THEORETICAL PRINCIPLES OF ISOTOPE METHODS FOR INVESTIGATING CHEMICAL REACTIONS

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• Document Release Date: February 4, 2014
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• Publication Date: May 21, 1959
• Content Type: REPORT

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THEORETICAL PRINCIPLES OF.ISOTOPE METHODS ?
? ; FOR INVESTIGATING CHEMICAL REACTIONS . ?
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S.. Z. Roglusky
Translated by:
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CONSULTANTS .BUREAU, INC.
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Technical Information Service Extension, OCkk Ridge, Tenn..
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A translation of:
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Tioreticheski'e Osnovy Izotopitykh Metodov 4ucheniya KhiMicheskikh ?
'Reaktsy S: Z. Roginsky Moskva, Izdatelstvo Akactemy Isiauk gSSR, 195.6, 614.P,
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AC.ADEMY OF scit.tvhis USSR
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INSTITUTE OF P1-1.YSI(.7. Al, CHEMISTRY
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? :.......THEO?RETICAL. 11.RINCIPLES O. F
.IS,OTOPET Ob. :*F R: INV ES Q AT ING ?
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CHEMICAL REACTIONS- '
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ACAD.EMI/ OF SCIENcES USSR PRFSS
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PREFACE '
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The'postwardevelopnieni.of chemistry ha's been inarked?by the rapidly increasing?importance of .isotopes
and isotope methods ef ttivesiigation. The time has gone when it 'might hay,: been possible, iii a .1thol?if timde.rate
size written by one,authoi, to present all the basic' infortnatibn on isotOpes and to give an account of their appli-
cations in various branches of science or.etictvin different branches of chemistry alone. A LharaLteristi: feature
of pur times is the ptiblicatibn and success of special inono.graphs and synipositinis devoted to individtial isotopes.
and sometimes e'veit to individual compounds, and of an exZensive specialrzed,literature on isotope IC( linigneS?
The' position is' much less satisfahory With regard to literature on the theory of the nnusual plietconn:na which the
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laboratory investigator imiets whetrusing?isotopes hi his Work.
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? ? I?have repeatedly found by?experience 'what serious obstacle's to the extensive use of isotope iiirthods in ,
chemistry, biology, and technology are pr.esenteri by ?an'inadequate acquaintance?ol Many resear: h workers with
the screntific principles of,isotope chemisiry?and by:i lack oF books which pres'ent thein sisteniatit auy and'eoni.-
pletely..The.research:worker whii first cbmtnences work with.isotopes' is perplexed by the ,iikestion of the adinis- ?:
sibility of the use. of isotopes ,as tagged atoms when the physical and chemical propertie's 1)1 isotopic 1 ompounds
are not completely identical. The Chemical effects:or radiations emitted by radioactive substaaes often appear
to him to.offeran inspperable obstacle, and he expects radioactive isotopes to have unusual ( lietnital and bio-.
logidal properties due to instability or their atomic nuclei. Having Overcome the'se apprehensions, the beginner
sometimes goes to the other extreme, completely ignoring isotopic eorrectibhs whe'n theemagnitude is appreci-
able, and entirely forgetting -the chemiCal effects of radiation.. Many disappointments' and. errors have be: n ?
caused by negleci of ?isotopic exchange. and inadequate understanding-of kts inechanisin and kinetics'.
It is pot' easy to gain a correct understanding of these matters' from the Journal literature, as it 'is very, ex-
tensive and mu'ltili'ngual. Moie.over.; many'investiga'tionsbased on statistical thermodynamicS and molecplar,
spectroscopy are difficult and insufficiently accessible to the: chemist.
A complete utilization of the possibilities of isotope methods in any given: field is' only possible if they are .
used in considered eoniunction .with other methods, and' With a thorough 'understanding of the field of application.
The present monograph is essentially centered on the, application of isotopes to itivestigations of the .mechanisms
af chernical transformations and of the reactivity orsubstances. Various aspects of this central problem of mod-:
ern theoretical chemistry afe being studied by physical chemists, organic chemists, and technologists, Its status .
determines to a:considerable extent the level of the whole 'of theoretical .chemistry. Tlierefor- s comPlete util-
ization of the ratent possibilities of isotope methods fbr investigatiOns of chemical' teactions simultaneomly re, .
quires a good knowledge of certain sections of isotope chemistfy and of the theoretical fundamentals of.( licrnica4
kinetics. Fortunately, we.have a rich scientific literatnie on Chemical krnetics, which?cont,ains ey.cellent Mono-
graphs, symposiums, and?reviews, and considerable attention is devoted to its theoretical principles in tbe new .
teaching courses of physical chemistry and in?the.latest editions of universi?ty text bmiks. A systematic presenta?-
tion of these -principles was therefore considered to be superfluous to* this bo6k. General problems of kincmi s' are
touched upon?only in direct relation to any actual problems of isotope chemistry under ciinsideration. A few ex-
ceptions have been made in the case.of prbblems whic.h haye been .inidequAtely treated in our literature on kin-
etics or which are usdally discussed withont sufficient attention to features important in relation to the theory of
isotope effects, This-applies to nucleophilic and 'electrophilic characteristics of exchange reactions, to the elec-
tron mechanism of oxidation-reduction reactions, and to the mechanism and role of tainctmeric changes.
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? Our 'fundamental ideas of chemicai?processes live been substantially changed by the discoery of isotopes
and their extensive use. Simple and complex individual substances have in most cases proved to be mixtures of
substances which;altheugh very'similar in properties, are nonetheless different and separable. What :liad been ?
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? foroit rly rt raided as a single chemical reaction usually proved?to?(.onsit of a stun of parallel reactions betweeh
lord? ides differing in chemical cbsup.osition. 'Comparisons of physit al altd ?physicOchemical properties of iso-
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topic. ithstan, es have revealed and clarified features in the 'structure of ( hentiCal compounds which are very sig:'
. tali( ant in r( lation to their reaetiv'hy. The concept of chemical change if.seff required radical rev)sion. The
'?. di (;) ( ry of Mitopes rev.ealcd :i new, formerly hidden world Of isotope exchange.processes, which accompany
tlu. usual : lie?itij?cal re:.ictio'ns, hut which ?rem also in total 'absence of the latter; Lsotopic processes are more
.1(iniit roils anti hied than elementary processes. Al the same time, they rtio in some respects simpler arid more
? ? ( .'nv( 'tient to investigate. For example, complkations which hinder measuremeni of .the trite rates of "elementary".
? r Ilk in ii al?rca( rions caused. by heat liberation are eliminated. Because di the complete symmetry of the acti.va-
? : lion bariier, the t al( illation of absolute rates of reaction is greatlisiinplffied, almost all processes follow the. ?
?(-iiiit .1 ineti( .law., et( A's, at the satire time,'all reaction types and i techanism's Met among'the usual?clicmicar
. pro? s1/4(s are represented in isotope ex.change,?theie is now a natural' tendeney to use isotope' eRchan'ge for study- ? .
. tug et neral t1iicct ions of the mechanism of chemical reiiclions, their kinetics, and teactivities of subgtances:
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. ? for x Ion.; 'time differences in the rates' or chemical reactions of molecules of different isotopic cornfuml-
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.tions w( re coirtidored a's a complication in work with tracer atoll's, which in some instances could be utilized . ? .
for' partial ?;eparation of isotopes.' The work of recent years has shown 'convincinily that smdie:s.of the magnitudes .
. ?of.loii( tit Isotopci orrections and of the effect of temperature on'them.can provide valuable and definite indica-%
. ?tions .i1 the ti,our( of?the determining stages' df various proceises, It is therefore to be expecsed that in the'ilear ;
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. flour(iiioasi nt irei itt pi these .corrections will berrime an integral part 'of every d4tailed investigation of chemieal
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. .? . I lie?posirion of isotope exchange and.isotope effei7ts ihstudies of cheinical processes, as outlined above;
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d( o?rinined ihe 'plan of present monograph.. The followiog are considered:. .' .: .
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? I. iliermodynainieal.is'otopic effects and differences. in the physical and physico?cherhical properties. of
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itioli( ides of.different isotopic c'Ompo.sition (( haptqr I and Sections I and II?of the Appendix). '? ' : . ? . ? ?
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'2. TI,e itinetics of isotopic exchango in simple and complicated 'conditions (Chapters II.and?Y). ?
:. Hie ineclianitm of isotopic exchange (Chapter III)..
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? s ' . 4 botope tfiects in the kineties of chemical mid physicochemical prccesses (Chapter IV.and Section III ?
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of the Appendix). ?
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? ?A 'review and gencialization of the i'esults obtained in' cheinical kineacs with the'aid of Isotopeg; and the
prospe( ts for. futther develop-tient of their ipplications in this.direction;Cculd have formed the contents of a
parato extensive. monograph. However, it seemed, wrong to ignore applications completely in "Theofetical
Print.tole,'?'? as without some acqitaintance with applications a 'Correct evaluation of the level reached by theory ??
't annot he made and the'prindipal talis which confront the theory cannot be defined. At the same tim, such. . ?
a dist ussion 'nay:provc. useful to the redder in selcting effective ways Of Utilization of the theoretical infdrrna- ??
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tion ns I work. These considerations determined the nature of the final chapter: ?. ?
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Thc, principal directions of the use?of isOtopes in. chemicarkirietics (Chapter VI):?
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he position and significance of any, given method of investigation in thd9evelopment of a-particular ?
held are. determined,, on the one hand, by the specific characteristics .0( the metbod and. its leVel of development,
'and on the other, by tit& theoretical and practical then-lades of the field of application. Both these factors vary,
and in( reasingly rapidly for newer methods and more dynamic fields. The iole played by the: method Th ihe ?
(eta, an.1 the prospects of further applications, vary acc.ordingly. 'Despite the very impressiye successes iu ex-
perimental techniques,:there are no signs of ?stabilization?in the techniques of work.witItstable and taclioactilie. ? ?.
isotopes. On the ( o'ntrary, stimulated by the demands of atomic power and other applicationi,..the development
? of isotope Methods Is proceeding at a pace unusual even for the period?of 'ftitorm and .rush"through which thp,
natural sciences are passing. 'Chemical kinetics as an independent scientific disCipline is, in its tlirn, still very
young' and in the process of becoming established. Its experimental material is growing al &vast rate-, while the
theoretical concepts, and problems are. being continuously Modified. While the methods and the field of applica-?
lion .are in such a state, the question of the place and prospects of isotope Methods in the 'study of?themicarpro?
cesses cannot be considered from a static viewpoint. For correct orientation it is ne.cessary to detect' the princi-
pal trends of development and to evaluate as correctly as possible the significance of the different development
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. directions. *In tae reu:snt state of IsotopechethIstry and chelnical ktnetirs the tial,klity of theet?oncepts ancleval- .
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,? ? In this monograph most attention is devoted Cohomogoneotts.processts as.the slutplsci andbeff understood: ?
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* .. Among the heterogeneous reaction 's, only some' of the Aimplest peo(?(..sse.s at olid- g7ts at sold ?Milli) interfaces ? .
'are conslclereQ, It is proposed to'coiisider the laws of isotope displac.cnitent aliC.1 exchange iii tolid pletses, an tile
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.? main applications of isotopes to heterogenepus catalysis'andtopochomistry,5inSm.u.7tIter ?,1;orli. :?.' . . . ?
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. nuireinents of research wotkers studying.chentical pro(.?esse.s. In coseqt.tenee, a nettill?er of (triesstimits impo'rtatit? .. ? ?
? . .in chemtcal kinetics have been inadequately studied. We have attempted to fill some sof thveS
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. examination of sonic questions with ege questions convitniont methods:of theoretical analysis avid of new ex- .
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. perimental datIt. This applies.,:in?patticular, to thtt kinqics 0.f?cottiplex exchange, the.gtneral solutions for
. .a.thich are gi.ven apparently "i?or. the first time. ?For greater Accessibility, the cext.inelndes minterons.(?;(amples
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. aiul fluinesical data, Inuit was rioi inteirded to cover all tile enormAs experimentai. material w'ffli( h has accu- ?%
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tables of thermodynamic functions. of Isotopic mol?eales, evtilibrium conAants for isoropic ran!exchanAc data ..
. ? ? ? one kinetic isotopic effects.
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. . 4s no books or reviews approaehinr, this innogr.app in seharecter have hitherto been published e?th(er
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. . ewn or in the foreign literature? ups and shortcomins itt?tht present V'orktire.inevii4)1?, anti wt.` (?;i11. be
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^ ful tc7bave oar (attention drawn to them 4y 4taders! Jt is to be Ijoited, however, that even in the plesiax imper-?
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?fcct Torm "Theoretical Principles" will be useful ro people commencing creative t ork with isotoites, atid.wilf . ? ..
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? ? ? ? ? . assist.a further extension of.the use.s of the latter in rese.arch?practice. .? . ? .
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. *In conchtsioNit is my.pleas,ant duty.to thank.O.M.. Totes and.O.V. KryJcpv, Clueread ihe.witole ho(11. in .
.. ant hnuscript form, A.I. S atenshteig anj V.G. Levich, who reacriedividtial.clsaix'ers tord..(iffered, value-11)1e vriti(.al?
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f ? ? ? . comments and ailvitte?Q.M. Vinograckw for active and systethatie.lielp.with the?mantiscmipt,'/A.A rly.?,hevioll ? ?
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fOr discasions of?cehain'questions of oielecular spec.trosc7Ty?.a.ne6.M Gal?iinsek4a fol. aid.in tronVilation of ?
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? . 'Mad bl.:ejt suI?gested by A.M. 13/trretrov (ll) and?k/. Crcokes (.1886) ?ha Existence o?isotopes is caused by trit:' ? ? ?
... ? ? ? . ? ? ? 00'
? ? ? ? ? ? ' . ? . ?
?
?! ? di ?
? ?prt sence of different Iflurtert of noutrons in?the nVett fora given?Oumb4 8f p?otons. : .
? ... ? ?
?
?? ? ? ? ?? .
? ? ?. ?., ? ? ? . . ? ? ??
? ? ? ? ? ? ? e? ? ?,,
?? ? ?
? I'? Otoms of.clifferent?elements contatning4te same numbers of ntlicleons in tit%ir nuclei are terped isobars, .?
? ? ? ? .. ? 4,
. . ? ?
. . . agil.afonis of tAccame?isoetgpe, differing in thplir contents cif Intranuclear.evrey and cow?quentl)c?with differot.n. . ?
es. : ? ? r4dttlet.ive pr op er ties , areskflown as isomers. Of these tlar8e.terrws, tge last (isomers) is west id organic cLentis- ' ?
. os . ? ? ? 10,', ?
? - ? , . ? ?.? . ? ? ?
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icy in .a 'totally. lit fereht isense;. . ? . . . ? . ? ? ?. ? ?
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? ? ? : 6. Examplteof Nuclear Isotope% Lsobars,?and Lsomvs ? ? .
.
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% ? ? ? ?I-1'4 1-1: (D); 1-13 (F). ...?
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Isotopes** ?? ? ? ?? ?
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? ? ** ?? di,f: .
ering?in isot.opiecomposition or arrajigemont of isotopes within tfie rnolecult4; this often leads lo?confdsi?on. ? .r.? ? .
. .? .1 anle 2.111ustIakes,eytnctualtlemples, tht syst'ern of nomene.latufolecntly priogcfsed by Olusin[4]. ? ???? ?
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. ? ? ?
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in isotopic composition and?ar.tangeqpnt of is(atopcs,isobtopitc.rtioleculd. Itis avplicable tt mqlecitles differ- ?
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. . .
4
S.
?
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.. ? , ,
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. ? .. rangerrserrt 'V the isotope's w.ithin the mstleculies, i.o., by the iso.toPie structure and not Ale isofopi.c comiSosition. ? se . . :6
.5:5 .Isotopic-imeric rtio'lqcules hav7a trie.sarn mass?nen&r. If ill; mass numter is:the s;rnt t ut the isotopiecon1P-1 . ? . ?
.?
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?? ? isotopic excbange involhs electron transfer; an othvs/ tratVer of atoms ez simpledtionoatonti to?ts., accompanted
,
? by.ruppfe of some chlmicarbonds an n formatiott of?others; itiaye-t other. neutrrd Po?olcAlles, ce-mitplr..x ions, or
?
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actions of another eletnebt. Finally, there are known instances' of isotopie'exchangch are caused py. transfer
. . e whi.
? of entire 1'11(11c:cults witliont.Pliptlir.e of original or formation of 11W chemical bonds, i.e.,?isotopic exchange with
.:?.physi?cal pr?ocesseic for?iiiitig its basis. With such'characttriitics of the effect?it is not easy to give a terse?and . .
..sirict definition., find inost?of the 'formulations met in'the sciCntific literature are applicable only to definite ?
?, : parligular types?of-i :th
sotopic: e>,ange.?'In'this bock we shall iipplit the?term Is_st_topic exchange_to al_g_.2.12?ess not
..? "le:iding to or?din'ary chemical or physlcOcheinical changes of a system, which raiults in a chan e Of isoto e ?
di?strihution.be.twe' cli di pent clItetnica l forms,..ilifferent pliaseseor within the Im.___A?Ss* This definitiori.does
?
. not restric t isotopic exchange to praesscs of any clef inite?type or mechanism, but the commonest and most im- ?
: . .
__ .. .
??? . ? portant fosn'ts of isolo?pic ex( hange are'llte results of e'llemiral changes of a special kind. Isotopic exchange was,
, . iiiihnown in the.old, "preisotopic" chentistry, and it does not 'fit. into tile usual concept of chemical change.? The
. most typical isotopic oxeliange, react ions do not essentially differ in their ,inner mechanism in any way?from or- ?
? ? dinary.c lietnical reactions, but the result of isotopic ex.chadge is hot a different distribution of elements within ? ?
Mole( iilLs,?or betv;c1nt molecules or. phates, but a differCia distribution of isotopes. The deCinitibn given is not
.?? ?
very illustrativo. '?'ro make, Its ineaning clearer, we cite a few examples.
.? : . ?? ? ,
. ?? ? ? ,
. E ample 1,ii,otopic exchanm_c_A iron between 'ferric' and ferrot We make a mixed solution?of
?. - -- -----T--r-. .
. ferric 'cidoridc ?.)ntaining ilie'radic)activ.e iron isotope Fe'''' and inactive ferrous chloride. After some time we , ?
. ex' trac.t.reC:13 from the solution by means Of ethyl ether, and measure its radioactivity. The greatei the time
? that the mixtirm was left before extractiiiii, the greater will be the decrease in the radio'activity?of the ferric
? chlorkde aid the equivalent increasd of. the railiciactivity remainiUg in the solution. If the expetiment.is suffi?-
?? :( ientay long', the rashoactivities of the two salts, peF atoin' of iron, will become equal. Ordinary chemical pro-:.
? tes,es did, not (went in the system. The chanye of activity i?s the.consequence of some special type 'of process,'
? .witic'll ca,n?bc. t,chentatically.teprescrtted by the..equaiion '? ' ?
. .: ? ? ?
. ?
? "Fe( :r3 + P0...12.-4 FCCI.3 + 55F9C13,.? ? ?
1
re? 2-1 F03+
? .P1' ?
11 Chapter
one.of'tlie? types oll.10 e_neous isotopic. excharige, the mechanism of which is discussed in. ?, ? ??
.* . ?
ritii
? ??
? ? Exang_i_ Isoto_p_is_e2Lchange between_pota'ssitirn io ? dide and ne' Vapor of moleculat iodine con
-
II.
taining?an admixture of 8-day iodine radioisotope I is passed over crystals of potassium iodide containing the ??
. .
?T31 ?
Ordy,stable iodine isotope of mass number.127. On pa.ssing over the potassium iodide, the iodine vapor will giv,e
np.sonie of its atoms of the 131 tadioisotope,?replacing them by an equal'number of atoms of the ordinary 12'i .
iodrile isotope.' In this instance also the, process is not accompanied by detectable chethieal changes, but the
potassium iocride acquires radioactivity which. it did not previously have, while the radio.ctivity of. the iodine .
vapor decreases. This. is a consequence of isotopic eNchange between iodine 127 and -iodine 131, This reaction.
is'11(.!ter.o.ge11eousc ? its equation .
. .
127 + '17/ Tr r?,1131 .L
+
: ,1.27
I I ???.- 2
.? ?
?
(2)
? . . . .
? reprtsents a' hetet? ,eneous themical roc.ess of ilie isoto lc t e. . ? ,
..?
. ELcarjipl.:_e_3. 'Bowie excliaireen. liquid mercand its vpoOn bringing liquid merqry tagged .
? ' with one of iiszadiodctive isotopes, for examle Hg2a3, into contact with ordinary mercury v or it is easy to ' ??
? 'detect the appearance of radioactivity ja the vapor and its decrease' in the 'liquid. This is:the?re:sult of a hetero- '
geneocs isotopiC exchange between liquid and vapor, which May be represented as follats.:*,
...
. ?
?
*A more detailed clasification of isotopic .exchange based on the natitire of .the transferred particles.is given
. ?
in, 24, Chapter III ?
? ? Of the seven stable mercury isotopes, we have included -in Equation (3) the?comnibiiest,,He (natural oc-?
. .
currencp?29.6%) L 21?
8
??
??
.?
'16
? 1111ffinaler?
? . ? ?
? 1g202 ng203 I Ig;203 1-1g202
liquid ? vapor liquid vapnr
?
? ? ? . ..?
-? - . ?
. ? .
In this Jnstance'the isotopfc'exchangO is based on evaporation and i?undensation, i 'e.,? a comhinai Ion of ?
? ? . .?
,
two physIcrrhemical processes. ? -.
^ ?? ? . . . ? ? ? .?
. .?
In all of these thrse examples, with'far-am?ching differences of pliase.c.cinditions.and mechaniOn ?of the iso-
tonic exchange, the? process involves displacement or change'nf cif individual' atoins cif the elements
concerned. We lloW cite sortie examples?cif?isotopic exchange in Salticlinc4 atoms hut mole( tilos art- evcitanged
. ?
? E:sample isotopic exchangepf carbon bet-ween benzene.?apd its yapcir. ithi the use 'of bewene tajv,Zd
with C14. or it is easito 'observe isotopic exdhange of carbon between liquid and.gaceon, ctystailine alid gas-
. ?
eotts, and liquid and crystallin.benzenc. it can .be.slioWn that in-this heteroggneons isotopic exchange ii c ? -'
change.of.C. atOms or CH groups occurs between different. molecules. Only-Whole 'Go6 wolecuIC :we:ex( hanged,:
and, the mechanism of-the isotopic eieliange is physicochemical as in Exaini.de 3 It should be mita Mal the
same results would be obtained in experitnents' with hydrogen-agged?henzeire with the use of tritiiiin or deutori- ?
t1111.
Erample 5. ?Isotepic exchange of?Carbon or nitrogen between KCN:and (CN)2 and bstweeu KrN? and H( N.
?
? . 'By tagging the cyanogen carbon or nitrogen in the gas phase, h is'possible to bring about the:tea( dohs'
???
. ? ?
etc.
Kci2N1.4 (ON1:)
. ,
b) ?K.C"N" IleilNid '2?N14.? ? ? ? ?
?
KCi2N14 +.11Q2N1.6 --> KC:12N". 11('PN".. ? ? ?
. . . ? . .. . .
?? . By- our deflnition, Reactions (4, a) and (4, b) represent isotopic exchanke 'of. i?arlion, and ?Reac ti.on (4, ( ), . ??
.
t-i
isotopic exchange nrnitrogeri. .However, actually in?all three cases the e,schange is not betwc?en C.: and (21-2:1 ?
N14 and N15, hilt ben;feen (C12N14)-: ions or C,12N14 radicals with (C,1,114)--, C141\114 Or ((1241?5) - and C12N15 ions Or
radicals ,respectiy.ely The is&o.pis? exchange here.is the consequence of eicchanebetween diatomi( sraclicals.or ?
.. _.
ions,? Examples.of the participation of more complex groups in Such ex?clianO?can ch?sily be found ?
. ? ? . ? ,
? ?"
. ?Example 6. Isotopic eiaange between sulfur dioxide and trioxide. Miktures? of sulfur dioxide with oxysen.
. and suffur trioxide do-not contain' either'sulfur atoms 'or SO radicals. However, iscitopic.(?,i'i hatwe between or-
?
dinarjt 502 and SO3 tagged with S35 faClioactive sulfur proceeds rapidly in'firesence of Pt-, V205, and other ?cata -
lysts even in. conditions' in Nhick, owing to establishqd equilibrium, no apparenrchemi'i al tea( tion occurs. Iso- ?
topic sulfur' exchange ? ? .
,?
?
?
?? S320.2 S3503 S3602 S320 ?
a
occurs in consequence of the invisible reversible cherdica,1 reaction 'of oxygentranster
S3202 + 11.202ct, S3203.;
s35.03C2
S3602+'1/202
(1)
The transfer. of oxygen. atoms -is perceived 'as isotopic sulfur exchange. If in.the smile 'system in eqUilibrilIM
? ?
not sulfur butoxygen is tagged,-it is possible to observe isotopic exchange of oxygen bet ween .'S016011' and SOY,
based on reversible addition and?remoyal 6.f-oxygen.
Example 7. Isotopic exchange of carbon in methyleyclobexane. When methylcyciohexahe otagged with
CIA in the side.Chain is passed over aluminosilicate catalysts, there is a decrease of the C14 conteni in the
methyl group, with its simultaneous appearance,in the ring structure. It seerns'likely that the following reaction.
Qccurs:
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
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'.?
9
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
-----""'""'""glanZarf ?
?
fun at the sante lime
? ? ?
??
.. .
(:',It2 ? ??? ? ? C I I, ? ..
?? ill(3( \ICIi???t',112 ? 11;c()cil. 2- cm.
? i I ?
? \ . ? ? ?
. Irac ? or, 11,( cif, ? ,
?
? ? Ili, . or, ?.
?
112,C/c1I?C11,
? ? ? Cil
? ? ?2
* .
. ?
? ?? ?
. ?
. ? ? ???
? . ?
a tid oilier isotopic isomers are formed [3]. ? ? ''
. ... .
?
. ? !his is an .example of iniiamelecillar.isoiopie dxchange. The. next example
.? ?? nut i asy to distinguish from. intermolecular exchange. ??
. '
E ample 8.. Hydrogcn?regrotiping:of Phenol. A.I. Brodsky And his assotiate
.?
???
.? ?
?
?
?
shows that such exchange is
[241 investigated Isotopic ispr
--? ?
itterizat?ian of plienol?tagged with deutoriuni in the hydroxyl group
. ?
.. ? .
. ?
?????
'1 :j ?
N51.)/ ? .
. I ? ?? ? ?
or' .?
?* ? ? [ 11 ? .
? ??
D.
?
.?
?? ?? ? ?
Tile pror?ess proved to be slow: ijitc?rinfaie.cu1arl..e.2cchanse_with the.participation of two molectiles. .
? ? ?? ? .
? ? ? ?
Apar4 front istopfc exchange by mechanisms analogous to.those illustrated.in Examples 1-8, exchange .
based.ott?tinbittations. of two or,more such mechanisms is possible, in particular, elecIrpn.transfer?is often ac'
( bnipaniedliy transfer of i.ttoin, simrle?ions, or?mor. complex particles. Transfer of radicals or moleenles'may
1-10 lollowedsby transfer of simple ions andatorns,,?eleclrerntransfer,.ete.? ? ?
? ? . , ? . . ? .
Sucli..flistance,s will be. mot in Chapter III, tlevoted to the mechanism of isotopic exchange. .
? ?
._Isot.pac Iffect?s?? ?? ??
? ?
? ???. . .
Research workers c? ommencing?work?with isotope i for /he fitst.t.ime are .often perplexed by the question of. ?
tlie. irtagnitude of isotope effects, arid primarily of the degree of deviation from the normal values. of chemical .
e, 1.11J Librium constants and rates or chemical...processes when particular' isotopes of a gi.ven?eletnent are replated
by?others, of different. niass and with cliffetent nuclear properties. 'In cOnsequenee,doubts Arise with regard to:the
. ? . ? ? ? ?
possibility oi judging tbe behavior of elements With the normal isotopic composition by the. b.ehavidr? of isotopes
? ? ?
itri?rodm.e.d a'rt.ificially as tztged atoms. . . ? ?
? ? ? . .
1 hese doubts, like the frequent fear that stil?ile and radioactive isotopes .are*not cherni:Cally equivalent, are
..
witlinin serious basis.. The. instability, of the atomie nucleus, manifested in radioactiVe disintegration, is 'associated
with :the inurnate structure of the nucleits, whichis in'ho way reflected in the chemicalliehavior of the atoms. ?
Neither !lit: valency, nor chemical bond stability, nor reactivity show any practical changei.ln: the tiansition hem'
..an itiarlive isotope to a radioactiVelsotope of 'the same .element. Radioactivity 'will mainfest:itsell only at the
moment o.f disintegration; and the observed radioactive effects occur with complete. chemical identity of the .
tniginal' radioactiv.e:elements with the ordinary stable. atoms of the same elements.* In contrast to the instability
of tile nut lens, which has no influence whatever on the .chemical behaVior of the afom lip to ihe instant of its
? .
* we will not .deal here with the chemical action of radiation grinned dnring radioactive decay, which' is. the sub-
_ _____ . .. ?
. it:, t .of the extensive and rapidly developing radia.tion che.mi,stry, or with the special properties of the so-called
hot atinns whielr are (*Med during disintegration. .
. :
. ? ' . ? ?
?
10
?
. .'?
1.1
'.E
????
? ?
,4?1 ? ;
. ? .?
. ?
?
? . ? ; ? .? ? .
? ????
disintegra:iion, the mass and seine other properties f the nucleus have a..tkfinite, but in tht.'ina "i'd cases..
? very sma1.1,influence on the cheMical properties. ' ??
. ? . .
. .?
.Thedifferences in ?the. physical and physidochernic? al properties of iSdtope.s incl.ease with ;e1.a.ti.vC1Y grc?at.er
? ? slifferences.in the masses of the corresponding lsotenes. ,It is eidilent that isotope effect's shotthi be'gropteni hI
. the case of.hydroge'n, in which the masses of the two rare ieotopes eket mass of tilt.
or_inar.y protium iso -? ?
? 'tope by almost 100/o for 'deuterium (D) and .by almost 200/0 for tritfuln m'ass of. radon tive cdrilon
used most frequenq as a source of tracer, atoms; exceeds the inass?of en by only The' differt in cc oI?.ihic
masses of C11 and ?C13 from the mass of C2 are ri hall* of ihis (about.8.55(,). The isotope. elle( 11 4re ?r.repondiuigIi.
much less.
??
. ? ? . ?
. . t . . ? ..
The sodium?rathoactive isotopes Na22 and Na2.4 liffer froM?the ordinary?Na23 isor?ope? in mass by less than. ?
'/(t$ and the radioactive phosphOriis isotope P3.2, by 3% from PI'. .?? .? ? ? .
. . ? . . . ?
? ? . ? '
For all thg heavier elements the differences between' the masses df ."ta,gged" and (*dinar y. isotopes do.not
.?. ..?, ? ? .
exceed these values and are often as low as rp or e.ven less. Li:such oases the' nidgnitude of the is,,tope eff et 4 c ?
Is so small that no corrections .need be,introiluced When .isotopes are. uied'as tagged' atimis. Sin! t' i.ii studios of..
. chemical reactions ills more often necessar.y io deal with molectiles Composed of light elements hydror,ed, ;
.. . . .
. .ca.rbon, nitrogen, and?oxygen -.- isotope effects cannot be entirely neglected in chemical litiet il s,*?atid Mt ir ,niag- ?
nitude and?methods for, its calculation require special t:onsideration. . . ?. .
. ? '
? ? ? .
. ? Calculations of isotope. effects in chemical thermodynatincs and. kinetic are basi?d on?alit: sta:tistif il. the,'.ry
. ? of chemical equilibria, different formulations ant. approxiniations of this theo.r.y.being wsed? in di.f ter, tit 1st s. ?
We will, therefore briefly?consider its essential point_ and exalt-tine the magnitude 'or?the ( orrections whit ii f`ollow
from n this.theory for the equilibrium constants (Chapter I) and absolute rates' (Chapter IV) with variations of-the '
? Isotope composition. Tables are given to shop, the extent to Which the derivatirms from 7Iie statistical 4.11(.0n, of:
? isotope effects agree with experimental data. .? '
. ? . . . . .. . ?? ? , ? . . . ? -.
?? . ?
? .? Various approximations-ate used in determinations of iiotope iifTedts act circling to the 4ysteatinder
elation and the dccuracy with which the problem is to be seilved.. For. isotdpes of ilie'lleaey eienienis, -.1er,, aft- . ?
..pioxirnatiOn is' often adeq?uate, the cheinical properties of isotopic atoms 'and of molecules differing in igotopic .
? coMposition.being.assumed identical. As. is known, the discovery of isotopes itself was the result of tilt: clif.?, cry.
by ?a number of.autborS [5] of the complete identity pf the chemical properties of; a;?ionitini, ( orrespondi?h?g, to ?
Th21?', and ordinary thorium: consisting of 100% of Th232 isotope; Midi)) radium amid mksothoritini [1.1. .
. . , ..
?
. ? ?
..?
We shall tam atoms wniCh' aie to. ?mpletely identical in the cheinical, sense lint whwhoIf dif ter.- in orher pr.o-' . .
?" ? ?
perties( such as stability of the nucl.eul kifficiently to permit separate?detection; ideal isotipes.. The properties ?
? o? f a molecule should remain'unchanged.on?replaceinent Of .sorne ideal isotopes.in it by others ? We shall tise the
?? term ideal tagged mOlecules to denote molecules of arromalous isOtopic coMposition and idiaiticai ( la.mic al ' ??
? ' p? roperties. Isotopes which are close to being ideaf .usualry differ very little in then physico: limn( al propnrtiei ? ... ??
This is. also true for the properties of.ordinary?and ideal tagged inoleCules. Wd shall apply 111. tenfrldcal iso- .
? toPic exchange to isotopic?exchan?F with the participation of ideal isotopes arid ideal tagged Moleculei; In the ? ?
. ?
Sagfe degree of apProximation We can speak of ideal equilibrium cif isotopic .exchange, the.magnitude of ideal. ?
' ? isotonic corrections', etc,? The above concepts bear.the same relation ? ?
to real isotopic exchange. reactions in chem-
. ?
icar.thermodynaMics and kinetics as the concents of an ideal gas dr all ideal?solid crystal lattice to real gases'arigl .. .
- ,real crystals in molecular .
physics.. . ? ? ? . . . t.. . .
. . .. . . . i
' .
Consideration.of general theoretical queitions can be suitably 'commenced with reference to sit( Ii kit alli.ed
systems. In the subsequent first'apProximation the' same quesilons?arc examined With considt:ratioti of the priii-
? ?
. . Cipal effects directly caused by differences of .isotope mass. Only in.?special cases does it .become necessary tt,
consider the additional small effects ciusedhy.differences in the electronic, magnetic, 'and other properties ( )1 ?
. , .
isotopes.'
? ? .. . ? .
. ?
? ?
. Isdt6pic corrections can be determinocipurely,by calculation, with the use (')f general equations which iii-
'elude atomic nlasses; or theyta.n be derived frorn ddterminations of certain physical:, primaray spectrosGgpic
.
constants of the molecules. The- second:method, which is predominant in statiitical thermodynamics., requires ...?
extensive initial data and in principle yields the more accura:te results. The first method, less at-Curate but situ- ?
?
.pfer, is.often used for calculations of isotopic corrections in chemical kinetics (Chapier IV) ?
?
? ?
?
r
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
? ? ?
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
. .k4...Iso?to2e??E1fects.in?Ch.ernica1 Equilibria ? . ? .? ? ? .?
? ? .
' ?
? .? influehre of Isbiopic composition:on chemical eq.itilibrium coftstants Ls *met both in ordinary ch.emidal
' rea'etions*.and in isotop.ic exchangd. For example, the dissociation conitants of 'deuterium molecule, D2, or trl-
thin,' T2. of the mixed niolecules HD, HT, and b.T, differ froth the dissociatidn Constant Of H2 (Ti.ble 3.).??
. ? : ? .
. ? . ? ?
TABLE; . ???
. Dissochition Constants?of l.Aolecular'HYdrogen of Different
' Isotopic CI:impositions [71 .
. ? . ?
?
. .
. T; ?K?,
. ? 1000
1600,
? ? . ?
2000
? ?
2500 ?
? ?
? .
?
?
?
?
?
?
. Hi
. HD
D,
? 11T
? .:P2
?
?
? ? ?
?6:0-10-14
2.0140-18
? i.11
2 . i0 0-1g
. 3,01?10-1.8
. .
3%90
1;57.10-10
2.70.10-16
'1.49.10-10
244
? ?? ? . :
. .
2.?90.19-0
1.36.10-?
? 2,49?10-?
1.3200-.0 ?
2.35:10-8??
?
3.28:10-4
3.21.10-4 ?
5.94.10-4 .
? ? ?
. ?
????????
Similar distinction's., although less Th magnitkle,.are found for any other element and for any other reac-
? troll, foi. example, for the formation of Acetylene from. methane or the dissOcia?tion of hYdrogen iodide into hy-
' ?drogen and iodine. ? Equations (9) and: (10) represent these reaCtiOns?for different isotopic cornpositiOns -of the ? ?
: .0)riginal tholecules;
. ?
. ? ?
etc.
?
?
.?
.?
. ?
?
a.) 114 ","-42 31-12;
? ti) 201)4 -,21 + 31)2:
C)..2C12144 '
?
.
?
. ?
. ? ?
??
. ? ?
. . .
? . . ?
?.,
. . . ? . . ? . S. ?
. ??? ? . ..
. . . .? ? ?? ? ? ? ? .
? ... ? ?? ??.
. ? ? ? . . . . . . .. ? . ': .?
? ? ? ?
It must be pointed out .that In a chemical 'process the inittah stat es from which the calclilations for the gyttisti?ca.1 ? .? ?
.. ? ?
sums of the initial and final substances arc made:are different, and t; reduce illehi to a?common.origin, thefa?c-
tor . ? ? .
I
. . ? ?? ? ? . .. s .
.. ??? ?
? ? ? ? ? ?
? ? '
. . ? ?? . ? ?
.
?
* . ?
? ? ? ? ? .. ? ? ? ? . ? .? ? .
? ??
? exp ? Eo init -En filial
-
? e . ? (Ii7b)
.. ? ? . 2-Q0ART ? ?%, ?
?? . . ?kT ? ? ' ? . ? ' ?
.? .
? ? ? ?
.?. . ? ?
. ? ? ? . . ' ? ' ?
? *
There 00 1s the heat elTect.of the proGess at 0. is intrqduced. int.o the corxespottding?form?las, And in pzirricular. . ? .
. ? .? ? ?
.. . loci) (33), after siibstitutlon'bf Z.? for Z. For isotopic pchanere,Acttons Q0 repte..sena: the different e ivtween?ti?te
. ??.? .
? ? ? ? ze ro-po'lfit energies o{ th.t Curespo?u din.g ritolecules. ? : ,? ?? .? .? ?
? ? ? . ? ? ? ?? ???? .
?:In ?.
?. ? ?
?? .?
???
Equatiorts C55)?and (57a), tu is ord of the characteristic freRuencies (If the molecule Since: v rat-Otssimie .
. ? ?? . .- . ?
? ary values fri'prn 0 iciitifinoity Z
.cit!a.tion,(57)?form's an infinite gebnietrfeal prtlwession,ilic?den4t2inator. ? ? ?
. ..
?
? . lett) kT.in whiceh is less than mnity
? ? . ? ? ? ? .
?? . . ? ? ? ? ?
? ?? . :
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? ?t"'. ?
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a
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i
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: ?
?
5.? ?
? . in this instance the?first term no = l.? Hence ? ? ?
?
?? ? ? ? ??
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?
?
?'"
? ' ?
?
or
?
.." ? ?
s ?
? ? ? ? ? ?? ??? ? ..
??
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?
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As is ktur?Wth.e.sum of the germs?of a geometrical progresoivn is ? ?
Since,?w'2*en 'V =?0
? ?
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? ? ? ? = a ti- 603:?-1- a0Y2 ''-r- ?..*: a"
??
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'? ? ilbr = .2 e-he6rikir ?
?
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. ? ncx?conT - 0. and LI? 2,
? ? ?
?
.; ?
??:6: v=v06. ? ?
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o=o ?
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Zvibr-;-?
? ?? 4,
? , 00'4.: ... .' ''? ? ? 555
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i?____?:,-iiiC:itl.kl: ',:. ?
?
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dr ?
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$ ? ? i. ?
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71, ? ? ?
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: : ? : ????? ?(..:...q: ...... ..........;
.?
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. % (.((,20.(a))).? ??
.?
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COO
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? ? ? ..: ??????? . ? ? ? ?? . ?.? ? ??? ? 1... ?
? ? ? ??
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4
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? : ?? ? ?
? ? ? ? if :=. 14:(1)/kT.' ??
?
t? . ? ?? ? ? . ? ?? ? ?? ? ? ? ? ? ? ? ? ? ?
. ? . ?? . ? .2 ? ??? ?? ? ? ? ? ? ? : .?
_. ? ? S ? ? .
?: ? ??
. ? .
? ? ? ... The vibtaiion.;bilell.diatomic it.olecules are?enly spernxirrii.tely reprvented b?:.; the harmoni( o:(??;11ator ?? ? ?
. ? ? ? %mode/. At Itisla vibration apIplittf4es, i.e., at higl; Z,, the detiatiotis?Mconie F.r. large tlaat i?Tina&itTn.(rM) bet nines .. ?
? ?
? ? . ? ?? ? ? ?
: ? ?
..? ? inapplical)le.? Therefore :t?very?high T,?wIlph.brg,h vilraticoil?1?eyellare excirtd, Equation; (V.) 2i11.1?(10) "0e -
? ? ?
? ? ?? ? . ? ?? ? ?
: cOlne i9applicable?yh? formnra: ? ? ?
.. . ?.? ?? ? ? ? .
? . . '? ??? ? . ? . . ?
.. . ? ? . .
. ?? . ? ? ? ?: ? ? .? : . . .
. . ? ? , .., ? ? ? ? .
? ? ?
. . .
. . % . - ? ?*Evibr 4.= hccoo(v.+.1t2)?-?\?nwo(v .4 Y2). . , ? ? ? ? ? ? ? ? ? ? ? l' '4) t ?? ??
. ?? ? ?? ? ?
? ? ? : . ? ? ? ? ? . . ?
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?
? ? ? .?? ? ? ?.. ? .. ? ??? ?? ? ? ? : : . ? : ?
? ?
. ?
. ' . which inclvdes. two serms of?the,mies, refliplica?ble?witclin wider llenits .In 7:quat::.n (6`2), ',cos LIR .:tifliarnivni - ? ?? ?
?? . ? ? .
. ? ".? ?? : ?
? ? ?t?. ? .
? city mnstqnt, doetennined?from?sp u...
?ectrcogtt
ic da. It is.inv:rsely propretnaleo ti,:e frcAtun lity wo?.?.?J;flo the
vorrJeut of inertia o th?anglecult.? .?
? ??
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Pot. exact carGulatron.s oT trierinodyniinit: quantities fitrthv?appr?oximativre are of tep need; ?tiore?the?tutt? ? ? .
? : ? ? . ? .. .. ?
? ... ?? vial influencp of tl*e v'ibrational and?rotaIipa41 mbuorr.. Qf Km polecule?is'ta!siii into ro?nsiditraticAt, and rjle v?i- ?
..
? ? ?? ?? brational awl rotatical en?rgle..1 apd their ipe'otra arecongidert'd?tointly'r.l.5,117]. The exprsio;t?for the: gnelgy? ?
? ? ??
.? ?? ?? ? ?? ?
.. ?
? ? ? ? ' 'of a 'diatomic moleoulethcn assurn?es the foirli .
.? .
.? . ? .
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? ?
? . ? . 77_,. 0 t v 1 bi. -..-- .11 0 4- 11c [we; - x6)0212 + liTov's -115. ????1 -I- ? ?
a ? ..*?:,
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,? Is. ???? %S. ?;i1, . ?? .:??
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.?
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.? .? .
-j-; ht {Bo [?1 (4+41 11-CL-yrist,) + p?.72?(i -1- 1)44- ? ? ? r.? ?? . . ? ? '.
. . ? ..... .. ? 0,.. ?
? ?
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? ? ?? 00 ?
?
? in this expression Ek is thozero-!poin't eilergy; hc[wov + 160v????ytuov- + .? ) is the willravional co'hi?ponittc
. ? . ? ? ? ?
? ? ? ? ?
, . . .
? .? ? : ? . . ...? ? . ? ? ? ? . . ?
a . '
.. . . ? ? . .
? ; ? . .? ? ?? ? ? ? ? ?. ??
? ? ? ? % ?
. ..
? ? . ,
? ?? ? .. .1'
. ? . '? : ? . . ? ? ? ? ?
? ? ? ? ? ?
? ? : .? .
. ? ? ?
? ? ?
..? ? ?
? .?
? ?S ? ? ?
. ? ? ? ? ?
? . ?
? ?
. ? ? ..
..?
? ? .? . ?
. ?
. ? ?
Declassified in Part - Sanitized Copy Approved for Relea
? 50 -Yr 2014/
? - - 1 43
?
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
111111110
?
?
?
?
?
?
. ?
? . .
? . ? .
? e' ?
? ? ? ?
??
? cif degeneration. F1g??8,c shoigs the internal Inotidns.of Atoms corresporidfng to nine fundamental plane' vibra-
? tion'frequencies of a hexalomic molecule, such as ethylene. The total number of such frequencies is 12, riot ?
fncluding.the,tdrsiolfar vibratio'n frequencies orthe tnetliyl groups.
. ? .
? ? ?
?
? ?
?
?
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?? ?
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. ?
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- ' ? ? ? . ?
? . :
?
. . ? ? . .
?
? ?
? . .. . ? ?
?
?
?
? .
? ?
... .
? ? ?
?
? ?
?
?
. ? ?
. .
? ? . ? . . ? ? ? . : ?
L ?. ?
?
H. ? ? ? . ? r
' ? ? ? .
? . . ? . ? .
? ?? .
?
? ? ?
? . ? ?
?
? ?
? ?
? ? ?
?
? ? ?
? ?
? ?
?
?
?
? ? . ? ? ? ?
? ? ?
I
? ? . ?
?
fi
? . . . ?? ? ? ? .. .
?
?
?
? . ?
? ? .
? ? ? ?
? ? : ?
? ?
? . , ? . .
?
?
?
. ?
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?
?? . . ?
. . ?
? ?
?
? ?
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?
?
?
?
? ?
?
? ? ? ? ?
?
? ? ? :C . ? . ti ? s ? 4.
?
?
. . . . ? .?
. ? .
Fig.' N. FoNns or plane' vibrations of?benzene molecules, observed in Raman spectra (rows
. . i and: 2) and infrared absOrption'spectra (row 3): VibratiOns degenerate.relative to.each .
. . ogler are shown in.ihe same squares. C) C)'Vibrations of carbon atoms; ? H) VibiationS of by-
? dro.gen atoms according to Kohlrausch. .
. ... ? ? . ?
. .. ..
? ..
? .
. . . .
? . ? ?
. . .
? ? . .? .
? ' .
' Fig.. 9 .shows the.rrynions of atoms.correspOniling to sik fundamental frequencies of the SF6.moleeule. With-
? ?
.
? ,
our (fegenciration; ih this caseate I-Olt-Hula 3n - 6 giies the 'number ()Catch erequencies to be 15. Finally, Fig.'
10 gives a diagra:m bf the spe.ctrosCoPicalty observed .plane. vibritions of the carbpn arid hydrogen atoms of the.
.? . ? ? . .
' benzene ring. ?
.. 2. ? ??.. ? ? ?
? ? .
. ? ? . ? ?? ? ?
?? .
? ? .
.. . .
.? A syncm of independeirt harmonic linear oscillators is often used as a model.for the vibrations of poly-.
? ?
? atomic nuilectiles and atoms in crystals.. .For such a system, with 3n y osciltators, the vibrational statistical
?*.suiti is ihe preducf.11 , ivhicireontain.s -3n - y.fac.torsPf the form (1? e. -
T)1,
?? :where.coi is the natural'
, frequency of the i..-th.type. of yibrations (see Figs. 8-1.0)
?.
. ? ...
.. ?? . ? . ?
. ? 3n-y ? ' ? a'n-y.
.??
, . ' Z*vibr =1.11 ,,,__e?ht.ca iikr.): ==. n ,,,__.,_?).._,..
.? ? .... ? ? ? ? ?
. ? , ? . ?
. ? .
??
.
?
? .
? ? ?
? : ?
On 'the basis ,cif,the results obta:ined for individual partial statistical surits, an.approximate expression for
the statistical sum of the internal energy of a?diatorpic molecule.of mass m and moment of inertia I cari.be ?
written ill the folloVcing form: .: ? .? .
? ? ?
??
?or
ZjnZr ??Zrot
ie1g5p(2rWakT)lia?87c2/kTfl-t412 ? .
crii.3/i; (1 ?
' rgspl6jri Tr3 y...77,0.7,`/.1.0.2,* -u/2
'
.? ? a46 (1 ? C--u)
. : . .
?
??
?? .
(61) ?
(67a)
Analogot(s expressiorrs for a linear triatomic molecule or for palyatomic molecules of various :forms can
'easily be derived.. ? .
? . ?
? 28
?
??
??
?
???
? . .
. . ? ? . . ?
? ? ? ? ? . ? ?
. . ? ; : ? . .? ? ?
. . ?
. . Caleulations with the* use o.f 'Equation (67).and otheis gliten In .the ten are bastrd'on measureinents of fun- ?
. damental frequencies, anhatmonieity eonstanis, molecillar roiation., monients, arid other coefficients detetinin.ed ..
from ipectroscopic data'. Tables 5, 7, 9; and.15 thdw.the influence of variations pf Isotopic eolnpisitton.on tite-;e?
. ? ?
. . -values. Numerical data for molecules sham.] in these:tat:46 wer.4 obtained frofn band spectra. in the Visible rad .
. ..
?ultrayiolet regions, ?frPm infrared specfra, rrom Ranian.itiectra, and. from ntlerowalie spectra ?at %yam' lengths of
..
OA. to 3 ?cm.. Microwave spectronletry,.despite iis brief exiktenee, has .greatly enriched our. inf&mation On Mole- .
.. .
? . .
cular energy levels, shapes, and dimenslons [/9]. Witli its aid.it is easy to defect isotope, effects in the speotta
. . ? of compounds of Suclirelatively heavy elements as bromine. arid'seienimil,.and in principle it 4 possibl(f to in- ..
? . vestigate such effects, even for.compounds of the hea?viest elements Vezitt, Morcury, thorium, etc.). It is to be
. .
.. .
expeted that new and effective methods for isotopic analysis' of chemical compounds will be cicycloped oil .this '
. . .
????
. basis in the' near future.. . . ,
.
? .?? * ? :
?
. ? . . ? ... .
.? ? ' : ? . ? ?
"
.? ?
.? ?8 . Fundam.ental EquatiOnl fcir Isotopic EKchan.ge Eqhilibrium
. - ? -..- -.--- .- -- ?-- - , . .
. . . .
, ' We shall now apply the theory discussed in.' th.::. precediiii sectiomi to'isoroptc ex.chan.ge equilibfiiiiii For ...
'clarity,.we will begin with the simplest reaction's. of.this .type, in which an atom of one isotope replaces?An atofn . ?
of anothei in a diatomic mo.lectile? '
?
. ?
. ? ?
. . . ? ? ? ? : ?
? A$C X.V: A X X
? . . . ? , . ?
? ? ? ?
The equilibrium' constant for such Foaction can be written as
? ?
Accordihg to the rule stated on pa.gg 16; ind' &illations (33), (.5'2a), and?Ci7a,b) it follows.that.
??
? zu yo
K AX .X +0.(RT
? ?? ZO ? ? n e = el-Q.,tnT*
?Ali Z. . ?
?
? . .
:X
where Q0 is the heat of the isotOpic exchange reaction at absOrute zero, per'moie.
??
. .
According to Equation (70),'K is 'a ratio of'tsb. fractions. The mitifierator? and deno.minatur if the..first
contain.the statistical sums fordiatomic molecules A.X,differin Hi the isotop:ii-i.cbilipoilion of X. The. second
'traction similarly consists of the statistical sums for the. X and X atolns? .Consectu.ently, (-Mc:illation of Ko reduc.es
.to calculationpf two ratibs:of the statiifical sums of molecules differing from each 'Other in isotopic 'composition ?
only.: This general ?charactetistic of isotopit-exchange equilibria, applicable?to 'molecules of any degie'e of coin- ?
plexity, as has been shown by Urey and his ?associat[ 20, 21], Bkgeleisen and Mayei (22], Tatevsky f 23), atid
. ?
others, considerably Simplifies calculations of isbtopic exchinge [,12/1]...
In tbrgiven?appeoximation, the statistical sum for'a.diatotnie mplecule Is the product of die translationdl,
rotational, and?vibrationaisurris. There are no vibrational of rotaiional stniis for free,ato.ms, and at not very
. high temperatures only /he fadtor gel remains of rhe electronic sum's, and?gsri: of the nuclear sums
. ?
(f4i). ? ? ?
?? ? .
. .
? (9)
? 47(1)
Or
??? a') ZIAX. ?-? zi - geigspzt tr Z?k?rot4 yilit? ? ?
I
x Z3 '?gelg g?a tr.
? . ? . P
. ?
Denoting.Z?A by z.1 and.Z3( by Z4, we obtain the following expressIons for tile frar dons
^ ?
? o
= Z is the produ.et 7,:visiZtrZr91. ' ?
geli gspl 1.1 tr.z/rot?21 vihr
gel 2 sp2Zi.tr Z2 For vitir
: .
??
? (70'
?Ax ?zx
-dud .
70 ,
'AX 'X.
??
(72). ?
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??
?: ? ? ?
. .?
. ? -
?
;
. .
Sot- molectiLes eontaining
?? ? .
? ' . ?
. ?
? add tlietefere.we have
? ? .
Declassified in Part - Sanitized Co .y Ap roved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
? ? . .
? 24 ? a2filleth(1".e.-.44). ?
? . ? .77. =
? ? al '121021/i (i ?
2
?
. . ? ? ?
. .
one atoll, .of the exchanging isotripes 'each,*tlie.symmetry nuinbers are. ecOal
? al =02;
. ??? : ?
. 11.(1t1 3\II; (1 - e's).
:
?
? . . . . . ? 16 ---- Ta R.; ) (1- e')?
1
? . . . . ?
? ? ? ' ? The yminCtiy numbers?Which are contained in z,(1 and 41 May also be eitual,for molecules of the type ?
.. ..
? A XII in dic condition that all the n atoms iti the molecule occupy Mutually indl.stinguishable positions, such as
the 4 c'hlorine atoms in*CG14 or the 6 hydrogen 4?Coms in'benzene;anil ate.ompletely'exchanged. ?
. - . . '
'ciao ?
? ? aC135 't CC136.
. . 4 . . 4 ? ?
. .
? ? ? . ?Qe
. .
In other 'cases the ratio9-1 difftIrs.fro.m unity and cannot' be neglectetl.. ? ?
. .
.02 .
. . , ? " ?
? ? ?
. . % .. f , ? . . ?
The statis.tica..1 urn or a free atom with Consideration of the electroliFc and spin factors" with nonexcited
..
... ..
electronic levels can he written, according to Equatign? CUL. as. ? ..
. . . . . .
. ? ? . ? : . ? ' .. g ig (2nmkTO ? . ? :
z _ sp . .
. ' ? . : h3 ?
?
(n)
'enc. . ? .?
.? ?
.? ?
. ? ? ?
Z? z ?? (geig ' )3. h3 (27rmakT.)1/61, ? . ?
,._..2c _ .._.2... . sp ? ?
? . . - = 4 (geigs )4../1.3 (.2nriz4kT)112V
? ? . . .
' Caucelling equal factors in 'the numerator and denornipator, and guf.:Istitutin for. the ratio
?
.atoms' o( the twQ iso.t9pes m311114 he ratio of their atOrnic weights 1\43/M4, we have . ?
. .
. ? .
:* ' ..?
. . .Zs. ? Spa Of-.1)3/.
. ? . Z4 ? gsp i kt1114 )
. ? . . .
. ? = ? -4 ? ? ? .
?
?
.? (74a)
of ihe masses of the ?
. .?
The electronic. suits also vanish at.high.temperatnres, when the..presence 9f electronically excited.4toins cannot
? ?
. , .
be neglected.' This.Wdue to. 'the negligible differencen the values of the:eneigy leveis'and the corres'ponding'
fre'quency differences for all atoms exeept hydrogen. However,:as Table 6 .shows, 'even for hydrogen the.effect
is nqt geas, since Aco fOr the tyrp,lines?giver! is only' 22.3 and 1.14 Crn-.1. For, He the: iiotople shift is approxi-
mately an order of magnitude lowet and the tw.o?vaities of Aw..given In.the table am only 0:85 and 1.40 cm4
Th t.: diffescncds diminish with increasing A tonic ntimber. For argon, maximum Aw.= '0.100, etc.
- ?
^ ? ?
. E.qu'ating gspa and gsp4, ',ie hive the equation . ?
? Z3 ? (M3 \312 " ? . . . .? .
? ?
.? . . . Z4.- M4 i ' ? ' ? .. .? ?
. ? . . ? ?
- ?.
In the...exponent of the last facto; of Equation (70) Q0 may be repla.9ed by the difference of?two zero,point
energies per mole
? ? . ?? ? ? .. . .
' ? ? ? ?
. . 1?Qo = E02 *-.- EH: '' .* : .. .. CIO
. ? s .
. .
using the connection of Eoi and .E with co2 and wi respectively, and.also? die possibility of conversion f.E/RT ? .
into E/kT by division ofjhe numerator' and 'denominator by?the Avogadro.nnmber N,:we hake, with' the Use of
(75a) .
.the,previeusly intrOduced contraCtion hcw/kT u,
? ?
, ? . . . .
?
*gel ancl gsp are 'omitted in passing froni.(72) to .(72a)'.. In the case of 843 this is Justified by geli
? gsp 2 in* the ...general case remains. .
?
? ? ?
. 3.9
?? ?
?
?
?
?
? ??
?
: '1' A Ell E 6
. ?
Comparative pata on Isotopic Displacement, in?Spectra of.Light Element.s [261*
? ?
????
?
?
? .e * 2 *
? . . :!Us
. .? ? . e
1
. " Element Wave Type
. length of ?
? ' X; A' ,of
?
.1
? ? Transition ? ? ?
.?
Isotives
studied
AX 'eq.,
A
64.0 C Xp.,
cu)'-1 :
.? ? . ' ?
1215.7, ?
6562,13 ?
? ? 152S 2p "P
' 3.(1 Lai)
.? ?.
Ill ?---'112
? 110
? ?
5015.7 ? I*
' S888.6
? ? ? . ?
? ?
? ? 2.s1S...-3p'[ ?
2 s'S - 3p3P
?
. ? .
.2 s2S 21i?2P
. 2 OS - 2p .
Li ?
. ?
6707.8
5484.7
, II
? ?
110- 1113 4
0.329 .22 300'
. 1 7114 .4..144. 't
? .
0 21'3 .0 849
,0212 ?*. 1 404 . .
Lid ? 0.160
0 342 ? ,
?
2497:7:
3451.4"
i ?
II ?
.. ?
? ? ? 2 p2.1).4 - as2S,/5 ?
..2 2p2ID2 ? .
? .100 - 11'1
' . ?
C'
2478.5' .1 : 2p3s
2836.7 II *. 2'5232 P.1.
??
0- -
-0 (AO
? 0 .104 ?
' ? .
- .0?069
- 9.049
' . ? 'N . 9629.6. ? :3s213.1.;.-
. ? 8242.5 , 3s4P./, --- 44 Pas,. .
? ?
.?
0,052 ?
? 0 041
8446'.4-
'7157.4
6233.3
?
as 'Si - 3 p 31).1 .
3s 'D2 -.3p1D2 ?
413P2- 3t13132
010 ___ ()1
Ne
Mg
7173..9
7032.4
33238
2852.1
4571,1
8806:8
.2795.5
?
. ? ?
?3p2pa -- 3s Is; ?
3p2jh0 -"- 3s I.% ?
% ?
2ki2111/11-.- 1-11, 219./, ?
3s2 'So 7- 3s3p
. 3s2 'So 3:d3p3P, ?
? 3s3p1P, 35311 ?Dr
. 3s2S:/, - 3p21)./,
? .?
NO"- N?2
?
Mg2?.
. CI 4310.1
.4s6S2- 4 p
?
? ? ?
. A 7147.0.
4510,7. 'I ?
*4'579,4 II
? 4s 1S6 -- 4p "I)4 ?
Pis S2-" 5p 3P5
4s 2p,i; 41, ?
:6:100
0 056
'0084
?
?
? 0,035
0 026
0.029
'0 005 ?
0,817
.0 066
808
? Gl" C137 . 0,008
A 3? ?- Ar4? . (1.009
' 0 010
(1.021
?
0 3O. ?
.1,14 ?
?.
? . (77) ?
. ? ? ?
:
???
0
070
0
060 ?
.
?
?
? .0
14.*
? 0
11
.??
0
47 '
? 0? 0G8
: .'0.052
260
_
0 061 '
. 0 083
0 0.85
0 102
:
0.035 ?
O 018
0 W8
0 1.20.
7699%0. ? 4 -4 p?Psi, ? 106?-?!-(41
?
? I iefers to neutrdl,and ri to toniied;atoms.
?
Declassified in Part - Sanitized Co.y Ap?roved for Release ? 50-Yr 2014/04/24 ? CIA RDP81 01043R00370021n 7
0 005 0.008
??
. ?
? 31 ? ? ?
????.
.?
Declassified in Part - Sanitized Co .y Ap roved for Release ? 50-Yr 2014/04/24: CIA-RDP81-01043R003700230005-7
. .. ? ? .
.., ?
,
. ? ?
? Subst[tict in of tlre'expjoss(*o.ns'obt'artied for the inaixidnal factors in Equation *(70) ?gives EqttatIOn 78)..
. .:..
?
.? ? ? ? til . . ? . ?
. . . ' ? ..- -
? (12/1 /if Of iVls (1-e-7Y?g) e ? ?2 . ? ? . (78) ? ?.
. Klsot ei(ch= -1 k m.) ?
.? .. u -. . ?
. 2 i .
.. ? ?
? . (1._e). 'e 2 .
. . . .
. ? '; .. .??
. . ?
. . i MC ceniation can be?simplified further. with the aidof Equation.(7.9). which is?a spedia".1 case ef.the Teller- ?? '
,
.. . . ? ? ? ? ??
? . .
.16 (.111111 Cp: : troseopic?theorent[253.? ? ? . ? ? . ' ? '
. ?
? 11. Cif i* 4\111u2'
? ' J2 \ M2 M3:1 ILI ??? ??
. .
: . . . .
. ?
. . . .
? ' ' ? .. ?
? I licreforc, multiplying and dividing the right hand side of Etitiation (78) by u, -*we obtain th.elinal Ecluation (80);.? ?
? iii.v:1114b tI,c only spec.ific constants are o and 1.1,?or, more accurately,. co, ?w?liich ?is contained..iti.these functions. .
. ._. . . ? . . .? ; .
. . ? . - u, ..
?
. .. ,
,-; 2 . (i '_.4z)
.
. . .
KIWI eicc.1:-. a, u, u. ? . .
. _
e 2. (t ___?e-its) :?
Ft jc to be kicte..d that the?same?yalue of?Ki is obtainc.d for 'the equilibrium in the somewhat tnore
. 1...c1opic exc hange pro( ess involving the diso'ciatiOn of AX atrd. AX molecules into atoms
(70)
. ?
? AX --1?.A -1- )5,1
*. . ? .?
? A.X.-t? A +
ihe equilibrium constants of these Iwo reactions ?
' ?
. ? ? ?rf ? [?Al[X] ?
? , ."dtss tiosi '
.? '