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A study of the exchange of iodine between ethyl iodide and sodium iodide in formamide Worsfold, Catherine Elizabeth 1951

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A STUDY OP THE EXCHANGE OF IODINE BETWEEN ETHYL IODIDE AND SODIUM IODIDE IN FORMAMIDE by Led Ay Ca -I CATHARINE ELIZABETH WORSFOLD A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of CHEMISTRY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF ARTS. Members of the Department of Chemistry THE UNIVERSITY OF.BRITISH COLUMBIA April, 1951 Abstract The exchange system G0H_I — 1* was studied in ethyl alcohol solution. <• 5 The average rate constant for this reaction was 29.9 x 10 ^  moles litre sec at 50.1°C, The exchange of iodine between ethyl iodide and iodide ion was found to be complicated by a reaction of ethyl iodide with the solvent.. The kinetics; of the simultaneous reaction of ethyl iodide with formamide and the exchange reaction were treated theoretically. Experi-mentally the ethyl iodide - formamide reaction was found to be of a complex nature. The measured exchange rate constant was approximately -2 -1 -1 o 1 x 10 mole lit r e sec at 25 C which is greater than the rate constant of the same reaction in alcohol solution. The exchange system I - IO^ was also studied and k for this reaction was approximately 1 x 10*""* -1 -1 o moles litre sec at 30,8 C. Acknowledgment I wish to express my most sincere gratitude to Dr. Milton Kirsch for his inspiring guidance, patience, and untiring assistance throughout this research project. Thanks are due also to the National Research Council for financial aid and to the Atomic Energy Project at Chalk River for prompt deliveries of radioactive sodium iodide (I ) used in this investigation. April, 1 9 5 1 Catharine Elizabeth Worsfold TABLE OP CONTENTS INTRODUCTION Exchange Reactions. . . . . 2 Halogen Exchange Reactions 3 KINETICS OF EXCHANGE REACTIONS Derivation of the Rate Constant Expression 8 EXPERIMENTAL I. Ethyl Iodide-Iodide Ion Exchange in Ethyl Alcohol. . . . 11 Preparation of Materials 11 Procedure -. 11 Results . . . . . 12 II. Ethyl Iodide-Iodide Ion Exchange in Formamide. . . . . . 14 Preparation of Materials. 14 Preliminary Investigation of the Behaviour of Sodium Iodide, Ethyl Iodide, and Silver Nitrate in Formamide . . . . . . . . . . . . . . . 15 (1) Solubilities . 15 (2) Separation of Ethyl Iodide from Sodium Iodide 16 (a) Distillation 16 (b) Solvent Extraction 17 (c) Oxidation . . . 19 (3) Precipitation of the Silver Iodides 20 The Use of KIO^ for the Separation of Ethyl Iodide,? from Sodium Iodide 21 Theoretical Consideration of the Kinetics of the Reaction between Ethyl Iodide and Formamide with the Simultaneous Exchange of Ethyl Iodide with Radioactive Iodide Ion . . . . . 22 The Rate of Reaction of Ethyl Iodide with Formamide. 25 Measurement of the Exchange Rate Constant . . . . . . 26 The Exchange of Iodide Ion with Iodate Ion in Aqueous Formamide. . . . . . . . . . . . . . . . . 28 The Exchange between I 2 in CCl^ and Ethyl Iodide in Formamide 30 DISCUSSION OF RESULTS AND SUGGESTIONS FOR FURTHER RESEARCH BIBLIOGRAPHY APPENDIX INTRODUCTION Fefore ar t i f i c i a l l y produced radioactive isotopes became readily available there were many processes of interest to the chemist which could not be studied simply because there was no means whereby a particular element could be "tagged." With the possible exception of the lightest elements, where the percentage mass difference between the isotopes of an element is the greatest, there is no chemical means of distinguishing between isotopes. Thus, the isotopic composition remains essentially constant throughout a chemical or biological process. Only Tl, Pb, and Bi (and several other elements in the middle of the periodic table whose radioactive isotopic content is very small) possess both stable and naturally radioactive Isotopes which could be used to investigate reactions. By means of a mass spectrograph i t is possible, though often tedious, to follow reactions with stable tracers. Even with the great increase in production of radioactive tracers from nuclear piles there is s t i l l a definite limitation on their use since some elements do not possess radioactive isotopes of suitable half-life. Among these are oxygen, nitrogen, helium, lithium, and boron for which the use of separated stable isotopes as tracers is a very valuable technique (1). Deuterium has found many applications as a hydrogen tracer and oxygen and nitrogen enriched with 0^ and N*-5 respectively are essential for many important purposes. However, a great number of elements do possess a r t i f i c i a l radioisotopes of suitable half-life for chemical studies and with these i t is possible to trace a "marked* atom by the radiations i t emits. EVen a brief survey of the literature on tracers and radio chemistry that has accumulated in the space of the few years that radioactive indi-cators have been available is far beyond the scope of this work. (2) This discussion will be concerned only with one phase of tracer appli-cations-—their use in exchange reactions in general and halogen exchanges in particular. References 1 to 9 include general background material on isotopes and their uses. Exchange Reactions An exchange reaction i s , as the name implies, a replacement reaction in which the reactants and products are chemically identical. Because of this chemical identity exchange reactions can be studied only by means of tracers. Consider a simple exchange of the type AB V+ B^ ^ AB£ f m Jk where an asterisk indicates a radioactive nuclide. Since the products are the same as the reactants (except for the small mass difference of the added isotope) the rate constants of the forward and reverse reactions are practically equal. Kinetic data may be used to show the mechanism of reactions, to study the character and stability of bonds, and to establish the effect of solvent on reaction rates. The following discussion is not intended to be a complete resume of attempted exchange reactions but is designed to indicate briefly the nature of the experiments which have been done cm exchange systems. In fact, with few exceptions, only halogen exchanges will be considered. One of the earliest exchange experiments was performed by Hevesy in 1920 By means of ThB; (pb2-1-2) he demonstrated the rapid exchange of lead ions between PbCl2 and Pb(1103)2 in aqueous solution. He also showed the rapid exchange of lead atoms between Pb(Ac)2 and Pb(Ac)^ in acetic acid solution. In the fi r s t case one would expect exchange since both these salts: give rise to chemically identical Pb ions. In the case of the acetates: the exchange presumably occurs through a reversible interconversion of plumbous and plumbic ions. (3) With the increased production of radionuclides in the 1930"s, very many exchange reactions were studied. In 1935, the mechanism of the Walden inversion was investigated fa*-5). It was shown that the rate of substitution of iodide for the iodine in secondary octyl iodide and the velocity of racemization under similar conditions are the same. This gave direct confirmation that Walden inversion involves substitution. In 1937, Wilson and Dickinson ^ ) calculated the rate of oxidation and reduction of iodine from the exchange which takes place at equilib-rium between radioactive pentavalent arsenic (As76) and trivalent arsenic. The reaction was carried out in acid solution in the presence of iodide ion and free iodine. Using the assumption that the exchange occurs through the oxidation and reduction of iodine the rates were found to agree with the kinetic expression given by Roebuck for the same reaction remote from equilibrium. While these and many other experiments indicate the utilization of exchange reaction in the study of the mechanisms of other reactions, many exchange reactions have been studied with the hope of reaching a better understanding of the mechanism of the exchange itself. In parti-cular, the exchange of halogens with corresponding halides has been studied in a variety of solvents under different conditions. Halogen Exchange Reactions Hull, Schiflett, and Lind studied exchanges of radioiodine and reported that: l) I 2 and I~ exchange freely in aqueous solution presumably by the formation of Lj*", 2') I 2 and I0^~ in IN sulphuric acid do not exchange at an appreciable speed, but in 20N hot H2S0^ 10rl5$ of the radioactive iodine appears in the 10^" suggesting oxidation-reduction at a measurable rate, 3) no exchange occurs between C2H5I or CH3I and active I 2 even after 15 minutes at 90°C but i f active Nal and inactive C2H5I are dissolved in alcohol and heated to 100°C, exchange does occur, L) I2 and iodoform do not exchange in ether solution, and 5) iodoform does not exchange with active Nal in alcohol. Bromine-bromide exchange in aqueous solution was studied by Grosse and Agruss who concluded that the exchange is fairly slow, being governed by the rate of hydrloysis of bromine. Roginski and Gopshtein however, stated that this exchange was rapid. Dodson and Fowler inves-tigated both bromine-bromide and iodine-iodide exchanges and found that both reactions were practically complete in 60 seconds. Long and Olson reported that the exchange between C.I2. and Cl" was immeasurably fast. Juliusberger, Topley, and Weiss showed that appreciable exchange takes place in 1 - 2. minutes between CH3I and active Nal in alcohol solu-tion at room temperature. McKay reported qualitative exchange data for the reaction between several aliphatic and aromatic iodides, and sodium iodide. At room temperature a l l y l and methyl iodides exchange with active Nal in alcohol or acetone solution. Tinder the same conditions no exchange was found with ethyl, propyl, isopropyl, and methylene iodide, nor does iodoform exchange in acetone solution. However, at 100°C, methylene, propyl, isopropyl, and isoamyl iodides exchange in approxi-mately 15 minutes. Nal*-ethyl iodide exchange was practically complete after 15 minutes at 50 - 55°G. No exchange between active Nal and phenyl iodide, p-nitroiodobenzene, or p-iodoaniline could be detected at 100°C. Iodoacetic acid exchanges with iodide ion in aqueous solution at room temperature but ft -iodopropionic acid does not. M- and p-iodobenzoic acids showed no exchange with Nal in acetone solution. Contrary to the work of Juliusberger et al methyl iodide-iodine exchange in alcohol (5) takes place i n 15 minutes at 100°C but not i n 2 — 3 minutes at room temperature. The kinetics of the exchange between iodide ion and several alkyl iodides was studied by Seelig and Hull ^ 2 ^ . The rate constant at various temperatures led to values for the activation energy of 21,270, 20,770, and 23,850 calories per mole for ethyl, propyl, and isopropyl iodides respectively. The higher activation energy for isopropyl than for normal propyl iodide i s similar to the results obtained by Sugden and his co-workers ( 2 2)> (23), ( 2 4 ) f i n their study of the corresponding bromides. Later work ^2^) o n the exchange of iodide ion with ethyl iodide i n alcohol solution yielded an energy of activation of 19 K calories per mole. Further work on exchanges of this type (alkyl iodide-iodine ion exchange) was done i n an attempt to show the effect of the degree of ionization of the inorganic iodide on the rate constant. The exchange of iodine between several inorganic iodides and n-butyl iodide was studied i n acetonitrile solution ( 2^). In 1944 R. Daudel, P. Daudel, and Martin studied the exchange reactions of Br" ions with CBr4, SiBr^, and SnBr^,and observed complete exchange between Br" and ShBr^ i n two minutes. No exchange took place i n the CBr^ - Br" system. They also observed no exchange between Cl~ and 010^", CI" and C103~, 803" and So^ s, Te03s and Te0^ s, and As03» and AsO^* which are i n oxidation reduction systems. Redox exchanges involving simple ions such as Fe - Fe are rapid. It has been reported (2^) that contrary to previous negative results, the exchange reaction K I 4 + KIO3 ^  KI + KT*03 does occur at high temperatures. In sealed tubes at 250°C one-third of (6) the radioactivity of the KE* was transferred to the KIO3 in 2 hours. The activation energy was found to be 32 K calories per mole. The exchange of lithium bromide with phenylethyl bromide in acetone was studied by Hughes et al ( 29) # Later Evans and Sugden showed that the bimolecular velocity constant for the exchange reaction between Li Br and alkyl bromides in anhydrous: acetone varies with the dilution. The similar reaction between Nal and alkyl iodides in methyl alcohol shows no effect of dilution. That exchange can occur by neutral atoms was shown by the reaction of carbon tetrabromide and elementary btomine in the gas phase (31 ) # reaction appeared to be homogeneous and the rate was found to be directly proportional to the concentration of CBr^ and to the square root of the bromine concentration. They felt that this indicated a mechanism involving bromine atoms' and i f the exchange occurs between CBr^ and bromine atoms the energy of activation of this bimolecular process is zero. They also studied the reaction in the liquid phase and the mechanism appeared to be the same as in the gas phase. No exchange occurred at room temperature. Some work has been done on the heterogeneous exchange between silver halide precipitates and halide ions in aqueous solution. P. Daudel (^2) studied the exchange of AgBr with KBr and found rapid exchange. More recent work reports the results of exchange reactions between Agl - KT' and KE in aqueous solution. At room temperature the exchange Agl - KE* was. found to be much more rapid than Agl* - KE. In the Agl - KE* exchange there appeared to be a rapid adsorption of I*" ions followed by slow exchange within the grains of the precipitate. Since exchange in the reverse direction is accompanied by adsorption of inactive ions only, the apparent overall rate of exchange is i n i t i a l l y smaller. (7) In 1944- Daudel classified exchange reactions into two general types: l) those which occur by the formation of an intermediate compound, e I*- * I 2 ^ [ I 3 * - ] - T- + I 2 * and 2') those resulting from continual dissociation and association of the reacting molecules', e.g. the exchange of Fb^ between PbCl^ and Pb(N03)2 Many exchanges reactions can be placed in one or the other of these two categories ^ 5 ) , (36)^ (8) KINETICS: OF EXCHANGE REACTIONS  Derivation of the Rate Constant Expression Consider an exchange reaction of the type AB +• B^" ^  AE* +> Br k m u v n The standard method of derivation of an expression for the exchange rate constant for an ion exchanging with one of the atoms of a polar molecule is as follows: Let the concentration in moles per lit r e at time t of CAB] . m [AB* J - v [B~] . n [ B * - J - U The differential equation for the rate of formation of AB * is dv s k(mu) - k(nv). (l) dt assuming that the rate of the forward reaction equals that of the reverse reaction. Now the total activity may be assumed to be constant. If possible the radioactive isotopes used will have a half-life very much greater than the time of reaction or a l l the measured activities may be referred back to a specific time. Therefore u - v » a constant, d. Substituting for u in (l) we get dv s km(d-v) - knv (2) dt To simplify the solution of (2) i t is further assumed that since the radio-active material is present only as a tracer its concentration is very much smaller than that of the non-radioactive species. That i s , v<<m and u«.n. Therefore m and n may be considered constant during the course of the reaction. With this approximation the solution of (2) is k = - _ i l n f l -v (l + n\ [3\ (m ¥ n)t L u * v ' m U v \ represents the fraction of the total activity which has exchanged in time t.. As the activities appear only in the form of a ratio i t is not necessary to determine the absolute disintegration rate of the (9) products; a determination of the specific activities (activity / weight) is sufficient. Consideration of the above derivation led the author to derive another expression for the rate constant by a more general method in which the question of mathematical rigour in assuming m and n constant is overcome. A new notation is adopted for convenience in subsequent derivations. In the reaction k let the concentration in moles per li t r e be as follows: At time t, [AB] a a-x - X = 7 The differential equations for the reaction are dx dt k(ay - bx) and dy -k (ay - bx) (5) dt and d(x 4 y ) dt o, therefore x 4 -y - a constant, d. do) It should be noted that the expression for the rate of exchange is identical with that of the previous case. However, a and b are now constants by definition. This equation could be used where the concen-trations of the radioactive species are of the same order of magnitude as the concentrations of the inactive materials. Substituting x r d - y into (S) and integrating between the limits Y • Yo r b to Y, - Y and t r o to t 2 t, we get Equation (6) reduces to equation (3) when the concentration of the radio-active species is small compared with that of the inactive material. (6) / / (11) I ETHYL IODIDE-IODIDE ION EXCHANGE IN ETHYL ALCOHOL Before proceeding to the study of the exchange reaction of ethyl iodide with iodide ion (Nal) in formamide, i t was decided that the reaction should be studied in a solvent for which quantitative results had previously been obtained in order that there might be a check on the experimental technique. For this purpose, ethyl alcohol was chosen as solvent and the technique used was similar to that of Seeling and Hull ^ Preparation of Materials Ethyl iodide, supplied by Eastman Kodak Comparer, was purified by vacuum distillation and kept in a dark bottle in contact with mercury. Commercial 95% ethyl alcohol, also distilled under vacuum, was dried with CaO before using. The sodium iodide was Merck, reagent grade. Radio-iodide 1*31 (half-life S days) was obtained in the chemical form of sodium iodide from the National Research Council Atomic Energy Project at Chalk River. Procedure 5 mis. of ,0L N ethyl iodide was allowed to react with the same quantity and concentration of sodium iodide (containing radioactive 1*31) in sealed test tubes for various lengths of time at constant temperature. After exchange, the test tubes were removed from the constant temperature bath and the reaction quenched by rapid immersion in dry-ice-acetone slush. Separation of ethyl iodide from sodium iodide was effected by vacuum distillation in an apparatus almost identical with that used by (21) Seeling and Hull ' and the iodides were precipitated with alcoholic silver nitrate solution, centrifuged, and washed. A slurry of the silver iodide precipitate in diethyl ether was pipetted onto tared aluminum (12) planchets, and was dried and weighed before counting. The activity of the silver iodide was determined by means of a Geiger-Muller counter with suitable corrections for background. Results The values obtained for the rate constant for the exchange of iodide ion with ethyl iodide i n ethyl alcohol at 50.1°G are shown i n Table I TABLE I Ethyl Iodide-Iodide Ion Exchange i n Ethyl Alcohol Temperature 50.1°C Concentration of Nal =• .02M = x Concentration of C2H5I » .02M r a -< x / Ratio Specific k x 10^  Time. Mgs'. Agl Total Counts;/Min of Agl Act i v i t i e s -1 -1 (minutes) EtI Nal EtI NaT (b - y ) " Moles l i t r e sec 15 29.3 19,9 562 8000 . 0457 23.0s 30 37.4 20.5 939 5850 . 0810 24.7 30 19.6 21.6 801 8309 .0958 29.5 60 27.9 50.3 2725 17360 .220 42.1 60 23.9 28.0 1966 11162 .171 36.9 120 27.9 27.8 2746 6920 . 283 29.0 120 24.4 26.7 2477 6632 .289 30.1 150 27.1 20.9 2690 5240 . 285 23.7 150 18.8 26.6 2304 6891 .329 30.2 Average k - 29.9 x 10"^ A • Sample calculation ' ' k m -2.303 lOg t(a*b) E - b - y f l » x M = -2.303 logfl - 19.2 (L * .02YI 15(60)(.02 * .02) L 19.2 * 402V .02/J (13) The average value of the rate constant at 50.1°C was found to be 29.9 x 10"^ moles"* l i t r e sec"*. The average value reported by Seeling and Hull ^ at 50.05°C i s 28.9 - 3 x 10*^. A later investigation of this * (2K\ same reaction was made by Neiman and Prosenko . Since they l i s t no results i n the neighbourhood of 50°C, their values for k i n moles l i t r e sec at various temperatures were plotted against temperature and interpolation of the graph led to an approximate value of k = 25-30 x 10 at 50°C. Thus i t was supposed that since this procedure yielded satisfactory results for ethyl iodide-iodine ion exchange i n the ethyl alcohol, a similar technique might be employed for the study of the same reaction i n a different solvent. iu) II ETHYL IODIDE-IODIDE ION EXCHANGE IN FORMAMIDE Preparation of Materials Sodium iodide, ethyl iodide, and silver nitrate were prepared as outlined previously. I*"" was, as before, obtained from Chalk River. Formamide. obtained from the Eastman Kodak Company was purified by (37) vacuum distillation w ' and freezing by means of a salt-ice mixture. The yellow brown discolouration present in the original formamide remained in the distilling flask and the resultant distillate was clear and colourless. The refractive index of the purified formamide was always found to be between the handbook value of 1 . 4 4 . 5 3 0 at 2 2 . 5 ° C and 1 . 4 4 9 1 1 at 1 5°C (38) reported by Timmermans and Hennaut-Roland . , 3 1 1 refractive index measurements were made at approximately 2 1°C using an Abbe' refractometer (39) with a tungsten light source. According to Brann , formamide will show no decomposition, discolouration, or other apparent change even after seven months exposure to daylight. It is hygroscopic, but Brann found that the amount of moisture absorbed was not enough to affect its freezing point. A boiling point determination was not used as a criterion of purity because formamide decomposes at its boiling point and there is l i t t l e accurate vapour pressure-temperature data available. Melting point determinations gave a spread of values in the neighbourhood of 0 - 2°Ci. The most fre-? quently quoted value of the melting point is 2 . 5 5 ° C ^ \ The spread in melting points was attributed in part to the difficulty encountered in observation in this temperature region due to frosting. As a further criterion of purity, the density of formamide was determined by means of a o (39) Westphal balance at 2 1 . 0 C. According to Smith N ' the specific gravity (15) 20 t of formamide, d = 1.13339 and the temperature dependence d r 1.13510 21 21 0. 00084756 (t° - 18) yi e l d s a value d^ . 1.13255732 or d - 1.1346 which i s comparable with the handbook value of d r 1.134 at 21°C. The density of the d i s t i l l e d formamide used i n t h i s investigation was 21 d r 1.133 - 1.135. Preliminary Investigation of the Behaviour of Sodium Iodide. E t h y l Iodide, and S i l v e r Nitrate i n Formamide 1. S o l u b i l i t i e s Sodium iodide was r e a d i l y soluble i n formamide. Eth y l iodide dissolved s u f f i c i e n t l y i n a few minutes at room temperature to y i e l d a .04 M solution which was a high enough concentration f o r exchange studies. Aqueous s i l v e r n i t r a t e r a p i d l y decomposed i n formamide presumably forming (40) some HCONH&g and free s i l v e r . The addition of ethyl alcohol during the p r e c i p i t a t i o n of Agl from Nal appeared to decrease the decomposition to some extent, but the s i l v e r precipitate from ethyl iodide decomposed immediately. Lead n i t r a t e was t r i e d as a precipitant agent but the P b l 9 was too soluble to be useful. Ethyl iodide gave no precipitate at a l l with PbfMO^g. •It was then thought that i f the presence of s i l v e r ions caused the decomposition of formamide, i t could possible be prevented by the addition of ammonia to form a complex with the unprecipitated s i l v e r ion. This hypothesis was e a s i l y v e r i f i e d . I f 6N NH..0H was added to an approximately 4 equal volume of .04M Nal or E t I i n formamide, aqueous or alcoholic AgNO^ forms a quantitative p r e c i p i t a t e of s i l v e r iodide which shows no sign of decomposition. When f i r s t formed i n formamide, the s i l v e r iodide i s white, not yellow. In order to prove that t h i s precipitate was i n r e a l i t y Agl, and (16) not some unknown compound of silver and formamide, a few quantitative determinations were done on the precipitate. A recovery of greater than 95% of the theoretical yield was obtained in each determination. Some loss was.incurred because of the colloidal nature of the silver iodide in the s supernatant liquid. Heating the Agl in concentrated nitric acid liberated free iodine. There seemed l i t t l e doubt that this substance was Agl but there remained the question of its colour. It was found that the precipitate always changed to a pale yellow colour by the time i t was washed with ammonia, water, alcohol, or ether. This phenomenum may be explained by the fact that formamide i s a weak reducing agent and may prevent surface oxidation 0 to free Lj. In order to mount for counting, the Agl should be washed at least twice with dilute ammonia and twice with ethyl alcohol before suspending i t in ether and transferring i t to the planchets. If the washing process is not done thoroughly, Agl decomposes fairly rapidly. 2. Separation of Ethyl Iodide from Sodium Iodide ai) Distillation Since formamide has a relatively high boiling point compared with alcohol, a low temperature vacuum distillation to separate ethyl iodide from sodium iodide after the exchange should result in the distillation of ethyl iodide only. A number of t r i a l distillations showed that the amount of ethyl iodide in 5 mis. of a .04N solution was too small to trap efficiently. Therefore ethyl alcohol was added to the distilling flask to act as a carrier for the ethyl iodide. Repeated distillations showed that no trace of ethyl iodide could be found in the distillate. Alternative methods of trapping were tried. For example, an attempt was made to trap (17) the ethyl iodide in the receiving vessel by means of alcoholic silver nitrate. A l l attempts to separate ethyl iodide from formamide by low temperature distillation were unsuccessful, b) Solvent Extraction Several solvents were tried in an effort to find one that would preferentially extract ethyl iodide from formamide and so afford a fairly rapid method of separation of ethyl iodide from sodium iodide. (i) Benzene Benzene, although apparently completely immiscible with formamide, separated only very slowly from the formamide layer. When pure ethyl iodide, formamide, and benzene were shaken together an emulsion formed which did not break easily even on the addition of large amounts of NaNO^  as a salting-out agent. The addition of alcoholic AgNO-j to each of the two phases showed that some of the ethyl iodide was present in the benzene layer but this apparent partial extraction may have been due to small amounts of formamide present in the top layer as an emulsion. When a formamide solution of ethyl iodide was shaken with benzene, a similar kind of emulsion formed which settled out into two clear layers in about 24 hours. However, the benzene layer contained no trace of ethyl iodide. These experiments were repeated at low temperature (approximately 6°C which is just above the freezing point of benzene) with the same results—that i s , the layers did not separate quickly enough for benzene to be used in the separation of ethyl iodide. (ii) Carbon Tetrachloride and Chloroform (Both of these solvents behaved in the same way) After shaking a formamide solution of ethyl iodide with CCT^» no ethyl iodide could be found in the CCI^ layer, even after the CCT^ was (18) shaken with aqueous NaOH and heated for a long time. This latter pro-cedure was designed to hydrolyse any ethyl iodide to sodium iodide but no trace of iodide ion could be detected. This process was repeated several times at .room temperature and at 0°C with the same result. (Iii) Diethyl Ether Ether was completely immiscible with formamide and the mixture readily separated into two phases. However, no ethyl iodide was extracted by this process. In addition, the formamide turned a yellow colour after a few minutes- in contact with the ether. The yellow colour could be attributed to either a partial decomposition of the formamide or to some change in the ethyl iodide, perhaps some oxidation to free iodine. At any rate this solvent was of no use. (iv) N-heptane. Cyclohexane. and Amyl Acetate No ethyl iodide could be found in either the n-heptane, cyclohexane, or amyl acetate layer. (v) N^butyl Phthalate A trace of ethyl iodide was found in the n-butyl phthalate layer by testing with alcoholic AgNO^ . However, the extraction was by no means quantitative and too many separations would be required for this solvent to be of use in the exchange reaction. (vie) Acetophenone The acetophenone layer formed a small precipitate on the addition of AgNO^  which rapidly decomposed. Further, as with benzene, the phase separation was slow. Even after standing for two days the formamide layer was s t i l l a l i t t l e cloudy. (vii) Anisole The results with anisole were almost identical to those obtained when acetophenone was used with the exception that in this case i t was the anisole layer which remained cloudy. (19) (viii) Acetone, Dioxane, and Bthyl Acetate These solvents were a l l miscible with formamide. Since the results of this search for a solvent were discouraging another means of separation was sought. The most important criteria of a good separation technique are the rapidity and completeness of the sep-aration at a low enough temperature that the exchange reaction is quenched during the process. On the basis of these criteria i t was thought that an oxidizing agent might be found which would preferentially oxidize the iodide ion from Nal leaving the ethyl iodide untouched. It should then be simple to extract rapidly the resulting free iodine with a solvent such as; carbon tetrachloride or chloroform. c) Oxidation (i) Ferric Chloride Ferric chloride in dilute HCI liberated I 2 from both the Nal and C2H/jIsolutions. (ii) Copper Sulphate Cupric salts oxidize iodide ion by the reaction 2 Cu + 41 Cu^-*^* In the presence of very dilute HgSO^  no reproducible results were obtained using this oxidizing agent. The reaction appeared to be very sensitive to pH and to the order of addition of reagents. Sometimes a white precipi-tate of CU2I2 was formed but no trace of free iodine could be detected by starch indicator. No attempt was made to explain these apparent anomalies at the time. (Iii) Ceric Sulphate Cb(So,)0l oxidized both the sodium and ethyl iodides to free iodine, (iv) Potassium Iodate The oxidation of iodide ion by KIO^ proceeds by the reaction: I0 3" -v 6H* 4 51" -*3l2 * 3H20. (20) The reaction stops at this stage in weakly acid solution (0.1 to 2.ON HCl). However, i f the acid concentration exceeds 4 N , I 2 is converted to I 01 according to the equation: KEO^  + 2I 2 + 6HC1 —» KC1 + 5ICI •* IR^Q* It appeared that in formamide there is conversion to iodine monochloride at lower acid concentration than in water; but in 0.1 - 1.0M HCl solution I 2 was rapidly liberated from Nal. No oxidation of the ethyliodide was observed.. Qualitative experiments showed that a l l the free iodine could rapidly be extracted by CC1.• The experiment was repeated at the temper-4 ature of a salt-ice bath using the following procedure. The formamide solution was frozen in a separatory funnel. To i t was added an aqueous solution of KIO-j containing a few drops of HCl. This mixture was shaken, and, as the formamide melted, the Nal reacted with the KIO^ and the free iodine liberated went immediately to the CCl^ layer. A l l the free Ig was removed in three extractions requiring only a few minutes. No free iodine was extracted by a similar procedure using ethyl iodide in for-mamide. This separation would appear to be superior to the distillation (21) employed by Seeling and Hull . 3'. Precipitation of the Silver Iodides The next problem in establishing a technique for the measurement of the exchange rate constant was to find a method of converting the free iodine from the KEO3 oxidation to a form that permits easy weighings. AsvjO^  could not be used to reduce I 2 to iodide ion because of the subse-quent formation of Ag^ AsO^ or Ag^ KsOy Sodium thoisulphate reduces I 2 but i t was found that i t also caused a rapid decomposition of the AgNO^ . It was finally decided to hydrolyse the carbon tetrachloride solution of I2 by shaking with aqueous NaOH. The products of this hydro-lysis are 10" and I~, and therefore one half of the iodide is no longer available for precipitation as Agl. However, this loss does not affect ( 2 1 ) the; specific activity of the Agl. After hydrolysis, the solution is neutralized with dilute nitric acid and then made slightly basic with NH^ OH before the addition of AgNO^ . The presence of excess 10 ^  should not affect the precipitation of ethyl iodide by AgNO^  since, as mentioned before, NH^ OH must be added to prevent decomposition in formamide solution. Silver iodate is soluble in ammonia and will remain in solution. It appeared that a method for measuring the exchange rate constant had at last been found. Complications by other exchange reactions were thought to be avoided. There should be no exchange between iodide ion and iodate ion during the oxidation since exchange reactions of this type ( 2 8 ) have been observed only under drastic conditions. It is even less likely that there would be any exchange between ethyl iodide and 10^. Since the oxidation of the iodide ion takes place at the melting point of the formamide solution and the free iodine is removed immediately By CGX^  there should be l i t t l e chance of either I 2 - IO3 or I 2 - ethyl iodide exchange. The Use of Potassium Iodate for the Separation of Ethyl Iodide  from Sodium Iodide Because some time had elapsed since the discovery of the use of potassium iodate to separate Nal from ethyl iodide the experiment was repeated quantitatively. As before, KIO3 in dilute acid solution com-pletely oxidized the iodide ion from a formamide solution of Nal. However, this time the ethyl iodideyformamide solution was also oxidized to free iodine by KIO^. The same ethyl iodide solution had been used in both experiments; but i t was noted that this solution had been freshly prepared when no oxidation with potassium iodate was observed. A new freshly prepared solution of ethyl iodide in formamide gave only a slight (22) test with silver nitrate. Heating this solution to about 70°C for 5 minutes, cooling, and adding ammoniacal silver nitrate gave a bulky-precipitate of Agl. Similarly, after heating for 2 - 3 minutes, at 90°, the ethyl iodide-formamide solution could be oxidized by 103" to give I 2 . No oxidation occurs with potassium iodate in a freshly prepared solution at room temperature but i f i t is left for two days oxidation i s appreciable. This behaviour suggested that ethyl iodide reacts with formamide slowly at room temperature and rapidly when hot, with iodide ion being one of the products. If the rate of reaction of ethyl iodide with solvent were slow in comparison with the rate of exchange i t should be possible to measure the latter rate constant using freshly prepared ethyl iodide. If, however the rates were comparable, the reaction with solvent would have to be considered in the calculation of the rate constant for exchange. This latter possibility led-, to a theoretical investigation of the kinetics of these simultaneous reactions. Theoretical consideration of the kinetics of the reaction between ethyl  iodide and formamide with the similtaneous exchange of ethyl iodide  with radioactive iodide ion. To derive an expression for the exchange rate constant i t was assumed that the reaction of ethyl iodide with formamide was a reversible bimolecular process, that might be represented by the equation for the replacement of one of the amino hydrogens of formamide with an ethyl group. i.e. HCONEy 4 C 2H 5I p i HCONHC2H5 • H*«« I" A reaction of -this type would account for the production of iodide ions on (23) aging o f the formamide s o l u t i o n o f E t I . A l though there was no e x p e r i -mental r eason t o suppose t h a t the r e a c t i o n i s a c t u a l l y r e v e r s i b l e , such t reatment should l e a d to a gene ra l exp re s s ion t h a t cou ld be s i m p l i f i e d where the r a t e cons tant o f the r eve r se r e a c t i o n i s v i r t u a l l y z e r o . The exchange r e a c t i o n o f e t h y l i o d i d e w i t h r a d i o a c t i v e i o d i d e i o n and the r e a c t i o n o f e t h y l i o d i d e w i t h formamide may be w r i t t e n s y m b o l i c a l l y . A E +• A B 4 • B" ( i ) k AB + HO. ^± AC + BT + H * ( i i ) *2 » k i . AB? + HC; ^ AC + 1 " • H + ( i i i ) k 2 where HC rep resen t s a formamide m o l e c u l e . As b e f o r e , the change i n r a t e s due to s m a l l i s o t o p i c mass d i f f e r e n c e s were neg lec ted and the r a t e cons tan t s o f the forward and reverse r e a c t i o n s o f ( i ) assumed to be the same. S i m i -l a r l y , the forward r a t e constant f o r ( i i ) equals: t h a t f o r ( i i i ) , and the r a t e constant f o r the reverse r e a c t i o n i n ( i i ) equals t h a t f o r the r eve r se r e a c t i o n i n ( i i i ) . I f i t i s a l s o assumed t ha t the o n l y source o f hydrogen i o n i s the e t h y l iodide-formamide r e a c t i o n , the d i f f e r e n t i a l equa t ions fo r the r a t e s a r e : , 2 dx r k ( a - x ) y -V k j ( a - x ) z - k (b - y ) x - k 2 fc - z \ x ( l ) d t \ 2 / d y = k ( b - y ) x 4. k-,(b - y ) - k(a x ) y - k 2 fc - z\y (2) d t \ X ) 2 . 2. ' dz - k P fc - z | x k 5 fc - z^ y - k-, (a - x ) z - k i (b - y ) z (3) d t \ 2 ) \ 2 } X where the terms are d e f i n e d as i n the Appendix . I f i t can be assumed t h a t £H *J remains constant by c a r r y i n g out the r e a c t i o n i n the presence o f excess hydrogen i o n o r i f the products o f r e a c t i o n ( i i ) are ACH* and B" r a t h e r than AC V B* 4 H*, t hen the d i f f e r e n t i a l equat ions become (24) dx r k(a - x)y 4- k^(a - x)z *P k(b - y)x - ^ ( c - z)x dt dy = k(b - y)x + k-,(b - y)z - k(a - x)y - k 2(c - z)y dt dz r -^ 2^ ° " z ^ x *"" k 2 ( c ~ "* ^ l ^ 6 1 ~ x^7' " ^O- 1 — y)z dt (4) (5) (6) The expression for the concentration of x from (4), (5) and (6) at any time t is derived in the Appendix. [A + i B"] t X - 4 0 6 +{A •ySB'Jt + & +«KBj t' * e C"B - DA B oh [A + BJ [A +O< B ] t "\ -» +-(e - 1)U DO^D «t- xo (_A + ^  B J J I J B where A - k(a +- b) +- k 2(c - d) + k^d d - r f y f z B = a(k - k x) C" s k^ad Q.r = integration constant z xo •+ yo xo yo (7) c^or^ = f(c - d)k ? * ( a •» b -» d) kj| C"(c - d)k 2 - kn (a 4 b » d)] ^ - 4(a + b)dkn If the reactions of AB' and AB* with C ( i i &iii) are irreversible, (7) reduces to x =LCe * ( A -78 k j t *[& - dk-J t +e [A - dk^ t elf (A k j t L A - /* k i ] +_e_ 1 -1 I + D(,-<)U. D -+ [A k l j J ^ J ^ where A r k(a + b) 4 k-jd B- »• D = a(k - k x) xo (8) (25) s- k-,ad *6 +' yo ' or =• ^ ( a + b «• &.)] - \] (-k-^ a • b • d f - A.(a -*b)dki The rate constant k does not appear explicitly in either (7) or (8). The solution of equations (l), (2), and (3) is even more complex (see Appendix) suggesting that, i f the rate of reaction of ethyl iodide with solvent is of the same order of magnitude as the rate of exchange, i t would be virtually impossible to obtain the exchange rate constant. The Rate of Reaction of Ethyl Iodide with Formamide The reaction of ethyl iodide with formamide was. followed by the rate of formation of iodide ion. An ethyl iodide solution in formamide was kept in a constant temperature bath. At various times, five ml. portions were removed and the iodide ion formed was oxidized by potassium iodate to iodine. The iodine, after extraction with carbon tetrachloride, was titrated with sodium thiosulphate. Figure 1 indicates the results obtained. Curve (1) was obtained at 25°C, and curve (2) at 30.8°C. The fact that these curves extrapolate to zero iodide-ion concentration within experi-mental error indicates that ethyl iodide is at most, only slightly ionized in formamide. The S-shaped rate curves obtained may indicate that the reaction i s auto catalytic or that 1$. is a stepwise process. Curve (3) shows- the results of an experiment, designed to permit a decision to be made between these alternatives. An equal amount of Nal was added to the ethyl iodide solution at 30.8°C and in plotting the curve, the amount of sodium thiosulphate required to titrate the iodine from sodium iodide was subtracted from the total volume of Na2S203. The curve indicates that the presence of excess iodide ion suppressed, to some extent, the reaction with solvent and that the reaction was not autocatalytic with respect to iodide G R A P H I T H E R A T E O F R E A C T I O N O F E T H Y L I O D I D E WITH F O R M A M I D E Complete Rtaction - 1-53 ml. C HOURS) loo (26) ion. Possible autocatalysis by hydrogen ion was not investigated. Fortunately, however, the reaction of ethyl iodide with formamide was fairly slow. If the rate of the exchange reaction were of the order of magnitude of the rate in alcohol, this reaction with solvent could be neglected. Measurement of the Exchange Rate Constant The rate of exchange of ethyl iodide with sodium iodide in formamide was measured by the following procedure: Five Ml. of ,04 M C2H5I (freshly prepared) was thoroughly mixed with 5 ml. of .04 M Nal in a separatory flask. When this mixture attained the temperature of the bath, a small amount of active sodium iodide was added. After the desired time, the reaction was quenched by immersing the flask in dry-ice-acetone slush. To the frozen mixture was added carbon tetra-chloride and an aqueous solution of potassium iodate containing a small amount of dilute HCI. As the formamide solution thawed, the liberated iodine was extracted. This carbon tetrachloride solution of iodine (from Nal) was shaken with aqueous NaOH to hydrolyse iodine to I~ and 10 . Before precipitation with AgNO-j, the solution was neutralized with dilute nitric acid and then made basic with dilute NH^ OH. The ethyl iodide solution was heated in the presence of NH^ OH for several minutes to increase the amount of iodide ion by the reaction of ethyl iodide with formamide. The presence of base reduced the possibility of reduction of excess potassium iodate by I~ as i t was formed. It was necessary to cool the mixture thoroughly before adding AgNO^ .to prevent decomposition. The precipitates of Agl were washed twice with dilute ammonia and twice with alcohol before suspending in ether and deposition on tared watch glasses. (Watch glasses were found to be superior to aluminum planchets.) As before, the samples were counted and suitable correction (27) was made to the measured activity of the Agl because of the inactive iodine introduced from the potassium iodate oxidation. TABLE. II Exchange of Ethyl Iodide with Sodium Iodide in Formamide Concentration of Ethyl Iodide = .02M Concentration of Sodium Iodide r .02M ? Ratio Specific k x 10 -1 Temp. °C. Time (minutes) Mgs- Agl. EtI Nal Total Counts / Min of Agl EtI Nal Activities [bay] lb-si-Moles 1; 19.5 3 35.5 21.7 602 6597 \ :J .053 • 1.53 19.5 4 19.2 23.5 850 7400 .123 2.92 19.5 6 14.7 19.7 1700 6137 .271 " 5.55 25.0 3 39.9 34.8 468 11250 .0351 1.01 25.0 3 5.4 31.2 253 4740 .236 8.81 25.0 3.25 U.8 20.7 85 953 .0935 1.27 25.0 6 5.3 25.2 139 3660 .153 2.52 25.0 9 4.1 17.4 46 2120 .0843 .862 25.0 12 9.5 25.0 738 8350 .187 .718 25.0 12 4.1 15.5 320 1800 .402 5.70 25.0 18 2.0 18.2 362 10240 .244 .647 25.0 24 13.2 23.1 243 3060 .122 .488 30.8 3 13.6 18.4 369 14613 .0389 1.12 30.8 3 1.7 14.5 812 18510 .272 10.9 30.8 6 19.0 12.3 958 16950 .0389 .560 30.8 6 15.3 11.7 1699 20605 .0577 .847 (28) The results of this exchange reaction are shown in Table II. The low yields of Agl from ethyl iodide in some experiments was due to insuf-ficient heating of the ethyl iodide solution before the addition of AgNO^ . The inconsistency of the k values led to an investigation of possible interfering exchanges. The Exchange of Iodide Ion with Iodate Ion in Aqueous Formamide If there were appreciable exchange between iodide ion and potassium iodate during the separation of Nal from ethyl iodide, the resulting specific activity of the silver iodide would be lowered. To duplicate as closely as possible the conditions of the separation, equal amounts of aqueous potassium iodate and Nal in (formamide were used. However, the reaction was investigated at 30.8°C for convenience. Two methods of separation were used: 1) The iodide was separated by precipitation with "AgNO^  in the presence of ammonia. The Agl was removed by centrifuging and the excess silver ion removed by the addition of KE followed immediately by the addition of dilute HNO3 until the solution was just acid. The presence of acid caused the reduction of potassium iodate by I" to iodine which was extracted immed-iately by CCI4. As before, the iodine solution was hydrolysed by NaOH, neutralized with dilute HNO^ , and precipitated with AgNO^ . 2) The iodide was separated by precipitation with AgNO-j in the presence of ammonia. After centrifuging out the Agl, the solution was neutralized with dilute HNO^  and the iodate was weighed as AglO^. The rate constants calculated are shown in Table III (29) TABLE III  Exchange Between 10^" and I*" Concentration of I~ 9 .02M Concentration of 10^" - .02M Temperature 30.8°C Method I Time (minutes) k x (moles "** litre sec"*"'") 6 7.9 10 2.6 30 1.2 660 2.7 60 .83 120 .91 Method II 5 18.0 10 13.4 20 11.7 60 1.85 The results from the f i r s t method should be closer to the true value of k than those from the second since the latter method increased the difficulty of obtaining a sharp separation of the Agl because of its colloidal nature. If a l l the Agl were not removed by centrifuging, the activity of the AglO^ would be increased resulting in high k values. In method I, the major error was due to counting. Since five-sixths of the iodine in the Agl (from the iodate) came from added inactive KI, the observed counting rates were low. and in the determination of the specific activity, the counting errors were multiplied by a factor of six. There (30) is: also the possibility of exchange of 10^ with added KI during the removal of the excess silver ion. However, the time required for this removal was very short and the error from this source was probably negligible. Both methods used set an upper limit to the rate constant for the exchange between I and 10^ » It appears that the rate constant for this exchange is not larger than 1 - 3 x 10~ 4. This value is of the order of 100 times smaller than the rate constant for the exchange between ethyl iodide and iodide ion. Therefore, possible exchange of I0^~ with i " should not seriously affect the use of potassium iodate to separate Nal from ethyl iodide in formamide. The Exchange Between Iodine in GGl^ and Ethyl Iodide in Formamide Another possible interfering exchange reaction is the exchange of free iodine in CCl^ with ethyl iodide during the separation. To study this possibility, a solution of radioactive iodine in CCl^ was shaken with a formamide solution.of ethyl iodide. It was found that the iodine was completely removed from the CC1. layer. Later experiments showed that the 4 amount of free iodine which could be extracted from formamide by CCl^ depended on the amount of water in the formamide layer. A solution of iodine in formamide was initial l y a yellow to brown colour depending on the concen-tration. However, the colour disappeared in several minutes and i t was found on the addition of AgNO^  that the iodine had reacted with formamide to yield iodide ions. In fact, the presence of aqueous potassium iodate containing a drop of HCl markedly affected the partition and most of the iodine could be extracted by carbon tetrachloride i f sufficient iodate were present to insure oxidation of I as i t is formed. Time did not permit a quantitative study of the partition of iodine between carbon tetrachloride (31) and aqueous formamide. Further, the possible exchange of iodine in CC1 i with ethyl iodide in formamide could not be measured by this method. (32) Discussion of Results and Suggestions for Further Research. Although the observed rate constants for the exchange of ethyl iodide with iodide ion varied by a factor of 20 - 30, the order of magnitude of the rate of exchange is probably significant. The major experimental errors were introduced during the separation. 1) Not a l l the free iodine may have been extracted by CCl^. During the exchange measurements, no particular care was taken to keep the con-centration of 10^" the same in each sample since the possibility that iodine was more soluble in formamide than in carbon tetrachloride was not recognized at the time. However, any I~ formed by reaction of iodine with formamide would be oxidized immediately by the potassium iodate. Any free iodine remaining in the formamide layer would be converted during the heating to i " , thus increasing the specific activity of Agl from ethyl iodide. This error would result in high k values. 2) The possibility of exchange between iodine and IO^" is probably small. Myers and Kennedy studied this exchange in aqueous and per-chloric acid solutions as a function of IO3", and H concentrations and found that at room temperature the half l i f e of the reaction was of the order of hours. 3) Exchange between ethyl iodide and iodate ion might possibly present a significant error but the reduction in specific activity of the resulting Agl is probably less than the increase due to l ) . From these considerations i t is felt that the observed k values are -2 -1 -1 high' and that k is actually of the order of 1 x 10 moles litre sec . For example, of the 9 k values obtained at 25°, two (8.81 and 5.7) are very much greater than the other seven values which only vary by a factor of 5. The average of these seven values is 1..06 x 10 . For the same exchange (33) reaction in alcohol the k value at 20°C = .92 x l ( f 4 and at 30°C = 2.5 x 10~4 which is of the order of 100 times slower than the exchange in formamide. The smallest observed rate constant in formamide was .488 x 10~2 at 25° which is about 30 times greater than that in alcohol. The k values for 10-j" - I exchange as explained before, also probably-present an upper limit. At 30.8°C, the value of k is about 1 x 10~4. The reaction of ethyl iodide with formamide appears to be a complex reaction. If catalysed by hydrogen ion, or other added substances, this reaction might be fast enough compared with the exchange to require the use of a complex rate expression similar to those obtained in the appendix. Although many problems have already presented themselves, suggestions for further research may be conveniently summarized. l) Before further exchange reactions in formamide are studied there should be a thorough kinetic study of the reaction of the solvent with alkyl halides. A knowledge of the products of the reaction might suggest possible catalysts. 2') Before exchanges of the alkyl halide-halide ion type: can be studied, conductance measurements should be made to establish the degree of ioni-zation of substances in formamide. 3) If the potassium iodate method of separation is to be used, the partition of iodine between CCl^ and aqueous formamide should be determined as a function of the iodate ion and water concentrations. The nature of the reaction of iodine with formamide, its kinetics, its products, also poses problems for further investigation. 4) Because of the difficulties encountered in the separation by potassium iodate, other methods of separation were tried. Even with the knowledge that ethyl iodide reacted with the solvent, no satisfactory (34) separation could be found. Many solvent extraction methods were attempted, a l l with no success. However, time did not permit an exhaustive search. The exchange reaction might better be studied using a higher alkyl halide which should,not react as rapidly with formamide and which might be extracted by a non polar solvent. Formamide, because of its very high dielectric constant (4-2) (43) (44) should prove to be a very interesting solvent for kinetic studies par-ticularly of reactions of the exchange type. Studies of reaction kinetics in this solvent should provide valuable information of use in the establish-ment of a very important aspect of kinetics—the effect of solvent on reaction rates. However, l i t t l e progress, can be made with exchanges in formamide until the basic reactions of this solvent with simple substances are well established. BTBIiOIGRAPHY The Chemical Institute of Canada, Proceedings: of the Conference on Nuclear Chemistry, McMaster University, Canada, May (194-7). Friedlander, Gr., and Kennedy, J., Introduction to Radiochemistry. New York, John Wiley and Sons, Inc., 7194-9). Hahn, Q...; Applied Radio chemistry, Cornell University Press, (1936). Kamen, M. D., Radioactive Tracers in Biology, New York, Academic Press, (194-7). Wahl, A. C.- (Editor), Radioactivity Applied to Chemistry. New York John Wiley and Sons, Inc., to be published. Calvin, M.., Heidelberger, C, Reid, J. C., Tolbert, B. M., and Yankevich, P. F., Isotopic Carbon. New York, John Wiley and Sons, Inc., (1949). Seaborg, G. T-, Chem. Rev. 27, 199, (1940). Hevesy, G., and Paneth, F. A., A Manual of Radioactivity. Oxford University Press, (1938)7 Wilson, D. W., Nier, A. 0., and Reimann, S. P., Preparation and Measurement of Isotopic Tracers, J. W. Edwards Co., (1946). Hughes, E. D., Juliusberger, F.,.Masterman, S., Topley, B., and Weiss, J., J. 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L0, 793, II84, (1918). ) Lenormant, H., Compt. Rend. 222. 1293 (1946). (41) Myers, 0. E. and Kennedy, J. W., J.Am. Chem. Soc. 72, 897, (1950) (42) Vasenko, E. N., J.. Phys. Chem. (U.S.S.R.) 21, 361-4, (1947) (43) Burdun, G. D. and Kantor, P. B., Doklady Akad. Nauk. 67, 985-8 (1949) (44) Leader, G. R., J. Am. Chem. Soc. 73_, 856, (1951) (i) APPENDIX For the reactions AB * B AB + B~ AB C ^ * B AB + C _±£» HAC -> B " at time t l e t LB} = x [ABJ e-a - x [ B . J - y/ [AB 7] = bry [.C ] -s z [HAC J = C - Z at t = 0 [AB3 +> [B 3 9 a L B ' J = - X G [ABJ + [ B ] --b [B] [ H A C J " * [c]-_ c [c] = z Q the d i f f e r e n t i a l equations for the-rates of reaction are: dx/dt = k(a - x)y -<• k-^a - x)z - k(b - y)x - k2(c - z)x (1) dy/dt k(b - y)x + k-^b - y)z - k(a - x)y - k 2 ( c - z)y (2) dz/dt ^ k2(c - z)x T k2(c - z)y - k^(a - x)z - ki'(b - y)z (3) Adding (1), (2), and (3) gives d (x •* y• •» z) T L 0 , . x *• y + z = a constant, d dt Adding (1) and (2) gives d (x v y) = kWa-* b - x - y)z - k2(c - z)(x + y) dt. Substituting x * y - u and z - d. - u we get du - a quadratic i n u dt du =. (ki - k 2 ) u 2 - |(c - d)k„ • •* k, (a -» b * d)]u + (a + b)dk-, dt L -(4) Let the roots of the quadratic be*^andy9 . Assume that the (iii discriminant i s positive where e = o •» i» Substituting z d - u, y =. u - x into ( 1 ) gives (M Equation (6) i s a f i r s t order l i n e a r d i f f e r e n t i a l equation and therefore the integrating factor i s ^ ^ ^ Therefore ^ L ^ (c« + D-UL> At * * t f where c" = 4 , *<A t t> » Now | b ^ ' l J - C J L B 0 ) WhereeA •= k(a * be) ;•+ kg(ce- d) ) « * k-^ d B 3 » k 2 - k x D » a(k - ki) C" ^ k xad C . s r integration: c o n s t a n t x x y^ -ex? x o n -P Equation (7) gives x, the concentration of B i n terms of. t-and the rate constants k , , kQ,, and; k. A similar expressions; can be found f o r y,ttie concentration of B , from the r e l a t i o n x * y u. I f k^ and k^ were measured independently ofk,, (7)}cowld. be regarded: as an expressiongjfcvlngF'x in.iterms of:. t;and k only. By means of a computing machine, a table of values for x could be calculated f o r certain a r b i t r a r y values of t ad k . From the measured values of ttand x, k could then be found from such atableebyinterpolation. To solve (l),(2),and (3) (page 23) ,vt i£ noted that, as in;, tke solutdm of (4);, (5) »and(6), (page24) x * y v z - d and substituting as before where A,B,and C,1 are constant c o e f f i c i e n t s . In p r i n c i p l e , the roots of t h i s cubic may be found and by p a r t i a l f r a c t i o n s i t may be possible to obtain a solution f o r z. However i t i s evident that the solution will' be even more complicated than (7). 


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