 .4425 3.5 x 10'2 M Maleic Acid 1600 .173 .4478 1905 .172 .4496 2200 .171 .4506 2500 .169 .4542 3.55 x 10'3.3 U(IV)’ 105 .187 .4257 9.00 x 10'3 M T1(III) 400 .175 .4455 1.76 M 3* 700 .170 .4498 1.06 M NaCth 1000 .165 .4585 2.9 1500 .164 .4605 9.00 x 10‘3 fl. Maleic Acid 1600 .157 .4725 1900 .154 .4777 2200 .150 .4852 2500 .145 .4953 3.62 x 10"3 M U(IV) ‘ 100 .191 .4156 9.00 x 10‘3 fl T1(III) 400 .170 .4451 1.76 M_ 3* 700 .165 .4556 1.06 E. NeCIO,+ 1000 .165 .4567 2.9 1200 .161 .4606 6.75 x 10"3 M Maleic Acid 1520 .160 .4626 1605 .158 .4655 1900 .155 .4707 2200 .151 .4781 2500 .150 .4804 Original Data from Table XX — Continued Time A log Tl/U 5.62 x 10"3 M. U(IV)‘ 105 .195 .4081 9.00 x 10"3 ! T1(III) 400 .168 .4489 1.76 M 3* 700 .155 .4707 1.06 H, NaCth 1000 .148 .4847 2.9 1500 .144 .4928 4.50 x 10"3 E. Maleic Acid 1600 .158 .5046 1900 .152 .5184 2200 .126 .5317 2500 .122 .5430 5.40 x 10'3.!. U(IV)’ 100 .182 .4576 9.00 x 10'3 M T1(III) 400 .155 .4825 1.76 M. 3* 700 .145 .5025 1.06 M NeCIO,+ 1000 .140 .5150 2.9 1500 .155 .5241 4.50 x 10"3 E. Maleic Acid 1600 .150 .5545 1900 .126 .5441 2200 .120 .5598 2500 .117 .5673 3.48 x 10-3.! U(IV)‘ 100 .187 .4262 9.00 x 10—3.! T1(III) 400 .165 .4609 1.76 E. 3* 700 .146 .4957 1.06 E. NaClO# 1005 .154 .5210 2.9 1500 .128 .5356 5.5 x 10'3 M Maleic Acid 1600 .125 .5480 1900 .116 .5658 2200 .110 .5833 2500 .105 .5968 126 Original Data from Table XX - Continued Time A log Tl/U 5.60 x 10"3 E. U(IV)‘ 100 .194 .4106 9.00 x 10'3 fl. T1(III) 400 .175 .4581 1.76 M. 3* 700 .159 .4646 1.06 M NaClOM 1000 .144 .4959 2.9 1500 .132 .5196 2.25 x 10‘3 fl Maleic Acid 1600 .125 .5412 1900 .115 .5619 2200 .110 .5762 2500 .104 .5932 3.60 x 10'3 E. U(IV)‘ 100 .194 .4106 9.00 x 10-3.3 T1(III) 400 .180 .4502 1.76 E, 3* 700 .167 .4509 1.06 M Nac101+ 1000 .155 .4719 2.9 1500 .145 .4915 9.00 x 10'* M Maleic Acid 1600 .155 .5151 1910 .126 .5329 2200 .118 .5544 2500 .110 .5762 3.51 x 10"3 M. 3(Iv)‘ 100 .189 .4225 9.00 x 10'3 M T1(III) 400 .174 .4444 1.76 M_ 3* 700 .165 .4624 1.06 M, NAC1O,+ 1000 .151 .4840 2.9 1500 .145 .5011 3.5 x 10'* M Maleic Acid 1605 .155 .5181 1900 .125 .5407 2215 .119 .5565 2500 .112 .5751 Original Data from Table XX - Continued Time A log Tl/U 5.51 x 10-3.3 U(IV)‘ 100 .190 .4206 9.00 x 10‘3 M T1(III) 400 .178 .4582 1.76 E. 3* 700 .168 .4545 1.06 M Na0104 1000 .160 .4684 2.9 1500 .150 .4865 3.5 x 10'5 M Maleic Acid 1600 .144 .4987 1905 .157 .5151 2200 .150 .5285 2505 .124 .5434 3.40 x 10"3 M U(IV)‘ 100 .185 .4558 9.00 x 10'3 M T1(III) 400 .158 .4771 1.76 M 3* 700 .145 .5025 1.06 N. NeClO,+ 1000 .158 .5167 2.9 1300 .135 .5280 4.50 x 10'3 M Maleic Acid 1600 .126 .5441 1900 .122 .5555 2200 .117 .5673 2500 .112 .5814 3.47 x 10'3 E. U(IV)‘ 100 .185 .4525 9.00 x 10"3 M T1(III) 400 .155 .4787 1.76 M 3* 700 .147 .4951 1.06 M NaCIO4 1000 .142 .5045 2.9 1500 .140 .5092 4.50 x 10"3 M Maleic Acid 1600 .156 .5179 1900 .133 .5241 2200 .130 .5307 2500 .129 .5334 128 Original Data from Table XX - Continued Time A 10g Tl/U 3.52 x 10'"3 !. U(IV)‘ 100 .189 .4218 9.00 x 10'3 E. T1(III) 400 .162 .4657 1.76 M 3* 700 .151 .4836 1.06 M NeCIOL+ 1000 .146 .4956 2.9 1500 .142 .5017 4.50 x 10‘3 X Maleic Acid 1600 .158 .5101 1900 .135 .5176 2205 .152 .5240 2500 .130 .5279 ORIGINAL DATA FROM TABLE XXI 85) Time A log Tl/U 2.81 x 10-3.fl U(Iv) ‘ 100 .156 .5109 9.00 x 10'3 M_ T1(III) 400 .148 .5267 1-76.3 3* 700 .142 .5586 1.06 E. NaClOk 1000 .156 .5524 2.9 1500 .129 .5686 9.00 x 10'} fl Maleic Acid 1600 .124 .5814 35.0°C. Temperature 1910 .119 .5948 2200 .114 .6090 2500 .110 .6206 3.09 x 10"3 M U(IV)' 110 .172 .4689 9.00 x 10'3 M. T1(III) 400 .164 .4826 1.76 M 3+ 720 .160 .4897 1.06 M. NaC104 1000 .155 .4982 2.9 1506 .150 .5081 9.00 x 10'3 !. Maleic Acid 1600 .147 .5150 24.9°c. Temperature 1900 .145 .5185 2200 .141 .5269 2500 .137 .5356 129 Original Data from Table XXI - Continued Time A log Tl/U 5.55 x 10"3 M U(IV)“ 100 .192 .4165 9.00 x 10'3 ! T1(III) 400 .174 .4454 1.76 M 3* 700 .167 .4545 1.06 M NaClO4 1000 .165 .4585 2.9 1500 .164 .4605 9.00 x 10"3 !. Ma1eic Acid 1600 .165 .4614 15.0°C. Temperature 1900 .162 .4655 2200 .161 .4652 2500 .160 .4675 4.24 x 10"3 H. 3(Iv)‘ 155 .257 .3296 9.00 x 10’3 !. T1(III) 560 .252 .5546 1.76 M 3* 1000 .226 .5404 1.06 E. NaClOM 1500 .220 .5471 2.9 2000 .214 .3539 9.00 x 10-3.! Ma1eic Acid 5000 .205 .5658 5.00C. Temperature 4000 .198 .3729 5000 .195 .5766 6000 .192 .5802 7000 .190 .3833 8000 .190 .3833 9000 .189 .3847 10000 .189 .3847 5.17 x 10"3 !. U(IV)* 105 .162 .4816 9.00 x 10"3 M_ T1(III) 400 .129 .5497 1.76 M_ 3* 700 .104 .6182 1.06 E. NaC10# 1000 .084 .6890 2.9 1500 .069 .7589 9.00 x 10-4.fl. Ma1eic Acid 1600 .058 .8199 35.0°C. Temperature 1900 .050 .3746 2200 .042 .9296 2500 .036 .9980 Original Data from Table XXI - Continued Time A log Tl/U 5.55 x 10-3.! U(IV)’ 100 .185 .4595 9.00 x 10"3 M T1(III) 415 .167 .4648 1.76 M 3* 700 .155 .4860 1.06 M NaCIOLF 1020 .145 .5060 2.9 1500 .156 .5254 9.00 x 10'* M Ma1eic Acid 1600 .125 .5507 24.9°C. Temperature 1900 .118 .5697 2200 .109 .5936 2500 .109 .5936 5.45 x 10"3 M. U(IV)‘ 105 .195 .4165 9.00 x 10"3 M T1(III) 400 .189 .4252 1.76 H, 3* 705 .185 .4509 1.06 M NaC10,+ 1000 .180 .4578 2.9 1500 .177 .4450 9.00 x 10'* fl Ma1eic Acid 1900 .170 .4559 15.0°c. Temperature 2200 .166 .4606 2500 .162 .4675 5.78 x 10-3.! U(IV)‘ 150 .210 .5815 9.00 x 10’3 M_ T1(III) 500 .212 .3788 1.76 M 3* 1000 .210 .5815 1.06 M NaClO 4 1500 .208 .5855 2.9 2000 .205 .3870 9.00 x 10'* !. Ma1eic Acid 5000 .202 .5915 5.0°C. Temperature 4000 .197 .3979 5000 .194 .4018 6100 .190 .4072 7000 2188 .4096 8000 .185 .4143 9000 .185 .4168 10010 .179 .4228 Original Data from Table XXI - Continued Time A log T1 /U 5.14 x 10'3 !. U(IV). 100 .166 .4761 9.00 x 10"3 M T1(III) 465 .155 .5581 1.76 M 3* 700 .119 .5772 1.06 M NaClO,+ 1000 .102 .6272 2.9 1500 .088 .6750 9.00 x 10"5 M Ma1eic Acid 1620 .075 .7410 35.0°C. Temperature 1900 .064 .7882 2200 .056 .8565 2500 .048 .8920 3.51 x 10'3 M_ U(IV)* 150 .181 .4457 9.00 x 10'3 E. T1(III) 420 .172 .4582 1.76 E, 3* 700 .165 .4726 1.06 M NaC10# 1000 .154 .4891 2.9 1500 .146 .5047 9.00 x 10'5 fl. Ma1eic Acid 1650 .158 .5214 24.9°C. Temperature 1900 .130 .5395 2240 .124 .5546 2500 .118 .5708 3.49 x 10-3.fl U(IV)‘ 100 .198 .4106 9.00 x 10‘3 E. T1(III) 500 .191 .4200 1.76 M 3* 700 .188 .4241 1.06 !. NaC104 1000 .185 .4289 2.9 1500 .181 .4549 9.00 x 10'5 !. Ma1eic Acid 1605 .179 .4574 15.00C. Temperature 1900 .175 .4435 2200 .173 .4475 2505 .169 .4558 Original Data from Table XXI - Continued Time A log Tl/U 3.72 x 10'3 fl. 3(Iv)* 165 .209 .5851 9.00 x 10’3 !. T1(III) 500 .207 .5879 1.76 M 3* 1000 .204 .3915 1.06 M NaClOA 1500 .201 .3950 2.9 2000 .200 .5966 9.00 x 10‘5 !. Ma1eic Acid 2500 .198 .3995 5.00C. Temperature 3000 .196 .4018 4000 .195 .4062 5000 .191 .4086 6000 .188 .4126 7000 .185 .4175 8000 .182 .4216 9000 .180 .4241 10000 .179 .4259 3.52 x 10-3.! U(IV) ‘ 100 .200 .4062 9.00 x 10'3 E. T1(III) 405 .194 .4145 1.76 M 3* 700 .191 .4185 1.06 M NaC104 1000 .187 .4242 2.9 1500 .184 .4285 9.00 x 10-5.N Ma1eic Acid 1655 .181 .4555 15.0°C. Temperature 1900 .178 .4578 2200 .175 .4422 2500 .173 .4458 133 APPENDIX METHOD OF LEAST SQUARES When the data from kinetic runs are graphed in the normal manner for a second order reaction with two reactants, one of two situations prevails. Either the data yield a straight line or a curve which becomes straight after x seconds. In either case 55 the method of least squares was applied to the straight portion of the line sO that the best possible fit of points to a line might be obtained. The MISTIC digital computer Of Michigan State University was used to carry out the necessary computations. Essentially MISTIC56 is a binary computer. However it is not necessary to provide MISTIC with binary data. Rather a decimal order input is programmed and the computer itself does the computations necessary to change the data from a decimal base to a binary base. It is also possible to build in a decimal readout program. All the programs used with the least squaring required a decimal data input and the answers were provided in decimal form. MISTIC can compute only with fractions. Thus it is necessary to introduce one or more scaling factors so that the data will be presented to the computer in proper fractional form. After the answer is obtained the scaling factor is reintroduced to obtain the output in prOper form. The MISTIC can store only 1024 words of 40 bits each. Therefore care must be taken in some programs to be sure that more information is not provided to the computer than it can store. This is soon to be changed with the introduction of a core memory. For example space limitations require that no more than fifty 134 problems be presented to program 7. There simply is no more room to store any more information. For a collection of points the method of least squares is essentially the determination of the equation of the straight line which has the prOperty that the sum of the squares of the distances from the points to the line will be a mifimum. The equation obtained is of the form: where m is the slope of the line, and b is the intercept of the line on the ordinate axis. The slope and the intercept of a line can be obtained by the solution of the two equations following. - nzxiyi " Z xiiyi nixi2 (Sari-)2 m 1) 2 b = 2x1 zyi ' zxiyi :3. 2) — 2 -— 2 ani - (in) In these equations n is the number of points being Operated upon, xi, and y1 are the coordinates of point, pi. There are three programs involved in the least squares method. They are denoted as the 6N, Ranes' L2 and 7 programs! The first program6N, takes the data provided and produces matrix equations which is the equivalent of equations 1 and 2. The ‘ Many thanks are due to Dr. R. L. Schwendeman who developed these programs for the computer and who so generously loaned them to the author. 8002840001 8002840002 1902626000 8002840000 L400140001 80028405F6 -5000263L6 81004265FJ 4000122000 7J5LFL4001 40001265L8 L4002263F- 423FFL5001 L4000L4000 265F-L05LL 703LL-53F7 4000081004 50000L45LL 525FLL45L0 425L5L5001 L400026000 40002L05L4 425L8255L9 5000140000 L15F9L45L4 425F9L45L8 425L800027 80008000ON 4000127511 465F6604-8 7LLLLLLLL6 223L-00001 0046*— 135 Table XXIII The 6N Program -5F468L L44L4211L 814FL025L 2210L402F L5F661F lOlF-JF 40FL1F 401FL52F 4OFL58L L44L468L L52F427L L025L52F L524L401F 41F814F L025L402F 526LL424L 40F814F 501F402F L025L525L 7525L-5F 401F5025L 75FOO39F L42F2616L 000F002F 00F005F 000F0010F OO3+OOF0011F 0072+ 40F +5F 4211L 92131F 92515F L5F 324L 92708F 265L92644F 19F L6F 40F 003322 00000000J 00F 503F 002F 7J6L 0020F 465L 92133F L58L 221014F 227L 261N 40F 1963-3 50F 40F 7512L 0036F 824F 1040F L5F L4F 327L 22F 00F 0010F 005+ 50100F50000L 26046FL5O57F 42012F46012F 41042F41045F 41044FL5038F 40045F26012F 0012+ 50000F74000F L4042F40042F L5000LL4036F 40000LF5043F 40043FL0041F 43020F-5000F 26000L00000F 0020+ L5042F50000L 26072F41043F 41042FF5044F 40044FL0040F 36028FL5012F L0041F40012F 41043F26012F 0028+ 92770FF5045F 40045FL0040F 52004LL5057F 46012F41044F 26012F92706F 92551F24999F 0035+ OFFOFF OOlFOOlF 00100F00100F OOFOOlF 201019N 136 Table XXIV The Ranes' L2 Program 8002840001 00F00160F L522L425L 7JF4OF 8002840002 OOFOOF 492F41F L556LL467L 1902626000 OOFOOF L51L4222L 4056LL068L 8002840000 00F00200F 4227LL522L 5677LL54F L400140001 00F0050F 4214L4216L 80028405F6 00F0021F 4218LL54F L471L464F -5000263L6 L56F4290F L42L4615L L05F527L 81004265FJ 40-550103 4616L4619L L55FL467L 4000122000. 263OFL511~7 4621L4625L 405FL072L 7J5LFL4001 46136F46138F L567L4221L 562LL565L 40001265L8 1020F42156F 4625LL5F 42-4L522L L4002263F- 4228FL5156F L6F5680L 4250LL524L 425FFL5001 L0155F42121F L5F66F 4675L4662L L4000L4000 46113FL0155F 4321L2620L L568L4650L 263F-L43LL 4692FL 020F 5066L75F 2776L-5F 745LL-55F7 4614OF42140F 66F4723L 50F74F 4000081004 413F2271F L4F4OF 50000L25LL 00159F00159F -121L405F L42F5254L 525FLL45LO 814F0020F L5F40F 5065L7J-4 425L5L5001 4624F92155F 505FL5F 2645LL55OL L400026000 401F7J1F L067L4O50L 40002L05L4 92131FL5-3 501023—4L4F L075L5678L 425L8253L9 50F524F 40FL42F L550L4258L 5000140000 2651FL525F 5627L4715L 4260LL5F L15F9L45L4 L4155F4225F L51F40F L6F5655L 425F9L45L8 L028F5625F L522LL066L L5F66F 425L800027 12152FL5F 4222L4227L L62F-162L 800080000N 26550FOFF L525LL467L 40F1562L 40001275L1 0068+ 4625L4621L L075L36w8 465F6604-8 413FL51L L070L5621L L474L2647L 800000000+ 4222L50-6 L515LL061L 00F0010000 225L-00001 40-5502L 5239LL569L 0000000J7 005+ 26-7414F 4056L5065L L4095FLL4095F 001F001F LJ1-4401-4 7J-340-3 NOl-4L42F 801FOOF 80-500-5 50FL6F N01023-3L6F N0-5L6F 0040F2551L 0027F2255L -5F401F 2279L2249L L516L4681L 50F-3F 5219L2618L 0030+ -5F4611L L410L4214L 814F2215L 751F0059F 401F5020L L52F74F -5F40F 814F502OL 4O2FL018L 565LL5F 661F-51F 40FL511L L4L4611L L52FL0194 401F52F 0059F5216L 256L1958F Table 41F236L 8OFOOlOF OOFOOlZF OOFOOlOF 0051+ 40FL116L -4L461L 4214L366L L5F365L 92706F225L 92642F002F J08L7J17L 428L228L OO63F19F L6F1039F 75l5LOO36F 824F104OF L51LL016L 461L5610L 92965F22F OOFOOlOF -41F001023F 001F+91000F OO500+ 00F00160F OOFOOF 00F00200F 00F0050F 00F0021F N01-4L42F 401F7J1F LJ1-4401-4 ~451F4652F 50133F7J—4 137 XXIV (con't) 40-4L590F 92131FL5-3 00550. L5500F405F L5501F404F 4O5FL5502F 406FL5505F 407FL5504F 408FL5505F 40138FL55O6F 4091FL5507F 40l36FL5308F 4052FL5509F 4121FL5510F 4025F249F 249N 8002840001 8002840002 1902626000 8002840000 L400140001 80028405F6 -5000265L6 81004265FJ 4000122000 7J3LFL4001 40001265L8 L4002263F- 425FFL5001 L4000L4000 265F-L05LL 703LL-53F7 4000081004 50000L45LL 525FLL45LO 425L5L5001 L400026000 40002L05L4 425L8255L9 5000140000 L1559L45L4 425F9L45L8 425L800027 80008000ON 40001275L1 465F6604-8 7LLLLLLLL6 223L-00001 00250+ 92770F9257F5 138 Table XXV The 7 Program 26999FOOOOOF 0051+ 26250N00252+ OOFOOF 5007OF50000L 001FO0F 26256F24999F 00F00280F 00F001F 005+ 41037F92535F 0045+ 92159F92515F 50051F41056F L5055F42015F 41037FL5000F 42014F42044F 40058FL4O59F 50280F50004L 40059FL5058F 26256F41059F 50006F50004L 26015F00000F 26262F92965F L5001LL4041F 0015+ 42001LF5057F 41056F50000F 40057FL0040F 75070F40000F L4054F56055F F5000L42000L 22001L00000F 42001LF5056F 4OO56FL0041F 0055+ 5602OF22000L 92965FL5059F 50006F50001L 0020+ 26262F92965F L5014FL4O52F L5044F42004L 46014FF5057F 50051FL1000F 40057FL0040F 50006F50005L 36045FL4054F 26262FF5056F 36005L26015F 4OO56FL0041F L5014F46006L 34999F92131F L5000F50051F 92515FL5055F 50011F50007L L4056F42044F 26262F92155F 41059F26044F 92515F26015F 00236+ ~5F468L L44L4211L 814FL025L 2210L402F L5F661F 101F-JF 40FL1F 401FL52F 40FL58L L44L468L L52F427L L025L52F L524L401F 41F814F L025L402F 526LL424L 40F814F 501F402F L025L525L 7525L-5F 401F5025L 75FOO39F L42F26160 000F002F 00F005F OOOFOOlOF 00262+ 4OF+5F 426L4615L 367L5116L L6F1039F L515LL013L 139 Table XXV (con't) 4615L5212L 92965F22F J011L7J16L 4211LL5F 3210L92606F 2211L92642F 0051F19F 265L7517L 001F825F 225L00F OOF823F 001F+91000F 50F00F 0035+ OFFOFF 24232N 140 second program, Ranes' L2 then solves this matrix equation for the ”best" slope and intercept. The final program 7 takes data from both of the previous programs and calculates mxi, biand yi and prints these along with the yiobtained experimentally so that they may be compared. The programs are as follows. As an example one reaction will be followed through the procedure. The data after the necessary calculations appears below. 2232 Log T123 100 0.4014 450 0.4195 700 0.4309 1000 0.4470 1505 0.4606 1600 0.4771 1900 0.4904 2200 0.5046 2500 0.5225 The data is supplied to the MISTIC on a punched data tape. The data are presented as follows: Table XXVI Typical Data Supplied to MISTIC 0040+ 00F003F 00F009F 265N +OOlOO+OO430+OO700+OlOOO+01305+01600+01900+02200+02500 +01+01+01+01+01+01+01+01+01 141 +04014+O4193+04309+O4470+O4606+04771+O4904+O5046+05223N Each problem consists of seven lines of data as shown above. Without going into great detail, the purpose of eich line will be shown. Line one gives a direction as to where lines two and three are stored in the computer memory. The sixth digit in line two is equal to one more than the number of variables in the equation being considered. For a straight line this is equal to three. The sixth number in line three is equal to the number of points in the data. This is the only number in the first four lines that will vary under normal circumstances. Finally line four is an order to the computer to transfer control to one of the programs in its memory. In MISTIC a number is indicated by prefacing it by a + or a - sign. No spaces are necessary. Notice that in lines five. six and seven all numbers have been prefaced by a + sign. Line five contains the x coordinates for the points under consideration. Notice that all of the numbers have been multiplied by 1015 the scaling factor for this portion of the data. Line six is a line necessary to complete the matrix which will produce the linear equations. As many +Ol's are insertem as there are points being considered. In line seven all numbers have been multiplied by 103*, the scaling factor for these data. These are the y coordinates of the points being considered. The last piece of data is followed by an N and at the end of all data sets, the number 2635N is inw serted. The N is necessary since it indicates the end of a set 142 of data and the 2635N is nucessary to allow the computer to shut Off. Since the MISTIC Operator is unfamiliar with the program, it is also necessary to furnish him with Operating instructions. These are reproduced below. Program How Started StOp Order 6N Bootstrap 20 1019 Input Black Switch OFF ‘—-—47 of 6N .____2, ~ we L2 Bootstrap 7 Bootstrap 24 232 Output Black switch 24 999 from L2 Input Black switch OFF ~~w-~~9 of 6N After the ON calculation has 6N contains the following data. +00206479250 +00117350000 +00564266000N +00117350000 Comments Insert input for 6N If black switch set to "ignore". Retain input for 6N for later use. Insert output from 6N and black switch through ____ problems. Do 22E remove output from L2 from punch until 7 is completely read in. Insert output from L2 Insert output from 6N If the black switch sen "ignore". been made the output from 3) \J'l v (J‘\ ‘ J 143 +00090000000 7) +00412480000N- 8) This information is necessary only to the computer, consequently it is not normally printed. Written in matrix form it appears as 00206479250 00117350000 x 00564266000 00117350000 00090000000 y — 00412480000 9) If time is denoted as x and the log Tl/U readings as y, then the data as previously given represents summations of the various entries. 3) E: x: 6) 2: xi 4) 3? xi 7) n 5) z xiyi 8) z yi This information is then inserted into the computer after the Ranes' L2 program. The output of the program contains the following information. -04944655615 10) -39383858242 11) +10000000000 12) The decimal point in the answer follows immediately the figure one in the scaling factor. Rewriting these they appear as follows. -0.4944655615 13) -3-9393858242 14) +1.0000000000 15) where 13) is the slope, 14) is the intercept and 15) is the 144 scaling factor. To correct these numbers for the scaling factors previously introduced, it is necessary to multiply 13) by 10-4 and 14) by 10’1. Now if the output from 6N is used as an input for program 7 along with the information from Ranes' L2, the following inform- ation is obtained. Table XXVII Output Of Program 7. +10000000000 -000049 -003958 -005988 -005985 -000215 -005958 -004151 ~004161 -000546 -005958 -004284 -004278 -000494 -005958 -004455 -004459 -000645 -005958 -004584 -004574 -000791 ~003938 -004750 -004759 -000939 -003938 -004878 -004871 -001088 -005958 -005026 -005012 -OO1256 ~005958 -005175 -005189 Again a scaling factor for locating the decimal point is provided. The four columns from left to right are xim, b, yi (calculated), (and yi (experimental). Using this data a comparision of the exper- ,imental points and the calculated points can easily be made. CHEMISTRY LIBRARY OCT 1 2 '01: GRN STQTE UNIV. LIBRARIES Ill! IWIHIWI \ HIHWIIWIIHHI 9 9631 12 300994 HICHI '3