Studies in Chemical Kinetics Citation Wilson, John Norton (1939) Studies in Chemical Kinetics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ryw6-gc28. https://resolver.caltech.edu/CaltechTHESIS:01032025-232452716 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Dickinson, Roscoe Gilkey (advisor) Pauling, Linus (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1939 Record Number: CaltechTHESIS:01032025-232452716 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:01032025-232452716 DOI: 10.7907/ryw6-gc28 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16944 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 07 Jan 2025 22:38 Last Modified: 07 Jan 2025 22:38 Thesis Files PDF - Final Version See Usage Policy. 30MB Repository Staff Only: item control page

[;tudies in Chemical :Kinetics a Thesis by Jolm Norton Wilson, M. A. In Partial .ii"ulf illment of the: RequirEments for the Degree oi' Doctor of Philosophy, California Institute of Technology Pasadena, California 1939 The: candidatE is happy to express his grateful apprec:iation for the instruction which hE has re- CE"=iVed :f'rcm the mE:'mbers of' the- staf f of the Chemistr,/ Di v.: i.sion of the Cal i f ornia .Institute of' ·rech- nology during the past threE ye4r~ of study. In particular his thar,.ks are due to Professor· Loscoe G. Dickinson. and to Professor Linus Pauli1:ig, Chair- ~nan of the Division, for their patient gL.i.Ldance, c;:: itic:ism. and encourage:nent. 0 Studies In ChemicaLJ.~1£§ Page Studies of :Exchange :·~eactions of Eadie- Part 1: active Isotopes Introduction •.••.••...•...•••.••••...••.•.• 1 TechniaUE· of Radioact.ivit·v rA:easurements • • • • J 3 ·.a. Fart l (a.) Measu1•er.ue.nt o:f a Reaction Ea.te at Equilibrium by Means of~ a had1o- active Indicator Part l (b) •• ••• •• • • • • • ••• • • • • • • • • • •• • 5 An Atteirnpted Lxc:ha.:nge of Phosphorus betwt€H Pho.s pho:r-01).S and. PLoerh.ori.c A.cids Part l (c) • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • •• • • 1.:xchange heactions ot· Eadioactive Bro- ......... ...... ........... . . .. ..... .. :i:;romide .. ..... .. . ... .. .. . . .. . . .. ..... . . .. . mine: 12 ~ .Excha:ngE: Lxpe:r-imc:nts with EthylEne ~ 14 Stannic Bromides • • • • • • • • • • • • • • • • • • • • • • • • • • • 17 Thermal and Fhotocllunical r:.xchange fart 2 Phoru"~ Trifluoride and Chlorine . . . ... . . .. . . 2& A Theoretical Jiscussion of the Liese- Part 4 -t- :. "... 0!)• Of ..... ,-:, C' .-i -,o-1 e C,Q"l 0 ... r-'b ._ .... ••"' t e'•••••••••••••••••••• b i bli ograpl1y ••.•••••••. • ••••••.•.•.••• • .•••••••••....... • ~ u.i11marv J • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •. • • • • \,J 1 Part 1. Stu.dies of hxch = .1nge Reactions of Radioactive Isotopes ------·-------------------- Introduction: A process in which interchange of atoms of the same element tak , s place bet,veen two different c omfH>Urk.S of that element we shall call an isotopic exchange reaction-. 'l'he study of ·these reactions is made possible by the fa.ct that the isotopes of a given element differ f'rom one ar.l.other in their chE.m1ical properties to only a very small extent. In order to cetrry out ;;;uch a study, however, methods mu c. t be available for v rying ,J.nd. for· determining the amount of one isotope which is present. in a mixture o:t· isotopes of tile same el€ment. The method which w~1s used in the investigatior:s re1Jorted in the follov.ing pages is b :1sed on the fa.ct th...t rad.Loactive isotopes of' most of the elements can be art..1.f l cially produced by methods recently developed in nuclea.r physics e.g. by bombard.rne.:1.t of' an element with neutrons or fast deuteror.s. If a radioactive isotope· is to t,e useful for the stud~/ of an exchang e reaction it is of co...i.:cse necessary ttHt the "hali:'-lifeu of the radioactive indicator be of the order of m-:::.gra tude of the time re(1uired f·or the exchange reaction to oe: cur to an appreciable exte-nt and for th€ ex:;·;er imental ma:nipulatior:..s to te made. A detailed disquisition on the results at pr·esent available from the investigation of' exchange reactions will not be given here, since excellent SU;illllaries of' the experimental data so 2 :far obtained by th€ us E: of radioactive i ~otopes as we 11 as by othe r methods have recently been ",ublished ( 1, 2) • A brlef description of tht t:,: 1,e of work which h iis bE;En doL.e will be given, however, in order to re Lite th€ resu.l ts presented in the: present di s s Ertation to th ose obtained by other investiga- tors. The elements whose exchange reactions h,ilve beEn sti.1died by the use or" thei r- radioactive isotopes include chlorine (with a radioactive is oto 1 ,e wh ose half-life is ~-·1 minutes), tromine (three it:oto .. 6s: half-lives of 18 ;:ninutes, 4.2 hours and 36 hours), iod.1.ne (25 minutes), sulphur (80 days), .i:ihosi.-,1iorus ( 14 days), arsenic (26 :, hours), and manganese ( 166 minutes). Most of' the work done has beE:n of' a qualitative nature; the results have· shown whether a given exchange occurs rai.·idly, slowly, or not at all (within the time lLrnits imposE:d by the half-life of the isotop~ us ed). Some very significant quanti- tative results have howev€:r been obtalned by Hugh~s, ToplE.cy, and their co-workers -who h a ve shv11vn that the rat€ of' halogen betwc€L. lithium br omide and 01 exch:,ir.ige oe. phenyl ethyl br omide or be,tween sodium iodide and secor~ary octyl iodide i s equal to the r c1te oi· race :nisation of the optically act . . ve org&1J..ic halide by th€ metallic halide·. 'I 'his result gi.ves fairl~/ direct Ex;>erimEnta 1 evidence f'or th€· valid.it,)" of the theory thc1.t race:uisation r rocEeds by an exchange mechan . . sm, with one in- ve·r sion of the opticu.l activit.:1 per ex.change. .\ .nother investi- gation from whose results some significant conclusions can be 3 drawn has been carried o,.;.t by Polisaar, v,ho showe d ,..,,n thE:' basis of' ,s_ E tudy of exch:a.nge react.1one. o:C ma.x:i.ganesc: b€: tween sum€ of 0 its c cmpournis that thE. prEviously accE.pted mH:hanis::u for the oxidation of oxalic acid by Jhrmanganate c 0 u.ld not be E.rrtirtly correct. Somt: results of biological importa nce hav€ beu1 obtained by various investigators :from a study of' exchange reactions of pl1osphorus .in organic c ompou:nds such as the phospholipids. vitro The-se e.x:i,,eriments ha.ve teen c-:induct.ed. both in and in living animals. 'I'ht investiga:tion.s reported in the:: follov,ing pages ir:;,clude a study o:i' thE. ioo:;.r~e-catalsse:d exchange of' arsenic between arsenious ~1d arsenic acids, an at te.mpted E:xcL.rnge 01: 1. t.osphorus ..,e·t¼ E. en phosphoric a.nd phosphor0us acids, arm a stud;;· of a number of exch,1ng€ 1•eact .... ons of bromine. It was possible to :follow the arsenic rsaction in detail, and to concli..i.de thd.t tl .. t, kinetics o:f the 1~eaction bet'VI Een arsenious. acid and iodint are the sa~11c at eq(..!.ilibrium as they are remote f"r '",m e q c1il.ibrium. Tht phosp.twru.s exchange was not f ounci. to occur to any measureable ex·tent. No q_uanti tati ve study was :nade of' the rates of' th€: exchangt reactions of bromine whicl1 were: investig ,ted, but some new qualitative results werf obtained. '!.'eclmicp..1e of hadioactivity MeaS ;.l!'e:nEonts: The radioactivtr: isotopes of bromine and of ars<:;nic used in tne experimEnts werf prEpared by thE irr:idiation of' a:;_)propriate materials with slow neutrons f'rom a racion-bE-ryll1.um s '"A.trce cor.tai..nir:ig :from fifti to two hundred and fifty millicuries of radon. Both s0i..irce and ~arget were placed near the c~ntre of a paraffin sphere about ~O inches in diameter. The material was irradiated for a time chosen to give maxLnurn activity in the sample, accordiP.g 4 to the equation wher·e I H a.nd J are res ;,,ective Jy t h~ h ,~.lf- lives 01 radon and The r,11.dioactiv i ty ffiE;,isw·e-mFnts were :n:J.de by means of a sensitive Lauri tse u c;_u1irtz-1·.1.t-cr E.illctroscope filled v;ith air r;;.t a t rnosphEric preu.:,; u re , \~it.h a c,1pacit., of" about 0 .13 cm. and a m.e asured. fH:.nsitiv.l.t.i of' 1.0 volts ,., er scale division, or ion-pairs per division . abou t b x 105 The sampl e to be msa.sw•ed wus c on• ve r·ted to a i'orm i n which it, could be fi.n~ly l) Ov,dered; th.i s powder v.; '"'· evenly P '.lcked into a CJ lindr ic ~':. l dep:r·ession about one millimeter deep and five or seve n cs r~imeters in aiameter position ciir'<2Ctl;y' below the aluminum window oi' t he electro• scope . t hick . The el e-ctroscope was ea l ibr :itcd for ncm-linea.rit.i of scaJ.t b..v tl"H u t. e of a uraniun1 sourc e . are rep orted in t h( f ollo ~-.i 1::g pages . 5 [Reprint from the Journal of the American Chemical Society, 119, 13~8 (1937).] [CONTRIBUTION FROM THE GATES AND CRELLIN LABORATORIES OF CHEMISTRY, CALIFORNIA INSTITUTE OF TECHNOLOGY, No. 592] Measurement of a Reaction Rate at Ectllilibrium by Means of a Radioactive Indicator. The Reaction betw,en Arsenic Acid and Iodine Bv J. NORTON WILSON AND RoscoE G. DICKINSON In the study of chemical kinetics and equilibrium, it is customary to correlate the specific rates k1 and kr for a pair of forward and reverse reactions with the corresponding equilibrium constant K, in accordance with the equation kr/k, = K In making empirical tests of this relation, however, the specific rates k1 and kr are in general measured with the system considerably displaced from equilibrium in order that accurate values may be obtained more easily. Hence it is of interest to appreciate t.hat such methods do not eliminate the possibility that k1 and kr might actually change as equilibrium is appror..~hed, but in such a way as to keep the ratio kr/kr approximately constant. The use of radioactive indicators, which have become an important chemical tool, permits the measurement of rates at equilibrium and thus makes it possible to place the ki- netic theory of equilibrium on a sounder experimental foundation. In the present paper are described some experiments involving reactions on which previous rate\ and equilibrium 2 measurements have been made by customary methods; these reactions are the oxidation of arsenious acid by iodine, and its reverse H 3AsOa + 13 - + H,O :::;:::=:: H 3AsO, + 31- + 2H+ (1) Experimental Procedure.- A radioactive arsenic with a half period of twenty-six hours is formed from ordinary arsenic by neutron capture. 3 To utilize this we exposed 15 to 20 g. of pure crystalline arsenic (Kahlbaum) for two to three days to a radon-beryllium source of neutrons whose initial strength was 200 to 300 millicuries ; the exposure occurred in a large block of paraffiu. The arsenic (1 ) J. R. Roebuck, J. Phys. Chem., 6, 365 (1902); 9, 727 (1905) ; W. C. Bray . ibid., 9, 578 ( 1905) ; H . A. Liebhafsky, ibid. , 35, 1648 (1931). (2) E.W. Washburn and E. K. Strachan, ibid., 36, 681 (1913). (3) F. A. Paneth and J. W. J. Fay, Nature, 135, 820 (1935). 6 July, 1937 RADIOACTIVE INDICATOR IN THE ARSENIC ACID-IODIDE TITRATION was then burned to arsenious oxide in a stream of air and a weighed amount of oxide dissolved in a measured volume of 1 N standard sodium hydroxide solution, which was then diluted to the desired concentration. The reaction mixtures were then prepared from standard solutions of arsenic acid, hydrochloric acid, and the radioactive arsenite . The mixtures so prepared were brought to thermostat temperature and a measured volume of standard potassium iodide at the same temperature was added. The mixtures were such that at equilibrium comparatively little free iodine should be present. The color due to free iodine developed immediately on the addition of the potassium iodide and became constant within a minute or two, indicating a rapid approach of equilibrium . The solutions were kept at a temperature constant to within 0.1 ° for a measured period of from four to seventeen hours. During this period exchange of radioactive arsenic between the tri- and pentavalent states occurred presumably through reactions with iodide and iodine. The exchange was then quenched by dilution with water and addition of an excess of ammonium hydroxide sufficient to make the solution 0.6 N in the latter reagent. The arsenate was then immediately precipitated as magnesium ammonium arsenate by the addition of magneannnammonium nitrate solution. The precipitate was flShed with 0 .6 N ammonium hydroxide, filtered, dried, and ignited to magnesium pyroarsenate which was then p-ound to a fine powder. A fixed weighed amount of the powder was placed in a shallow cylindrical depression 0.1 cm . deep and 5 cm. in diameter in a thick sheet of brass; the powder was pressed down to fill the depression fully and evenly . The brass sheet was then placed in a reproducible position under a quartz fiber electroscope and the activity of the arsenic mea5ured . Separate fillings of the brass container gave results with a maximum deviation from the mean of about 3% of the net activity. The electroscope was calibrated for linearity of scale. Natural leak was measured frequently and corrected for. About one-fifth of the original radioactive arsenite solution was oxidized to arsenate with sodium hypobromite and was then prec-ipitated, ignited, and its activity measured just as with the exchange samples. All activities were corrected to the same time using the half period twenty-six hours. In some preliminary experiments the usual reaction mixtures containing arsenate, radioactive arsenite, and hydrochloric acid were made up with the omission of iodide. Even after the solution was boiled for three hours, the subsequently precipitated arsenate exhibited no activity. This shows that any direct exchange between the tri- and pentavalent arsenic is negligibly slow, and that .the method of separating the arsenate did not 'i tself induce exchange. Incidentally, a similar Jack of exchange in alkaline solution (~1 N sodium hydroxide) was also found after three hours of boiling. Treatment of Results I In the experiments described here, the initial concentrations of trivalent and pentavalent arsenic were not significantly different from the 1359 equilibrium concentrations, and it is assumed that substantially all of the exchange occurred under equilibrium conditions; further justification for this is given below. We shall accordingly first obtain relations valid for the case where the initial solution is at chemical equilibrium. Let a and {J be the respective fractions (corrected for radioactive decay) of pentavalent and trivalent arsenic which are radioactive at any time t measured from the beginning of exchange; if initially only the trivalent arsenic is radioactive then at t = 0, {J = f:Jo and a = 0. Let (Asv) and (Asm) be the total concentrations (at. wts. X voI.- 1) of arsenic in the respective valence states. The total concentration of radioactive arsenic (corrected for decay) is a(Asv) + {J(Asm); since this remains constant, it follows that a(AsV) + tl(AsIII) = tlo(Asm) (2) Let R be the (constant) rate (atomic wts. X vol. - 1 :X 'time- 1) at which arsenic passes from the trivalent to the pentavalent state or the reverse. Withoutteference to the orders of the reactions involved, tbe rate at which radioactive pentavalent arsenic is formed is given by the rate R at which trivalent arsenic passes to the pentavalent state multiplied by the fraction (3 of trivalent arsenic which is radioactive, i.e., (3R. Similarly the rate at which radioactive pentavalent arsenic disappears is aR. The net rate at which the concentration a(As v) of pentavalent radioactive arsenic increases is the difference between these two terms, i.e. (da(AsV) / dt) = (tl - a)R (3) Writing (As) = (.~sm) + (Asv), and substituting for ,8 from (2), we obtain da R [ (As) ] dt = (AsV) /3o - (AsIII) a (4 ) Integrating, and inserting the condition a = 0 at t = 0 R = _ I (AsV)(AsIII) In [i _ ~ (As) ] t (As) tlo (Aslll) (5 ) Since a/ ,80 as well as the other quantities on the right are measurable, R may be calculated for the particular solution used. In the present experiments the quantity a/ f3o has been taken as the ratio of the electroscopic activity of pyroarsenate from a solution which has exchanged for a time t to that of pyroarsenate from the original unexchanged arsenite. On the assumption that a given arsenic atom passed from one valence state to another only J. NORTON WILSON AND R OSCOE G. DICKINSON 1360 through oxidation or reduction by iodine or iodide, the rate R may now be identified with the rate of the oxidation of arsenious acid by iodine or the equal rate of reduction of arsenic acid by iodide. The results of such experiments are given in the table. Columns 2 to 6 give the empirical composition of the solutions as made up. The empirically measured rates are given in moles X liters- 1 X min. - 1 in the column headed R. Vot: ·59 oxidation may be tested by determining whether the rates of exchange depend on concentrations in the manner to be expected from Roebuck's kinetic studies. In order to do this, we have calculated specific rate constants for the reduction of Asv by placing R = k(HaAsO4)(H +)(J - ), the right-hand member being Roebuck's expression . As was done by Roebuck, we have taken (HaAsO4 ) = (Asv) and (H +) as the formal hydrochloric acid concentration. The values of k thus M E ASUREMENT OF THE RAT E OF O X IDATIO N AN D R E DU CTION AT E QUILIBRIUM AN D TH E CALCULATION OF SPE CIFIC RATE CONSTANTS ~ - - - - - - - - F orm u la weig hts p er lite r H , AsO, N a Cl Kl No. H,AsO, HCI 1 0 .120 2 3 4 5 6 7 .114 8 9 10 11 12 . 107 . 105 . 125 .125 . 125 . 125 . 107 . 105 . 151 . 151 0. 119 . 113 . 100 .098 .273 .406 .203 .273 .099 . 098 . 096 .096 0.130 0. 121 . 114 .236 .100 . 196 . 107 .100 .098 .081 .098 .081 .081 .098 . 163 .081 . 196 . 100 . 107 . . 100 . 074 . 079 .237 . 074 0. 0091 .0086 .0408 .100 . 100 .100 .100 .100 .0405 • • . 100 .0536 ,0} 07 n ->, (I, - ), 0.0091 .0086 .0407 2 .5 X 10- 7 6.5 X 10 - 1 4. 5 X 10 - 6 1.9 X 10-• 1,5 X 10-• 7.1 X 10- 4 2.6· X 10-• 1.0 X 10-1 .099 .099 .098 . . 099 .097 .0403 .099 • 05.16 .,0107 -~~J. ~ 10-1 ~ l, ~ io,-• ~ X 10 - 1 -2i..~ .10:-' ~ In the columns headed (J 3 - ), and (f:")., :are given the concentrations of 1- and of I a- in tlie various solutions at equilibrium. These were calculated for the runs at 25 ° using the constant 2 K = (HaAsO.)(H+)2(1 -)a = 5 5 X 10 -2 (HaAsOa)(Is-) ,) • For the runs at 35 ° a value of K (3.8 X 10- 2) was estimated from that at 25°, and that at 0° (1.6 X 10- 1) measured by Roebuck. 1 Here (HaAsO4) and (HaAsOa) have been taken as (Asv) and (Asm), respectively, and (H +) as the formal concentration of hydrochloric acid. This is adequate since (Ia-), was in all cases small and is needed only to calculate a small correction to (J-), and to show the small amount of reaction required to reach chemical equilibrium. A more detailed analysis of the rate of exchange which considered the fact that Ia - was initially absent rather than at its equilibrium concentration, led to an expression similar to (5) but with t replaced by t -(1 / a ) (l - e- at) where a = R/ (J3- ),. Because of the small values of (J3- ), in the experiments the use of this expression gives values of R differing by less than 1% from those given by equation (5) . The assumption that radioactive exchange occurred only through iodine- iodide reduction and .. Ac tivity, Time!, Temp., k X 10', oc. corr. a / {Jo min. Rat.e R X 10• 0.062 .072 .226 .333 . 265 .208 .280 .212 . 256 .350 .342 .231 952 617 555 732 789 657 839 361 278 408 713 1001 0 .85 25 .0 6 1,4;3 25. 0 6.2 5.38 25 .2 6.7 7.80 , 25 .2 7.4 20 .3 24 .6 7.9 31.1 24.6 8 .2 6.5 12 .6 24 . 6 24 .6 6.6 27.8 35 .0 . 16 . 1 12 . 6 14 . l 35.0 13 . 7 6. 75 · 35.1 16 .5 2. 78 35. 1 11 .3 are given in moles- 2 X liters 2 X min. - 1 under k (corr.); a small temperature correction to 25° (or 35°) has been applied when the experiments were made at temperatures slightly different from these. At a given temperature the values of k show reasonably good constancy. The assumptions may be further examined by comparing the absolute values of the constants with those of Roebuck. 1 As recalculated by Liebhafsky, Roebuck's measurements of this specific rate give the values 6.3 X 10- 3 at 0° and 1.6 X 10-2 at 10° (units: moles - 2 X liters 2 X min. - 1). If these be extrapolated to 25° using the Arrhenius equation, the value 0.057 is obtained in satisfactory agreement with the mean value 0.071 from the exchange measurements; extrapolated to 35°, Roebuck's values give 0.125 and the exchange measurements 0.154. 4 The Arrhenius heat of activation is calculated from Roebuck's measurements to be 14,300 cal. per mole; the exchange measurements give the value 14,100. It appears then that the radioactive exchange occurs . mainly through the oxidation and reductiofi • ~f the iodine, and that the kinetics of the oxidation and reduction at equilib- pbtained (4) In calculatin&' the mean values of k the results of experiments 1 and 2 have been omitted because of t he slllall precision of a / /30; uperiment 12 also has been omitted. July, 1937 RADIOACTIVE INDICATOR IN THE ARSENIC Acrn-IODIDE TITRATION rium are the same as those remote from equilibrium. The authors are indebted to the W. K. Kellogg Radiation Laboratory at this Institute for the preparation of neutron sources used in this investigation. Summary Radioactive trivalent arsenic does not exchange with non-radioactive pentavalent arsenic in dilute acid or alkaline solutions in the absence of other easily oxidizable or reducible substances. In the presence of iodine in acid solution, however, an 1361 exchange takes place at a measurable rate. On the assumption that the exchange occurs through the oxidation and reduction of the iodine, we have calculated the rates of oxidation and reduction at chemical equilibrium from measurements of rates of exchange in systems containing iodide ion and small amounts of free iodine. The rates of oxidation and reduction measured in this way are in agreement with the kinetic expressions shown by Roebuck to hold for the same reactions remote from equilibrium, and lead to specific rate constants which agree with those measured by him. PASADENA, CALIF. RECEIVED APRIL 7, 1937 9 [Reprinted from the Journal of the American Chemical Society, 60, 2697 (1938) . J [CONTRIBUTION FROM THE GATES AND CRELLIN LABORATORIES OF CHEMISTRY, CALIFORNIA INSTITUTE OF TECHNOLOGY, No. 652] ' An Atteµipted Exchange of Phosphorus between Phosphorous and Phosphoric Acids BY J. NORTON WILSON The hydration of hypophosphoric acid, which takes place according to the equation H,P20& + H20-+ H aPOa + HaPO, (1) b~ shown 1•2 to has proceed at a rate which is first .Qlder with respect to hypophosphoric acid and creases with increasing hydrogen ion conion. It has been suggested 1 that this ac s irreversible, but it seems probable arr librium may be reached in which the cent ation of hypophosphoric acid remaining too small to be detected readily by chemical methods. If the structure of hypophosphoric acid is such that the phosphorus atoms are equivalent, as in the structure (HOh P-P (OH)2 which has been l i suggested on the basis of X-ray absorption spectra and chemical properties by Nylen and Stelling 3 and by Hantzsch, 4 the reverse of reaction (1) should lead to an exchange of radioactive phosphorus between phosphorous and phosphoric acids according to the following mechanism (the radioactive phosphorus atom is denoted by an asterisk) HaP*O, + HaPOa ~ H20 aP * - POaH2 + H20 ~ HaP*Oa + HaPO. (2) An attempt has been made to detect this exchange using radioactive phosphorus6 obtained (1) Van Name and Huff, Am. J. Sci., 45, 103, 18 (1918) . (2) Blaser, Z. physik. Ch em ., A167, 441 (1934). (3) Nylen and Stelling, Z. anorg. allgem. Chem . , 212, 169 (1933); ibid., 218, 301 (1934) . (4) Hantzsch , ibid., 221, 63 (1934) . (5) This material was supplied through the generosity of Professor Edwin ~illan of the Radiation Laboratory of the University of CaUforni as a by-product of the formation of radio-sulfur by bombardment of sulfur with fast deuterons. The material was separated from most of the accompanying sulfur and oxidized to phosphoric acid; a small amount of ordinary phosphoric acid was added as a carrier. The phosphate was precipitated as magnesium ammonium phosphate and converted to lead phosphate which was treated with hydrogen sulfide to liberate radioactive phosphoric acid. The reaction mixtures were made up from this material and "c. P.'' phosphorous and phosphoric acids. The phosphorous acid used was found to contain a small amount of phosphoric; this was determined and corrected for. In order to determine whether exchange had occurred the mixture was diluted and the phosphate precipitated as magnesium ammonium phosphate; this was dissolved in acid and reprecipitated to remove co-precipitated phosphite. The phosphate precipitate was dried and its electroscopic activity measured. The phosphite contained in the filtrates was oxidized with bromine and similarly precipitated; the electroscopic activity of this precipitate was determined as before. Occurrence of activity in the latter precipitate would be evidence either of exchange or faulty separation. The reaction mixtures were made up in duplicate; one of the pair, used as a blank, was sub~ jected immediately after mixing to the separation process and radioactivity measurements described above; the other was sealed in a glass 10 J. NORTON WILSON 2698 Vol. 60 ATTEMPTED EXCHANGE OF PHOSPHORUS BETWEEN PHOSPHOROUS AND PHOSPHORIC Acms: No. (H,PO,) (H,PO,) I II III IV V VI 0.76 .46 .60 .62 . 36 .36 t, Other reagents min. 0.72 1440 .43 NaOH, 2.86 1400 .68 HCI, 5.31 11,500 .70 HCI, 5.51 21,200 .35 HCI, 5.63 18,900 .35 HCI, 5.63 37,900 Activity P03, div./min. T, °C. 100 100 100 20-25 25 25 +0.004 ± 0.005 0 . 79 .002 ± .005 0.92 + .006 ± .006 4.85 + .013 ± .006 4.20 + .010 ± .010 49.0 + .006 ± . 004 24.8 ampoule and allowed to stand for a convenient time before separation. The probability of error due to faulty separation was greatly decreased in experiments V and VI in which after the precipitation and separation of the radioactive phosphate some inactive phosphoric acid equal in amount to that originally present in the solution was mixed with the phosphite in the filtrates and precipitated in the same way. This treatment should remove practically all of any radioactive phosphoric acid left in solution after the first precipitation. Measurement of the activity of the resulting precipitate inc:1,f.; cated that about 0.1 % of the radiophosp acid originally present was left in solution a ter the first precipitation. After the extra precipitation the phosphite in the filtrate was oxidized and precipitated as in the earlier experiments. From the observed extent of an exchange occurring during the time t in accordance with the mechanism suggested in (2), one can calculate the rate at which reaction (1) and its reverse proceed at equilibrium. If the first order rate constant k1 for the hydration of hypophosphoric acid is known, one can calculate from this result the equilibrium constant K, defined as K = (H4P2Os)/ (H 3PO4) (H 3PO3). It may be shown that for the case where exchange occurs to a very small extent over a long time a good approximation is K = 2 (3 (HaPO,)k1t ao EXPERIMENTAL RESULTS {J/a.o, blank {J/a.o ( 5 ± 6) X 10±6 X 10- 3 (-2 ± 5) X 10- 3 ±5 X 10- 3 ( 1 ± 1) X 10- 3 ± 1 X 10- 3 ( 3 ± 1) X 10- 3 ± 1 X 10- 3 ( ~ ± 2) X 10-• (1 ± 1) X 10-• ( 2 ± 2) X 10-• (1 + 1) X 10-• 3 which has been taken as the ratio of these activities. The values of {3/ a 0 for the "blank" experiments are also included. The normal leak of the electroscope was about 0.07 division per minute; fluctuations about this value were large enough to make a comparatively large uncertainty in the value of the activity of the phosphite precipitate. This uncertainty was estimated from the root mean square deviation from the mean of a number of alternate measurements of the normal leak and the phosphite activity. The results of experiments V and VI are the most reliable because of the care used to eliminate the error due to faulty separation. It is apparent that in no case was definite evidence of exchange obtained. It can be stated, however, that the extent of exchange was less than a certai1_1 value determined by the estimated uncertainty; on the basis of the assumptiQJts made a limit can then be placed on the value of the equilibrium constant K. Thus in experiment VI, {3/ao was very probably less than 5 X 10-4; k1 for the given conditions may be estimated from the data of Van Name and Huffl to be 1.0 X 10-3 min. - 1. Then K < 8 X 10-5 mole- 1 liters at 25° in 5.6 formal hydrochloric acid. Unfortunately, an alternative conclusion is possible: that the phosphorus atoms in hypophosphoric acid are not equivalent, as for instance in the structure (HO)2 P-0-P (OH)2 proposed on l (3) where a 0 is the fraction of phosphoric acid initially radioactive corrected for radioactive decay to the time t and {3 is the fraction of phosphorous acid radioactive at time t. In the following table are listed the concentrations, in formula weights per liter, of the reagents used in the experiments; the time t between the original mixing of the solutions and the separation of the phosphate; the temperature; the electroscopic activities of equal weights of the precipitates from the phosphite and phosphate fractions, corrected for radioactive decay and for the normal leak of the electroscope; and the values of f3 / ao, . Activity PO,, div./min. the basis of some slight chemical evidence by Blaser and Halpern. 6 If this is the case it is unlikely that the reverse of reaction (1) would lead to exchange. According to the evidence at present available, 1•2 however, it seems quite probable that the molecule contains two equivalent phosphorus atoms bonded to one another. The author is grateful to Professor R. G. Dickinson for his advice, criticism and encouragement in connection with this investigation. Summary No exchange of radioactive phosphorus between (6) Blaser and Halpern, z. anor/l allgem. Chem., 2111, 33 (1933) . 11 Nov., 1938 ATTEMPTED EXCH ANGE OF PHOSPHORUS IN ITS ACIDS phosphorous and phosphoric acids in acid or alkaline solution was found to occur beyond the limits of experimental error. The results indicate that if the phosphorus atoms in hypophosphoric acid are equivalent, the equilibrium constant for the 2699 formation of hypophosphoric acid from phosphorous and phosphoric acids is less than 8 X 10 - 0 mole- 1 liters at 25° in 5.6 formal hydrochloric acid. PASADENA, CALIF. RECEIVED JUNE 13, 1938 12 Part 1 (c) An atte :.rr_p t was nhde t o fi nd a s imp le i i..-otopi c exchange re .,ction v, b.0 2-; e r i: 1.te e:ould l:,e c0 nvenientlJ' 111eaaijl'ed, in the hope th,.:i:. t the reLttive chemica.l s1m1,.; licity .o:f su.cl1 a reaction might permit a straightf'orward i nte1· £,r-€tatio .. of th~ obser·ved The at tempt ,v ,is not :t succe ::J .Sfu1 one, but ci id 1e:.1d to th e L"iiBcover:1 of' so:1;e exchange reactions L ot pr t::vious ly re_..orted. Brief investigations ·were made of exchange t·eactions of' r ,1.dl:i.oactive 1Sl.ementary bromine in C,.-i.rbon tetrachlo:ciae solution with thE· f'oJ.lov..i ng substances: sta:rmic bromide, . .nd trichlorbrom methane, arsenous bromide, etci.ylene di bromide, the l J.s t bo th t.l.E:rmally and photoch.fc ,r:ically. P:r-epar·c.':i.tion of reagents:- Ca rbon Letracl1 loride: ... A good gr ,:-de or carton tetr "c nloride wh l<.:.t h ,..d teen _purified v..-ith .::!.qua regi a and c ,a•E:i'ully d.i:..:.tilled wa.s dried with .P20,::,__, and redistLlled. The f'r 0.ction boiling 1-<.: thyle:ne dibrcmide :- A st 0.d€,nt prep ,'3.r .tion w.,-is was.t1€d ·~ith disti ll0 d dried ove r P20.:; and d istilled, the v :fr , ction toiling in t he r ange 1~0... 1~➔ 2°C beir..g retained. WiAt€:r , Bromine:- 'l'he best com.mere ia1 g;rad c otta.irnt,lE: -w_, s d..:i.stil..Led. over so dium bromide a.nd th€'2n from P ,3 Oi:: in an all-glass still. V ::tannie Dromide :- This c .Jm, ,ound w:::ts prep.1.red by <.-. -~ utiously adding 0 ;,1c.il J piect::s oi' pure tin to a. S~) lution of 2~ grams of 13 After 7. 5 £"I' :~ms bromine., in 72 grct::,ia of carbon di$~lf id.e . of tin had been added t.iH& mixture w.1.s allov~ed to stand at r oom t.e;nijerature f'or four hours. into an a1.l-glass still and thE c .,.rbon .:iiG~ ~fide:· was uls t:i.lled of'f , with s •Jme of the bromine. oi' e;te; ; m rlc b:romidE:;. acc.ompliJ:Shed by adcling C.ci.rbon tetrac:t1i.or1de; and dietilling, the bromine be ing c .;. :cr ied over with th E c :::rbon tetrac hl.or..i. a.e . S edistilli:itio n ot' this materi a.1 yiela,e.¢. a colo:;rl ess mat0ria l with a slu .r_p melting _;,:i oint .::1.r:d a distillat.ton r ,:1.rig:e oi 0.2°c. Ar Le L ic: tribromide; ... A Kah lbau:u product was .,.,uri:fied 217°C being r~tai:ne:d,, Trichlorbrorn ~11E:th.1n(; :- I,. s6lution o:i.· sixty gr3.rn s of b vdiu.m h,:rdrox1de i n 2.S~ ml . of 'ii'.i::Lte:c wa..s 1t1.0.ded at room temJ)el",itu..r-e to :10 cc. of a1cohol- freE. chlorof orm. Th.rt ~11.ixtuu?. i!,a,6 e:ooled h.yclrox.1.de i s present t hE:· r€:iction is agonizingl:/ slow ; under th€ condi tiorls dt:s.cribed at ove t l.e- r eaction i s fl ,L o.;.t t wo-thirds days in an ice-ba.:thl the non-aque ou s L ~yer w,::;-1.s separatf:-d, and 14 distilled, dried \ti th lr:lriur.i pErchlor :~ti2 .::1.nd t wice dlstilled thr,;,1u.gh a t'r,~ction:Atir;g column. The f .i.n,11 produ t was color.. 1. less and coiled at 1M.8°C, thl:; b viling point b-ei.ng c0nsta11t ¼ithin 0.2°c. fladioactive Bromine:- For thii experiments ""i th ethylene bromide, arsenou.s and st,i ri.nic bro,:uj_des , radioactive bromine W;1.S prep ired by d.i.rect exposure of E:lemE-nt,zll"J' bro.mine ..in a soft-gl;.1ss c0.r..ta.iner to elo\::/ neutrons in pdrarfin . 15 g;ra.;ns \'¥ ere irrad.J..<l ted ,:At a t i:.Jle . Solutior~s oi' this m.:·1terial in c.J.rbon t-etra.chioriae vH:re m .de up by direct we .1.g.r~in.g. Lxc.h-.:..1 .ge L xp0t·.J.mcn:ts with hthylen.e Br,.mlide:• Solutions of ttb.ylt;ne bromid~ i:1.Hd ra.dioact.ivt· b:r•o:ui.ne in c t i.rbon. tet.raellloride 1diLr -e p:r·epared by d.irect \\0:.i.gL,irig. V.: eighed an1oi..mt :·, 01· tlH~SE; &ulutio:ns were .,:-1 i:r.ed in a gl.d.SS ,J.ill~.; oule which wae. then SE:-;1.lE::d, bruught to an a ,;. ,rro pric::, te terfl1i €r>d:tv1.re in the dark, and kf::'rt unaer tnH3e conditions for a cvnvei.de ~;.t t..1.me. The ampou:LEt 't;?Ll.b e: ,_,oled anc opencdt its cGLte L t1:i we r e tr.=.:;,ni=iferred to a glass-stopf:.t; rud fl -::tsk a nd shaken with 4 n. suci1u.w nitrite s ,' .!lution until tJ. o: org:~H.ic li quid wa,b culorlEH:H,. cess req-..1.ired about f'ov.r minutes . This pro- PrelLninar-y exµ, er· i.rtE;nts showEd that the ef:fect of .sodium nitrite on the a.U<1l bromide under· tl.cl::ie c -Jnu.it.L:,,ns v, a.s n€g:J.. .i t)bltc . Th.E., a.queoue l~yt2r v.·as then 8€JJ•il' i.ted from tlle orga.nic maten;i :.ii. l ,m d made a.s,,pro :-.i.rril.tely 1 N in. ammoniurn hyo.rc.,....1de. The 0r0mide w.:a.s the.:. prec :i ="ita:ted as silver brori1ide ; tht ::rnlution was heated to boiling amd filt-2red. The preci i.: itat ,., was washed with hot W r.tt1.::r , dried in an oven at 130°C, we,ighed, and powder-ed in a mortar. The 15 electro.sc op:i.c activi t:r of a k:th )'w,:n t;eight of" tL.i~ ;;-:o'l,der was the or.1gin.J.l rolution o:f r . .,.dioactive br ;;;rnine useu a.a .s. *'blt:mk'1 • The a pp ,il'ii.::nt exten.t to Vihlch , :;•x.ch,1nge h i d occur·red c ould Le l'. ,ete,. ·£uJ.nE:a by a cow1Yari$lill o:r the electroec ,:p:ic ac:tivitJ Es of the two pr 1c ci;;.,i t.d.t,. ::, per gr-,1.m of s.:i. lvE',r bromide, co1 ree,;tt·d :for r s.dio,J.ctive oeca.i to tht:, same til'ili'!. As is sho~}n in t,Le detaJ.led r€·froLu ts tabulated below, no e:xch ,.nge beyond ·u1e limits of e;;;.p er ime ntal error \vas :t.' ..,und to O<.:LUZ"• 16 ;.s oi The:r nm.l .E.xcha.nge Experi;,H,nt.3 with Bromine :ind Ethylene Bromide. Co:n.c. Br~ of' Cone . of' C2 84. £Ta · iment (mol pe:rc e nt) (mol percent) .) 7.0 !) 24 I) 2,1 t) 28 28 .8 Apparent Lxchange c<> 'I i,,fi(f; (min) • (perc ent) 25 114 o.o 100 30 o.6 + 5 65 3,.3 + 5 Tempera.tu.re 100 -5 ♦ - 17 Excha:r.ge :2xperin;ents wi th ;,:rsenous and. Stannic Lr0mides: - Reaction mixtures Wt~r e .made ur, cU::, before by m.ixing weighed amour.:.tc o f c urbo E tetrachloride solutions of radJ.oactlve bromine and the me:tallic brc,nide, tut were st.t'bj ect~;d .i Ji.'.aediately u nt il al.l tl.:.t.: Lirominc had b een removed. Thie process was cv w-1-.: l E. tE.,d about thirt,y-five minutes d.fter t IH:: 01· .i.g1.nal rn ixiug o f t.hc . oL,t ions had oc.:curr~d; the stannic 01· ar·seno ,1s LronL. de In t.h Eo case of' st ..mnic bro- zoL1ti on was hJcirol:,,·sed by boiling and decanted t r.J.".Jug.r. a i 'ilter. The Lrom:Lde in t he filtrfat e w:t.s 9r cci_pitatc1d as s.1lve:r tro,;:iide prepared for r ,~·, dioactivity measure:.Je1-ts in the ;narmer preThe rE.,s :idue of arsEn.ious Lro.;,ide was dis soJve:d in .r.ot. w..d:. er anu the : -:. ~ lution w,:is u1dde a:ika ].ine ,ui th ami;wnium hydroxide. ~-=- ilvEr bromide v.as then p:r E:Cir.·i t .: t-Eo. directly from this 5olution. Th , occurr c n<..:e of radioactivity· in these p recipitat es ¥Wuld give <lirect ev:.;.J.encc o±: t he; oc c u.;.·rc1ee of' an exchange. The results obt ained were ~s r ol l o~c : tlH:': initi .: l mixing of the: soluti un and the con- 18 c iusion of t.hE. bro:nine d-"-s t1. 1lat.i.0n v,as ~"30 minutes. 'I'lH:=, a pp:...rent extent o:r e:-:ch ,nge was 101 % • (b) With a solution which w ,:iS 2.0 mol '-;; Snbr 4 and 4.2 r.uol % Br\~ at 25°c, the time r·eq_uired f'or separation was 35 minut es and th e a;,,parEnt €xtent of exche.nge wa s 110 %• In both these cases the r;. the exc1.1ange Wd.S a i::;par e;-ntly c omple te i n th E: time reqJ.ire:d fo r sepc.1.: catlon. muEt Lot The po ~. S.i. b:..l.J. ty be :forgotten, howev~:r, that a small a ;::w1..u1t of -v,ate r pr <- sent as a ., i.m, ur:1.ty 111ay hctve b r;. e n resp ons ...ble for· U1€ r b.;.., idi ty of' thE- exchange. Lxpi£.r ime nts with 'l'r-ichl o:cbrom met:r~:i n€ . The first €X;.,erim€:i,.ts were c or:ducted in the E-a.me -way as the exp er irr.~nt.s wi th ethyl.E:- ne br omide, e xce f it tJL, t the bromine -was e:x:tr,::.cted. :fru:n the or gS:.r, ic mater Ltl by s haking \<.-i th 1 N s odium hydroxide solution. This extra ct v,.,.s treated vi'..i. th n i tr ,:;us acid to red u.G e the hy1;obrom.i te to bro mide whlc h w~rn t.nen _µreci p i t 1.t ed ,f rom a mmonia.cal s olutio n ao ~-ilver br omid~ . If any exchange oc curr ed in these ex.p e1·i.rnents it wu .s within the lirni ts of €Xi:eri;nental error. i .xpcr iments Wfl•e then ma.,.ie to dete .;. ·mine whe th er t he e xchange c 0u.ld lit, induceu. photoc L €.,-"l c a11y. fl. photoch€ dlic ,1. l e,xchange wao i nde-ed found to occu.r, but i ts detailE d stud,1 \>;as abar,doned beca.1se of e:xv er iH1ent :il. dii'fi.cu J.t ies . The ex1, E"-rirnu1tal tech- nique V:Jil i. be d esc:r·ibed i n s owE· detail, howEvEr, since s ,jmE: of· the met L~;ds which were develop ('.d f or rundling r . :,d.ioactive bro- 19 mine may be -of' valu e to anyone interested in a further study of' this, or si:iailar reactions. The high absorption coe:t"'f'icient of bromine :for visible light and the length of time required f'or the ex_pe:ciments neces si tated the fJI· ep :i.r dtion of di lute solutions of' highly radioac tive bromine. :For this purp ose th E radL.1 ,~cti ve bromine re:::ml t ir;g fr,,m the, exposure oi' 200 to 300 grams of ethylene broidd.e in a soft glas s vessel t o slow neutrons for a period of 24 to 48 hours was extracted accordi1:.g to th E< Iue t l1--.;, d of' Erbach.er and Philipp (4) by shaking the llqu.id for about ten minutes with a di l ute aqueous solution of sodium bro.nide (about 4 • .r-~ x l O- - f ormal). This extract was then eva k) ora t (: d to a volume or one or tvo cc., cooled, and shaken for twE:nty winutes with 10 to 20 cc. of a solution of bromine in carbon tetrachloride (0.01 to 0.1 formal). In tht: r·esulting exchange reaction most of the r a di c:activity went into the c .•rbon tetra- chloride solution. The solution of radioactive br ,_,mine thus obtained was separated from. t i:le aqueous layer, dri€d by snaking with P205 , and distilled in an all glass still. 1'he time elapsing betv.-Een the re,n0val of the ethylene:, t romide :fr0;n the neutron source and the c .,ncL,. e,ion of' th€: distillation of the rauiuactive br omine £oluti0n was about one hour and tlurty minutes. TlH: 21.mount o:t' activity to be expected in the bromine solution resul ti:r.g from such a treatment rn,ty be sstJ.rnated f'rom the results of an exper- iment in v,hich a 150 gram samr: le of ethylenE: bromide was exposed to a neutron source, initially estima ted t o c o t.tain 35 :nilliCLlries of r ~ldon, for 74 hours, 20 this being the time re quired t'or th€, bromine isot0rA~ with 36-hour h a lf' pe ri od to re d.ch its m..1.ximwn c o i:.:ceutration. The radioactive bromine was extrii.cted by s hak ing the lic"uid for six minutes with a solution of 1.0 gram ot· sodium bromide in 30 cc. o:f water. The aqueous layer wc, S sepa.r•atE1:d and th€ sodium bromide obtaineo. by ev st;.:-oration to dryness . 1lnJ. l_ysis of' the measLJ""ed r a dioa.ct ivi ty of' this sodium br cmi <.ie as a f'unction of' time enabled an estim;,tte to be made o:f thE: total Electroscop ic activity at the t i me eXi; osur e to ne ...ttruns ceased, ,:1.nd of' the distribution of the res p ., :nsibility :for th i s activity a".Ilong the vari 0us radioactive bromine isotopes. Estimated elsctroscopic activ.ity Half p erioc. of bro~inE. .is otopE stopped l<'r a ction of' total activity ~· I nun . . 8 . 15:- o.:i.v. o.?4 at time exposu.re 4 . 2 hours 2 .14 div./min. 36 hours ~ • I min. • 0. ,..,11 a.iv. " Normal leak 11 o.o? 0.07 div.Im.in. of E:lectroscope By ·way of c mnpar 1son i t mc1y be re ~narked t b . . t e x1~0su.re of' 15 gr arns of , ure bromine to the s ea.me nm..tron sour·ce, usir~ the m€thods described for the pre pa.r -1.tion of· r ,.. dio ,.,,ct.i.ve bro- mine for thE exp eriments with ethylene bronude , \-voulci be expected t o yield a total act i vity of 1.5 div. p er minute or less: a much s maller total activ i t y distributed ove-r .::. much larger amount of bromine. Evidt::ntly the u s e of the c 0Lcen- 21 tration technique de s cribed above i s we ll worth v,h ilc: , in S.1.) lte o:f the extra time i nvolved. Sln.ce the preliminary experiments previous1)' described h ::i .d sr. own the r .1tE. of th e t t t r .'. £Li l excha 1-:ige rEact.lon to be negigfbly small, the phot, oc11emical ex_;,e riments wei-'e conducted as follows:.. The re:i ction solution \Yas made up i.n a blackened 50 c c • volume tric flask using the di lute s olution o:f r aui oactive bromine, a measured volume of a st;;11rlard 2 -.; J..ution of trici1lor- brom .metha ne t a nd enough carb on tetr a ch l oride t -.: ;n::1.ke t he total vol ume 5 0 cc. After mixing, th E: solution was ana l ysed for br omint by ti tr .1ti ng a f'e~v cc. with t hi os ulf ate after tre a t• ment with pota Lsium iodide. ThE: s olution was then s epar ... t cd i nto halves, one; :t'or u. Le as a "blanku, th€ othB·r i or exposure In view of' th€ f ::.. ct t hat the presence o.i. OY'lfgen i s .kn.:.r.:,11 to exert an ii11~; 01•tan t inf' luen c:e on th€ r a t e oi s o;ne phot ochc,mic ,:1.l halog-enation re acti ons (5) (6) (7) an eff· ort v~as made in most of ,:,he e xperime nts to E: l i minate ,nos t oi' the air f rom the reaction vessels in the :f o llowi ng way : the who l e solution of trichlorbrom me,thane and bromine was sealed in a 250 c c . Erlenmey(U' flask c 0nnected by g lasf, t ub ing t o a vacuum system and to t wo sma1ler i'la ,;.; ks, one of t h css being a photoche.raic a l re a ction vec se l. The so l ution wa;.; f rozen w__;_ th liquid air an. :.,. the s ys te;n \ W:l.G ev a cu j.t f d by means of a Hyv a c ln€;chanical p urnp . It is do;...btful ·.vhethE:r t he part ial pre ssure of air the system was reduce d bi:. low abo'...lt 1 mm. 01· mErc u:cy. in The tl:'.•ree interc0rm.1Scted fl a sks W€:re t he:n s ea led off fro,n th€ vacuum 22 system; the s ol ,.1tion wa s allowed to melt, was mi )l_ed by shaking, and transf'er:red t o the s ma ... ler fli:i.sk s, approximately half the i:.0lution g o ing to each. The smaller flasks were then sealed off from th€: re t: t of' the syetem. per:t'ormed in se ~uidar.kness. All the se operations were The: photoc hcnic .,. l re dction ve ssel, which :n.ow c ont ained half t h e s oluti on, was transf err ed to a thermosta t and, after a suit able time h a d ela.psed f'or temp era- ture eq ..dlibrium to be re cJ.ched (about twenty 1:ninutes) was exp o sed to light. The flask c ontaining the oth er half' of' t he solution, ·which was t o s erve as a blank, wae: kep t in the dark at apprGxima tely the sa:ne te mp era.ture during this time. !d:'ter th€ exposure to light wa s comp leted, both s olutions v~ere cooled with ice. were trans:ferred to glass-stopperE:d dar k bottles; c,'.l. ch of the sol..1tioni.; was tht:n an.al.: sed for bromine by ti tra:t .1.1,.g a i'ew cc. Lqual volu:11es of the t wo crornine s :Jlutions v,,ere now ll1€a.s--'red out wlth a p i pet and s hak ell v,ith 5 cc. o f 1 N s odium hydroxiae s olution until colorle!; s. The a queous extracts were dili.1tEld to 100 cc. and separa.tEd from the organic material. The~e op erations were also carr i ed ou t in semidarkr1ess. ~:> .:i.nce the amou.r1t of Lrornine in thes e extra cts wis insuff i c 1errt t o ,yi eld a conven ient amount of .silver bromide precL.:ita.te for r adioactivity measurements, 25.0 cc. of 1 N sodium bro,nide (non-radiaactive) was now added to eac r, sulution. This w~s f ollo~ed 23 by 5 cc. of 1 N s ,_;dium nitrite. Each s ol ution was made slightly acid w... th nitric acid, b oile:d, and made allc.1l inE wi th 5 exces s of' 6 N a:mwonium hydroxide. Cl• Silver nitrate solution was added and the resulting .fJI' <: ci piti:.ite 91· silvtS:r bro.miue prepared f'or radioactivity measurem~nts. exchange h a d occu1-rE:d was c a lcuLated from the rel.:i.t.Lve elE: ctroscopic a ctivities of equal w01ghts of the prec.1 1.:.1.tdt (: s prepared from tbe nbla nk" and from the £olution ·which had been ex"':osed to light, c ..:,rrected tor the difference, if any, in th e. :.aea.sured c once ntrations of bromine in the 11 blank'1 and the 11 r€action 11 s olutions. The photoche:.nic a l re action cell h ad the shape of' a flat cylinder ,:ibout 2.0 cm. thick .. nd 3.7 cm. in diameter, with a glas ::: s ide-tube which l:ierved for filling the cell :.l.nd also for the accommoda tion of a md.gnetically o,:.; era ted stirrer. The retAction cell was suspended in an a i.r therI.fw~t -"-t and illumi• nated with ·the roughly collimated bea.;n f'r or11 a 500 w£nt tungcten lamp rumnng at 100 vol ts. of the r adiation e,:nitted by the l a:.uy e ntE;red thE collimdting system where it was pa :. . sed through a f'iltu· trausrnitting chiefly in th€ s pE:ctr al region fr om 5000 to 6100 ~$l..• No mea£urements of the amount of light absorbed in the rE: c.tC!'tion cell were made, :ror r eas ons which will a ppear later. A test of thE; technL:,ue was made by c arrying out a t LE:rmal exchaqge re;_1ction in th e s .:. 1. int way: the solution ;,va s prepared 24 as :for- the photochemical ex_uer-imtnts and separated in vacuo lnt,o two parts, one of which was im.medi : 1 tely subjected. to the extraction process described above, while the other wa.s kept in the dark at a high temperature :for a Ci.Jnve Eient time bef'ore receiving the sa..me tre :,tment. limin:iry experiment s , the rad.1oactivity J1eas.;r•em€Lts indicated tha t no exchange beyond ttl€ limits of' experimental error h .id occm·red. • Nevertheless, it w-1.s not found pos ,, .J..bl.0 to repro- duce the res1.1lts of the:: .;)hotochE-;nical experin1ents ., and the attempt to study the photoche.Hical re a.ction i n detail v,a@ aban- doned because of the excessive labour involved in each ex; erir.aent and the d . . ff iculty of' doing precise work wi t,h the speed necebsi tated by the short half- life of r ",dioactive bromir1e • If further w0rk ie to be done with this reaction a set of' c onditions will h ave to be found under which rate :..rieai:l ure ;11ents can be ma de, a nd so:mE; improve i.ae 11ts in techLi que 1Nill be required The dlf.ficulty in reproducing thE' experiments may be ;,b.l"tly due to a d1f'f'erence in thE: concentra.tion of CClsBr in the t'Vlo portions into ·whlch the original soL1tion is divided, corresponding tc tl:te observed difft::r·E.nce in the corresponding bromin6 con.. centrations. This eff'ect may l,e overcoinE o;y- proper temperao(ivi.sio'1- ture equalisation in the system in which the ,·e;rYu:-a1.tie11 16 made. The need for and effectiveness of the tre :.tment for the removal of oxygen must also be studied. The experimental results glven in the follov;ing tables indic ate that a photochemical exchange does occur, and that 25 under th0 c o nditions o:i: experiments 8 to 13 inc.L... t:dve it is pr 1:1.ctica.i..ly c omplete in th e time allowed. Comparison of exp erime:nt 2 with 6Xptriments 4 to 9 incluslve suggests a The resu.lt of' e xr.; eriment 3 is probably due t (> sume gross experimental error. Com_paris ., n of th€ 1·esul.ts with one another irn:iic a tes tha t in expe.r·imcnts 9 d.nd 12 exch.'.::.\.nge was probabl.y 100 % c Gm;)lete, and thd t the experiment,.:.i. l error is of the ord€r oi" 15 %• Res\lts of Exchange Experiments with :Bromine and Tr1ch1orbrornmethane '11'.nerma.l Experiments Ti me IQ%, Cone. of CC1 2 Br (min.) -) .± 10 10% Cone. of Br 2 Temp . 00-. 4 7 .± 10 Cone. of :Br 2 in Experiment (moles/liter) 250 40 Apparent F.x- Est imat ed. t ent of zxUncha.ng;e certainty Reaction Solution {moles/liter) 0.62 95° 10% (perce~t) 0.36 0.82 9 .± 10 in bli¥}k (moles/liter) l o.6 50 2 11:;0 0..3 1.c-0 3 l i;:,4 _;'f:; 0. 0824 -3 .± 10 0.0032g 70 0.00320 76° 4• •The s ame tech."1ique was u sed in this exp eriment a s in the photochei.nica l exp eriments r:-- C\l Time of ex- Apparent 'e> Photochemical Exchange Experiments with Bromine and Trichlorbrommetha.ne Cone. of CC1:l:Br 0.0035 --·- -- ·-----0.0412 0.039 o.ol-i,o 76 76 30 30 oc 20 75 25 160 40 light (min.~ 971., 86% 98% 11% 4/ii 86% Cone. of :Br 2 in 5* 0.008 0.0063 0.0324 76 20 100% tent of Exchange 6 0.0054 0.0033 0.0206 76 40 S5% Temp. posure to 7 -----0.003g 0.0206 76 25 100% Experiment 8 0.0034 0.0037 0.062 100 86 (moles/liter) 9 0.0033 0.0036 0.040 100 Cone. of Br 2 in blank (moles/liter) 10 0.0031 0 .. 0048 0.039 reaction solution (moles/liter) 11 0.004) ------ (,f 12 0.00:;l The light u.sed. in t h is experiment v;as not filtered.• 13 • 28 Summ,iry : - The results of' this s ection may be -sw1.m.iari sea. as follows: no defir. . i te ev .i.denc € w.:oi. s f ound for the oc cun.·c nc e ot· thermal isotopic Exchange of brominl'.: betw, , en bromine c:ind trichlorbrom methane or ethylene ditromidE: in CJ,rbon tetrachlori de s01;...Lion. A thermal exchari..ge betwe0n bromine ;i.nd ars e: nou.s bromide or stannic bromide, and a photochemical exchange between br-o.;nine and trichlorbrom methane -were :found to occur readil./ ln c : .U'bon tetrachloride solution. 29 Part 2:The Hate o:r the Heaction bet~n Phosphorus Tri:f luorige a nd Chlorine. Many years ago Moissan (8) discovered that gaasous phosphorus tri.fluoride combines in glass vessels w..i. th chlorine according to the equation PF::, + Cl2 -· Pl1'3Cl2 Tt.i€ reaction ·was later studied by c. Polenc (9), w.r.o was unable to find any othsr products .J.nd demonst1... at t d ty Vf:ry r0ugh volUJ1e measurements that the re·-~c tion appe a r s to go to co,:,pleti on accor-ding to the above equation a t room tei.nperature. In the present report are presented the res 1.1lt ~ of a study of the kinetics of this re action, wl1.i.ch was investigated in the hope tha.t it might be birnolecu Ltr. Unfortun,3tely for this hope, the reaction proved to be heter ogeneous. The phosphorus trifluoride used in the se experiments was kindly prep ,.red by Prot·. Don M. Yost L·y a method w11 ich he has described elsewhere (10). The purified mate:cial was obtained as needed :from a l arge Pyrex storage bulb through a stop-cock. l,1oissan (8) has shown tha t in th E- presence o:.:. a trac e of \tl a.ter vap our phos_pboru~ tri£ luorlde attacks glass ra.e;ldly ; since the storagE: bulb used in thE',Se experim€nts shuv.red no €Vidence of such action even af'tEr several months, the gas wa s i-r ob a bly quite dry. CommercL.1.l tank c hlorine was used.; the gas vvas V1ashe.d with potassium permanganate s ..:. l ution, pa.'6se<i through 30 a long calc :..um chloride tu.Lie ~tnd v,as condensed by means of' liquid a:Lr into s mall we,,ighed Pyrex bulbs with cap illa:r·.y tips. 'I'.h~ .ce•?iCtion was followed in a.11 a.11- gl.::i.s£, syst bn by preBsure .ne:::t.SUl"E:ff1ents made: by ra£ans of a glass diaphragm ''clickn gauge t:ack.td by a mercury manometer . lxper· imE:,nts 2 to 10 :.Lncl\.-1sive were: made at 0°C accor·ding to thE f'ollovd ng technique: a Pyrex reaction vessel, wi106e volume w ,s iJ.bo:--<t 300 cc., was ev ~cu at .ed by means of a mE.:rcury dif'fusion pump to a pressure of' 10- 5 m:11 . while being baked a t 150°c. /\. dry-ice trap was interposed betwe en the rEact1on veosel and the 1;umps. The connection t.o the p.J.rnps was then clo sed ot:f by si1 e2m s of a s top--cock, and a s amp le of phosphorus trifluoride was ir~troduced from the st,orage bulb into the reaction vessel and its cormecting tubing, wl;.ose volume v.as aLout 30 cc. 'The prei.rnurE:, of the g ;;.S a t room te:mp€•ra:ture Wd.S tLen m€asured, and the sample w:.ts c 0nde nsEd by means o:f' liquid a. ir into a smr.ill side tube sealed into the re ,:1.c tion vessel. A glass bulb containil1g a known weight ot· cb.Jorine vD . s then croken with a ms.:,gnetic ham:11er which was loc a ted nea r th e r&aC; tl. -011 ves s el as part of· the connecting tubing ref€rred to ; i 0ove. 'l'be chlorin€ diff'u sed into the reaction ve.ssel v.here it was condensed with the phosphorus trifluoride. measure:nents st1 c,wed that a.11 the chlorine h.a.d bE:en c ::>,i.dE::ns ed the rciction b ,.llb was se::i.led off fro,n the rest o:L the : :i.pp;'lratus and the reac tants were- a llowed to evapor,:. te into the re action vessel which vc ,s inLnediate1y surrounded by a.n ice 31 bath. The re1... ction was 'the1.;. followed by means ot' pressure mea burements. The initLil pressures ot.' the re acta.: at.s were calcul,:.1.t td i 'r0m the initia l ly measured pressure of' pho.i-,p!.orue trit'laoride in the reaction vessel ano. its con.riection~, , the known weight of chlo:rir.e, :,nd thE, ac:curately knovm volumes of the reaction vessel and of its cormections. The vapors were aBsl.llfled to act as perfect gases • .After the completi on of' an ex1.:.er iment the products were c onde nsed in the sio.e-tube which w E1.S then sealed of'f . It was observed that the c ., ;:den.sed products on war1ning up to room temp era ture f"ormE:d a liquid which rap idly atta(ked the glass c ;:;nv:i. ining it; smaJ.l :flocks of :flui'i'y white material Degan to a Jip e 1:J. r in the liquid ::.1.nd increas~d in a.,U(1unt until 1.,1. thin a f'ew hours the initially cle r liquid co ntents o:t the tube were r-epL.. ce<l by a gelatinous mass v~hich \-\.. s v.hite or yello i.·. aepending on whE,ther phosphorus trii luoride or u·;.loJ·ine hrJ.d b€en 0 The nature of present in {;Xce.:,s. in th(:. reaction rn.ixtu:ce . thib rEaction vo.1s not investigated; its occurrc:nce m,:.Ly indicate that a tra.ee of v-1atEr va or was pre bent. Polenc ( ~) observed that dry g ;tseous PF'aCl2 does not a ttack glass uoticeably a.t room te;rr;,era·u.u:·e ; slight etc h ing of the 1~ec1.ction V€ss el used in thes€ ex1_;er·iments t L .e ,1oticE·d only .,.f'ter : :.-everal r t,llf.;; had b c(·n made, eacr;. extending over s,e·v erul days . 'Nhen the re a ction ve. 2sel w._.. s opened ::Jfter a run a faint cloud of smoke usually i ' ormed from the hydrolysis of Plt'aC l2 32 wr...ich h a d. rwt been frozen out with liquid a ir . rea.s-on the l'Ei ,e:tion· ve s sel wa s washe d w1. th d:i.Gtilled. ·wa ter 'l.'his prec a \.ltion '.IVJ.s n ot ta.ken between r ·uns 2 and 3; the hy drolysis :>r o6ucts p ·e s ent on thE: ,Mills of the r-e a c.:tion vess€l acceler ~':. t E:d the re action in ru.n 3 con• siderably. tt.1. s,t from 20 % to 50 % of' the reaction o<:c\..i.r-:ceo. l>Ei'ore the f'l rst pressure measurement c culd bs ;:n ade) presumably because of a rapid r·euction t -~ ki ng place in the liq uid iJh &..6e ·r.;.h ile Ult re a cta.nts were evaporating f'r :>m th e side-tube in which the:,,· h :.i.d b £.E.n. c 0r.d.e . s cd togetL er. This r ....;,,id reaction in tiH:1 l i q J.id w,:.s also observed. .l.n a separ a.t 12 isxpe 1·imu1t in v,,hi ch chlor.i.ne a nd excei:iis phosphoru.e tr .i.:fluoridE.: wer€ c.. -- hd E.n s ed together in a sma.: ll gla ss tut-e which had bEen evacu;:1.ted. disappeared V d 'J r a pidly. Th .,t p art of' tla. re _,ction v1Lic:h c o uld tie f'o11o l: E:d by ord er wi th re spect to e c1ch rea ctant, with a SJ: -ec 1:fic rat e r oughly prop or t i ona l t o t h e s r1ecific s ..irfa.ce of the vessel. In order to study this l a ttE.r e: ff ect th E s ::;;)e cif'ic surf':.1ce 11va s • d• v . cI'.l.E: .c .trom a 'u out· 1O• c. v cm . -l t o or- . '7 cm. -l , tl1e 1 arger value b eing obtained with a re a ction vero Eel p ;;,c kE d .,, .... th thin gla~.s rods over wh ich thE g.1se QUS c cLte r.ts v.,e:::·e c irculatcd 33 by means of a glass piston with an iron core aetuatr;;d. by a eol0noid. Some a ttempts were made to V :i., ry the n .J.ture of the surfa ce: in ex;.- erirnent 9 the reaction vess e l w~,._s r.1.nzed with a solution of ;, ot:::i, ~sium ch lo ride, d.r ;_ ined, dried, a.mi b,;i.ked in va c uu.111 in exi:;eriment 10 th e inside 01· the r eaction flask was silver-ed ch,.:;:aical Jy and treat ed with c hl or ine to leave a c oating of s1.J.ver c h loride, ': c. n d v,as then ri r.1sed wi th dlstilled wate r , dried, d.nd baked under vacuum. ments 2 to 10 wi1.l be d iscussed l::1ter J.nd tl1E:. techn iq_ue used in c .:.,.rrying t hem out will be rtferred to a~\ th€ "first technique 11 • V/i th such a 1 lrge: p.irt o1~ thE. re.J.ction occu.r·riug in the liquid ph c1;e it a ,;_-)p eared un likely th-:1t it \'rould be p o.s.~ible with the techn ique ju;;., t de:scribEd to st0.dy th e re .;1.Ction in a satis f actory way ov€.r♦ a \,ide r ::.r..ge of i n iti:~l. p rE•.::; s11r1t::s . Ex_;_;,(rimE,nts werE· then c arried .,ut ut:.ing a rea ction ve ss el A c ·. . ,..vcuie:nt, W.l. thin v/hich tLe ch.lo:r· ine bulb CC·Ul cl bE: broken. 1.1L1o unt of 1:il.t ,)Sphorus tr .l.f'l u;)ride vh:.S _;_ ntroduced into the pre ... vi ously ev ,-.cu:1t(:,d r e.> ction vessel and c 0r::.densed in a. ,. l.de-tube. Th€ reaction vccs81 wus then sca led off i'rom tl1E: re.st of' the app.9.r:1tus i.ind the )hosphorus tr ii'l..10r .i.dE -wn.s a11ov.'ed t.0 eva- porate . arournl t he react-ion v essel. by meuns 0:f p u llcyt-, ann a counter• weight, a.nd t hE i11.i. t.iaJ preBsure of phos _phoru£ tr .:i.f'l-. .wrlde ~'he gla ss 1:ulb c cFl :lining a ·, E,ighE·d a ,.aou.nt of chl orine VL i.S broken, :1nd th e initial pressure was :.neas~•td as soon ae the chlori ne h ad v ,:1r;; ::irised. ln t:his cast v cr'J little 34 r€action occurred bei'ore the first pressure ;neasure,.;1ent w.:.tS made; hsnce the whole course of the reaction could be i'ollo\'\ied . Unf'ortunately , hovH3ver, the expe riments carr-i€d out acc:ording to this proce dur e, were much less reproduceable than thosE made with the firbt technique, possibly because it w_-.s now lm;.•ossible to L .tke out th 1,:! re 1 , tion vess€1 since it C L,Lt , .. ined a bulb of' l iquid chlorJ..ne. Ii... small and variable amount of water remaining adsorbed on thE' gla.st, surfaces ~ua;y huve bE e:n responsible of t-hf. s_p~,c1.fic rates anr.i in U1e ct1ar .:.i.cte _ oi' tl-:.. 1:; kin€tics . Th € .spc cil'ic rates mE: :a.su..red at 25°C L,y t .Li.is meti:...oci , and calci.~l.,.: i. ted on t.l:1€: t .:lsi.s of a r a t € :f 1.rst order 11v i tJ.. :r-E:s p0: ct to E.cach r-e ae:tant, v~e:;.-e co nsiderably smaller 1,1:.an t.L:i.v,ii, e measured at o 0 c by thE first t echniqu.e; to ascertain ·whE'ther tr1e aypa.rent IJEg::t.t;..ve temp er ,n.t..u•e coe f f iciE,nt was eLtirely u0.e to Ll.1.c change in EX_p eriment :1 1 _procedure an e:xp erime1:1t ( No. 15) using the S€ccnd technique v,as run for• a time at 25°C d.l'.ld the temperature W :::tS the 1~ l,:)v.;ered to 0° C, whereupon the rate o:f re 1-: tction increased In th t sa;ne exf1E.r irnent the; watt elEctr:Lc light a nd reflector p laced ad.j~cent to the reacti on vE.ssel; tlHi rezu i tar,t incr E ase 1n s :. E. C .:.d'ic rate all other exverimen.ts made -WLtl,. either th€ f'irst or sEc <md technique, the re :;:1.c ti on VE;ssel was protected fr om light by means of a black cloth. 35 a re iKtion ve s sel wh ose inner surf\ice was co at ed v;ith .,.Jd..rd.:t':fin. In this cas e the decrease in pre s sure wa s very slow, ..:::.nd may well hav e been due to re a ctions othcl' than thE. c .Jmbination of chlorine and phosphor•us trifluoride. This result indicates tha t the rate o:f the homogeneous re action is n egligible c 0mpared to that of thE: heterogeneous reaction at 25°c. In the :t'ol J.owing table a.re listed the te!:!1perature, the initial pressures p 0 of' the r€,acta.nts t and the average apparent second order r .1 te const .nt k...i, an average o:f thE v .il ues calc ·~ la ted from point to pcint by means o :i. th l expression _ -1 A i) . c o.tumn . ' . .v . .. k -In the .neac.ed k2 'care t.~Dulat t d ----...--; "' P lo -1+1 3 Pc--2 I t:,. t _ the values of k 2 divided by th1.: spec if' .i.c surf'a c e (here V is . ' ) the tot a l volume o1 th€: re :-:1ction vesse1 :1nd. ~-, its total sur:face.) The extent of' the devi a tions :from a sec und order r tttt! EX-.i:- res- s.i.on is sh ov. , n in the cur ves in Figure 1, in which the rec ... pro- ¥ cal of k 2 ;:, is plotted against the total pressure P • l 'heee cur·ves cover the r ~':!r.ge over which meas . .tr·€:ments were m.,.de , a.nd may therefore be us ed to calcula te the fr ·.K tion of th€ reaction which occurred before pressure me.-::Lsureme nts were st J.rted. Additional in.formation of this kinci i i:; f'urnished bJ columns in the tablt which contain va,lues of' k 3 ranges of the reaction: averaged ovtr V. ;.rious 0 to 20 % completion, 20 to 40 % etc. A s tudy of' the table and the curves leads to th€ :follow- ing obs ervations: between exp eriJnents 2, 4, and 8, which were made in vessels whose surf aces had be€n tre .lted in a pproximately the sa.11,e way , 36 i.e. by was.b ing with distilled w~:ter ai'ter a previous run, drying , and baking wider v -.,,cuum. In these experiments the c unstant. during th0 r...in, .: aid ther~'. is :f"" ir .o.Ji:sT~ eru0nt oetween val.ues of k;;3¥. i'."ro;;n oni.:· f:'Xper► imen1, to another, ·though the .;;) 5.7 in experiment a. The rate theref' ore lilppears to be pro- portional to the Sp (".c1fic surface so long as the n ,ture o.f the surface remains the same. In ex;>eriment 5 , in which the fr reaction took pla ce on new gla.s 1J , the Vcl. lue of k 2 ..... is seen to ..:.. manner; in €!XJJ er.unent ? , in which tbE f:H.irface was 25 ¼i glass wh.ich had been treated as in expcr imEmt 2, arni 75;b nev; glass , tht C:.ll"Ve is S€en to Le i nte rmedid.te be t,wt':'en 2 and :.:;, and perhaps by c oinc i.dence t,o be v'2r-;y· IHktrly the curve wnic.h v,ould be obtained by uci.d:i..ng 25 % of 2 and '/t) % of 5 . 'l'b.E:0 E results indicate that the rate on Zl(;'W glass f' ol i owe a d1tt·erent SXJII"easion from th:~t on us ed :1nd washe:d glas s., and. that it c .:m be ref/ re s ented d .t. the presr:ur-es used as The reaction wao net studied over u. tuf:ficient r ,1nge of ini t i:1.l prf:: s1.:ureG to ullov, the sig• :nifie:..m ce of' the corw t .1nt " du tu tie dc-terminE',d. 37 P1i'3 Cl2 on the new glass &ur:t'a.ce. 1'he reaction appears to go f ,ister on a silve.r chloride s -u rf'ace t1.1a.r1 on gla ss ( Experiment 10). On the othEr hand t.:nc behaviour of the 1~e~ct.ion on gla ,s treciJ.ted wi t11 KCl (Lxperirnent, G) is surprisingly similar to that on glass treated a s i.n expe:r-imento 2, 4, ands. 'I'hils f.lict is in c 011.trast ¥Tith tht: results o:f Peae e (11) who found tha t the sar,1€ ti--eat• rne.nt of the surfa ce of g lae .s :reaction v E.SE,c ls w:i. th YCl decreased the velocity of oxida.tion oi meth,::1.ne bi a factor o:r' ten. The l ack of co r1.sis tency .among t,he result £ of· ·1_.b.e exp eri- serrt.ed at the e:nd. o:f th is section • '£ he occurreLc e of extrema • i; :..ng • • • S a.s a r••unction o.a.+> . +·•ne = curves sno~ the rec :i.procal o f ' kay .l• r·• tlH: totE,l pres s ure p indic •'3.tE'B t hat the d ,1ta. :for a.r.i,y one experi~ ment made with the f:-ec ond. tecl'tnique carmot bE fitted by a sin.gle tE:r:rn oi' the :fa:nl.LL,r U;1.:n.gmuir rate express.i on(.12) • n is ::..n integer which may a.s f, ume the v :-tlues ·r11:1,s last o, 1, or 2, and, the partial pre,osures _D--·-etc. are given in terms of the ,, / '.t' 3 i :t~itial pressures p~,-~3 etc. and t11e total pres s ure p by the .;.· · ,!.i equations: 38 In all the experiments at both_0°C and 25cc ( except tha t, in the pa.r 1f:f'ined vessel) th.& final p:r-ess;1re e.pproache:d within 1 :i the pt·es~m:re calculated for c cu:p lete reaction. No analysis was .:rH.we of the products. Becaus e of the d.1.f'i' .1cu1ty of even app1•,n.:i1nately reprod:uc.ingthe exp eriments unle.sfil, obsE:rv,' :itione were 11:::i i ted to only U1e latt€r p.art of the x·eact1on th€ ·~york wa ; .;. d:i.r;; c ,,nt.1nued. .No attempt "-'ill be made to discuss the :.u.echa:rus:n o:t' this a_.;<parently very co mplicated react i on on the b d. b~& of tJ1E- ,.n eaf -;t' E experi ment,al results reported here . 39 f,:;::l C: ,...,: ~ H •1±"'1 :ti ! ~ t:t . H ,- - l L ~ C) N ft. " ~~ - _,_ ·- ~f .l. T' :; ..... ~~~L t 40 .. '. n ·I J__ -i- ti I T ' 0 au ~ (X) rn + : ±~ r •, ,____j ~ - & 1·0YI Y1 j H c :ct: ·! +• H c+ mt:1+ i-+ ::j: 1....1.. t-L l- ! ti' r+ ·t -+--'--4 • _., +A"·i I: - L t ... :~ -lttj:j:ff;l:!:I ~ Cl 2 po k2 v/s -l V~lues of k 2 during the reactim: Rate of the Reactien between PF 3 and Cl 2 "'3 Ppov _g;g -~ -1 ~t (cm-moles sec-1) 0-20% 20-40 16.3 22 17.g 40-:,-0 22.7 1"'- -7 26 17.8 ,0-10 86 21.6 15.2 33 17.2 70-80% oo l 18.2 24.2 89 108 T-emperature cm4 moles 0 16.00 15.00 13.2s 14.0 l .1• "lJ 113 '' 0 16.28 19.6 Experimen t ( cm. Hg) . 2 0 17.20 l:;,.75 14.26 16.90 19.56 16.49 PPFa Pc12 3 4 0 14.35 21.2 41.2 6.26 k2 ~ - ,.I~ 0 17.52 18.58 21.40 15.9 6.32 (cm.HF ) sec- 1 7 0 20.so 19.7g 6.61 ~-15 5.50 6.1 19.6 g 0 18.16 5.63 6.3 12.16 9 25 20.03 6.4 i:;_ 1g.2 29.s 10 25 26.44 9.45 27.30 16.06 13 0 11 12 25 21.0 17.11 32• 14.5 11 6.39 5.61 5.9 30• 16.6 ~ ..: 6 ..,.; 5.26 6.o 13 . 19. 3 .,,I . 13 21.60 17.11 230 . 19.2 14 25 25 21.6o 17.11 0 ',)t- 22• 6.6 5.17 6.08 34 to 43 13.8 15 (a) 25 21 .. 60 19.5 16.0 15•(b) 0 25.0 12.5 15** ( c) 25 16 • Reaction Vessel illumina ted with 100 watt lamp. ••Rea ction Ves s el cooled to 0° after startiug experiment 15a at 25°. 42 Nll,ture of the Surface of the Re,1ction Vessels Experiment Specific Si:rface 2 0.90 Washed with distilled ~ater ai'ter previous 3 0.90 run. l3aked O"Ut Coated with products of hydrolysis of phosphorus halides from No. 2. :Baked cut. 4 0. 90 Treated as in No . 2. 5 1.63 New glass. washed -v'!ith cone. 'HNO:;p distilled 7 i;,: 71=; .)• '.) water. Baked out. Vessel from No. ~ washed with distilled wa ter, packed with new glass rods which s/v = arn-.i Trea t ment of Surf'a.ee :Before Reaction had been washed with cone. HN0 3 and 8 ~. 75 9 0.90 10 0. 90 11 0. 95 distilled water. D,.ked out Washed with distilled water after experiment 7. :Baked out. Vessel from No. 2. rinsed with KCl, drained, dried, baked out. Vessel from No . 2, coated with AgCl , washed with distilled water, baked out. New glass• washed with cone. HN03 • distilled water. Not baked out. 12,13 0.9) 16 Washed with distilled water after previot1s run. 14,15 o.9j Mot baked out. Coa ted with paraffin. 43 'rhe addition reaction between phos 1:!hor-us tr:i.f1 \. wride and chlorine t :~kes pL:.tee very r-:. \p:i.dly in the liquid phase in gli~; -;, s vessels, and in th!i: g ;1~s phaLe procee<..\s pract.Lcally to by tht f ollo ~-.ing observations: 1) '£ he rate in gle..ss veesels is approxiiwcit~li pro• than one-tenth as great as in a 01.mi l.--. .r glass 3) 'I'he reaction on glass appeI.:i.r- ::~ to .hdve a negative temperati..lI·e coei'f ic:J.errt, being r v -.lg.r:. ly tw.ice of the glass, Th@ r ate o::C th(, g .is reaetion at 0°C in k;iass r-e:Ktion - ~tO)F3) :::: k;;Ci?:B'a) (Cl:i) wherE: Q · V s/v ib the BJH, cii'ic su:r·f "'l ce of t h0 re i c::tion vest:; el a.mi k is a pproxim.i.tely 20 :noles •l cm SE:C -1 • by this Et.i<..:pre bs ion, pos s ibly becauce v~i t:b. the technique 4 44 emp loyed in the exJ; eri1i1 entsrthe re dction vess el c cu1o. Lot be I temr,er ature r p.p.i d ly attacks glas s. 45 Par·t 3:- A Theoretical Discu Hsion of the Liesegang Phenomenon. In 1896 n. E. LiesEigang discovered that i:f' a pr€ici . p ita.te wam, i'ormed by the dif:tus.io:n of one reage nt into a gel which c ontained th1:: s e,c: ._,1 ;.d re agont, tb~ precipitate in m-lny c ,lses wa.o discontinuous, occurring in a series of' discrete layers or b-:J.nds. This phenomenon, nhmed after its discoverer, is al&o kno~vn as ttperi0dic 11 or t 1 rhythmic" precipitation, ane1 the discrete bands are ltnLwm as nLiesega:n.g rir.i,gs'1• A qualitative explana tion of' the eff<:lct ·was first proposed by Will1elm Ostwald ( 13) , who s uggested th .'it the ph enomenon is essentially due to the formation in the gel of supe·rsatu:r-ated s olutions which become w1stable after a certa.in limiting sup ersaturation is rE.ac:hed. He a hH .;, suggested tLat tL.is 11mi ting supe r·saturati on i s char a cteris ed by a limiting valu i:.:. oi· an ion c,;,ncentration pr oduct, similar in form to, but gre ater in magnitude than the solubility· product of the substa nce being pre;c .Lp i tated. Since Omitwald' s suggestion a numLe,r of' alter ·nat1ve theories h av e: been suggested ( 14), involvi ng ads or ption of so lute from the: gel by the newly formed precip itate (15), or pr oposing that the fundarnent e.l process is not crystallisation f'r vm a s upu·- saturated solution, but rather inv 0l ve s so:ne l imit ing c oncentration for the coagiJlation of a c olloidal s c·l o:f tJ:1e prE·CJ. 1;;itate (16). .i\l though there i s evidenc e thd.t t li.e se :factors may ,.J:6 bee ome im1,orta:nt in s,pe c ial c ases , it the b.J,sis. of Ost¥,i a ld' s suggestion , wh ich wil l ac cordir.igly b e made the basin :Cor the w·ork presented her E. !,f ost quant i tative stu.d ilfrs of the ph enoi~1enon have been c ..,nd ucted in tl1e f'ollo¥\ing wa y: a 1ong na 1row tube i s filled with a ge l c 0nt a ining initially a c o:nstant concentration of one re u.ge1;.t v~h ich we may call the internal reagent. This ·tube is di 1)ped into a bath containing a bo lution of the second re ~ent which is allowed t o dif'fu i e into th t tu1'.ie. caJ..l t Lis r€agent the entering re agent. I ts c ,:.>nce ntr ation a t the entrance t.0 tht t0.Le is kept c Oi,S t ~nt t ·,1 st ... rr ing and by th e u E;e of a s u:ffi cie·ntly l arge v olw:nE: o:f solution. To lnsure uniform results the s ys t em mu:c:t be 1,rot ect Eci aga .lnst variations in temper .;;.tu.re and in l ight intE:nsi ty. Under these conditions the fo llowing e C:;_ u.ations are f ound to hold.: (1) x.n X n- 1 (2) - K - constant wherE xn is tht~ clist ,r,nce f'rom the endof thE.: tub e in c: 0nta ct v,ith the ,. elution to the n'th ri ng , and. t L~ i s the t.ime, measured f rom the b eg,.innino- of the e x:;;eriment , wt1en the r i n ,1 y :first beg inis to form. -~ ~ ~ This time can be prE:cisely measured; the ring a ppears suddenly as a very t hin ·band w..·., ich tlH:m grows 47 1.n t h ickness until the :nex t ring :forms. The i' irs t of the equa.tion-s just menti.oned was developed theoretically by Morse und Pierce ( l?) who tested i •t in a series of painstaki:ng experiments a nd obt ained excellent. agr e erne.nt. The second is an empirical relation wh ich wa s suggE:sted by Schleus sner ( 1 8 ) and by J ablczynski ( 1 ~). The object Gi' th€; present discus :-s i on i s to present a derivation of e quation (2) and to show hov,. the value of K de p E: nds on thE, othE: I const __ ,. nts of the ring £,y s tem. Let us con.sider t he diffusion of the ent ,~ring rtf- age:nt f'rom a regi on where its concentr ation has th e constant v alue C0 into a long t1.ibe c ontaining the .i nternf.i.l reag ent whic h cm e form a prec i ;: i tat€ wi tl:1 the enter i ng reagent a nd is initiall y at a wdforrn c oncentration 0.? t hrou,ghout the tub€• l. - and Ci be the v a• .i able concentrati ons of the ente:cin6 and inte:r·nal r@.'!l.g cnts res , ectivel.:i- within the tube. th€; Lett be time mt:'.tsur€d from the teginri.ing of the experiaient, and x th€ dista nc e measured from the End of the tube wl:iich i b in conta ct wi th the enter ing reag ent. 111 accord:.:¾. nc e with the experime nta l f'act ths,t in order to p:r·oduce ring syste:.ns :for \;. hich e quations ll) and (2) hold true it is usually necessru\y to use a low initial concentration of the inter nal r ei:ig 1: nt an,J a rtlat:lvely hig h c oncentration of the entering re agE nt, we sha .l l re s trict our discus - si on to tht ca ;,_ e where c0e .,,,,,, ''- Coi. It then seems reasonable to a.c sume t ,h .,.t immediately preceding the formation of a. r ing 48 the concentration 01· internal. r ea.geHt at tlie place wr~ere the ring is to :form i s not. very d.iffc:r~,nt from the i n itial con- centration Ci; this assumption receives eupport from the exp erimentrtl work of' Eugh(l;S (20) who h a s conduct ed qua.n.ti.ta- tive 1.il.tii l.)·ses ox· thin sections .o f gt ls in 1,vhich ring sy$ t ems were f 'crming. Thr assumption which we shall a ctually use will be c0nsid.eratly ;nore dra,stic, however: we assume 1) Th@ concentration o:t: internal reagent at the place whe:r·e a ri.tig is just a·bout to f' urm has a critical value C\ \lihich is co.n.st,.m t for .al l the rings in a system formed witli. given initial c0ncentrations of reagents, a nd is not ve rj' different fr om the ini tia. l co nce ntration c1. 2) In accordance with Ostwald's the ory, \';e a@i:jume that v1hEn preci ~.i tation occurs, tha t so.r:nE: :function of the concentrations Ce and c1 has ;a c-:n1sta.nt value" 'l'his ass umption combined with ast:umption ( 1) leads us to state that for the· :formation of' a ring the entering re i.il.gent ruust also be presEont in a critical c 0ncentr:1tion Ce wh ich is constant fo:r a.U the rings in a g ive n s;ystem. c1 h ave values such that J u Gt before p:rec.1.i!i tation occurs that a c0nsiderable degree of supersaturation exists. 49 >> that Ce C.\, so that the formation of a ri:ng ·w il l not seri ous ¼ affect tht:; d.11':tusion of' the entering re,agent. We assume fm""ther that t.he d iffu.sion of' each rea.gE:-nt o1:,eys Fick ' s dif'f'usion in equation 2 TI .: : 11) , with a constant V•i'.tlue of' the diffusion coefficif:nt D, though this c0e:ffic ient is kn0vrn to Vcu•y with the concentration. We may no\lJ visualise the process of ring formation ,vi th the h e:, l p oi the:: fol :_ o·-,'J; ing cur·ves in t;hi ch the conct::. ntra tions Ce and Ci tire p lotted as functions of x at clif'fe:t'ent times . In Curve I, prEcipi.tation is about to t .~kE: 1. ll...1.ce at xn_ 1 ; in Curve II pr€-cip itation has oc:curred and the concentration of internal re ugen-t at xn•l has fa.:len pr ..ctical ly to z.ero . i\ large co1:;.centration gradient has b~e:n set up causing r;.1,.,ld diffusion ot internal reagent from the surrov.ncUng region to _:\.t the sar!le time the dii'• 1 , where it i f• prGcipitated. f'usio:n o:f ent,ering re .s.g~r.. t is S (',ffi€\', hat disturbed; Y, € shall x 11• ignore tb,is E:f'fE..c:t in our quantitative c vnsiderati c.,ns . In Curve III the diffusion of internal re ,i;l,g ent to Xil-l has continued for sc:ne timeJ the disturbar1ce ln th(; dlf':fu::don of entering reagent c i:iused b,/ ring formati on has s,.uoothed i tse11· It is evident th,J.t one of the f\.1.ndamEint al causes of tho discontinuity in the p:cE cip i tate is the great di:ff'erence in the dif fusion gradients 50 I I I - :t I C,:. 1/ ')C - x.- 51 which c ,:.;ntrol the diffusion of t he 1·eagents. af'ter the f \ .ir :m fation of' a ri ng, 'the abrupt changii: i n the C(Hl- cen tr<J.ti c,n of internal re agent c auses i t to o.i1'fu:::; e toward t h e new r ing so r a -',J idly tha t a reg ion beyond the r1ng i s depleted of' i ntermil re a.gent s ui'f :i.c1EntlJ t o r,revent spont ane (hiS pre- It il6 only d.f'ter some ti me, wh~,n t h e L trge c oncentr•a.t i on gradients h ,,J.ve been s moothed out , ti1&tt t he entering rt:;a.,gft nt is able to 11 CJ3ltch up 0 , s o to ep eak , v.i th tlH intern.a l re a.gent and again bt• ing about prEcipitation . With this picture in mi nd we m;ay now c ,tI'r.Y ,,ut a.n approxi- ma te ma t.t.e.ma.ti.cal treatment o:f the process . On th1: ba.s i e of our a s sumption ( 3) we may set up the follov;;iz.ig b s1 Lai.df.lI' ,1 c ondi - tions for the diffusi on of en.etering reagent: C e ;:; Ce ::; - o, X ~ o. co for X ::: o, t > o. e 0 :for t The t olu.tion of F ick •s equation for the:i:;e boundary c oLditions is shown in the theory of he ttt c cnducti on to be : 2C 0 00 e J 'J:~ .,,,....=x- (3) 2Jn e t where w is an integration variable . If' t·or t he :f0r mat:ion of each r ir;iY C == Ce = c unst ant , then the lower l i 1;,1 it of i.n.te• -= e gration must be constant and we obt ain 52 This iz the equation of .Morse and P ierce and vtaB obtained by them ty- a similar but in eome respects incorrect treatment .. 1.nation made ill ignor::tng the in:f'lui::nce of preci_pitation on the di:t'fusi on of' entering reagent. Ot.1 the basis of assumption (1) and our q_ualitatiV€· dis• lovd:ng a.pprox.imate boundary conditions for the dif'fusion ot' the internftl !'€ 1gem.t iiuring the formation of the ( n•l) 1 st :i:-ingi C i Q ;.,; C i The correa:ponding solution of the dif'-fusion equation valid in I 2.JD.,(t•tn 1 )' .j. (4) .- o where n is the diffusion coef'i.'icient o:f thE: inteornal reagent. 1 In accordance with asfn.1.mption ( l), wh€in preci;;i tation 'l'hen 2C<? 1 Tr, I Q dro 53 Substituting in eq~ation (6) for tn and tn-l in terms of :xn and xn-l' by the use of' equation ~ 1) , v,,e obtain (7) = ~¥-f- k2 This is the empirical relation of' Schleussner and Ja"clceynski (equation 2). 'l'he most precise experimental data available see.m to be tho s e of' Morse and Pierce (17) on the formation of' s.1lver chromate, rings by clif':fusion of silver nitrate into g eliilA.tin gels contain.L..n g pot~ssium chrom~\te. values of k 1 , ki a.1.1d K calculated :trom their data for a single It appears that ka is c onstant -within the precision of xn .. xl'l•l. In Table II is preeH:mted a list of th€ values of k1, ki and K calculated from each of the experiments o:f U1orse and Pierce and in Table· III a.t the end of this section the mea.ri values of these constants for given values of the .initial cone entr·ati ons.. The experimental values of K are also co1n- pared with the V!;ilues ca.lculat0d from equation 7. It should be emphasized th .:i.t the relations presented in this discussion have ·been develope:d fox· very spE:cial boundary C(mditions . 54 Table I CompilECl from Morse and Pierce I s D2:i.t a: ExpEr-iment 2. . 1 d.if:Cus .1.n,g into gela.ti11 c onta.1.ni.ng - 1-J K2CrO~ 75 t sec. 1.5g2 2. 88 o.537 124:5 o.675 1420 0. 6 11 1607 ,) .649 1825 0.694 2068 0.7:-18 2345 o.?85 2ob8 o.834 :3000 0. 888 3395 1.06 2 o.940 ~~82:4 1. 058 o. ss,s 4305 1.065 1.056 4 842 1 .12s 5443 1.188 6102 1.2so 6870 1.071 2.64 1. 524 1. 034 2.65 2.bO 1.518 1.520 1.523 1 J• ✓ 17.0 23 21 22 20 16 19 i~15 12 11 9 17 18 10 8 0.00333 0.00333 0.00333 1.0 1.0 1.0 1 .. 0 1.0 1.0 1.0 0. 50 0.50 0.50 16.0 0.00333 0.00333 0. 00333 0.00333 0.00333 0.00333 0.00333 • Valu e not 1:, sed in computi.ng means 15.5 1Si•5 o.. , o 0.50 0.00667 0.00333 0.00333 o.oo667 0.00667 0.00667 0.00667 0.00667 0.00667 0.50 0.50 1 .. 0 1.0 1.0 16.9 17.7 16.6 16.& 17.3 16.3 16. 7 16. 5 1~ -,)• 5 16.6 16.6 16.7 15.7 , I; 7 2 16.1, 1.• 0 0.00667 0.00667 0.00667 2.0 2.0 2.0 2.0 16.3 16.3 16.0 in gel (mol/ i,) diffusing into gel (mol/ t) co Cone. of K:i?Cr0 4 Oonc. of AgN03 :t' 5 6 3 4 E¼p er iruen t number 1.299 0.9165 0.9120 0.9132 0 .. 9094 0.9094 0.9331 0. 9309 o. 9333 0.9276 0.9339 0.9274 o. 9334 2.. s1 2.81 0.9444 0.9450• 0 .. 955 • 0.933s 0.9411 o.93s5 o.9 i;:, 0g o.. 9512 0.9-515 0.9514 n X 2.76 1.335 l.J13 2.g1 2 •.g, 2.78 2. 76 2 .. 82 2.so -:,C.:• 7ll.• 2. 7~ 2.61 2.·S9 2.26• 2.02• 2 .. 63 2.65 2.67 2.68 2.69 2.63 ~ •.63 1.311 1.292 1J+;3 1.477 1.468 1.466 1.467 1.462 1.~62 1.377 1.3S4• 1.549 1.533 1.523 1.524 1. 700• 1.663 1.671 1.656 cm. sec.- 2 ftD- tn-1 /tn 1. X n-l X 103 ...!,t:! X X 11 _L X 102 X Pierce on t h e formation of silver chromate rin;:::s i n ,i'e1 a:tin. Calcula.t ion s based on da ta by Morse and Table II 01 01 56 calcuh;. te·d from equation (4) wi 11 be t oo high, th'G e:rx·or increas.- If. this ratio is in the neighborhood 01· o.5, however, e(.':.uatio::1 (4) should a ppronmate the· correct f'orrn :f'airl~/ closely and the error will be partly of' ka a.cc ord.ing to tl:ie me thod to be describsd lat€r·' • the othE:r hand Ce<., cl t lie probl(:'lf11 i s iJTUCh !Jl0?'€ Ii' on dii':ficult th:in the: one treated hH'EJ , becaus,e the dif:t'uai on o:f €:nter·i.t;g reagent i s much mor e serio 1.1sl;y· disturbed. be available no precise data for a c ase oi' r1.rig f'ormatlcn in whi ch Ce <. c1 ; and it iSe 1Em,1:1- probable that 0uch data would require a different treatment fr orn. t h,J.t given here. I t will t he c ,,nditi on C )) C. is ruert. e J. In c onnection wi th the disturbance oi.' the di ff ... sion thd.t an equation equivalent to equation (6) oi' the prestrnt pc.ii.per- ha.s been developed t.1y Bau,~r (21) on the basis of the c o:rrections ·d ach must be a pplied to th e: d.if':fusi u:n of tl:1e ent~r ing reagent in order to ace cunt for the €1'.t"ects o:r J;;trEci.p i t ate f' or:m.;.11 ti on. A complete trsa t rnt-nt ought to t dk.e .i.nto acc ount t,.oth the ;present results ,;ind -c,he results of B~UE-·r 1 s work. Such a di scussion bee 0we s vers cun:ibers c:me; moreover." the expE:r imental results 01· Am:non an,~: Ammon ( 2 2), -who s·tw.Ci.i ed by me-ans of' indic a :..ors U ::.e di:ff'usion of ruu;:rionia into a gel in which magnes.ium hydroxide r ings ·w er e f' orming , may be inte rpreted 57 as showing that ·t.he d.:i..sturbanc es :pr t>Ci.u.ced bJ p:t·eci.pita te :fvrilllll.• tion tend to sm-coth t:bi,mselv12s out in ;::;uch a ws:y tha-t the diffusion 01· ente.r·irig re: ai:(S nt may 'be represented by €:(iULltlon 1"1...t (3) vii th a dii'i'usion coe:fficient De larger th.tn "ch.a:r· ..:~ cterlsing unhinde:rEid diffusi .:m. ot' our own asal.lll.l1;ti 0ns ty calculating v ah.es of tJ::1E. c1· i tica.l c •::mce n trci tiuns Ce and I II. <\ fr-orn thG val .... Ee of' kJ. ru:.d k;a in 'l'able As w s•.S mentione.d ear li~ .. ·, the dat::.i i:n Ta.bl<i:· III are for bands of silver ch.com.1-.it~; un the b1.:i. sis of Osti.vald' s ideas It i s f'irst necessar'.Y to calculate the diff'usi on coe:fi'i- cleLte De. and D.1.; this ·we may do by a rnethod first suggested ..I. by 14oree and Pierce ( 1'/). From the values of ka in set ~ 4: and 5 of 'r&t,le III it fo:i:· the formation of ei!\ch ring, is ('.O nstant, S .J,il€: function of' Ce and C\ c\~ i-zi also the Sarne for the two Sets. tion of equation (3) leads. to 00 I 2 ~ ,x 10 1.466 ·-..- 58 2 :x o.so (8) ..Ju This relation ie satisfied by a value of De :;;: 1. 7 8 x 10· 6 By us€ of this const ur~ ~ e has been evilluated for Each @ ,et of experime:c.ts listed in Table III, the v .:~lues so obta ined a.re there tabulatE:-d. 'l'he calculation of Di m,;11.y now be c a1•r·iEd. c;u.t i.n th~ same way , using t he v o.l i..:.o&s of Ce and k 2 from sets 2 and 4 of 'l'ab"'le _a Substi t uting in e,.iua.tion (5) and afisuming Ci\ :;:; H = III. C~)IlSt ,. 't.N€ obtain .( l • Ll,~·2·. 5 X A'.:31 X . (•l •v... 2 ) a ( 3 3n 10• ·, · •· ••. ..:" X 10• B) 1 () .. 2 ) 2 ( O ·- •O~7 • X --1 0"'3) .i.,1 ... e:• w aw J' (9) 0 -h G . whi ch is satisfied by D,J. ::: 1.28 x 10 . . . c .m"' se,c pa:c€s f'£Avorably with the• v :i lu.e 1.1 x 10- 6 -1 • '£his c: om• .f'or potass.:i.um d.ichro- rna:te in water a t l6°C as eetimated from V,';l.J.ues in the Internatio:n .~tl Cri tica.1 Tables . Using this c onsta.nt the v du.es of' H c\ and of the product = c2e • c1. have been calcuL1ted and are listed in Table III. The value of H appe ,tl..rs to be reas onably const,u rt.. Since the assumption of consta ncy of H was made only in ev a lu,::i, ting Di 59 from sets 8 and 4 it a;}pears :frcrn th€t results :for Qets 1, 3 ;and 5 th~tt tirn data are- consistent with this asst.uu1;tion, A more complete test ovE:r a wider range of' ccnct:ntration ot: both enterin •. g and internal reagents would o-f co Llrse be desirable . The mean value of H obtained is 2.88 x 10· 7 mole.s 3 litres ... 3 • Hughes (20) has obtained the value 2 x 10... 7 by direct expeLi• ments in which increasingly dilute aolutions of silvc,:r nitrate were difi'used into a 5 % ge la:tin gel containing dilute J) otassium chromate until no prE·ci r itate was observed to :form. It will 6 l;)e noted that the v::tlue o:t' H here calc·iJ._lated is atout 10 times I f :further e:x-per•ime:nts i r:.c.ic.:1 te that the c 01:.St.,::ncy o:f E has a real significance it ~N::.i uld be of interest in the study of supersaturation ;·,herwmena to eva luate H for other preci_p i tates G1.:nd to study th€ effect on H of such factors as lJ.ght .1ntEansi t,;,r, natur£ and conc~:ntration 0 1: t he .gel etc. I t will l:e SE E:n that the va lues of Ce caJ.c.u1ated for the ex; ,eriments of MorsE· and Pi€-rce ,].re ttpproxi;:ucl.tely five to ten times as grea.t as th€ v rtlues of' c\' so that in this res L.;ect at le:::.1.1:.t the conditions are ftivor able for the, p:c€D£nt treatment. 'l'he fact tha.t thE: r ~:. tio c\/ci is in all c ,,.1. 2 e: s about 0 . 4 , however•, It should be worth whi 1.e to attempt to obtai1:i Etq_ually ,tJrec.is e data for cases in ,/Lich C w':'l.s more ne -n rly equal to or less e than and to investigate whether :for this c a se equations <\ , (1) and (2) still hold. 60 The treatment here presented is of' c o (..,rse far :Crom complete . 'I'he assu.mp4lcn cf· the: c ;.;nstancy of c , while it a"').i.,ears to be 1 c -. .-.1.1s i sten't, . with tht d 2:i. t a , seems so:nEr~~-hat arbitrary and should be d.erivab1€- fr---ra a thor ,:.:,ugh tre a:t.mcnt o:f the dif':twsion pro·· , f'or precipitation is c eP c1 q > R . An interesting r elation which ~LY ha ve some: b~t:irl.ng on this possibil.1.t.1 can be derived in thB following way : ue a sEwue that Let after the :f ormat ion of the ( n.- 1) 'st ril':l,g' that pr12 cipi tat.ion next oc curs where the product c,/Jci q is a But thE, va:J.e of x where prt.cipi- maximum vii th respe:ct to x . tation occurs wi ll bG -"n_, a:nd Ce' Ci v.: .i..11 h ave the cr1.t i cal Vct...i.U.E:S -Ce , -C . • i Then (10) or ( 11 ) Differentiating eq_uat ion ( :, ) wi th re s pect to x and rn:;.lti1>lying by x, And f'rom equation ( l ) , a t .1.£§.) xn ( ~ x • x=xn = X = ~ and t ... t n 2C% .. -,..,,ro - k:{ e ~ -~~-e ~ De t (12) 61 Similarly di1~:fere:ntiatiri.g e quation '1. , mllltiplying by x - leil:•l and applying t h e c ondition x == ~' t ::: 'tzi, v;e obtain by the US( of :equation (7), (13) 1C Substituting in (11) from (12) and (13) to eliminate 1 l C. l0 x1. 1;,;e ob tain ! - cc. 0 1 - - ~ 4Di e k2 .Jn e ~E; 1 ::: ------kl, xn 0 4De p r_,•i.c-e e k.1. .JD.,~ Xn- 1 and ( 14) This is a more explicit 1"'orm of the Sc .c1lE:us sner relation (equation (2)). The term on the rJ..ght hand side can be calculated for Niorse aild P ierc€c 's €xperimen.t.s with the aid of' the qua.nt.i. tie::s tabulated in Table III, using p :z 2 and Xr1-l The calculated a nd observed values :t'or♦ l ~ are listed in Table IIIand agree mrly v.:611 V.ii th onE. a.11othe1-. ma_y c onclw.de th~t the hJ,pothesis that ring for 1nati.on occurs . •) qat a pcint '"q,here the product Ce r C.i is a .;naxJ.:nu.m is not inco.usistent with the more detailed a.ssurnptions mad.e at the Vi e beginning of this tre atment, and. that it may be puss..i.ble to derive the; latt<2r,.:fr om the former. 62 Table III Ci X c.1., x 10 3 103 --------- --··--·---- -----" ,.... E;xper imie:nts 2.0 6 . 67 l i ~.:/0~ 2.66 1.058 2.68 3,4,5. 1.0 6.67 1.532 2. ;.)5 1.031 2.67 2,7,8. 0.50 6.67 1.377 2 . :) 1 1. Y.:8 2 . 63 18 ·1 ,., _,_.v ~3.83 1.465 2.79 1.485 1.40 o. r:; o 3 . 13 1.~110 2.ao 1. 4 14'1, 1.40 r; t ic . X 10' e 1 C-1 -:::0 \., { ,4 "n-1 l•- xn --. X,~ •l- 1 l.•-- xn Oqu . 14) (Obs) K ~1 -X ,, . 1 (Equ. 7) .... K = ~~, l~, l~, 13 l19,20, 21 1,.,, , lb , lo {..~2 , 23 . 31 X Experiments n-1 <.ObsJ 0.401 3.00 0.053 0.049 1.052 1.051 3 ,4,5. o.4oo 2.84 0.002 0.058 1.062 1.062 2,7,8. 0 . 394 ;3.,94 0.075 0.005 1.(174 1.070 18 o.419 2-84 0 . 066 o.069 1.075 1.074 l~t 1~, l~;: l~O, .L4,lo,lo 0 .420 2.ao 0.021 0.088 1.096 1.oso ~9,~0,21 {22,23. Legend: Units of' C°e ' Ce .:; 1noles Ag NO~ per- litre. Units of c1, c1 - moles F--zCrO., per litre. Mean value of ii.::: 2.88 x 10- 7 mole: 3 litres- 3 Difi'usion COE:i:i.1Cl€Ilts: Tl LS - 1.?8 X 10· 5 cm.& sec:· 1 Di .; 1.28 X 10- 5 c .1.f 63 Conclusion: I t has be:en p os si ble by meam~ o:t' s .;;:i1e; perhaps r a t h a· arbitrary as,:;um1.: t j_o ns to c ar ry out a trr,at mcnt of the Licsegang u.ra tion .pnenorneno n on the. b a sis of Wi : helm Osti;vald.'s sm'.)ersat • the ory. This treat ment c a1 i ot: co urse r E<:u.liJy be e:xt ended to c a ses otber U vu! th, s e involving supEcreatu.ration of crystallo:i.dal sc,lut.tons; for exi-. l.mple the knov-r1 exa,r1pl es oi ' Lies egang ring formation invo1vJ.ng p€riodic coagulation of' colloids can no doubt be dlscussii d in the same w.3..y. 'l'he pree.H:;nt trea tr:nc-nt c an h Ltrd1y be regarded, however, as a f undai.nent.a l one beca w, e of the at:1 hoc nature 01· the as ~u.mptions i nvolved. A tre at ment t ,:i.s00. on a satisi\:.i. ct 0rily general postu.la tlona l basis i s yet to be e:a 1·ried out . 64 Part .4: A Theory o:f the... Chromatographic ,Agsorption of a Single Solute. The technique of the so~called chrom,;1.to6-rra::/hic adsorption method of an a.lJs.i.s wa :.:. origirn1ted by the h u r sian botanist M. Tsv;ett (23) in H:106. He discovered tiLi.t if' a solution con.. taini:ng a mixtu.l"e of colored f;olutes is allowed to run through a vertical glas s tub€ packed vfith a suita ble powdered adsorbing r.naterial, ~ a partial separation of the constituents of the solution t ;. ikes place as shown by the occurrence of' a series of colored bands of the v arious solutes, form€d by adsorption on thE, yowdered material. This series of c 0lored bands is knova1 as a "chromatogram". The separation c8l'l be further increased by gram'': .i process known as "development o:f the cru--omato- there is poured thr ough the colurrm a SLLi.ta ble 6olvent which washes th€ colored bands down the tube at dif:t'erent rates, the· lowest-lying bands moving thi.:: fastest. In this develop- ment pr.;:,cess the segre~tion of the: various s olutes :..nto indi .. victual bands becomes more complete; i:f the process is cd.rried out in a sufficiently long tube wit h thf.!l use ol' a suff ic..i.ently large volu:11E: of solvent it is pos ::: i ble to e:frc ct C1Hiplete separation of the .d .nitial constituents of' the solution into a series of discrete bands sepa.ra.ted by c 1ear spa ces of adsorbent. 65 The technique just outlined h a s bec0me .1:n. recent ye ,;;;.r s a very important method for the separation, pu.r..L:fication and identification of small amounts of complex naturally occu.rr ing org,J.nic compoundsf these developments have bt1en ,:described at length by Zechmeister and Cholnoky (24) to who s e book the reader is re:,:f'erred for a more complete discussion. Although the nature of the phenomenon S E E: rns to be quali... tatively fairly well w1derstood (24) ther~ has be:zen carrJ.ed out so far no quanti tat iv€, trE:atment by which even an a 1>proxi ... mate prediction could be ma.de of' the width or of thf.: r a te o:f "development" oi.' the bands to be: expected in a g1.ven cr.;.romato&ll~am. The present treatment grew out of' a desire to be able to make such predictions in order to decide on the basis of known adsorption isotherms ·whether or not a given ::i.dsorbent might be expected to b€ useful for carrying out tht chromatographic separation of' a given set of subetanc es. It 11-as not eo f'ar been possible to c ::trry through a c omplete treatment; there will be presented here however a tentative th€oret.ical discussion of the: chromatogra,Jhy of a. single substance; it is; evident th.at this simpler problem must be solved be.fore the much more complicated .:iroblem of tlH~ c t,romatogTaJ_)hy 01 mixtures can be successfully attacked. Let us c unsider a long c 0lumn which c ontains M grams of adsorbent per centim&ter of its lGngth; we wish to calculate the distribution of adsorbed material in this c olurnn after a 66 volume v of a solution containing a solute at au init.ia.l concentr-ation C0 has been poured through it. We shall assume that the rates of adsorption. and desorption are much greater than the rate of' flow of solution pa~t any point in the tube so thr.:.t equ.1.librium between solution a..11d adsorbed materia l is always maintained. Let the isotherm which represents the adsorption of the given solute on the given adsorbent be q/m = t: (c) where q is the numb€r of millimoles of solute adsorbed on rt1 grams of adsorbent and in equilibrium with a solution whose concentration is c moles per liter. Then under equilibrium co1;cdi tions at any pQint in the c olu:rm where tl1e c onccr1tration oi' solute in tit€ liquid phase is c, there will be adsorbed Q milli.rnoles of' solu·te per centimeter length of the c olu.;Hn, where ( 1) Let the distance from the top of the column of adsorbent to any lower point in the c olwnn b~ x, and consider the changes in Q and c wl1ich occur at x when an element of volume dv of solution, whose conc€ntration at xis c, passes through a thin cross-sectional layer of the colu: .nn, of tlu.ckness ruc, on which is adsorbed initially an amount Q dx of solute. The number of millimoles of solute adsorbed on tlns layer will change by an amount ( ~ S)xdv dx, and the concentration of the solution will change by an amount (.ti) dx. ~ xv Th€ number oi· millimoles of solute cont .dned in the volwnt dv of solution will therE:fore 0 67 change by an amount ( ! Eut f; lnce matter is c on- ~)v dx dv. served, we: have 0) x dx ~ C) v dx av " ::: ('.) ( i~ ~ • dv + ( Tx Substituting for Q from equation , 1) of tlu.s section, we obta ln as the di1':ferentia l e ,:: uation f'or the fundamental process occur·ring in the chrom,1tographic adsor ption of' a single s ubstance (2 ) The general solution of this equation is c == IJ { v - x'M f' ( c) } where /J is an arbitrary funct ion and f' (c) is the fir st derivative of f (c). This equation will appl.'J to €:.i.ther the pro- ce s s of :formation of the chromatogra.rn or t he process of d.e-velopme:nt. Different boundary c ondi ti-.;ns will , however, a pply to the t wo C ii.s es. Let the cl:tromatogra:n be formed by ) ourir)g a v olurn.e v 1 of solution whose initial concentration is c 0 through the column, 'I'he approprLtte boundar.1 conditions are: ( 1) When V1 = o, f (c) = 0 for X ( 2) When vl > (3) V1Co .. o, f {c) = Jo A "'1. ::; dx = ~ o. (4) f(c 0 ) at X = o. (5) (c) dx. (6) - Jo M f The last is a conservation condition. The s olution of the different ial equa :_ion for t his case has been found to be 68 F'or O f: x For x ~ ___v_i__ M f 1 ( C0 ) > f' (c) (7) = ThE> discontinuous nature of th:1.s solution acc-Junts satisf~actory way fo:r thE sharpne;: 1.: c:hromatogra,,h ic exveriments; 01· the bands produced in solution is also in accordance tl1€ with thE: experimentul observation tha.t the intensit.Y in the band is uniform ( Q = M f a .Lil (c0 ) ;:;i 01' color c onstant) • 1'he solution (7) was discovii,red in an indirect way: The problem was tre ated not b~v difYerential methods but bJ a method of finite differer~es. For simplicity an adsorption isotherm q/m r.: Kc was assumed, ar.).d the column of' ao.sorbent was co 11side:red as being made up of' a succession of' thin layers 01' thick11Ess ¾ The volume V of soli..ltion of irn tial concentration c 0 was con- siderE:d as be.i.rig divided up into a number of' small volumes vim. The first of these elements oi' volume was now aJ.lowed to pass through th€ column of adsorbent step by step in su ch a way tlut eq 0..1librium was reached with each layer before the ele ;uent of volume passed on to the, nE,x)!:, layero The am.ount of solute adsorbed and the cha nge in conce ntration o:t' solute in t:he e1€ment of volume w.:::.i.s calculated for each step. The cal- cu.lations were repeated for the' similar passage of a SEcond ele:ne.nt of volurne, takirig into account the conditions lmposed by the previous pa.ssag~ of the :first. This process was con- t.i.nued until the whole volume V h ad b ,, en passed through the solution in this stepwise manner. The total a.mount of solute 69 qnm. adsorbed on the n 'th l.:J.y e.r- ait&r the passage of the m'th element of volu,ne vim could then be expressed as a S€ries: •• n(n+ll = sn-. i.mn . l 2J ~~ :t.:_ 12 ,1 + ma. .... s ~md. 1m-l} l +s and.Mand Q have their previous significance. Eli1ni nating s by mea:m, of' the e .x.pression x ::.: n.1 an expression s was obtained for ~,n = Q (V,x) Q(V,x) :::: tom terms { 1 + m Kmx \ n { n v) where the factor inside the square brack1,:;t.s is to be expanded by the binomial' expansion, the first term be,ing l, anc. only the first m terms are to be retained. To o·'bt,ain the solution to the problem it ;i.s then nE:cesr,ary to evaluate the limit of this ex) ression as m and n tend to inf'lnity, where n is HOW t h e r.tl.lmbEr of l ayers of adsorbent fr 0m the t jp of th€ colurnr.1 In order to reduce the problEim to a limit to the point x. in one parameter, thE: phys ically made that.!..n'il ' ., - .-:!.. where ax reas onable assumption is a. is a constant. 'l'he result is 70 f,i( x, V) = Lim ill ... (I,) _ I\11flc 0 ~ te m terms ) max (1 + KM)V a 'l'his limit has app arently never been ftvaluu.ted and its evaluation a ,;pears to be very difi' .1.cu J.t. Ar i t lil1letical com.1,,u.tation b asE:c.l on the Eixp a.nsi 0n h ov,e:vn:· s r..ow ed that as m Vid S given l arger a1;d l s.rger V .:i..Lu.€·s, ~ t he solution a_;,_iJroa ched tile form r, '-i:., ('\ 't = KMc 0 for 0 :::: 0 for X ~ X f V KM V > KM • 'f his indicatio n , c ombined. with the g enera l. s olution given in equation 3 ~ suggests t h -:Jt the s ,.'.i l u.tion for th e. given boundary c onditi ons should bt, gi ven by equations (7), d.!ld. thesE: are .indeed found to provide a sat:i.s:f,,ictory s olution. We ma;y now c onsider th e c asE. in wi'1ich a band al.ready .formed is ffdeveloped" by passagE t hrough th<:, column of a volume v 2 of sornE solvent not necessarily the same as thE: sulvent us1:;d in forming the band . Let the ads orption isotherm. for the 11 c1eveloping'1 solvent a nd the given ads orbent be, for the solute in question, q/m = F (c) (8) We shall assume tha t the band was formed in acco 1·danct with equation ( 7), i.e . tha t up to some po1.n.t x = x 1 , ·Q = Qo = We may a.lco write ( 0) 71 where cJ is the concentration of' solute which would be in equilibrium with Qo in the new solvent, and is not necessarily eq u.al to c 0 • The boundar•y conditions to be appliE:d are as follows: l) When v 2 = o, 0 2) Wh 13,n Va ~ x ~ x 1 , Q ; Q0 - ::; lA F (cJ) > o, at X :;;; o, Q :: M F' ( c) = 0 J0 M f ot· v 2 , 3) For all valU.f)S (c) dx :; = constant (11) J...0 (kdx = constant The solution of equation ( 2) f'or these c-~;ndi tions is Q == o for O V < x < ~ ;-_rt:•,, tco'i i'.li! li" \ CJ ) ana' for· x > x1 + .:vw V G (13) We reach the conc l usion the:n tllat th12 b 0.nd sh ould remain sharp during the process of develop.ment and that its width should remain constant as it .m oves dovL. the c ol~i.mr.:.. mentally the first conclusion is verified; the second holds only vu·y approximately. relations (7) and ( 13). It has proved di:ffic. ult however to carl'y out. c liroma.tograph.ic adsor ption experitnents in a qwliiti• tati ve arr::: repr(,duceat le v,ay. I t is a pparE.ntly .not e11s.i to utake th£ .s v :L i.itions :flow t:venly tb.rol...<\gh t,.he adsorber:.t: C faSES .Ln some most of' the flo\lii occurs adjacent to th€ wall oi· the tube wnich c ,. nf' inos the adsorbent ; v,hE,n thi.s 6.oes not occur flow is ;:no r e r ,J.pid thr ougL the center than through the out.er secti ons o:t· tl1€ column. (lQ) bither of th€se eff'ects causes the band$ to be widE:r than they should be according to eq_uation (7) and to increase in ,11 J.d.th as development proceeds, becaul-3 e the e:f:fective nwnber of' a-rams of adsorbent per unit length of' the column is (12) 72 decre-as.Gd below the va]lll.e which it would have if eff ectivE con- tact were 111.Ade bttween the solution and the entire surface of the adsorbent in the column, and varies moreoever from one region in the c ulunm to another. 11 Charmeling" of the column also occurs and leads to the same result. It should al so be borne in mirni that equations (7) and ( 13) were derived on tl1e basis of' an assumption that eq_uil.ibriurn between solution and adsorl)ed material is always llifJ.intained. If' this corn.ii tion is not fulfilled, i.e. if the rates of' adsorption and desorption ar-e not much more rar;id t,h~n the f'low of liquid through the tube, then the b tmd. :.t·ormed will be wider than it sh o~ld be according to ec_:,uations (7) and will increase in ·wldth as development proceeds . Furthermore in tl:lis treu.tment the efi' E: ct.s ot diffusion, v;hich will also t€nd to '"iden the band, ha.ve b , E.n nEglected. It should not occ asion surprise then if equations (? ) and {13) d ~, not ag1N:e precise1y v, ith the results of e;q:;eriment. Nevertt~eless a f ev, ex.1;:erimental results have been obtained ,.~'fl in,.agreemEnt with the relations given her€. For instance the band formed on f; ouri:ng 20 cc. of a. solution of picric Elcid in alcohol tr,rough a column of alumina. was 2.0 mm. ·wide; the v,idth p1 ·c dicted er.. th€- basis of adsorption rneasuremu:i.ts was 1 . 8 mm. In other cases however the observed width of the band has diff en:'. d fr om t.Le pr-0:dic:tE:d width by as much as ( l :factor of twoJ "channeling" of the adsorbent w J. S observed to occur in so ~n€' of' these casts :i.i.nd maJ ha ve been responsible for the discrepancy . According to equation ( 13), the dist::..nce the band 73 mov€s down the tube during develo,rmHmt should bt directly pro ... portional to the volwnE of' developing solvent. This has been f'ound. to be approximately true (within 1~) in an experiment in which eosin bam1s on a1.u,nina. werE deve lo :ped by waehir.,g with ·. , ·, wa.tEor and in an €'Xi1erilnent in. which fluorescein bands on alumina were developed by -wash.u:..g \d th benzene. The experi- ments iNhich have bBen done so far on the chrornutography ot: sir,gle substances are so 1.nconclusive that no detailed data will be presented here. .A. satist·actory exp erirnentail.. test of' equations (7) and (13) has yet to be made. The treatment presEnted here appEars however to h ,1ve suf:f:i.c ient s.i.gnif'icance to enable one to decide from me,asured adsorpt.Lon isotherms whethE:r a given adsorbent may l"JE ex;y ected to be usef\11 for •' effecting the eeparati::m of' a given set of' sub st .;.nces. It has not y-et bEoen found possible to develOi> a qua. .. tita.tlve trEi , t n1ent for the chronv:ttogra;;hy of' a s ~;,lution c.:.:mtaining two or more solutes. The principal difficu.lty lies in the fact that wh t n adsorptl on occurs fr om a Bolution containing sev eral solutes t.he amount o:f a given solute adsorbed is a :f\ mcti.on of the c c., ncentra.tion.s o:t all. the soluteG J.n the It a 1_.pea rs morEOV"Er that no general rules are known for predicting the form o:f this function in ter;n&. oi' the. adr.orp tion isotb<: rms of solution:,,:; of the individual s ,.;lutes (2fi) • It is usually true, however, that the s.olutes with the stronger adsorbing tendency displace f'rom the adsorbent thosE W.i.th a wEake,r adsorbing tendency. I:t" a ctromatogram is prepared 74 :from a solution of two solutes,, the first of which ter,ds to adsorb very strongly on the adsorbent while thE sec vnd has onl.y a ~uoder-u.te ten.denc,./ t, ,.) adsorb, the formation of an ad• sorption ba11d by the first solute w.il.1 be pract;;_cally uninfluenced by t he presence of the sec ..nc. solute; the latter will however- be force:d t0 idsor-b bElo t, tr~E: for-mfr, so that a part:i.al. sepdl"'a.tion o:C the sub st ..ne: es wi 11 take .::-' lace vvhn:i. the chromatogram ie :flrst f'or11H::d. shc)uld b€' given a,ri::;T0x:i.ruate.l.;y- t,y aquation ( 7), a;)propr l :" 'tel.:,.r .nod .1fied to t ake intc ac count the d.isi;la.ctd. origin o:C the ThErE wi 11 probably be between the t ·wo bands a region where both substances ar~ adsorb€d to so;nc extent. On developmtnt o:f this ba.nd syst€m, however, tnere wi.11. even... tually occur separation into brands in each oi' wili.ch tht concE.dl... tration of' one adsorbed solut€ is ... nif'orm, as may read:.i..ly be se-en by carrying out a qLi.ali tative d.:5.scussion of the develop;ner..t of dn initially non-uniform band. of a single solu.t.e:: on t.r1E ba sis o:f th-c results of our previou.s, tre atment. Summary: tr€cttment of the chromatographic adsorption oi' a single solute has 1ea·J to results by means of whl.ch fa r Clugh prediction of thE. w1dth of" the a.dsorpti on band and of the rate oi' its migration during development can be ma.de in terms of th.€ adsorption i 2oth erm of the- solute . 75 1. For a discussion of' exchange react.ions of· hydrogen, see 11 Che:: mie der Dt:uter·ium vert.indungcn", diskussionstagung cter Deutschen Bunsen Ges€ llschaft, September 1S·37; z. :fur L.lE::ktrochernie: L1-4 , 1-98 ( 1 8 ~➔ 8). 2. '.' Methoden u. } rgebnisse der Anwtndung von Isot open in o. Heitz, z. f'ur Elektroch ernie :1§, 100-116 der Chemie 11 , (lS:19). ~). . :J:r 'or referE:nces to papers bea ri ng on the exchange r E:act.i..ons of arsenic and phosphorus, see the app.roprlatE: sect.Lons of the text of' t b is dissertation. 4. E,rbacher and Philipp , z . phJ'·sik. Chem. 11.176, 160-88 (lS~', o ) 5. R. G. Dickins on a.nd J. A. Leermakers, J.A. c. s . 54, 3 852 (1932) 6. n. a. Dick inson and J. 1.,. Carrico, J-. A. c. s. 56 , 1473 (19?4) c. s. §§, 818 (1934) ?. /1. . T. Chapman , J. A. 8. E . l.VIoissan, Arm . Chim. et Pl"1ys. (6) §, 4~~ (1885) 9. c. Po lenc, Ann. Chim. at Phys. (6) .:i1, S48 (1881) M. Yost g, 6 34 1.nd T. F. Ander s on, J. Chem. Phys. 10. .J• 11. r-. . N. Peasca: and P. E , Chesebro, Proc. Nat. Acad :3 ci. (U.S. A.) 14, 472 ( 1928) 12. .For ,:;:, discussion of tlH:: Langmuir r :. :t te expression .i.n .i. ts v arL/us forms f1ee. i::;c hwab, Taylor i-ifL, Sp ence, pp. 21 8- ~~40, v ~i.n Nostrand , New York, ( l t137). 11 Catal;;1si s 11 , 76 13. WilhG l in Ostwald, "Lehrbuch du allgeu1einen Chemie", p. 778 Leipsig (1898 ). 14. For a general summary see L. s. Hedges , 11 Liesegang Rings", London (1912). 1.5. Br a di'or~, bi och.em J. ];1, 29, 474 ( 1920); Koll. ..., , , ,, , ) 0'± 16. ( l "' A<')') z,l,t;;e, z. 30, • Dhar and S en, Koll z. 1,1, 270-f: (1823); Dhar and Chatterji, 2 ( 19 25) i ibid 49, J ? ( 19~10 ). 17. E. w. iitlorse and G. VI . P ie:rce, z. physik . Chem 45, 589 ( 1803). 18. H. Sc:l:il.eussner, Koll. z. ~, 338 (1924 ). 19. r . J 'ablczynski, Ko11. z . 40, 22 (1926 ). 20 . E . B. Eughes , .BiochE,m. J • 28, 1086 ( 10:?4 ); Koll. ~: . 21. H. Bauer , z . physik . Cbem. 22. E . and G. Ammon, Loll. i'll • 24 . 11 ggz, 145 (1S34) . z. ?3, 204 (lS~b). 1?sw€tt, b €r Deutsch . Lotan. Ges. 24, 234 , 316 , 384 (lSOt>); ZechmE·ister and Cholnoky, " Die cbrom-9.tographischE:: .\ dsorptionsmeth ode'l Vienna, Springer ( H.108). SEe also P . 1,1. JenDen, " Die Ledeu.\:,ung der chromatographisc ne;1i .·:.dborptionsana.l,yse usw. 11 25 . Dissertation, Technische Hochschule , Fre u.ndlich, "Colloid and Cap illary Chcnistry", p .200 ff. Lon do n, M€thuen ( 1926 ). 77 Sumrnary of Results Part l(a) MEasurEm~nt of the rate of the iodin€-v.-:.ta1Jsed exchange of radioactive arsenic between arsC;nious and a.rs0nic acids .1..dic::itts tha t the kinetics ol' thE reaction ar·e the sa~ne rem ote from Equilibrium as they ,1.re at equi libr 1U111. l(b) h o exchange of rad:1.oactive 1JJ.osphorus betvvEU1 J;l10sphorous ctnd vhos phc,ric a cids was f'ound t u o(C;UI' in either alkaline or acid solution. l(c) h a pld and comple:t~l' exchange, of rc.10.1..oact.J..ve bromine was :found to occur thermally betweE:n bromine arid stannic bromides , and photoche nica .,ly tE.tweu . bromi.n.€ and triclllorcrom rrwth:0.ne in c ~u>t:on te:traclllor-idc soluti ons . No measure ,i.ble exchar.ge v~as obs1;:r-ved to occur thermally between bromine and ethylene bromide or trichlorbrom methane in carbon tetract.loride. Part 2 The r€action between g !1seous P1"3 and. chlor:.i.ne in glass vessels is almost l •..•mpletE: ly hetei· ogc11Ec~s and has at 0°C a negative tempcrat;.:u•e: coc:::f..LCient. Part 3 An a.,; ,proximat e thecretlc al treatmer:t oi' tlle J::,ro cess of thE.: formation of Liesega.ng r:u~gs hab bedl Part 4 A the oretical treatmt:nt of' thE ci:,.rom.atogra.!',hJ o:r. a sl £..gle so 1ut€ h ,::a.s lE ,id to equati ons by means oi' wl1ich r,:,ugL pred:;.ctions caL be r,.r:1de reg ..rdir3g the Width of the bt1n(;_ f ormEd fr ..m a. g~ven volume of solution and the rate at which the band will be develope:d by a givE·n sol.vent . 78 Propositions 1. The mechanism suggested by a nu.r.nber of authorsK to explain the anodic de position of PbO;a f'rom a rapidly stirred nitric acid solution of plumbous i on i nvolves the; sweeping oi' p lu.mbous ions, by means o:r stirring, to the a:node, wh€;re they can be oxidized. It :Ls here proposed thJ.t this Jewett, J. Phys. Chem. 33, 1024 (1929); 'I'opelmann, 283 ( 1907); Classen and Eall, ''Quantitative Analy·sis l.Jy ElE:ctrodepos i tion. 11 2. A spheric,11 bubble in a dH:lectric liquid ~k .ill not remain spherical under th€: infl'...l.ence 01 a homogeneou.s electric :field. 3. The solution of· the diffusion eq1..1.at1.on su.gg&sted by :i.!Nersole and Dot...gh ty* is .invalid. 4. The critic a l temperatures a i:d voJ.umes co;nputeu for the vapore; of ionic salts by Lorenz and Eerz!tr on tb.c b c:1.s .1s of empirical equations are of doubtful si 8•ni:fic :. .:. n ce • Kz. an.org . Chem. 138, 3~0 (1924); Landolt•.B.Brnstein Tabellsn, Erg. 1, P• 159. 5. For a crystalline normal hydroc arbon, the sum of' the entropy changes occurring on fusion and in transitions below the me:l t..Lng point is a line- ,:1.r :function of t.LE; number 79 . of Cd.rbon a t o:n.s 6. L li the e:hain. The ef'.fect o:f pr·e s sure on th0 s p~c.1fic rate of a c:ht'::,11ical reaGti0n is ·well e:xpres~ed b,/ thE: cc;uation where ,1\ and B are constants independent o.f th€ temperature T alh ~ thE. prEssure P . pared with unity OV €r t ir~ce LP is no t rn,:g ligi ble comthe pressure range i..l~ua1ly invef:ti- g ?J.tE'd, it, \:,,,..., iJ1d app e.far th,tt thE, nE.g lect o:f CO.tlpr·ess.i.b.J.liti es in t.llE; theoretical tre. ,.t:.uE:nt by .Lvans 3.nd PolanyiK is 1...o t jLrnti:fied. KTrans . }'araday Soc. 81, 875 ( 1935); 32, 133~-3 ( 1836) • 7. The so -c alled quantw:a ;110chan.ical theory- of the i'oru1..::,tion of' LiE: segar:ig E.i.r:gs or periodic precipitates is oi o.o . . . b tful va lidity despite the opini ons of Christ iansen and Wulff , z . physik. Che:;n. B26 , 187 (1~;34 ) :3hernvakin, J. Gen. Chem. U.S.S.Ii. 4, 444 , 111? (1B34) 'V --·----· ·----- ?Hk iforov, l.!_ Chim. Phys . 32, 585 (1035); 33, 250 (1936) Micha.left' , t-J.i kif orof'f, anc".t Schemyakin, Ko l l ~ 66, 8. The obse1~ed relationK between the distance s of succes• sive Liesegan.g rine,;s from t he origin of the ring GJstem can be acc0unte6. for on the basiF of simple ascwnptions. Koll. z. 31, 347; 34, 838 (1824) 80 K. Jablczynski, Koll. 0. z. 40, 22 ( h:126) The sharpness, extent, and rate oi 11 developrnentn 01· the bands produced in chro:natog:raphic adsorption ex:pe:ri:.r1e:.nts can be accounted for in a semi-quantitative WJlj on the basis. of' thE: as.su.mpt.ions that diffusion is negligibly slow and that equil.tbriu:m bE~twEen solution and adsorbent is reached very rapidly comparE::d to the velocity of flow of solution through the adsorbent . 10. It is certainly true ~ i f n and rare positive .integers, ) n L 1 = 0 i(i + l)(i + 2) ----(i + r • 1) - n(n + lHn + ,gL--(n .:L!:2. r + 1 and it is rEasonable to suppose that Lim \ m -- -m(!> e.::q.)anded by the ] t.1.nomial expan- sion to m t1:.:.rms 1 ~ r .± but = 0 t'or (! > = l for ~ ~ g ive rEcsuJ.ts t ·or the ,JiE:J.E:ctric cor.staLts of 1:., ._,..._::ir .iiquids which, though they do not agree Quantitatively with experiarE f~ i r l ~r self-cocsis tE nt 3.nd devi!;ltE fro::11 E.xperLnent mt:nt/in a way vd:1ich can be qualitatively accounted for 81 on the basis of i nt ermolecular interactions. 12. A si:fiplE: gr-aphic ,Et.J 1oe tb cd c •~n bE: u sed to f 'ac ... l i t atE: the interpretat i -:m , by nwans of Langmuir' s a dsorption. theorJ , of the rate of a heteroge neous g a s reaction. 13. In ca J.culating the concentrati ons of rea cti ng i ons at any 1;oint in a ti tra.t:.i. on , it i.s. usually a dvis a ble t o use approximate met.hods. These r:!l£ t hods unfortun,itely becorne inaccurate in tlH~ vicinity of' the equ ivalence 1,:.•0J..nt. Ey mE.a ns of s.1.mp le criteria it may be decided in simple cases (euch as the t .i .tration of chlor i de with silver ion, or th€: titration of ·wea}: a cid s wi th st-ro:ng b a ses) how close to the eq uivalence p 0J..nt the a 1.Jµroximat.1. ons usually maci.e c an b e :.1pp lied to obta.:i..n resu. J.t s of' arzy- desired. 'iCC t..tra.cy. practical value. These cr i t €:s ri a h a ve pedagog ic and