MAY 10

ISOTOPE EfFECTS ON CHEMICAL EOUlllBllIA

CENTRE FOR NEWFOUNDLAND STUDIES

TOTAL OF 10 PAGES ONLY MAY BE XEROXED

IWilhoul AUlhor',P.rminionl

PETER D. GOLDING

' .

""

".AThes i s

" . . ...<. J..'

J . . . .

Submitted in partial fulfillmentof the requirements.

·~or'.·,thC d~g;eC

^of.Doctor

~.hil~S~P~

.":

: .

f.~r~a1University of'New.foW1dland

,.':

,,"

.2"

Theaut~'wishes^to expr es.s hisgrat~ful.appr ecf.a t ion to Dr'.J.M."W.

Jcttt.

^Theinitiation and,maWration'

~f th~S ~ttdy

.

~OUld

^{not be}a malit; were

it

^{not for.Dr •.&ottI}

~ pat~eTlt supe~ision am en~o\u~g~~t.

^The'author also

~'res~es

^his'

sinc~re·thankstoDr.'O.J . Barnes who.in innumerable dtscuss icn s, has transtared vagueconcep t !" int,osound~iridalpractice.

.'Thest.imdat.ingrej~indero,f'Drs.E.Bullock~drr.x.Ralph•

....hethe.ri,\seriOus discussionor recreation.~s.;.provenin~alu:

able duringthe course of thi;'

study.

-«:~'\ ^{o '} Forthetechnical preparation'..

o,~ ~!1 ~les1; .

^{the autho::. ;}

~~'~tr:.^C.Piercey~ ~aticn:ly>yp'edthe manuscript~..

~~r.P.Kingwho devotcd"1ong hours "tod!"awin~the dfagrains, J:inal~y.theautho~grateful~y ~cknowledges.the graduate fellowships'awarded him byMttoorialUniversity.ofNcwfounlland

andth~'Nationa l Research Council of Canada..

"

.PREFACE

.Th, ini t i .,

in~rOdu~;on

^{to the}

th,;;s ~utlin,;

^the

^bas!<

pfu ro sophywhichpromptedth e rt:escntinvestigation. Prj-or to' c~rryi:ngout neasurcrentswhich could prove definitive in the

;cons iderat ion of substituenteffects onequiiibri~Isotope

~ - "

rectos .. studies ofthe protium acids,andtheir,corresponding

.dcut e Ti umsubst~tutedanalogues wereconduct~with,aviewto

examining theirsuitability. for measurement.-This investigation led'to 'a closer

-examinati~ ~f

^the'

~m~cal ~ ^{p .nysieai}

^,'proper-

ties ofPhenylsu~finylacetic'8.cidand,someretated,c~d, This additional investigation was not arrtdcdpatcdintheOTjginal scope.o f the work,and to acconrodate the~esu1t~lap~in..'

• continuity betweenthetwoar eas 0f study, the rhes f.s is conven-

. , ,

ie~t iydivid ed'int o Part I'andPart I~ , ~achpresenttng separate .Introducti6n.

,

EXpe;imental;- . ResultsandDiscussion chaptel%.

.

^~

....;..

•

/

-a

r

~. D.G•

... .. \

,"

..:

Th~,

thenood.ymimk equilibriUll

const,~tS. Kt{H)~'

^{of. fi;e'}

m~mOsubs.titu~cd

^acetic,

~i~s "RaMlXlI. ,,~ere

^{R·CI. Ph.}

PhD., .

PhS,and PhS02,ha.~,beenmeasuredcondcct tn e t .rt cet t v, The synthes~s

o f

~ve iS~~:icallYsebst .Ltut edace~icacids,R~2 ·

~ax:tI,where R^c Cl, PhD.'PhS,PhSO.andPhSl?i~are'described and the then:oo;amiC'

equi1i~ritml cons~t~,. Kt(D).~

^of

~h~ee'

^{of :/}

these.R..ci,~hO,and~are repor-ted, Thec~eulationof

s'e~on~ry

^isbtope

effe~ts

^{'of the}

se~~d

^{kindforthe-threeLsc- .:} t~ic^acid.,ai~:ROI2CXXJI/RrntCIXlH,where R"= ci,Pho,andPhS.

.

.

^{~ . .'}

.

has,been accmpf Ished by tile~prOpri~te,canPari son'of thermo- Idynamic'equiIibr i tunccnst.ents,Ktq:nIK_t(D),'~ by'thec~~rison.,^. .'::pf isoto pic•"Jslopes,. mtCD)'.

/~Cm .

^Theseal opes , m. t(D) and" mdH):,

r

a~cder i vedfromlin ear least squarestreatmentsoftheCl.assical .andShedl oyskyconduct anc eequa t acns, and theirconpariSon~s

demonstrat~^as~^superiorrneth~

fu

thecal cula tion of~sot"ope.

effects.

A linear' leastsqua r es interpolation ,toII\ini.nuJideviationof'

. "" . . :

Shedlovsky~tvatues~ith varia~ionC!(limit~&'equivalentcon -. .duceance(~)^iste~icdass'suitablemethodforthe ca l rul a t i on

. '

'. . '. .- .

Qfho.,11leeffect,ofsub~tt;uentvariationon the isotope effects repot -tedhere disqua lifi e s.th e~fuple^{mduct fv e}model.as,a legitt.

mate,

des~ip.tj.on

^of

s~condary i~ot~

effectsof" thesecona

.~ind.

^:

\"" , i . , ' -,.

".

;: ,':

..

"

.The

correi~tion

^of

dk~.llishin~r iSO~·OPe. eff~~t'

^per

d~uteri~ a~om

·

w~,t;h' increasin~'

^acidity'is,

als~ in~al·id~te~.

^by

^the

^present

re~~ '

·suits,

~

"" .Th.e

.~yntheses ,.f 9.'-:~. :ia~9.~D~dih~d.~

^..

~ena,;th"me,9-0Xi4e

^000..

efuoxenthcne-tq-oxr aearedescr-Ibed. .::rh,jecompoundshavebeen

'J~rtial1Y':dffiJ~eratcd

^at'their

respectivC'~~hYlene P!Jsiti~ns ~y

dis solution"inafkajjnedeuteri~oxide..SpectralevfdenceIndi.~.

interchouigeof~h.emet hy l ene,p ro t cn chemical'sf doesn0t:'., .occur fer

:~'ither c~lUld

^whenthe

sOlve1i~im

^is

~aried f~

^.

~imethYl~ul~oxide~d,to,t r i fluo roacet ic'acid. Thepropos~

conio~tiO~UllchaIlge,;f thioxanthene-lO-oxidefreerthepseud o- equatorial'array an-chlcroforn-dtotlJep~eudQaxialarray~': '

·t;ifluoroacetic

~dd

^is'o

~sidered,

•1

--.,;

,{

.fiREr-ACE ,

ABSTRi\LT'.

,1..INTOOOOCfIilll

:1-1. ,~^{the,oTi gi ?}~nd^Int eJTIrct ; tiono~. Isot ope 'EffcCts,,'.::•• .;t

.3'

',' ,'9','

F2. TheCal cu fat icn of Equi libriumConst a nts

from

Conductance~leasuremen~s^','

:<.: ^{.3 0·r}

1-3, rhecafc utarton.of Isot opcEffects'. S3

z-r.iGeneralInstrumenta ti on •.•.

2-2•.Conducta ncf

.

Instrunen tat io n.•

.2~3. Mat-era1S.' ,•

, \

61

62

'7

J. RESULlS

3: 3". IsotopeEffcct s '•.' _..--

. . ^{. . . . ..}

.'83

91

109

, .

..

:':"

".,'

4. DlSl'USSIOO

.. .

4-1."Th~nnodrnarni~'Equilib,riumConsta~ts l

4-·Z.'IsotoPe~fCcets .". ,.•

.>. .. .. " """.

"4-4. Sltmraf}' • •.'.• •'••• • "",

112

...

1'14

128 m

139

5-1. em'the Originofthe Hagnetic Noncquivalence "

.' 'ofthe

~~h~lcnc P~'tons

^{in ' .} Of.

. .. _. ^{\ '} _. ^"

\

'i' )

^~henyl:ulf,inYlaccticAcid.

,. ,," ":.

• • • •..14Z·

-5-2. The~oton-Dcutcronnx changcneecrt on of Phcny lsulfinyl acetIc Acid.• . . •

5·3.

N.~.0~cctTa

^of

pnrt~.allY

^r:xdu

~ ngcJ

PhcnyIsulfinylacctic Acid ..

J .

. . : j,'j

(1.

EXl

^lERHnttt

4¢l

e-i •.lnvt tumcntation'.,

i'{}/ . .

fi_2.'·~btcrials

7. IU'.SULtS/\NU DlsrusslOO-

.7-1 . 9-Thi <l·9 , 1O-d i Jl)'dro ph enant h renc-9-ox idc

I

7- 1..,Thicxan t hono- Ht-oxld c •.

• .•.1f>6

··_•.17 S

.1-S1'

••182

· . to,

•",208

,

I

APPENDIX I • Al'PE~DIXII APPENDIX-III APPENDIXIV

\

.. 217

';J

·.224

·.232 , ,253. .'. 268 .:.'.275

,"

r

...

.'.

.

^...

'"",

. ... .

•.. .

'

.-.' ,'.

I,

,

.

; .'

.

,,-

'1-:

-«

'.~

" ' -t"

J .

^'

:

,

',.,

... .. ... . . ...

.~

".".

'.:

..

'

'.,~ .'

: '>

_~.

..

^"..

. ~ .. . .

~'

.

.'

L

effects:'.

"

.

.

'.11.te'correl ati on.ofst ructural.changewithcorre spond,i ng' .

..'T'eac#Vi~changehaS'remained atopicofinte,resf.inthe field

=0 £~ntetp:)raryIilys ical~organicch~stfY" 'Stroctur~lvariat ions emraci nga....ide.rea~tiviiyrange havebeenstatisticallytieat~.

te .£.

(1»),andthephil~sophy^ofth~f:interPretai'i~'liasbeen. ca~f~iIyconsidered Ic.f.(-2»)..By <lefin ition. however,the

~ ~~t

^{'subtl e}

varlatio~

ⁱⁿ

struc~uTe '~t be _isotoPi~ ·sWJst~tution .

^t

-l. " ' .' . . .' ~ .. " " .'~ . '

'.~ ..,with thecor-re spondi ng,reactdvttyChangesdenotedas"isotope

. " .- L' ' . .",

r,

\\ . r: .

.,

.

^{' .} ' . ,

. ,. ..

In'the inte res tso~cterdty and cont in uity,thi s.p,resentat ic;m.- will

be .

rest~ictedto.the.coru.ide~atimofonl¥oneisotopi~pa~·r.· , 'muliel~hyd~en

hQ

anddeuterhn(0 ) . In~euseofchmi~l

equil~b~ia. -~. bator. _ef~ect

.i s

' define" b~ ~>~tl~ ~f ,Kcffl _t~

.K(D).K(H)beingthe"cquilibrit.r.lccnatant~rtainingto,thePrbt~

sws"t~'tuted s't~ture

^an1X(D)theequilibri lJll coru;tantapp'ropr ia te' tc the

d~terh.n analo~. Wh~'

^rate

me~u~ts a~

^of

in~~~t', '

tl.eis otope

e~ect '\s

^{desigru;,tedas t}he rati o of

"~~ eOrTespotd'ing:~ "

,nite

const3ni~

^k(H)to

.

^{k(D). When}

~he

^. ifo"top;^{" ,}

.e~fect

^{. isgreater.}

.

^.

thanWlity,'i.e."X(lI)!K(D»lor'k(H) !l<.(D)?,l ,itis sai d'to be-a d'nonnal "effect,and

whcn.i~ss·~an unitY. i; ~.

^{K(H)/K(D)<Lor.'}

k(H)/k.(D) <i. i~isdes cr ibedflS

an

"Inverse"01'"~~verse"Isot ope ef fec t.

.(:, . ^{'. . (}

, ,:A,

fu:th~~ cl~_Sifi~atioil

^Of..

~ ~toPe ~ffects d~cnds ~

^,;a

':'~'

.-'. <.C~i~eration~f,^the~~f,ec~.^of~.he^..~~ical.~rocess,~n./~e,^bond

linking the isotopicatansto.themolecular.r~sidues. If"this

partiCUla~ b<in~is '~{~red

^or

par'ti~lIY ruptu~?

at'pr-irnary..· isotQpe effect'tesult~;butif thebond remainsinta t t 'i n··.·the

1I:''O.J'

"

10

.

^::,~,

"

.

' - . --,, " : '

,reactanrs ,tr ens t t .ion-s t etes,':m~ ~iOduet~^'.theisotopeeffec~

.~ is':se~ondaI)''', ,.Eq~tiO~S',~.:)It~.~2j^serve;to iilustratea

g~~ryand asecondaryi~otope'e ffect respectively:

.. .

^" ~

Ph:.

rn

2-:CXX)5~)^+'D30( +)

~~ ', '

p h

~0I2.~ 0Xl~ -~'+^H30C+);,

','

,Ph~Oh'- CXXlI+'1!2.0 ...!illLa.

'Ph · Oh. -

CXXl<· ...H ;O . ~

^Ph.•

'.Oi~ '- .OXl C-)

^+H30

C

+) [ll

~h

^-e;th.-

aX:)D+D20 " '~

'<

-'Ph';CD.~:,-coo-r+fho,.!.C.QL..Ph.-CO2~

axl

^C-)+'~hOC:)

.Secondary i~otoP~^effectsi~w~ich^thebonds~m^theLso- topic,.substituents'totl,e-mol.ecUlarresitfuesundergo ;pa t i al .reor i entationh~VC·.b.:rndcscribed'h~,St r ei twe is er(3) "'as second- -

ary is otopeeff~~ts.of~e." firstkind"; Secondary is ot ope,".

~>

ItSi"nce

.h~dioXYl

^p'rotium

^and deuteri~

^ato,ns

exch,~~;

^very

'raPid~Y:

In-aqueous-~:dia.^,K£D)

miIst"

bedetenni.ne?iiJ.·D~~~( ~sequently .

K(H)/KCD)

6 £ '

c~~tiort[1]',i nqudcsnot.on lya

primary

iso~oPe

e~f.~C~>

but,':'1'150

~' ''s'olvent ,i50t:O~ ef~ect'.'"

_~.^._"^\_'1'^.

\

,

II"

. .

. .

eifects'of the "second

~ind;'

^are

thq~~

^In

Whi~

^no"

spat~al ~or­

ientatio,:"of the,bond occurs in the'equili~riunior

rate

process t1nder consideration. Ex~lesof secondary'Isotope effects

" of .

the

~~rst

^and

sec~d

^{kindlar e}respecttvety given by

Eq~t~ons' f~i'"

··arid(4] ..These examples'fom part of

i

's erie s of reactionsin-

ve'tigat~

by Strei"'ei,er,W>d,co -wor ken; (4), .! 'Ph

-~ _01, .

^{-H' B(')}

~

^{Ph :eel,H}

"'If

"O h . , ', (3] _ D

Ph' ,·

C , .-

H:;:B'o)

rn

₁ ^•

^..!ilL

^{Ph _(;?-D, 'o-h.'BH}

Ma~er

(Sa), Bfgelei'sen (5l,Helander

(6J-'.'~ ~th~rs -d~,

I ⁷⁾

have put'forwar d

rigoro~

^theories'based on.srattsrtcet

mec~nics

""and,the Redlich-Tellerproduct~e[see (8)] whichall~the accurate calcu:ationQf Isotope effects'In chemicalreactions.

:Although~ese'thoories may differ51igh~lY

i;

emphasis...~he

..differences are of iittle consequence in, the"present dfscusston.

, ~ , ^" "

The,catcinatfcn of isotope effects~rate processcs"\reqUireSa

"

, ..

.~icdgeof'the sote ctnarvibrati~~l'frequenc iesofthe:isotop-' i~l1ysubs ti t ut w sPecies.'in bot h thegTOlIlJ9andtransi tion sta t es , andin the case ofequili br i a. thesefrequencies mustbc .' availabl ef~r'boththereact ant s and prodUcts. Hence,thethea-', ret.iea lapproach proposedbyDige leisenand Melander is oflimite d' val uein its finalfonn, for the situationseldomoccursin~hich'"').

all.th c vi bra tional fr eq uenciesor the related force constants '.can beellq)irical 1yd.etermi nedte.r.

Bigelei~n

^""Wolfsberg eSc)]",

J\.n~abl~exceptIonistheinvestig at i on oft~ormi.cacid system byBelland crooks (12) . The)Ka differencebetweenHCOOHand ' IXJ)()I1obse rv ed bythese workers.was.in-

good

agree ment withthe theoret icallyconoute d valueusing

'on~y

enl>i rica lvibrational'fre- qucncies,

Howe~er" th~ ~asurcment and

assignmentofvi l?rati,onal"

freq uencfes'?~morecomplr;x.isotopi ca lly substi tutedmoleculesin a condensedphas e,in.whic h ra tes,andequilibri a areusuallyex- amined; .i s~ exc~dinglY,difficul~task.'Thus,an accurateca.l- eulati on.ofis?tope effects forequi.l ibriaandrates.is generally inq:l~ssib le.

*Thi s'isnot possiblefaT'rateproces s es since-the vibrationa l

.fr equenciesorrelated force cons t antsof.the transitionstat es'

arenotObse~ables. However. sever alseri~usat tempts have been madeto cal cula tekinet icisotopeeffectsby~loyingmul ticenter tr ans i t ionstate model sEc.f,wes thetser (9),Bell(10).andM:l:e

.. , "

-

- ' .

O'FerralIand Kouba (11)J.

\

13

IJ hv in··a

p~ir

^of

l~

^..

and ·D.,~ub~tituted\na:ogues

^is'

ia~~~

re l ah \'e to IT for- all.freq uenci es,t~ccompl~~thccr etfcajCX.~

.pressionscan be simplifiedto

a

dependenceon,zero:point energy t~nn.<;,qnd_the iso.tciPee~fc~venby

, ,' ' . ,'-h ," , -

··[5] ·!Q!2. expo'2'~ ^('6,\ (""),1.

, K(~) ^.'

where"h" isPlanck's cons t ant ,"k"isBolt,2:mann' s cons tant,'T"

isthe abs ot ute teep eret ur e,.and"ulV" representsthe difference in thefr~ucncysumsof,the respe ctiv.eproductsandreactants', Eq~atiQ~^[5] u;liesthat~'isotop eef~e~ts.a~cquant um effects~ that theydepend largely on doubl e d.iHerenccbe tween.the vi-

. , .

b~ationalfr equencysums of ,the productsand reactants?fthe iso t opic analogues..

Byappl ying further approxdraat.Ions Equation(5',] 'f'iY~e s~mp lified"togive

[6 J !ill!'-

K(D)

r

I

:In thisequationonly thesums of thosefrequen

7

i es',pr.imarily associatedwith the motionof~he hy.d~genat omatdothe<$Js~tion

of-interest'i n the non-de uteratedproductand'reactantarere -

.

.

quircd ,and these-sumsa~e~~presentedby L"'H and.Lvii';r~s~.-;

tiv e l y.,Theseapproximationswereemployed.by.stretteetserfor

..

'\."

the calculation ofis?top~effects'inrate Processes - lIowcver, si ncel.(U)/k(D)ca nbe relatedtb K(II)/K{D) (l3 P',then isot op e cff~tsarisi ngfromcqui Ifbrhmconsiderationsmaybeca t cutated. using Equation[6 ]; The constant."c" in Equat.ion(6 ]ha s athee- retre atva l ueof

rr-«,

hutSt~ci twc iscr(14)hasdeterminedthe

·;' a l ucof"~"^{to he'about.1.:5from a}ce;nsidc~ation^{of sul tabIe}

.;. ·''''-·sp~ctroscopiCdata; ByemployingEquation.[6] to approximate~

isotope .e ffect,thesumsofal itile vibrationalfrequenci es i,n

bot~,

^{'pai rs}

o r

.I sot optca l Iy ;ubs t i t ut ctl reactants

,~d pr&luct~'"

^a\..c

no longernecess ary,: In extreme ca ses,thes~t ionsmaybe,100- duccd toa cons i de r a tion oftwoor three vibrationsoreven a si ngle vibrati on. lnoweve r-,for more detailed calculatIcnsusi ng the coinpletc.thcory,sec 'Wolfs hcr g and Stern(lS)and Willi(16)].

Itisgenerallyacceptedtha t prothm-dcutcrjtmseconda ry tsotopoeffect~are primarilydependentuponze~ro-point'en~rgy

:~i.f..fercncesincurredingoing from reactantsto products.:

Kk(H; /k (O)is act ua lly;

r~lated

^to

[~(H)/k(D)]+

^{inwhich K(M)and}

K(D)

a re

the

quas'i -~~1ibrium

cons t antsbetween therespective reac tantsand thair transitionst a t es.

UThetheoreticalvalue of

a:

;es~lts-!ro m theapPlic~on-of the'"infinite mass-diatomi cosci llator"approximation, inwhich thehydro gen atom is

as~&ned

^to'beonly

~ibratiitg

ⁱⁿconjunc tion

~iththe III\.lch larger mass of the molecular!esidue.

,

/

rs

Thesedifferencesare in tu:ffi'.dcpcndcntuponforceconstant changeswh ichcanbeat t r ibut ed to stcr-Icinteract i ons (14,17,"

~8 ,

^{19, 20,n,22,}

lJ) .~

suc h-oloc t ron iceffe ct s

.~,

^hYPOTCon-·

jugaticn (14,

ir,

.24, 25,'26,27" 28) ~hyhrIdf aatIon (14, is,'19, 20',29.3!!!, andinduct io n(29,sn:

Strcttwciscr(32)has ascr -ibedsecondary isotopeeff ect sof .t~i'" ki~to.hyb ridi zat ionc~angcs .hutdescr -Ibes eff ectsof the second kind as thos ewhich "behave

~ik~

^{induc tive}

~ffcct':::

^,"

~F

ThC"~ccr i t e ria have beencr it icizedlJYHal.ev~.^{(29) \:Al0}

sta{cs

^l•"a"

~las'sificat ion sch~mc^{bas ed'on thepresenceorabsence}of Sigrlifi:

can tstru ctural changesin thereg ionof isotopic sllbs t.i tutioni~

likc~y,tosurv i ve longerthan oneb~scdon theoret,ical concepts , nomatter how wellcst ahlishcd theseseemto beat the

time".

Thiscrrr t ctsn-mey"..ell be consideredt}iVialsi ncest ruct ur a l

. · 4 ·

,change~^lIr.c.thcmsefve susual l yhased on theo.reticalcon~eJt~^(e.g, postu'lat cd.me:chani sms ) .. Indeed..In hi sreview (29).HaleJ i attempts elabora tion and inte rpr e t ationofsecondary isotope

~ffe::ts

^{.in termsof}

qualitati~~

t.hcor etical

-conc~pd

^{rel at edto'}

changes whichare el ec troni c in nature. .Hesta t e s ,"deuteri um bonded to carbon is effec t iv elymor eelec t ropos itive , butless .pol a r.habl e , thanprct tcn. ~rincipalfact or respon sible

(fo r thi s e.lec t rondc diffe ren ce).s ccesto betheanhanoonicity of thevibr a tionsinvolv i ng thenotions of the hydroge n,atces, whichleadsto differentaverazcbond Iengtbsandang~esin

16

'~,

deutcrated

ilJld

no)'malmol ecu les ".andhence, a differe ntcbarge-

<,di str ibution . This,hypothesisthat'~SC~OndaI)"Is o tope effectsof

".thescco,ndki ndbehavelike induc'tIve effects is suppor ted

W

:hc

.crrcctof de utcration(at po;itionsc and

a

tothecarboxyl,g~up)

ontheequilibria of thecarboxylic'acfds listedinTab ler. In .the.caseo~a few anrnoniUl}l ion acids (33. '34,35.36),whic hsh~w

behavioursi mi l ar,t o't hat ofthe

carboXY~iC

^{acidsin Table r,the'.}

eff ectis more marked; but thishasbeenra t i ona lized on thebas is of:opposing""i nduct i v e~dhypcrcon jugat'i v l!' ef fectsi~_t.~e^{car box-} ylic acids (29).

1fsecondary isotopeeffects behave Likeinductiveeffects.

the m"agnitudc of~ucheffects might.be expectedtovar-ywith structu~eand with.positiqn_of deuteration , andco~cqucnt1yb~

amenableto alinear free energy tr e atment in much the'same mannerasTa ftts (37) treatment of "largeS:~lC"tnduc ttve ..

effects. 'Indeed, St reitweiscr(32) has successfu t tv~pplied'the Taft equation toestimatethe magni tude of isotopeeffects in

-c,."cer-tain aromaticring compoundsfromthe.is~t~peeffectsofan

aliphaticseries. ' '.,.

. " Usingthe 'premise

thatC·t'~~e

effects at-c

a'dditi~e,

, .

' \ . .

^.

Scott andBarnes (38)havemodi~l$d.t~eTaft,equation(37)l~om

[7] lo~ 1Q X'''' (I.?21 t_0.025) oll:-,)4.76 to'

\

[0] .- ( 0 . 550:!:O. ~9)1:01' +.5.200t0.014

17

~.-

. .

lSOTQPJCPAlR

OII<IXJvtnICxoo

(01) )CXIXlV{CD, ),alXJi tmlf!DmlI OhO haxJVCDJQh CIXlJ

.OIJQl_zOXlVOI,CD2CIXl1

PhOI2COO1I/PhCDza:xli (. ) \(.) Ol,NJh/CDI~IJ

lill!lmPl,'

OBSERVED(REFERmCEl CALan.ATED

1.~35'(32) 1.04,(32)

1.08 t~'

^I.O}

'1.01 (34) \.014

1.08 (34), 1.021

'\

^1.12_1.13 ⁽₍₃₆₎^{34) .1. 021}_1.083

, "

r:

,

\,

1.3 2 (36) 1.18

.")'herec entncasarerc ntsof theK.(lil/K(D)"valu,e.srepor ted

in

^.(38)

forR-P.h0.'zCCO I/R-PhCDzanf.wher,c'R..II,4-~bo.4- NCh .arcgivc~

in Table

in.

p.28.

lie

.'wherealitis.t hc Tllft inductiveparameterfor asub~titucnt"t'

.' ,',, ' - . -J

atta,~lcJ:to.thc..~arboxyl_.~J1)~acarboxylic acid. ~lcn"X"

can bc.con.sidcreJ,asasubsti~utedmethylgroup(·CXIX,}~Lthen',

I

~,(Xz)

.,Thi smodificat ion is similarto Hall's (39) relationships ,which arc given

by

no?

pKa =...--l3.23~3.14to·

l fcr'-primaryttfninc~and

)

[Ill

f?Tsecondary amincs , In,thes e equationstheEo" pa rameterrefers

.to't he sum of,the Taft constants fOT~egroups attached to the'

nitrogcnatom. The1:0·val ueswere calculatedby SCot tand Barnes (38)for twenty-threecar~oxylicaci1s"listed inr.able.II.and used in thecorretunon,ofEo*andpKashown in FigureI. The correlation of0*andEo'"(see FigureII) gfves.a st rai ght li ne which docsnotpassthrough the originandthe slope.ofwhic~is nO,tunity. Ho.wever. thisplot indicates that the.premiseupo~

which themodificationof

the

Taft equationis dependentj name ly thatinduc tiveeffect sarc additive,isbyandlar gea good one: Although theccr re r et f on of ro."andpK_abasedonthemodification.

19

0

.T~1EII

ACID~G1lfDATA RELATED

To

mETAfTCDRRELATIOO FOR SUBsTl1UIl'nAmTteAClnS'f!AKENFRDM-(3B)]

':.:/ '

' .~

^X=CX1XZX)

ACID (X-COOl)

E&':.

~ X, X,. X, Eo:ll+

)

^{'.CF1CCXl-l. 0.23 .·F 9.30}

'

"

^{ccnmnCBr'lrnQl 0. 65}0.66 ^{'2.65 C1}B, ^CB,^{1 ci ,}B, ^B.7Il8.40

i "

"

QIF, lXOH 1.24 2:05 ^H' M69

,

(}fC12OXJI 1.29 1.94 C1 C1 6. 29!

- .

^{"(.) (+)}

(Oh )sN.Oh ax:l.l '1.83 1. 90: _(Qh)~N H

rna.hCCXl~ 2.43 1.30 CN 4. 62

OhFCOCH 2'-59 1.10

. \

^4.08

Qh{ox:t-Ih· 2.83 ~1: 05

'<WI ....

^;..

-

rn2Cl~I ZiB7 ·1.00 C1 'H 3. 8 8.

. .

Oh Brcoo:I' 2.90 0.92 BT 3.78

CP1Ql20X11 ~.O7 0.85 Cf,

C6H$CQ-I2.~1 3.12 0.85 Plil

(3"

^{Ohra:al 3.18 0.52 I 3.38}

OhOCHico:J-( 3.53 0.60 01,0

.

H H

noxn 3.77 0.49

~02(}h0-l1COl-1 3.81 0.50, NOzQh H H' 1.48

(

^{.... Cont 'd}

'\

,"

'.

\

/ .

20 TABLEI I(Cont'd)

X•,;'CIX, X,- ACIDrx-coon plCat,.

o' X, x, x,

1.0·+

(Cr.l1s) . Q KD:JI f 3.94 CaHs C"Il. 11

•

(C"1I5hC~-_t(

^{C"H. C"B' C.H." 2. 94}

ahC ~P1zaXU . 4:08 0.385 Qiz~l 2.52

.

C"lIs0h(D()H '4.3 1 0. 21 5 C"H. H' 1.5'

CF.OhQho::a l 0. 320 CFsOi.

"

^1.50

C.l'.D-lzO lzOX»I ..0.08 0 C"H.O '2,11 1.1 9 5

Oh CXJOH 0.00 H' H 1.47

{Ols),(} {( XXI-I 0<, 0 ', H 11.4 9

Ol.O!,O)OU -0. 1 0 en,

--n:

^0',98

OhOi. rn.OJOH .~.8 2 -0.115 OloCH. ·H 0. 8 8

OI.tH:i(Q-!.)OIOXJlI -0.2 1 Q-1.0h

0"

^0,39

(Oh).COX)l! .5.05 -O . ~O (H, 0 ', '.a-l,

- -. I _

t~1:1pKa.valueswpretakenfrom (41)'excep ttho s eofthe

• rnonol'lal o g e l'lOacet ic acidl'.wh ichweretaken fr om(42) .

";"e

to' ~a'u.> ~rc "k.~

^{'r om 'he}correlaU on. '"en hy

Eq~;ri~~

[8] (se e

Fi~UT~ J~.

^alld..

~~e~ n~t ~~T~~d.

^from'

Eq~ation

^{'(9 1.}

'.,;

0 ..

<:' :0

. r

.

'

.. zz·

,

^.

...

o o

N

e.

.

-.)

•~^{: 1}

,

-.

"" ~

",>.: ..

^-0~

~ oo : ~

W . , .. . . '1

.. . > :'ii~$Ji§

~f"'t/-

' .

23

.

^{' , ,}

~,

^,

(seeFigur~^{I),i s}inferiO~^to,thatO!ig~~'~ygi y1 by Taft

t

^a'

moreextens ivcrange'of structuresi.{emltraccdbyEquation (8J

,t h'an was

~<;ed .t~ e.';ta~liSh

^{F.qua·tion·}

['7;~ Dev~atiO~_ f~~.

^tfc

str i ct ,:i"dditivityof.inductivceffects

may

bea con.sequence'of - st e r le,eff:-ct s ,but these shoui d'be~egl~gible'

in

thecase of"

H. D, GI,andC!l) sUbstittionts[However,'see,Bartell's"invcsti- gat.Ion of nonbonded:nteractions(i s,19,

wj],

I

,

. .

'

'.

^{,,' , ,}

" , . .. .

The value of_0:'":.(D) was obtainedfro mequilIbrium constant

.

^{-' , ./ ~}

mca surcncntsmadeb~Rate~.~ &' (40).~thernJaiJVQ)J~"

system,'and si.J1lilarlythevalueof0' (CD))wastfutainedfrom'ah

\' investigation of.th'ef0l3)Jcip1/{aJ;.l

3~ ~ystem

^"by

'~treitweiser

~d

^Klein

(~ .

Subs t i tut i onof thepKa'sof CD,cXxi1'and' ,

,

" ,. ^{. .}

(CD, ) ,axJIJ Into'Bquat.lon18J i;oilowed,Scott.and:Barnes (~a)to, .\., ca~~a~~ .v~luesof0.482 md,-O.On for0'"(D)aridaft",rn3) , r .", :tl;sp'eCti yel y.,Theseval ues

'of ~"; '

^{(D) and ;;}

'((D~ ~~re

^{'t hen.used '}

~

,

~ ~~

^{.c onjW1ct i on}

li~th

^the":al ues ·ofoft'(A).oft(rn: , ),andoft'

~h)

{see Taql e II)to d lculate"theLa ';'val uesofthe,·,~oliow.~ng -~.!10.

topi cadd systems :

'00:u-i/rx::xx:fl , 0i3rn~aXl--vrn3rn1OJQH;'"'"

, " . (» '

«)

0I1rn10X1-1/OiJCD2(X)(]-t,PhOIzCXXl-l/PhCDzQXl-f,"Q{,l'tI1/CD1NH1,and

• (+) 1+) (J, • , • • •

(rn, )zNHz/ (CDl )zNl:lz • Fromthecalculatedzceva t uesSc o t t,-and'

""Barnes

',~38)

^have

recent~y ~~edi~te4

^the

iS~~OP~

^{effects;f.'the; .}

•latter syst eas,and theseare canpared (seeTabl e

p,

wi th exper-• , .iment-allyobserv~dval~s

_ dete:rmmed

byHa"l~~i^('34)and:-Rob~rtsq~

~ . "

.

^{' "} -,. .

.(36,43), Althoughthe predictions'ofthe isotopeeffects for theseacidsystemsare

qu·~.iit~tivel.>: ~;;ifiEi<i.

^the

obs_et'V~

^Iso-

to~"~~£ectsgenCra~lYexce~ded ~predi~(~"^effectsbr.-seve,ral

percent. . . . ij;.

.

^'

,'''',

. ,

14

TO'pro vi de'

~;e data' Wit~

^{Which.to test.}

~e'

^{lIa leVi}-Str ci·f.<

~ise~-~a~t ~Juc.tiV~tr ea trnCntofIsot opecffects ,Scot t~". . Barnes.(38.-44) carriedout conductance measurements todetermi ne

tl;~;~(i'I;-iK(n;

^_

;atio~'

^for

~hO' ,i~:to;i;w~ak '~cid

^{pairs ,- .. .} 4.NO~.·C~li,,·-·al2-axlV4-Mh ·C~h·~Q)2-co::lI^and.4'~W-c,II~-rn2-fJ:X»ii

".

4-~fcO-C~I~_-c:b~~~1~

^.

Th~~' ~:lso ~cd~t'~~incd

^the

isotop~,

^effect·

.of..thePhQl~aXWPhCD;(D(Hpai r.-The se aci dsys fcmswerechosen

«,r , . ' , ",

.t~.:est;t~~ a~cquacy.of the Induct ivctreat.ment ;.:s i~ce th~.i~duc~

."'.tivc.model"r e qui re sto.e fi,rstapprcximat.tc n that; Isotope.effcct.s

be

il~JepC<lTd~nt

^ofthenature

_~f

^{"anyg:pup'substi}

t~ted

^Inthe:

~-~

·':pof i.t.i on ofth~ring.dn the.a roraat Ics~dechain.

··Alt hough.the isotopeeffect ra'tlos'determinedbyScot t;aOl!.:d Barnes·(38,44);arc

i'~.

qualitativea;reel1)!!..nt'",:iththe

Halevi~ ·

^:

·~s7reit\o.'ei,ser~Taft.induct ive nodet , acompa~i~',?f.lInlogIOK(H) /

"KeD)'and~K~(H).has^beendeemedgr~<lterⁱⁿsignificanceand,

~.:-·~n7.erest"_" '~9

incl usion.of,t11f datafor

t~e ~cet'ic

^acid-system

(40) withthe.resultsof thelati~rthree arylacetic acid pairs :

~uige;ts

^a

tre~d

^{.i n'which'}

~e

isotope effect per

dcut~riWl

^atom dccl~es

as

the strengthof\~~acid, .in cr eas e s.(seeFigi.rr~^{Ill) .}

~·V;'J."Shiner.(l1)'or i g inallyp;o~sed

th:.

^fcrmnai/nlog'IGK(H)/

}\(O)inwhiCh n,"3,for0I1CDJfl/m1a:a-tandn "'·2fortheary f-

i:' " . . ,

ac~ti.C.'acids.,

-~.

·., .

2S

~

~

^{UX;"'J:(H)/K{P)YS.pK.,(H)'.[TAKENFJDI(44)]}

0:005

0.004

..,

0.003

·0 ..

^<,

~ 0.002

""

o

'"

9

0:001 -I,,'

9.000

12>

,'

.

.'

pKa(H) .

4.20 4.40 4.60" 4.&0

...•::'.,-'

-1.998..L.;...-'--'---O:.' - J . - _ - I ._ _...L...,:--I._~...J

3.80

. ,

26

' .

"' , . . '.

~ obseTVati~'~rgefrom~ecorrelation.o~ P~a(H)wi th

l/nlO~to.~(U~:K(D): : ^{: " , .' •, .}~

' .(1L

Th~redi.ct~dval.lieQf.i.ozof or,the dsotcpe effect or:the PhcH20XlHiphCD2COO{acidpair based on

a:

^1It(D)isnow much closer

"\~

^...

to,_,~theobserved_val~of 1.01. Le,the induct;ivetreatment

is

pait~al.1Yvcri~icd: ^{\ . ."}

(2) The isotope effect appears to be variableanddepends on the

~tnK:.~U~LOf ~e

^{acid(38 , 44)'•.}

This~s

not consistent'

wi~

,t he simPle

induc'tiv~

nxxiel. 'which-r equ t r e s that the"

in~­

.tiv'~'~ft~t^JX;Tdeuter-Ium atanbe Independent. of the molecular environment ofvthe fsotoptc substituent.'

.' The aim of thepresent work wasto furn~sh^furtherdata

"whi ch would test tbc-corretettonofdimi nishi ng isotope'eff ect per deuter-ium~tomwith Increasingacidity (see F.igurc III). The r.elativelr's tron~isotopic acid"pe tr sClPI2a:a-1jClCD2a:xJH,' PhOQ-l~OXlf/PhOCD.2<PJH.PhSOI2~I/PhSCDzCDJH,PhSOQ-lzOXlH/PhOOCD2- CXX>H,andP~S02Qh~j~hS(hClha:xJHwere chosen forinvestigation because previousstudies have shown the prot-iumacidstobesuit- - ( able for conductancemeasurements (42, 45,46).andthes ~pairs,

~d furnis~pointsint~lw pKaOU portion of the corretaetcn>

(sec Figure III). Aline ar leas.t"squares -treatmentof the data for the.carbcxyj.rc acids.examinedbyScc t.t and-games (38,.44)

~as'ell1P.l oyed to determine a tentative relationship between l/n-l~gl~K(H)/K(D)~d p~a(H). The resulting~ti~is

. ~

... . .

".-

. .

Thisrelationship was'~ioyedtopredict:t~isotop~effects

antiCip'at~, fo~. th~, lsotOPl~

^acfdpairs

'uOOe~

cCns ide ration"in I . ' . ... ' . . " -.

'.'..the~presenti~~~ t igati~-(s~·Table'111andF.iRU~IV).'. ".-.

",c'

~'.:....J

, . .,.

. .~ '

..

'r i

.

^{\. - ...}

~

. ..

'.

'.~

..

'

.

".

" ,"

' . '.-

';

.

••'1., :',

",.:"'.::.> .•~.;.

"\ .:

1\

~

mEPREDIciE:D ISOTOPEEFFECTS OF SONE CARBOXYLIC ACIDS

CALrui.ATED FInl A LINEAR LEAST.5QUARESTREAThlENf OF.OBSEWpKatH) A'ffi lsoIDPE'EFFEcr VALuEs

, '

K(H)jK(D)CALCIll.ATED Flal.0BSERVEi K(H)jK(D)

'1

PIDfIl.Jf .ACID

- '-- '-,

OhroJi., 4~MeOc,H ..rn20Xli C,HsClhOXlH. 4~N02C6H..O;hc:n;:H C6HsSGhaxlI C6HsOOhaxlI ClGhOXl-l C,HsSOGhCOJH. C6HsS020ha:a-l

..

^'

• pK.<H) -.

J:TAKFNFIOl (41)]

4.76 .4.36,

4.31. 3.88. 3.43 3.14

2:85"

.. 2.66 2.44

B:SJATIOO(12)

1.032 1.009 1.007 ,0:994 0.981 0.972

.-:.--..

0.964

.

.0.959

"

0;952

[TAKm'FRlJ'·{(44))

1.035 1:005. 1.008 0.996

~

./

^}'<

5·00 4·50

4-MeO-C.H.-C H.-COOH c.H.-CH.~COOH

• - EXPERIMENTAL'VALUE / -. - PREDICTEO VA~UE 0·004

0·006

r---....;.,---.--:---....

r-...,...;..-~

30

1- 2. TIlECALCUl.ATl~OF EQUlLI BRItNCONSTANfS mll roNrtJcrANCI. , NEASUlIDILVIS.

1-2a. A~nrrnooocrION11.) 1l1EmNIXJCTANQ;~1EmOD

As

several,excclicnt accoun tsofcond~tanc~measurements~ electrolyticsolutionsareavai~ablc(47'. 48, 49,'SO,?1,52)..

thisIntrcductionattempts onl y abri e f history ofthe calculation o~equilibrium constants from concerrtrntIon-equivajent; conductance da t a.:

.-rarl yconduc t ance theory at tempted_3distinctionbetween

. .

ctcctrcrytcs , classifying them asei~hcrweak orstron.g. Both ctu sstflcat .tonsevolvedfroma constdcrattonof the'<rcjntivccon- \., duc t ances oftheir.sojutIonsat cceparabfo concentrat ions,the strong electrolyteshavinglarccr,conductance s thanthew~ak•

.Electrolytes whichobeyed the OstwaldDilutionLaw(53) .

[13]

--'-

A

~ K.A2

•c O.

(

wcrc'cla'ssificdas weak elcctroi):,tes,* ~trongcfcctrofytcs

appearedtoIol lowrheSquare ~t^Law,empiricallyformulat~dby

"!Theparametersof cqui.valcnt"c onduct an c e(Il),limItingcquiva-

"

l~nt co~ductance

^"(Ae) .

c~~ceJration

^(c).and

equilibr-i~

^con-"

st ant(K

c) in Equations[13 ] and {14]aredefmedIlIOr~formally below.

31

Kohlrnusch (54) . This rel ationshi p is expressedby

[14] 1\ = Ao •.B(c)l:i

.i nwhi ch B isthelimiting,~lope. Thisdistincti,~n.howe ver.

was not sharply defined and inseve r al ins tances the ctasatttca- -~ions,

tended

too~erlap;

Modern electrolyte'theory classifieselectrol yt es as either ionogens

or

Ionophores. The formerare tyPifiedbycova l ent rmlecules~hich rapid~yproduce the noodjnami cally stab.Ie '" ionsby a dtssoctattonprocessin aqueous medta,"and the latterare,cl ec - -;

trolytes which existas.~oniclattiCes inthe pure fora. The specificconductan~of 7S0}utiondepends upon the nunbor of ions per cubiccentiJneterof solution(ni for thei^th kind of ion). their charges (zie)andtheir mobil i t ies (ui ) ' Le,- metr velocitiesper urut.offi el d strength(55). HenceJ-.t he

specificconduc tance , L.isdescribed by ,I

[IS]

~~Ct:~tainorganic reactions wh i chprod uceth,~~dym:Unicb.~lyun- .stable c arboniumionshave alsobeen~scrihed.as"Icnogeruc

'react Ions". The disti nctionbetween these-andthe aboveis .obvious'.

3Z

In pra crj cethespec.l.fdcconduc t::mceisanempiricalobse rvab le related"to theresi~tance(R).ofthesol utioriby

(]6J .L ;.. K/R

whereK isthe cellconstant . the detemine tfonof,whichisdes- .

cribe~

^{betos (see}

3~1. · uti.

<nIsrANTS,pp,83

~

^85):

,..The equivalentc0'.1duct ance (l\) of thesolutionj.sreadily ob tainedIrmthespec lf'ic conductancebyemployingthe relat ion- ship

C17J.

t .

inwhichtheconcentT~tion(e) is expressedin~lesper1000 g ofwat~r.*

F9r

asingl eneu.~~alsolute havf ng adegr~.o£ioniza- ti on(I,

t~onit

concen tration isDCandthe

~ot~l

^{chargeper molal}

unitis aeF, where F is a charge of oneFaraday . Inconj unction withEquations [15] arid [17] thi sle adst?

[18]

""Concent ra ti onis somet imesexpressedasequival ents perwrit volar.e of solve n t.~utin thepresent case of 1:1weakcarooxyt tc .acids'dissolved inwater.1l()1aJc~centrationswereusedinthe

calculat i on of equilibri unconstants.

33

whereu,andu,ar e theapp ropriate ionic mobil itiesof-t he specdespresent at

~

finitie

con:cen~ration.

.- ,

Hence ,the variationofd.heequival en t conduc tances'

of

Icno- phcr'es completelydissociatedin solvents ofh~ighdie lectric.con- '!>t ant isprimard;"

1f.

functionofthevarf a t t onof ionicmobi l iti es with~onc~tTation. AI,thoughthe mobilit>:.fact9Tremains imPor- tant for solutions of Icncgens, itis,sllP,crimposeduponthe more dominante~fe-ctofthe degreeof ionization.

Kohl rausch^I5"Law(56)implies that ionic mobilityat infin- , itedi Iution is lirnited

s~lely

^by

"10cali~ed

int eraction,wit hsol-

ventroolecules ,.,as no other Ions are withina finite distance.

Thus,thelimiting~quivalentconductanceat infin itedilu tion (11.₀)is the sum of the contri butionsof each ionicspecies.inde - pendentofthe natu reof theother ~edespr es ent. suchthat

and thiscanbe'also expressed by

[20] .:. Ao ^{<: AO..+).0.'}

4- From Equations [I8) and [19]

_I 211

maybeobt aine d.

«(u..+ u.)

.(uo+,+uO_)

34

From theor eticalcons i.dcratio~as~dOn.an'~ionatmosphe re"

model,DebyeandHucke] (57.58) proposedaneXPTe~:~ionfor the electrostat icpotent tal ata fini tedist ancefrom an'ion. This .expressionai l ows thecal.culat icn of the

'clectrost~ti~ ~rcc c~cr- '

gy*of anion relative to a neut r al particleof thesane massand, sizein

a

medium ofknowndi el ec tri cconstan~(D)

and

tcnoerature

(T)•.This,modelpro vi des an expressionrel ating themea n act Iv-

.

^.

ityco;fficient(ft)to the Ionic 5trc~gthof solu tion{I} .,the' tontcchargcs(ZI Z1) anda constant(A) described asthe Debye- -Hiickel limiting slop which ispr oportional

t~_ c ur;

^{2h. The .}

expres si onforthe me-

moial

ionic activitycoefficient(f~)is givenby

[22 ]

in'wh i ch'I

i! dc~ined

^by

~he

^equation

w~er~' ·z~

-:- the charge'on thei th ion at concent rationc i. Equation(2~]appli~_sto extremelydilu,t e solu tionsonly buti1;.

hasbe en empirically'modifiedto accomrodatehigher concentra- tions by altering the denminator andaddinga termcontainingci '

*Both the Born charging(61)andionatmosphere terms.are given hy thistre atment ,but-thesear e easilyseimrated. Thelatter .~enn ~nlyisconsi~eredⁱⁿth~sent,discussi on.

~. 3S

'[s ee(59)

am

^(60»:

Frana'calSi de nti onofEquatioos(13] ,[ 21Jani[22]anex-

pre s s'icnforthetheI'lllOdynamic"eq u ilihr iUll c:imstantof a weak ecnocarbcxytic acidis given'by

[24J

~nwhichf u istheacti~itycoef fi cien tofth;undis sociatedacid

~t

concentration

c .

^{Equations[13]','(22) and..[24]-canbecrnrbined.}

to yield

-,

',ror'

a 1:1'

e~ectT01;te'.

^{iffu.+1: Hence'a}

.~bt i~ShiP be7

^the.

"clas sical "equilibr itnconstant (Kc)described.~.Equation[13 ] am'the"thermd~ic,"equiliprilin cons tant(Kt).in Equat ion [24.]

isobta ined.

Usingthe

Deby~.t(ickci

^{lIJdel.Onsage r(62.}

63~

^{hasrational-....}

~1edtheSquare RootLawandsu::cessful l ypr edictedthemagnitude ofthe'limiti~^{slope(8) in}~tion[14 ]. Histreatmen t pcstu-"

late sb«lfac to rswhichiJ'!.fl~einterioni c rot ienin el~t~ly.

ti~

^{'s olut i ons}

..

subj ec tcll to an^..

e~ric'

^{: . field.}

The

^.

fir~t .

^factor'

isderived ,from~heopposi ngmo~ion.of ani~anditsoppos~tely

ch..:rg~dtena~sPheTe,an~ i.~knownas the electrophoretic ..

eff ec t .'-Thesecondfactor.therelaxationeffe ct.resultsfrom-

• v'

the~rturbatipno~the Ion atmospherebyan exte rna l~ield;.

The .

. )

...

,.;

-r-3/i

ionatmosphere is continually "decaying" ~."refcmfng"-a s the- iOl!moves throughthesolution.'Alth9ughthemathematicaltreat- ment0'£these effectsis outsidethe- scopeof thisthesis, the' resulting~ua"~ion whi~ac:~fIIlDdatesthese'eff ects is'relevant 'andis given by

-i~;~/' ~\--.,..6-

in ....hh ; h.'eis-the,etect rophorettccon~tantandy\5 the relaxation~

constan~:' ~~ nUllCr~cal valu~s

^{of B and"y}

~~d

^inthepresent

thes i s arebas e d on val uesof "the dielectricconst.ant

and

vtscos-

.

'. .,

-

it yof .water.(64) reconaendedby Fuoss andAccasctna(65). F"'ll3- '~:~:tion(261 isa limiting fonnulain which line arity witJ'"(ac)':iis

anticipatedupto concentratio nsof3!..0.001N, beyond which curvatureapp~inthepl~tscorrespo,ndingto~,p rogres si-ve de- creaseintheslopewithincreas ingconcef\tra~ion.

r..

!>llre erabcratetheore ticalequationsfor conductance have .been proposed by Pitts (66) and Fuoss and Ons'ger (67).

~e

Pitts"

equetfcnhas beensatisfactorilyappliedto theconductanceof.

.hydrochloric

a~id.

Thl"equation

propo~ed

^{by:Fuoss and}

~ag~­

tr eat sthe, ions~sspheres ratlie,r:tJ:lanpointcharges andt~es the Iorm.of' ~.

[27] ft·a ha".--S(c)':i .E(clogc) -.J(c) .in: which~^{isthe Onsager}"eOO'fficicnt (6+YAo) of.thelimit in g

.'

. .

"

':."1....

-37"

law'{'see Equation126)}.

~ .is

a c:onst an t"-defined

in

the

~am:

ya~~abies

^as

S~'and'J

^{isafunc tioniefined}

h~' ~on

^{si ze.}

~'Pitts.~d·thePuoss:~sagcrcq~tionS·.willnot~c ~~·S·

OLCi seJfur ther as beth arc'outside.~c:,cqx;of thepr esentw!,rk. Indeed.

-

the validityof thei'r

^.

applicat i on to acid

^.

solutions^.... has .bcc~~quest ioned inasmuchfS.th c sl?tr-c atscnt.s\cons i de rionic:

".ridgrat10nas"suhm:lri.nc·li~e"sot.Ion,whereas"pro t on"j Lallps;'

::mighthe

'Mti£~~:Jlor

^{'t hem}ig r ati onof

hy~niun .

^Icns._

I

·: ·t

','

-

^/

'.

'.~

.- / -

",..

",

.. ..•.

.

..

:

,_-:~.' '" .

K" :' ~~' .t..• .{l-4)~u~:

[24 ]

"1-2b:

INDIRECI'~:'

The·O~·sicaIPlot•.- Equation[24] pro vid es

an

e~resSi~n

·.f,?r

th~.C?lcui~tion'

^of

the~~. ~i·JibTi.lD C~~~ 'and

:.is statedas' . •,

":.

The

cla:~~~al ' app~xiinat'i~~~

^proposed

-by '!A~:rhenius

^{68)assimed

no

mobi'litY·.di f'foTen~ial ~ith vary~

^{concentrati onand}

negle~ted

" ;:::"~i~ ~~~e.":1f :?nTt.'~bili~

^Is

~s~~:n '

--

_~

_:

.:~.'

..

·[29]" K_c··_. ~

(l-ell •

'~ich'is theclassi~l~xpressiort p~edbytheA~iUs Dis~.:

·scct a t tonHypothesis. 'The Os twald'DilutionL3w'i$':obt a ined by

·

' .

.

'~. ~, . "

. .

^'.

. . .

^.

ccmi ni ng Equati ons [28]aM[29].·.Wi threarrangere nt these

•

'oYi~~~d

^'th·c.

e:xp~ss.i~n·.stat~

^previously

~ Equa~ion [ ~~J . namely~

;,.'

..

:~

.'.

. ...

: .... . .

,

.'

" ..L " + ~

.fLo; -Kc · fLo2•

...L

A -, r I 'o

. . " c.:.:-

AplotofyAagainsta-egenerates sol utionsfor

Ao

frOm.

•.-,theu«

int~~~~r~~

^{Kc:frar: theslcpe}

~lue .~f . l./Kc ~~":z .

.'~

.

iI'

'!"

!\.. . .

..iI

--~

"

39

"'. The Fuossand Kr aus !-lethod. -

~ss- and"IC~~

^t(9)'

hav~

propos~

^a

tre~tme.rit:·-~f·tij~~~-.:n~ ~~'~a wljich.accorrrnodat~s

~th 'io~~'~;~ge

^{tnterfontcforces}

~_

^{ion-mobil ities. Fmploying}

an ahbrcviat~'

^{fonn of-the'}

_FuosS.Dnsager'"Eq~tio~

^{{see'Equatic'n}

£271,Jfor

~l':;'- io~og~n .sqlU~iOns,

the proposed

:T~l~tionshiP :~iin

be~escrib~by

[30J '

. .

loIhich'

i~ --~

^.cubIc,equa ti onip a._~

_.

thedegree of_".

i~izat{ori. ~ssoc .

'

. .

Iat edwith the ion concentrationaC."A correc tedvalue ofa can .th en be obtainedfrOll!Equat:kl~130Jby successivesUbst~tut~onof"

~.in"~othecorrection factor; represented b; 'thebracket~"t ernin

the'denomi~torof the right handslue of Equation(3OJ..This.

'~terativeprocess~apidlyconvergesto yield,acorrectedval~eof

" . .

The

correcti on

fac~or

^1.'

S{ac/~/!lo

^{in the}denominato r-of

. J • . .. • .

.theright,hand sideo~Bquat.ion:POI-may be expressed as

,~ere

^{z is}

-S~A' C;:J'Ao :/2:'

At temat fv etv,the'continu: d fraction

,

can~des cr -ibedin,'te~ o~,

!,h. e

:f ollowing ccsfne relations hi.p

I

\.

-I .,

:[32) F{z)

<.

40' -!..

.

\

. The

degree ofioniz<lfio~.a..'then can he expressedin theubbrev-

. ' . r

iated form of. _...•."..:

a

(3J] ^{.:e:_ _A_}

",Hz)

. .

.COOlbinin"gEq_•.uations ._{. .}

{24~

_:

' 3nd~

_1-

'3~l

_'

~

^and_.

Tea'~ranging

_'. ^{'th e}_,^.se.to_. ^a:

form analogous

ta'

Bquation (

i

yie l ds .

. -<~'. -, '

(34]

M

.:1-.

t ..

~

. . .

^{. ,}

'tr

^f_uis,assuned tobe,~ity. - '\;.-. . . . Alinear.,lcas t~quarcstreatmentof theF( i ) j J\and!I.c.ft2

/

F(: ) variables,whichhave been calculated from anappr oximate value o£"/Io. leadsto ancwve j uc ofAa.the least squa re s Inter-

c ept.

Thi sgeneratedvalueof1\0is usedto,rep la cetheappr ox j -• matetoOused ini t i a lly and thecorre l at io n isrepeated . The iterath'~proces sis cont in ued Untiltwo successt vevatues.of!I~

~.arc thes~w,ithin.predetermin edpreci sion-l i mits . The fina l value':Iffloisus ed tocal ~late,Kt fr omllK_t

-!l.

_o²•thefina~

leastsquares slope:

TheShedlovskyI~kthod•.-.

By

repla cing0.with

A i!l.o ·

in'the

" . " :

abbreviatedPuoss-Onsage r Equation {see~uation[3D)) andrear- nl1;ging"the terns Shedlovs ky (70,109)proposed thefollowing

" - , ~

cuadrattcexpr e s s ion in

»,

. . . . . ,. . . -

^{. ..}

~i.S'S(~l.'func tion is 'Sometimes.c.xp~r~ss~.asa'.row<:rscrfqs,. suchthat

,

..L

)z/2.+(i.+z2/4 ) 'sJ2.•....!-·S(z)

"0. · '0 . .

./36)

-.which.canbesolved int~rms^oft.h~·^{z.vaT'i able(se e}F4~tion^{[3Ij }.,}

.·~~.syiclds

. ,

andnUllICr.icalv~lUfs ~r.SC:z)~ve^been.tab~lat~^{byDagget t (7.1)0•.}

Iff

uisas sumedtobe'unityandrquat.Ions (24Jand (36)arc

· canb.in~

1IIldi'car r an,:cU,the

cxpTcs'~ion ~s.

^1>.

_ 1_ •.

..L.

+ A^oc^of.^1.S( z) .lI^oS(.%) •. Ao ^{, 'l(}_t°"o2

--.o:·; ·Sol ut.ionOfth i s cquatton forJ(~-~;'achi~VcJ.in~ ~ersimi l ar.

•0 ~o.~~o{theprcvaou s met hodbutthe variable sin.thi~insta_~cc _ arc.gener atedv,iatbc.S(a )functionrathert~on'theF{z)func ti~ .

TIle Ivc s~klthOdo ^•·.Ives (72) hasucvetcpea,~~ethodforthe· calc ulation ofequilibril m:'const antsfromac~nsi~erationof a .' mOdified {o~oftheO~t,,'aldDilut ionLaw, 11\0.a·cid it yconst nnr .

. .

isexpressedas'"

Kt

A~ 'C'f.2

^{•/ .}

Ax{J\.

~

lI>"f u1

.. ..

..'"

in which Cuis.assumedto he-unityand

,t40J

\

'42

.whcrc\,is.th oswnofth,c equlva lentconduct ances ofthe ions

a t

ionicconccntratfon cc, !Ix.isobtainedbyapply i ng the abbrcv - i.ctcdtuoss -ons uge r Equation{secEquation[3D)) totheionized part of thesolu te .such that

in which'Sisthe Onsager slop e. ThenEqUat'~on'(39J",IlI3Y"be re':' written"as

[42]

The substitut io nof

lO ~2A(fo.'C!J\)'"

^for

f/

leadsto

wher e A is)he-ricbye-H9~ckelcOeffi cient.

Byempioyi~gan approximate valueof-Ao',a.1i~earleast .squaresptot\ofthe11.-+ S(A.c/Ax)"'-and

A2 'C: io·2A(A··~)

^..ftxt'-;Ao -

S(A·c/Ax)~ '

var i ablesleadsto

t~c

^.

gener a tionof anew val ue ofAo obt a ine d fromtheinterceptby extrapol ation. Thf s"newva l ueis incorporatedintoth~itera t i ve

, \

,

.

.. .

^{, .. . .} :

',proces sa1ld

the :C~~~lation

^isrepea'ted'.

The

appropri ate value

. . ' . . . I "

O,f:~tisaC":CI?tedwhenthe valueof!lpshows.noiJlt!rov~t.wi th-.. . .In.pr edet e ne tred precisionl~its..

., '

...

,\

"

,

· .~10;;:(

..( ':";1

.I-2e. DI~crMEnjjDS ~

n:Ii

IEIERMINATICNOF. K tBYD~REcr

",.".., SUBSflnITIcNOF,PREDETERMrNEn

Ito

VAL!)ES

44

Th~

Robinson-StokesMethod. -FTOIIl'activity

coefficient

and roobilityccnsrdcrartonsboth.SherrillandNoye s (73) and

-. ^{. ." .}

.

^{, ",} \.

MacInnes (74)def.ined the degreeof ionization(c) indiIute solutio~sof-weak elec troly tesas

[44]

-whereAiist~~equiva lent'conduct ance,of the hypothetical •.

fully- ionizedelectro lyte

d-i

look.concentra~ion

<.

By~lOYingan estfma tedvalue of~iobtai nedfrom Aoand a theoreticalequaj.Ionfor Aversus·c:"nich assumestheelectro- lyt eisatr cng(sec Salt Methodbelow).MacInnesandS~~lovsky (75)were ableto,succosstve.lyapproximat e thev~lue'of ato

con~ergencefrpm~i~lcal,equat i ons. Th,isimproved vatue.of a

was subsequentlyused to caleul.atc~t.from '[quation[24]~ithfu taken as unity.,

Ina moreextensivetreatment ,RobinsonaodStokes,(76) dividedthe square toot term of the onsagerLimitingLaw{sec Equation [;6])by the iiact,or (l+Ka)1lto a11o..,:.£orthe finite

,ilKis theionatmospherecons tantof theDebye.J li.i~kclTheo ry whicH canbC'putinto the formI(~. '"B~tlc'w~erecc is the -ionic strengt hof.t~esol ut i on and-Bedsa constant atgivent~era­

turefor

a

pa r ticula rmedium.

,.'

..

,45

size of theions (aR),which has an estimatedmean value of 4X

S

^{(17). The}resulting equationis .-

[45J Ai ='h

o_ (8.;. yAp)(ac)~ 1.;. Ba(ac)':i

Th~'activityc:oeffi ci en tf_t at theionic'c~nce~t~ncc is. .now given by

[46J ft,

The valueof Ai will no t beverysens itive'to''th e val uea~cribed

" ,

to mean ion~'i zc^ifthe ioni~ationof the weakelectrolyteisnet extensive (77).

The initial substitution'ofAo'~othi inEquat.Ion[44] leads"

to an apprccdnete va,l ueof .c..Subsequent introduct ionof this valueinto Equation[45Jyi e ldsari~:ovedvalueofAi' Iter a- tionof this process.feadsto rapi dconvergenceof c'whtchis., thenint roducedintoEq~tions'(46]and(24] to yie ld;val ue.of Kt·for each concentration-equ iv alentcon~uctancedatapoint., Theres ult in g Ktval~e~overthe en~j~~,~o~entrati~~range'are averag~,;od t~eass?dated~tanda.rddeviation is calculated.

'.The ShediovskyIr Me th od. -This directmethodwas designed.

by

Barnes (44)und Scott

£.!!!!..

(38, ·78)as a simplemodification of,the ShcdlovskyI Pethad descr-ibedprevi ousf y. A,predetermin:d value ofAa'is introd.uced int othe ShecIlovsky'¥quation {see

46.

.&;Iuation Da]}and,?Snoit erationis necessary .avalueo~Kt ',.

isgeneratedf'~;;ad~concentrattcn -ecutyatentconductance data P?~t. AsintheRob.~on-S~okesMethodthesevalu~~._o':J••t arc averaged,with~hCresulting5tan~rddeViajOn~~ingascribed to theerro r associatedwiththe~rmeasurcnrnt and calculation.

'> \ '.1

>~

\" ' .

-'

.'