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^~ :~ ^.,;: ;',:'", .: i,f:~~~~; :; .. .":.~. _ . ·:~ ,: ,:.. ;£ ~ ,~ : ·~;·:~ ~ ·:~ · · ·_\:. ~)~' · · ~<:;··~ ::r-;.·: ')·.:~ ~"~ : <:'f ..-- t~~ ·· ^{r. . r : .:.; .'} ,:~ ^{,: _ .:; ._} , ( ~ ^{. .} ~ .~:' ^{. . : .'' ,.,.: .}

... . " ~i5h·io;expr~.myd~pieDse'Or

gratitud e

_to7m)'.upe,.,:~i;:Pr$l~r-.~r~k

.

.., R . S~;th

^"Qt.

his~ ~'eat. hel~;-,ti~·uWi~g· a~~ice;'·CQD.:I~u~· ~eour.ag1!~Dt

^and

~t· . :~ii;n\ .~ida.~

^•.

ibrp~~~n~Hb~ ~

^{.. ,}

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^and

Oi~b&1r,;'an.

^{' . '.... . ,. -,',:...••.:.:...-••••...}

~ .:

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^•.,..

,.~. :

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•,

tamtnde:~tedto the.glas,bJow~~,Mr.~Do~eymour,Mr.TomPerk~'taDdMr,-~ '.,'._

~;W ':. '.~:

^Ma';tin

Hat~well

^"ror the constructionand repair

~1 8SS appar~tti,

^Iwould'like to '. . "1.:'

', .,,",

....

^{' ,....}

...

:-:.

':":'.. '.,; . 1 . _

r·~?1~~f~r21:;~i~~~9.!09:'}7~~:!Y?;!~~;\:~~!j3~~f]:~r2~\ ~f;~~'1'r ^{" .}

^c

, . ', . . .~. ^" Ab~t;~~t ^{. :. - .:::_.: ._':} ··:.::.:... . ~:· ^{. ..._ : ·..} f .'_:,~. :.~.~_~.·

^..

i ". ~' ^{. . ,} ... 'T~~ 'h~\-'·~ ~'ip;,.;.j ~r:;~ .. :p~,~ih:.~~ed ·~. ~~~,;,;b~~i~~rki~;ii, ^{• .}

:~.;

^r,.•

~

^thtc?fYandexperi.rneotal.observatiouconcemiol the ferrous-Iu nc iroosystem.;

.~

^':

~~;~J

....;,.._. " . . - ,: -.".- .:?

::..',. -'".'".In

part

l,"stirtingeffectsOD .1~~PO:te~tiometrie.titr&ti9n~.involv~n!,Fe:+.·a~d.."~._.:.-{:.;,

c~.~·'·a~e i.~~~j~~a~e~·.iD :·~m':.d.~~. :_:~T~~: ·.mix\~~e.: po.te~ii~i.~~.'~~i~~;~~~; :." ',1!;(

; ..,. .describe theexperimeD~.data.:.It''hubeen obserVed'thattherneuured'po~entlab. "!

.V :;

:~ ~

^while

th'e

SOlutl6n.is

~tirr~ ~nd

'while"itis

s~~ti()nary

^...

~ 'diie~~Dt:

^AE

'~~pres\Db ^{', th e '.. , . .;' :;}

F ^{~;:: ;,;} . . . , ' ^{' . : :} g iO '~,.'~i"~'U~'~'h'o :Si~~i~:;'~~~~t2 tEb~r;;;. '.h~.~d-POi~t,: ~h~~~~ d~" .;~'r ,th• . "~:~+{ d ,id ' .... · . . . . .., . ., _·~ . ..• .. - •....\ . , " : " . • . ' . :; .' .' . • .. _{~ '.~',} • :. .•. ••..' • . : . .. • , _ . .•.• . " ' .' ..•._ - . " . :." .• . • . .•• - . _~ , : . '.'. ' . ~~ •. - •. . . . . _{~ ,'} ". , • • . _{, : ,~.} • _{' ."',}

^{':. 1::....:.:•.,·.:,·,}

~.

^{r: .',::: :}

:!::ri:h:~:"~:;O~.hoq;.;;;:t\~r ~E.'b:D~': ~' eq~iV:I'~Tt':ilr~r;

i~'~

"Atheoretieal interpretation applyin'g.eleetroehemleelkin'eUesbas'been made-to\. _

~

^l

l _~r: " - ,'~i22~~B~~s~~t~\

speedeoatrol withdlgttaldisplayandprinting systemW&!Iused,

The

referenceand.

,;1 /~:~

&/ , _ .' :e;o . ·~·i Do'

^••.

~.~ ~I~~i~od~ ~,~. c.o~

^.:

' " .r ,u.:~te9_ "."

^..

ri?.~ '~~~ .. _S~~ .:~:~,~t.·al:.~o.-

^..

' .·.V.~ ^{. .} i~:,P . ~.i.b

^•..

, ~e' .~.·O .·,Ji,'. i . ~~! ^'.'. ;·.:i'~

. :., /,~,

':''-1\.low

overpoiential 'm~~~r~meDt- W8,Spr~·~~~~.~.,·~T.h!·iit~ik~~:~;: . .. :~

wer~ eill~ina~ed

by"maki'Dg

~n 'e~t;apolab;n'--i~' ~fiD'iie"'~tati~~

^{;peed or:lLpilot'}'or' ,," .:

~:~

~;.r~\ ,';.. . . ' , ~ ~ . {

^{I' :,'"}

't~ , :~ ~~=jj~ j~ ~J

:'.:

' " '","

w'.' .;}o.•

':' r '

::.~ ."

r·· ···

.-r'~. .

, .•}: J _y .' . . .

;

.

-~...

;; , '

,' ::.

f;~

.... .~~

F~~'~&~~~'"~nf!f't~';:'~~,~~~\)''::,~'~',"<;. :,~~t 't",~;;ft;('ttr;:';.'Ji~t:.',.'j~:;'f":": ::.:'~~-r,~":.:~: 1,}~<,;.c"~".':

6

ft_'f~•.Jf!

.», !

I' . . .

/ ! . ' . ^{,F ;}

¥; :;-. :' ~I

^{I , . -}

'inirot<~eti~D ^{. '. .'} .~~

. -", '"j . -,:',.•.'" : .. - '., -::':,) '-"<.'.. .: -

-~

^{:"; .", .: '.}

~

^",

~,~;

,:The:,purposeortbe:W9rka~fi~,l'^WIL'ltomelL'l~re^theb~t_^ratecODs~aDt^{for .}

-7'-;

Fe~'~~:

^Fe;+,+e'-

.~n

^8,

~i~;lliumf~tatiDg ·~~c el~cltr~d~. ~:!l;l2'!~e'

^case.orthiSwoi'"k; •,. .'.:;

.'t he

~ce~r _. r~~

&nal;sisol

ir~n'~a"us i~:

solutIQn':waS

ap~~reDt.·

^{.The'relaretheinvestiga:-}

~:;

~; -.,. " ", :', . ' -' - -',',- : , "" ,'

tionor_;t~eFe2++.Ce4+~t~tratio~reAc~U)D.beganand developedintoPertIpC{he .the9~·~b.i~b'^isabout,thes~irring e~es~'in'potentiometricredoxt1~ratio~~,'Si~c·e.the

~f~

·,1,x,-

, ~t;::·A~_

^{_ .__}

·_ efJeCts_~are~related~t~:electrochemical

kin eti"ts-and.heye.uci been,preViouslyreport ed'..' '1

~;.5~~,. ·. • :,:~.:::~~t;:.d:~~~~'d '.~;~t ^{• •• t ;;n} t~ib·~p"im7,~nY , 1'tb:,iti,:~uy ~~.c

),l

'<~,: '~,":!.~ .'~ ^t ,:.",.: .;:

..••.•.'...',:.•.'.'. '••:.•.;.'..•;... . .. ... .. ..

^{. ..}

. , .... .

. ^{:I ;~;r~d} p.~;i ^;'ro, nd';"ibf'i, ^~~;i~ ~h?'i~"ic iuv~tJ~etl~n,

e

v ario u s ~xP,n,";;, f ^{i n} _,u~qou'l' ^' .tt,mpti~g _~.ny ^'oacti,.t, P"Viou. wo,i,,~' 'h;plaii~un\, ~;d( ; . ~' ^" .;./.'.:, ;, .,., ^{. •}

studie~

^thli.

Fe2+ry<~~3';' ~ e- _reac~~on

^atplatinum:we.be,1ieve'

tb.a~

^{none until}

~no',Y

^'.

~ :i",~

t~k~~·!~~'l"~t car;·W u:;c1:.~,t'~t;;d" ^{. •nd} :ppar~tu, .nd ~U:b'i'hl:'PU" ^..• ' ,,' 0;

~ {:

^...

~

chemlcals..'

~, ',a...,~ovel .metho~

^otlow

overp~ten~ial

measurement

~bic~. hlLS ~ot

. ,',:

~.atiy met,~?~s: ~av,e

^been:

develoP~~

^..

~~, I~at~~Uie ,eiiui~~l?n'c.~

^point.

' sinc~_'~h~

^,J

first potentiometr icmratio~swere"r~porte~ rDI8g33; Mos~ort,~esemethods 'cllnt rp,"

.on

-ih~

bes"tway

~r,~ucin~.tli~ ~ui!aIence v~um~ r~o~:~be tii~ation,eur~ii~ .Thi~

^:.:

inter~t se~~~ .to

. .

.

^have

int~~.sified o~~'-the i~i

^{-, -}. .²⁰'

y~nr3.

,

· T~'re:c'

".,\

~~th~d9

-. ' .

oiic~e'.ral:

' .

;"

int erest~~,e use~t'o'accuratelyobt aintb~~qui!~lence·volu me.T~cy.nrc:

G~apbi~~; :netb~~ 'men\ion~d'in .

^most_.

t~iib<>Oks .

^'

~r'~~al):tic~l'~he~i:t~y:'

^{" -." . .}

.3. ~Curv,e-fitting wiih-c.~mput.er9.5. ^-.

1tQ~ever, ~Ii.

^or

tb'~e ~'~thod~" ~~~.h~i2~

^the:

matK~~atielli 'trea~m~nt~ w,liil~: tb~

,·:·exP~ri.me.ntal pr~~~~.u·;_es.r~~~i':'i~;n·t~;al.: . '-'~

^{: '-, ::\; " ..}

.'

ACc~:Hding

^to

o~~ w_~~~; t.b.~r~

^{is.siltri'e ffa",:}

-i~. t'~e ~n~e~tici~ai '~i_e.~~

^{-.It is}

n~c:~: ~ "

; !i , arX ~o:~(;n~i~er ·k.i~l!t.ie ~ffeetS .!s·.~ell ~,~tb~rm~ayn~~ic ~ela~ion~~ipg;

^·Ii,

b,~ .~~e'~

..

Jo~n'd

^.in.

o~(wor~" th~t 'th~ po~eri!i~l n~;:r· ~qu~~aieri~.~.i~ d.et~rmi,tie~ -b~.so~,~.ot~,~r

^".:.

. mechaDi~rP'ih\~D.th atenviSagediri thecon~entibnahiewdetailedabove.'Inpnrticu-..

. . ' ~~:r:':n:1:::::~;Ei~'f~i7~~t::~£::::?:iE~;i~!;:~::E.::~~:::· · ^.

~l)'}}--';",: ~~l;' ~"r'~'~ !!t" ~ '~A;'" ~.~,'

!\....

(:,~,:'W;..;':'~',x"'"....'r'.:t·,..~.\ ~':t·f:"?Il:;~,:"~=,,"j'i'~E:""''<,~:f~0'';'._<rPH'f'ti'<'~^\\:t<~

C' .' .. ^{'l. .' : ' , . . , . '} ' "<' ' ' ,'. '.' ," ,. . ' ;:'''-::'.~

, C Apter2 TbeEIf'"c:ts"rSt~rrlU' ODPotenliometrie-RedorT l lntlODS :

"- [ ;"In orde r_,

_\ ~ m~ _.

^the

ti:trat~'':luhODS we~1I ~D·j\!,&5teD·tbe acbleve~eDt

_{:::/ ,} ^ofeqaili-

I

brlu~&dj ua\fstir nDIisreeo~meDded.G Usually alll~etle .s~lrTerandbaT mag-

one t areus e IIIpolenhometne t1ttaho DI. Ilhub~~roundIDOUtworlt that the . trlc u.ured. Itet:l tlals ." dlffennt, depending

~D

,.-bet hettbe

r :

^is

bel~g

^{stirred ".}

~

^::

/

...or

u J~tionrry.l~ ~th

^eases.flersufficie n t

~tll'nDg

^to

~~

tbe solution Tab le2I,"

t.'.Jhows somerbservl!'tion,'from a typicalCe4+'"F~+ potentlom~~ictitration. .

I: :" -"" " . . ~.-' , .'.~ "

~:~:.-. ^.".'/";':' ..:rabie'

2.1:,

l'o.teD~illl^{DifferlRceBetweenP}t Electroden.Ag,AlGI,Sa.turatedKCI

!. :,~~~rere~ce ,El e~t~~,~ii FeS04 _~ 'C~S~~)~>. A~~~~S H2S0t,S~~t~m: '

~.;"

,.-

ti"')'f::';"{"'~~ "'r"!~;::r:':~~:~~' ; :::'j~:~:~ fl:!;r t::j)J~~:r:}::)~;~';'";!" f'~5~~';;'f!~

, ff'" /'

^Thetypicale~peti~entto-showthe,ph~n?_m~n~nWBSca~~~ed"ollt'wlth.~·re~?x.-· -.,:~~:~

l .::.

""

'::~' ·"';"": '·""

..,..'•.•.•••.

· r ..'.·. • . ." . .

^U_'.

^{r .'}

^'tltreucn

^Th. "::~:~I;:;) ^+. F."I'~J ^{. 7"} C,~(~q)+.Fo'+(,ql ^{'/'" .•.} ;':~

" with

c."

soM'"''''th'

m;""

A primar-y

,th,d~,d 6~(NiI;JiN03J

^..lrom

C.I', . Smi;h w~ :us~d. A.bout~.4

^gor

C~(NH~)2(NO~}5W:Bfl acc~ralelY ~d~hc~,'~~d\4 n ; ' .. ." : , :>

.cpnc~ntraled'

.'

s'ul~hu~ic

. "

,~cid

' .~-^(Ac'S.

'grn

.

de)'·~~.as .

^{added.', ..tothe}

.

-

e~riu~llY)

. ^salt

..

^and'

.

^tho

sollftior(wellstirr~.'rm2'minutes:"Tben?5iriL.-dlstilled."w'aterw'asCo.u~i;ouslY·D.dd9d ,down

't~e Sidior.t~e

^beakerover,8

pe~;od

^.or

~, '.fl,in~,i~.· .Thc··~~Olhcrmi~·,r~ll~ti'on

:-..:;~,

-.".{; ::/i

::dis'sol~ed' llnd lbe,s~ol~ii~n ~ad ~fed; 'f~ .~~ , (~n~sr~rr;d' 1l) .&i·2JD.O·:niL .v~I~·m~1~ij

^.''..

X.;:~

'ftasJ·.~Dd· ~~a~:,~p .. ,~ri::mar.~ ,~w;tb ~.i~tii\~dw·a'i:~: , The :·S~iu~i~n··~~" ~b·iuf o

^•.

~~r ~:: >~o

. ' moi.~.I C;'~~"d~'~.~OI:L-l~SP"~';OI,iio~.r F.3+ ~'b~de"~~i~;d,;W~ / :;~

~f ..: . '. ' : . ma .de"

^by..'

d;''?I~i ^{• . . . .}

^g•.

^{'bo.u .' . .}

^:.7..

^{7 8 . ,. . ....}

^01.

B~~.,.e.~

^.An..'.IY..

'.e.~ ^{. . . F e ..}

^SO._...

^{7lJf' ..} i~.'. l

^..

~

^or..0.

t. ': ' ." '.. _{;:.\ .:~}

~i . ..~mOI:~:2::::I;:;;~:::::0:::":;~ :~:;~,:::t:~no:;r~:;:~;~~~:~,) ': . ( ;1

[ t >. 'be~ker

^and

"ll,lixe~,.~eU'?~ USi~g':~~net'iC st.irri~g.·

^Then,'a

5.~

^m.L

'micr~b;~:~etie ^{-; .} ',~:

~~'/: ; .w!1'<I.1~ed·

^{Ior precise}

~it~a:l~on,," ,Tbe'

^{'rererenc.e·ele,ctr? de,was.a Ag,}

AgCI,'.sa:i.~ratcd· :':'~1;

,

'i ,:.·.:".".•.'.:.".' K,Cl

elec~r.od~~ --~~ pOl~n~ia) ~'~'rt?und ~_o

^be.207·ritV

'm~aslJred,' ~'g~!OS(~,'91an'4a~4, '~' '~y

~:.£ _ hydrogene~ect~de,~,.:r~e /'fQO~.f.n~ieator' ele~t~de_,.w~,~,~~~ti~um.:.~?il..c,~~:~t.~o,~,C': ..~~;

~k~~," For most,~?CP~ri~~nt5·"t~.e'pofe,?ti.als .,wet~ ,meas~reddllt'inglhe'.tilration:r-:it.h,:~n '~;. /¥

j~}:,'

^{'.:>'. ':}

Ori~n

^..

~:s~~r:~hM~del

^601.pH/m.V·

~et~~

^{..::," '. ..}

,:.~\{~~

Ii. . t) S~8"S~~:Et~:r:&:~i~t.::" xl

'~~~~,~h~'i11~;§;~~~~l¥{~~~~'

-:."u bi'

·1120:

~-

,

.

..

".:

.'.;'

:~ :\

..

><.~.

'-' '..

"'~

- ,

'_:.:

, "'Addedv olume

'~~~~i~,!m~

^{-EstiH!my'. A'E/mV}

' , 7)or KM~O!/rrU;

\

2£3'86 \

59~

21.478. '602 646 -44·^.._.

\ 26,84

21.590 627,\" . 675': -48

'", \,

,-

21;698' 97Q 034 +36 ~13,53

21.800 "1140\ 1,146 +.3 ~1I,llj·

\

D.,.rrom.Titr#W'W;'b 0001;m~I ;~;~;9r~~, ~.O;id ^{a n. , ' .}

o.Ol,rn61~L":1

^reS.o..as"

Re:d~ct~n~ i~' t~.l mol'L~l.H2S0~ a~d ~ ^mol·t.:

^L

t .

H

3P0₄:"

?

E~tirri~,imVc E.til~/my ~E/mV

'-:--'",~.

"22.000 546:6 61M ~11.4

".2 2.108 565.0 628.6 .~.O

22.210 .,SgS.4

647f~ :

^{'-51. 6}

'68~10 +1.8

730.0".:

- c.o

,'760.8 +4.8

181.0

"

^+1.2

.,

, " ,." . I. _ ' .

A:'big,jum~or, .aR"and,a, sign..change~an b~_o~ser.ved,:.in,thee~p~ri;meDtal resalts'

~n~,

^{th e}

,r~.gion·, ~r

^,sign,

;Ch;;;~e

^als,o

'c~~n;id~d '~ith" the en.d.'~oiDt:r~~

^{_.the .}

..

~.e~ond derlv~.t·iV~, ~etb~O~:: ~,~~ese'ob~e,rvatio~~

's u,ggeSt"

~.n()V~1 , ":;:t~~ or·~tl~at.~ng. > .

the-en d-~~int._in" titrations_~~volving-lrcewithoxidant~,suchee.eertum,~erman.,_.

g~li'~_te , a~d di~b~~m~e._-·~his.' m~thod ~ay

^not":be"

r~a'dily .

apPiicable,

~ofo·uiine

^-."

"!1n~y~~

^:but'

,~-

^still

o~i~~~;;St.

^{". ." "" -.}

··men ts.

\

, ·1:

.2.2:rittati0ll.s

o f

lron(I1)withAtgonF'rotcct ion•

: ... .. .,... . . ':'. . r

^{> . . ' .}

. Theconsideration~a.s:that..o xrge.nin·th~airmikht !1[c ctt.h-e·titr::Ltionthrough'

~xida.tion . o t

.ferrousiODS

tber.eby>c.h8..n,ging,tbeir·co~c~~tr~~ioli. 'I~ ~;dcr

^,to

~i nimb.~ ·:

air int erference,aspeciarcellsh~wDⁱⁿFig.2.1^WIl3~sed:^fotther~stoftheexperi,-

.

^'. '

..

"

.

"' ~: '

'.

Figure2.1en~extpage~I'

Ai~·a.

^{platinuintoilelectrode}

'wit~

eweter-eeeledarg6ri.'out!llt;

D: i~ a , ;ilvet,-silv~r'

'.chloride

snttir~t~d i<CI'-rcref~nc'e ei~~;r~de~ '~ 'is ;~ mi.C:~~,u;~~~~ :~"

^is

, tb~' a~:ion. i_hl~t::'

".0• (lao

be-a<lju;t~d

' ,

r~r b~bblin'g

'

~~

th'ro ugh the• 'f'

s~l~ti~~

"' ,

'to _{deg~ 'i~}

:."

_'b~ro;o

. the..

~·tar~·: ·

^.

of,t.heex·P!!rirm~.i,·oi~p'~~in~_j~,·~~~r_~.~e s,~,luti~,n,;hile^tlie,'~~I~t}?~.·,h~:·to.,~~ kept~

s.t ill:,bY'ope~ in gv.l~eE:,.25.00"'1'ftL,.~e2+sOI:ut iJJand2?.'.O~.mr,...Ce~~ sol~Uo~~~ro added'beforeobser.;i~g' qi~cell e:~.r. Tbi~^js~till.about^7'mLof,C~(t'·befor~·.

~~uivalen~~: _{' '} ' ~he' _.. rtst _{' .-}

^o{·

_. th~ t~4+.s~hiti~n _{'. ' ..','}

^was

'~dded fr~m t'~e '~icrobure~~~:' ·The~' _{<>: .}

_~ ^:

~~e.d.sciluti~~'w~slitur~t.ed wi~b~Jgonand~.~tirre4 ~or.5;'fr!.il1ut~tcr~~.ov~.~~_ • eclved0"1'~ ''Pol,oU ,lreadings were begunat the.n:1' this h\,bbllng,Omlng :

~

^the

still·p~riod:. th.~ ~al~~.· was,·a~j~~ted OP~:9' The'.read0r,r~r t~e ~till p.e,rl~d.·":e~(l:

:aga~~ take~\a..~.- th~ e:n~_

^or2

mi~

^{..uteewithelUt.atining.,}

s: ^rono~i\'lg

^teblee

^~ho~.:

titrationresu~tsusingtheabov~cell. ' . . ;. . ~'.'.' . '. •.

\ \

lJ.E/ mV.

'.1.2

-2.2'

;2.1, +.63.0 :-":':-,+13,5.

+5,5.

+1.I

;" S48 .? ".

507.0 618.8

7

^00.5,.", 1~.t3.6•.

.ti07,!

:,~162;2^"

557.5 -~.5

\ .\

"..501.6 -1.6

.

604.1 "- 1.6

628.8

..

_-1.4

861.5 "+ 58 .6

;1077."4 +.10.3

;

1114.4 +l.~

541.7 505.7 616.7, 854.4 '556.0:

500.0

602

. s

627.4 .0'20.3

"1163.3 .-1057.1 1112.6.

.. -r~;.~ . '. r~. ' a : 'mr:li~~ . ~r ': O~I~ol'l:' ~,,+

0.011mol·L-1CeHInH:8 04Cllfrie.d.Ou\ UnderA~n•.

:-.~_••-.-_....,...-l087,7

1116.3 20.00

20.698

·,20.79g.

:20.000

20;00"

'20.000

20,00"·• .21.OQ2

21.100 .21.204 22-.202' Add~ee⁴+..

"volum"e/mL.

.Compa rin g't bese. resul ts wit h

~he

^{resultsortitrationsj'nopenair,tbe}

AE's

are·obyi'

~.;• .- -. • • '• • . .. •.;..0-,, .',e ·. '_.. . ,>..

, AddedCeH ..

vol'u~/~L

...

Tab~c'

^2.8

D:~ia" T~~eD

^.,{rom·

~o~b~r' Tit,atio~ o~

^0.01

~oi'L-' ·F~:l+.

^versus

./ .O.Oil~bl·L-1_. Ce4₊in·HzS04C~'riedOut.Underk~~.:-

~ -,

. . . .

^'

...

,.T able 2.g

A

'Comparison of~E'Berore,'At anaAlteitb~E~d;Point^"inAi~~~d;,n.

.Argon rof" Two Tttraticns."or O:Ol'mol-L-1Fe2+ versus.

·'O.OIlmoH~-~feHin,H~S04"

,UNDERA~G~N

'Added volume ...ce4+/mL.

20,00 20,670

:20.7.10' .20.87'8

'"

'i :1.660

l>.E/,mV Added volume toE/roV

.,Ce⁴+'jmL

- '3

^{20.00 -1.5}

-3'

^20.608

.2 '

^20,7gS

-28,.'

-2~ 20,gOO

+4.

^20:gga

+g~

'+2

,Someecnclusicns~an^{be drawn}r~om,this.C?mpai'ison.

I.

Beto~e, t~~

^"erid-point,toE's'in

'open~r

^are'much

~~re

negativethanthey

a~e

ultderargon atmosphere.:

2',

'.Tb·er~' i!;tI:':pot~nti~~

^[ump,at

th~ end~p6int

^when

i~e

^sign'Qr

~E ~li"anges;'

^b.othin'

airan4--.ulldeHrgctt;-

. '

^{" . '}

3.'Alte; tlie,e~d.point;'-the AE'stend'to~e~o bu~,afarger.v,oiume~rCe⁴+.8C!lutio~',

,

"", ~u~t b~,':a(i~~d in'~he

^open

a:i~.~~tuat~on'io ~rin~ toE'n'e~~iY ,to ze~o

^"

,:4:,:,Anothe~cbservetlcni~'thai;i~:'general,the'r!!dox':~Iechode pot;~tia&differ

;,., _,-, , . ' . .." ;: ' . . I, ' ,' , '-"- , . '.,'

t··

~.

:;:..:

l ,5'~"" '::~'f:~~i? ,. .-\ , ;,. ,.... ~. ~ ? .'''' '': ' ··r~"" i;1',~'t>~;'?t:;~jI!'[;~"~"'J;,,~"i':Wf'[; 1.},":~~%

~:;;-. ^{- 21·" J}

t

^{r , .}'~~.~

h:":'"

i 3 Iron(O)--

.Ceri~m~(IV) Titrat,io~!l-~_t OthctConeenlr~tiof"

^{. .r,}

;~;~~

[

,J..; . .-: ··~a::,I~.::~P:i::.:u;~~t~2;~~:~:D:.:::~::;:~::;'~::~:.:; ^{a ::7&'} ·/'· f J

,. ' solutionswasconfirmed butdetailswere..difrerlht, e.g:with0.001mol·L·l ~lutlon,. ..>~~

. - . '. _ .~ .",_ ". ,_ ;.1.:

.thedill'et~n~es.o~·PO:.t ent.ialbetween"stirredand"UD!tirredcas~^we.rela,.serruther.:' -" :c';~

fromtbepoint ofsigncha nge ?rAE,'wbile with-O. l

~ol'L'1 ,?~utiOD!l A~'s

^{were ..}

~J}~

,small

~eept '~IO!le

^to

t~nt·-poi~t.· 'T~e_

^'point.

~.r si~·CbAD~~.appel\red

^notto

eoinc:id~

^{• ,"'..}

:~:~

~

.

^{.. '}

,

^{" . ' . .. ' . -} -

":

^.(:

.well.wi.ththe-end-pc inrdetermined byIirst orsecondderivati vemet hods,Tabll!S ;~~:f i·

; 7 ',:: '

,·Z.11

a~d 2~lZ iIIu!trat~ t~es~~·bs.:rv~tion's,

^-

">:"~

t~~,· ) . , ' ," ... . , ' , .-~ '. ,

^{I : .', .}

.,. ::::~~

l .;.:.;.:"'~':

^{:.....'- .}

T abl. 2.11 :::~~;~;,~~~'Q~;t:~;::O::;::.I~:;:~:;: :::~':;:;'::d"::;::~ . ."'j'ii ~

". per,i,!~liv~,~rea.t1~'l.ent'.

20.00

61' -.610 -a

62'

^63'

. ,

'63

^{707 ,+,146}

..~^'1000. 1088

+'

1123 .1122 tⁱ

-s.ci

r

1135 1134 -=Fl

\-

^{-0.38 7}

',OtherExperimen ts

".

, )',' in

~idcj.^to-ensureth~t ~~s,ervlltions ~er~-.not.^{dependent.cna'}p~r~icular^{instr u-}

.:...--/.('mcnt'aR.iLdl~mete;,'C~;'e~~;'ge~^PHM84research.pHmeter·~u^{use d(or}¥<)me,o(the

.' . " : ".,:,~, , ." ,,; .' : ; , , ' " " ' "

e.m.r. rneceurement s,without~significaotdifferenee.'Large.r platinumin4ieator'~ce-

tro.~,~" ~;V:,I~~~er,p~t~ntiaidi~ereDe~. ~et:~en Elti':'i~I;,aDd Eotilll w~il~ '?h:angi~g :t~c

"si,lver, silv er.chlorideretereeeeelectrode was'w ithout effect.

i~' ~~~~ eXp~une~'ts~'~wo~um ele,e~r~d'~ ,w.e~e

sta o'tcurrent<i a.b'out1.51IA"passelt'thro~gh·'tb~m",;""aI'vn.d' ..•...•••,.'" n

,

;~heOrY _{, '}

of.Stirrin'g

_• ~ii~

_~

_-

Air Bffects

_{r; ,} iD P~te~tio~efric"Redox _"

^Titra-

tlcns.

TO.gi~e:ath~retic~1expl~~atio"'Cor--'thepbencmene-tleteiledi~Chapt er'2,we . . mixed

pot'et:i~i~b:

The kineti c

~actOr9'

^erethen:

~'n~ide~e~

".by''dcri~in'g'

a.

rcl~tioD~hip^betweenth~^{'m easured}potcDtia:l~^and'th~stirri~g^{rat e} '; un~cr' ~h~,~~p~r.ime~.!aI cire.umstanc~tro.~·80~e,~~ic eq~ation,s~;f~iectr~d'ekinei~

-Jes.Tbe.'kinet~c ~reatmeDtshould biebletceuswer thetollowiogquesticps:

1..

~'hY:~

there a"

~ifl'~'ren~e:, betw~e';

^{E.tilTinlandE.ti ll}be(6re the.

end-Jl~lnt,in

^cpenc-

'~i, and whY 'd""it d!,~p;~a, in arn,g~

^{. .}

tmn'Ph~"? "

^{.. ' , '. .}

.",~~~,~:ttiere,r~ifl'er~~ce,be~~eenE1,lirrilis,~~d,~.tm_~.tt.er^tbe'end-point and',,\by

."is.itindependent,~tthepr~se~ceor'ah.setl,<eot,air?

.~

.. . ..: . :... " ' :. " , 0' \ . :.: ." , " : " , , ' , '.

3, ,W.hY·,d~~jhedil,ferenc~

0::

potentia.l,change sign'Ircmbefore,theend-point to

.

·.~r.t~~'~he',e~,d:~:'~~'~! ,/~

^.,"

3.1',Th~:Miiced'Pote~iialⁱⁿ~.R:OOoxS; stem.

\

_(3.i,1)

.

is .usua!IY '~~med ~

^{a'redoxcouple}

6XdR~d'i. :

^MOstphysical chemistry

t~tbo~ks

·'d_~al.

^o'nli.

~U~ ' t1~~,,,~~h~Vior

^of

this ~higie,re~ox·

.ott~D: 'eD~o~nie~stw~\or .·~orecouples,jffiullan~';'IY

'..

".

^-"',~", .::'^" .".\' ,

.

^{, " ." ..-}

_..SY8t~Ii~ ~.pot,e.nUal,which'reflectsth. ,ont' ih'''i,o",

u .r

a];[',o;,p[,; p,';" ,t'

. .

OXi+niek'~~~~(

'C~nsid~r

^tbe

·sit~3tio~. ~here

"t:wo couples

.~~l!'sim~It~'neou~ly ~reSent '~t, '~Ui!!~~i.\I~

withl!~chother. More'Important;if.all or anyone'oftherend ions u er~v~rsibl~, .

therate

·~f·;eaction

^is'fairly·rapid.the-

wh~le

^s;stem:romes

to'equilibriu~ .a~d 'all ~f'

^.

. -.J ' , .' , , ' •~ '. • ._ .' . •.••.

theconceDlr~t ioDS.re~aiD.e6.Dsh.nt. Thep~teDtialisthengiven.by Nernst~Illtions···':' -·

'. < .

':..:'

. . .

.whereEtqis'LbepoteDtia~.at equilibrium;''~ofistb~fQrma!~tential.~oran'i~divjdual .

~oup,le.. . .. ..'

"Thepotentia iis:tben~aleulated.by -Usingany.oneofthesecouples'ror'whicb',its

.'equilibrium

' .

eoncen trationa are

.. , ^{" .}

^.conveniently available,

^....

^{'..;. '. , - .}The measured^:_. pct^"eutial in :,.' .

equilib~ium

^{will be}

independe~t 6 r

any kinetic.ractors such'as'lf_{, . '.} and0.-'

[~

_'^parricu-

, "

'#'.lar,themeasur~d^{pctent lalsbouldnot}'change' :w'itb~tirring,once equili6rium hes

. ). '

. _{. , ::; .} ^{' .}

^.

rew.~i~ed~y~~emscome'tc; l!quiJibr!u~':~iilieachothe~.a..nd rlipidly:,Them~~~r~dpot~ntial^{drirts,riomthe}caleulat~d 1.'"' ''.''Vu"~"",,,.^{This ispartlybee'Buse}homogeneousredoxreactionsare rarely! a,t, because

onl~':'~ ~.in?~ity ~f,r:~ox :~~~.I~ ~~~ ~1~,c'i~~~~~micaIlY, reve~ibl~~,:

mustbeinvol,~"ed,

. .

kine1!cas,peet~·bave-t?beecneideredin'.,

'I=: :.E--~~q

" .' : " , '.". ,"/ .

-where E'isthem~'asu.re'dpotential..,,Wesh~1lusethe.following(!~nventions:

pos~tive,^theelectrcde.reacrionis,anodic andthe corresponding currentis defined as. .

\~ositiv~",Ot a"~Odi<e.Ur~entj ,~., neg~e o~er~o~eDtial" C,au~es ~egaiiv~.

^or

'c,athod~~

currenttofl.ow.,The. cverpotentjal'I is8.:kin.eticallyrelated parameter-as in'the

Q~'tl~r·Yol~~r'e~uQ.tio·nll:

^..

..: ,.".... ',' . ()io;F'I '" -:(l'-~jjniF-"

11=~J.i-hi::::;Jai[e~P( ~)- ,t';Xp(~H:, "' .

. .

^'

:

^.::., . . -.:' ,. ':':'.. ": :'"

.-:. . : " ". ^-

^\

,w~.er(l',the,su~:criPti,rep:~en~s',A9' Jn~ividualele~toc~c,~ical,rea,ctioli,couple~~d-jai

':

~:'i~·~h~· ~~.c'~·ang~ ~~r~en,t den~.;ty:

^lor

r~aciion

^'1.;',

Q;.~ ~~e

^tt.ansler

c~efficie~t ~~P!opri. '~

.:

:~'

^ate

,,~~

^the

i 'th.',e~ec~to~he~ii:al ,r~~tion;, ~nd" ni iS ~ n:~~ber

^of

'~Ie,c~r?,~s ttimsterr~~;

-,On"e can:dl'lI.vn'cu rrent~potent1alcurve'eccordingto.equation'(3,L8)iii Fig.3:1:

,.:An

eleci~de sy~tem' in,'whi~h t~o or-'~ore ~~uples'

^a;e

pre5e~~ '~'ge;h~r

ⁱⁿ

so~u- '

^..

ti~n

^.'but

n~t ,i~ '

equilibriufu

wit~ e~-Ch"o:he;,'is called '~'"POiY~lectr:de;,~~: "its t~~it;:-~'

,mentis

gr~~t1Y ·~irnplifi;d. ··by ~~: additivity 'p~in~i;le;

^The

princi~le·,is. b~ed'~il, :

^ihe

.

~;~~piion.:~liat

^t.he

c.ou~',es

^'present

a~~ i~de~~n'dentl;' ~l"

^{eachother.\Thus'}

·a~.'

^any.

given

poten~ial.

^the

ne't,.ob~e~ed ·curre.~t

^j's-their.algebraic'sum..There

~i.II

^{..be one}

potentialat'

~hicb ~he n,etobserve(lcurrent ~

^zero,'the:,point at'which't'heaPod'ic'.

:-- '.', i : "'-:., ' : ' ,:", ..' .,' ,'-' ',' .etir~e~t~u~tocne eouple.exlI.eUy.~alanees.~h.e.ca!hodi~..eurren~,~rtheother

Icr8.9y~iem:rest';ict.~dto

ju st

\:.vo.ccuplee.

E~;lll r

.

prcS~nt ;t~gethcr, at'~n

^electrode,.

·~~~'ni~udri ~ut;oi~OPPosite s.ig'~' "

.:

.

not,"only .'th~.~rates of.the. tW? -helr-reecticns Re.dl - OXI

+

nle- .endr OX;'*n2!".:.·-'Red2.blitelsethe rate

o f

theoverallredoxreaction tbattakesplace .

~etween:'the couR;1~ _a~ Emjx.'·: M~~ i!?p~;tantl· 'Emil.

^is

affectf~~bJ

^ma!1J

kjne.ti~'

'clfectswhich will'b-ediscussed'in

later

sectionsofthis

ch'api~r1' The ma"thematic~1.

-,.'

\rc'~t~~~t r~t . " ,

^,..'.

th

'

~

"

par~i~~'ar

'

p~;tS

, 'orco""uplcs Fc2," --. . +

/Fc3~,

^{,-" ,}

'02/H2bJ:~D

^{' " .'"}

d

^'

cc3+-;dc~+'

, ^will

3.2:·TheMixedPotential'inPotentiometri,cTiiration~:

>. "- ',

r

r· . Il.nd ·wii.·b·dich~mate~ioli :d~ .bot·sho;V t~~, .expected

po'tentia;!at,tl"qtlivalebce

heca~se

~lf ^{0 1.} irrov'''ibiH,~ ,~~d.''d

^with

^th' M~'-/~n'+ rt9o~. 'O"pl~!~vbi,h; ^,,}.lik.

^"b.,'

il~\".,,:.

^:'1'

CeH/Ce3~ _

couple,

J~' ^a: m~n.Y-.EI!~.,ro~, ~t"anster, :a~,? ^{p rb'Li:t.i}

^y

:O~Cll~ .\~rh~h

^'a

f N;.." ... ~Ul\\~~r.of s ,tcps... Th~ ~~ie~~ial,' ~ter ~~~ivll;leil~ce

^'in

"~be case o~ ~e1m.a~g~.~a.~~;.~t w~ :

~" .:.

^,'rg", d, i, .mixedpO' , n' io! i.volvingO, ....';.tiO..Ircm

".t",'.,'w. I.,••

m, in:" "")

~:~

^{';' .}

" """ . t'in ",~,; 'bO:~"h;:,';,r"rt~;"~~~i'n\ ,y,t,~"",

^well

"Rir.~;:"

^is

~.d~" .l.\r . .

'.fr,"'.• ':..._~.work.."Or.W!,!~ar~,8:Dd'FenwickI3Iu.~~a2,in.w~.~h.:pairs,or.dis,~.imi.lar,metalsl.~.g.,Pt .::.".

',J

r:r~(: : . .~;":..,an,d"

^Pod

~ere '~~ed ~~~.dete~t. pv~~nt"io'~et;k,c~d-J>O; tsl: in9t~~~ bj ~qle ~OnV~iiti~n~I_'

^{_ _•}

~~ . -~platin\.mmdn:ll.torecmbmedwltha retereaeeelectrode • -'... .. ,:

't

<""i

~~,\

":,.v'!'l,!'i"::':l;\k~J:\?l""'~

: ' . ' It:;

^1,\<'

" ~

^'..'"st::-L'::'{\,

"

::;-'~

• •

^I

'::>

~!-.I:-..i" ~\)i~~~; ~~i,'r'i~,

, :

,:,.,ltt:r

_J

f,f;\'jUl'~

_{: ~}

~ewartowici14 h~ ~ore ~ecent!yc~mbined

a plat'inurnand'

'~.

gold'

~i~ctrode

,

imme~sedin o:~.,m.ol'L~l ~z~~:'~ont~i~~~;a ~ious ~once:~;~tiOJ1Sor.:Fe2+'~nd'F~~+

^"

ionsas an~Iett~ometric^sensingd~vic!^ror~tLces-or^{oxygen.Sucheeell}~ith"(~e~+1 ^:

=-3.1x·-~O-.4mol-L:l·.an'dIFe~+1=O,9.,x·1O-4mol'L-1 had an?,rrd , Qr 4,gmY.in'1000.

ppmOZ.,electrolyticallygenerat e.<!'in,ArorN~'.the^platinumb~oo'ming^morep~sitiv~' ,,thehigher

't~,e~~2

^.ccnteat

~hi1e

^{the gold}electrode remefne

~onst~;n~, .:.A~·eO~si~n~

.[Fe2+)+:'iFe3~Jthe'seDsiti~ity-to~xyg~nincreasedwit~.lncreaseor'(Foz+1 andw~

lar ges.t

~,.

,Ii'at the lowest

~otal

^{IFc: +j.}

^+'

^[Fe

^{3 + j.}

^ThE

phe~9ni~na" wer~ ~m:~tIY.

we believe,

id;ntified ~:involving 'n'1hed pote~tia~

^W

~e2+,'~~,~~ti~~ atid:02"-r.;duc~ ~,

^{'.;', '}

'tion:",

~eve.rt~e~;,:·~~ith~~·Le~aitC?":'i~z·si.4.,:p~r~Wmard,'.'~tid, F~nw!~k's13' ob'scr~n~

^'

ti?~sin~lu~e~n'yof\hety'pe'present lyundercci~sid~rati?n,,:"'.,•.,

,

~

."Recalling Tabie 2.ia-

Chlipt~r

^2,the

'differ~Dce 'or

poten ti'ai

b~i'wee'n' 8ti~rinilLnd

.'.... . " , "•. 'll .:" . ' . . , - ,', " '. ..' . " '•.,

still (.6.E) wesazmv when t.he solut ion wasopen-t o theairwhile itwas cnly2 mv..

~,n a~erage

_'I ^wben'the,soluiit m_'

waS're~onably,

_{:.' -} prote'ded tiom',air.'_." Th_,e_{' .}

e~rieentration

. orFe3+in,our,work5"'is lar ge, not small

'as

inCha riot'scase,12 Furthermore,th1rair: a.andstir'r,ingeffectswerer~u.n~,b'yo~serving:the mainit~deor:.6.Eo,yhicb. has.been

f ' ," .. ., ' , . _,". . . "-

speciallyde1i,ned in our work, The higher the I1E.observed,the more stirring <

i~fiuenced

^,thl;!:

'~~I~'e or

^E;'",Vebeve

t~).

^reasons

t~'

^maket'he

ass~m~tioQ' t~a :

-mixed potentfal.iseStablished:

.''1 pifferentpotentialsbifts bet'weelt'unstirre d and"i""d/ ~" io,"were

,." :

th~ p_r~ebeF'.a~:e~ce or'

air, .

. 2 :

Bot~'stir;ing.;~~d.m'1xedpoi~,~ti~ls^"arekin"' i",IlY",I. tjdqn , nli' i,,.

For~redoxtitration;oxygen"cne omy.,.."yr,,,,li:f'component -,bas\ eeo'

sb~wn,

tobe.

iII\Po~t~~t

by"

carry'in~

outan"p'dn" ol:wilhI,"re'

ox:yg~n

p~~ent.:. ~he,r.~ror~,"a C~~~le ,~f , d.

2/H:.Q

pr~babl~" "~":II' 1~:'liI,,,'ioo

"y, ' , m.',Th, r~ac~OIi

. is

notmally .

• . ., 0,

4.

4H+~'4e-,~^2H20

:.-: - , ; " 6 e.H" _{+; Fe:~'~' :}

.'

~~:H"

^+F

e

^2f.

Si~ce

^this

re~:~i~n i~

^Yt'ry.

r\l:'"~th ooup~es C~~~/Ce)"; aDILFe3+'/!,e;~ ;~in~

^to"

'eq uilibriumrapid ly.From(hediscussiontobegiven in thelasf sect ioD,t.heporen-:

tia.1before equi;.leDc.e·in tb.e

.bse~ce

^otOXJ(l;ffl'

~.ab b~ obtai~~ :t~~" 1~1! ".N~rDit pq~~tion

....I?'most

.flOteDtiOm~tiic ti~rati~n$.

^the

~~[lerJn,en~

^ar!-'

_c3rri~ '~ut i~

^tb,e

•ope n ai,r.11~ t~eretoreimpo~~ant to,.s~~dyhow oxygen alfeels"tbe titratiOn:

.. ToanalySethepot en-t ialsinYolv.i~g^{oxygen,kineUctactorshavetobe}eoesid ered' sinct'"the.

~~tion {3.2.i·)

^{'is very}

i rr~"ve~iblel ~

^"!iDd'50

b~

^a.verylow

' exc~"¥ge

:~urr~~i. . ·d(:li~Jfy

^{. "or}

'&bo~t

^{' .}

'fO~IO·A:c~·'l.

^.''" :--:

" USi~(l;'e~ual~n

' , ~.^(3..1.8)'" torthe-"02/ H20"

'~YI-

^.;

tern,'the cuqcnt-pot ,entinl'ellr;Ye .can be drawnas thedot:.dasbed"linein Fig.'3.'"

The

.~E

'etirve'is very

f1"~~

^.•

l~. c~?I~i 'be

^{horizoDt.ai for,IL'}

hi(l;bIY"i~~~v'~'rSibl~

^c?UPjll.

. 'Soo.;e'ano'die

d~ta~tor

^the

,6~/H~O c"~uP.le

^in.o:JsM

lr~04'provid~b"y&ck~is ~Dd

~~i~1::;:1~:~

~~perirAt'Ota.i'conditions

;:~:~;E::'~

(JeStpur ity"of~a.gen't~

';:~':~S;:~5~:i~~:::~~'~~:

~D'd!simpl~('ie~DiDI: o~^{theelec trodes),}

:

woul~ pro~lbl: ~e, 1~:'

^..

r" ". "" "" . . ""-. . "

~ :Co mp"ariD", the'':'E'cl1r~es^{in·F ig. 3,1}torar~t^redox~~ple.~eh0a..sF.e~'!"Ir:.eh'."

."the cuivecaD have •st~p^siopearoll~d^tbe equili.briumpOwtsince tbiscoupleis

rai"rly\ev~~ibl~

^withaD' exchange

eu~r~Dt d~n~ii.Y- ~r

^about

~

^J:

~io:;'

"-A'em-t

"~Tb~ "

• .. ~;:;.~;:~:;~~:~;:i:i~: ~,I:±::I:: ~ ;~;':dd~~:~t:d::l~:~~:.:~: .

.

^.';\'

..il,~,.;";'" .nF~mRCR

.:

- .

'. .

. .

whereA istheg("()me~rieeleet rodaa.tea;rno'''"04 rnReremm"~,.n"r,u,~''',',n ''" ,

. .' '. ..•. ." .' • ... •. . 0"

In a,pproximatetreat~ents^orronveclivesy~t~rris.~

&?d

fl\a~~r~pond to·.~.·.

DR :' < '.'. . .- "- " :.

and6;'respeet ively,~'het"60 and6a' "the.l~ i('li.~t'l!,~ (irtheh~thdi~1I.1;tAC""

?lI.o tla y..~attheeleej.rodesurfaceunder tathod~and"anod icconditions.respec- tively.Thl"y willbedisclissoo il).a'lat ersec tio n: Cci Indeli:arethe bu'lk~ntl!ntrD..,."

lionsofoXidi,z~d^{andrede eedspecies,}res~~ti^...~lY.^{:It"isnccesSary}t~'ml'!nlion^tbat

il,acouldbevery"

mU~b

^smaller

lbaD .~.~ ~.hen 'tb e tilr~~ion

^isbe;ore

b~l'd~G't~"

equivalence.

~.e. "E

^curve

tb~D

^{hp tbe}

s~~pe

^{ofFig.3.3:" '}

Figure3.3 nextpage.

I~'^lias,beeD.1P~wn^{tnat a}sihg;~~o~pie;^has'an-equiii-br!~m^point,E.q,~t^{whi ch}th~

m~8surel pOl~~tialisindependent:

o r

stir ringorother kineticeffects.

A

8oluti~n·con•.

tlliniD~ O;oOl ~oH:t

Fe;'" and.0.000·mol·L^otFeH 11:(·0.5'mol'Lot

~'12S04

^WIUII

tCltC~

^...

Atmosphere-

\ 534

53•.

Bothta~~~,\bow,thatthe.equ!l.ibri<J m potentials- n.,otchange withst irring. The reasonist~a~nocu ~rentflows,att~eequilibrium'p.oteoti~.tHowever ~be.Stprr;will

. -be differentitweputtheFeHIFe^3to.n{ 0 2/H20coupleS':togeth~;. Themixed

."pot entialcanbeeeellr

rou:~~i

^{in:Flg:3.4.. ' :'- .}

~

^{, :}

~ .

Solut ion was'atirred2min,unstirred2 min,;tir~ed2'mtnet c.

1228 1220

1220 Eili11/mVve,Ag,AgCI,"snt'dKC~

1228 122U 1228 '

L The mixedpotent.ia~'EmiJe.isalwaysI,argerthan'the,s~nglecouple equilibrium .potential measureduDde~^argon.Table3;2.3 supports thisidea. inwhichthe.

,

p6ten~ials

_.

.

are measured^'.

un~er,o~henYise , idc'~tical condition;;

^"

i,~. .

·concent ration,'

,

.

,t·e~~ei,a.tur~,stirri~grate;etc.

Figure3.4·nex~page,'

Thm"onlyonepoint,Em;:,",'whi l no . .ieunen;'"flowing,Tb,cathodie', current ls,xaetlybalancedw;th'tbeanodic

e",e~t

^...

I~e

^{pOlenti;'Em;,' Thi,.}

diagramillustrates

.

.:'-,

two,exi;erim~ntal ~~serv.ations;

,

'--

Table3.2.2 Measured 'Equilibrium Potentialsfor-theCoupleMuZ+/MnO.:InAr

:---, \. '- . .. . .

Atmospher~* ,

I .

...

^{." .. . .}

3.3Th~_~ittiati~,nImme di atelyarter.~'t~y"a1enee·

Inthis region-orthetitr~tiontwofe atures arediffere ntIrotnth'eregionbefore' equivalence..The first

i s th~.o.E

^{is'alwayspositive,}

wheth~r

^or

no~

^the

solutio~

^is

open to the f1.ir.9'unde ren.

ar~~ll' a~mosph~re, (o~~ared

^{:to the}

^ncgnti::

^values..

observed

ber~r~ eq~i~~te~ce.

^,The

s~nd

^{is tha;,t:.he}

dWeventuanY.t~nd ~

^tetefnr.

beyoed- e qujvelen e e.:.~

The'first

f~atu re~y'b~ eX:Plai~_~'~Y

^the

ge~eraLion or·oxyse~., Si~ce

thil-titrn-

tion'has pasi~: eq~i~ale~ce,

^there

~ ~p:re oXida~i

^in,

thes~i~tion,

^for

e~am~I~:'Ce4t,

~nO~\

^{'or'Cr2qr-:..}

they~ 'l:i:aYe ~uc~ big.h~o~idili~g p~tent;ahd~at ihey'c~:lU ld p'~~i~iy" :,

r.ea.ct with

w~t~r, e~g.,:'i.ri

^-thecase

~r-Ce"',,:. ' , "

·(3.3.1 )I.

"Scmeox y gen~produced b';. thei~3ction.^eventhough-^{ata verylow},oooce~t~Bti~oi• I

;an equilibriumcouldbeestablishedin theabsen~e

o r

airand oxyge'n.co'uldbe"the'

com~b~e~t ~hic·~ . t~~~~he~.,

^with'

an~her

^-

redo~

^_

co~pl~

^{.prod ucesa.}

nl~~d

^_

'p~tC~~~iil,

Th~rerore,it-.may notma t teritthe solutionis-inair or'in,aninert'atmo sphereas

Th~

^{current ..}

pot~~tla.l ~u.~ve

^Ior

t~~.G~~:,~~~+ .cb~pJe

^would

^be

^as

;0 ~~g, 3,6,

T~e'difr~:rent,magn itudes'or~,~8.n.~I'~;-areeeusedb{the-'differingcOllcentrll.!iollSor· CeH.:.end.

'Q.~~+. recalling eqiJ - ati~D! : (3,~,31 '''and

^{'(3.2.4 ),-the}

~n.ceotrat~~ '

^or

cerium(ID ).b,eing great erihiln ~h~tor.ceri~~(I,y).~~arequivalence'- Themixed poteatlal -estebllsh edbythe'c~up.les' Cea+jC,eHandOi(HzO.rnaybe aeenbyputti ng' their.

:~rte~~p~tf7nti!I' ~un:~

^{toget heras}

^in-.Fig, !.7.~ ^{) .}

! " . . . '

•

The '~lx;d

potenti"arislocated

~~t'~ee~ ihe, 'quilib~~~

'Pot entials of tbe"02/H₂₀ coupleand

t~e de':

^/Ce4

+

-'couple:

iDAtb~ r.nge l.~'V

^to

i~

^{V vs.}Ag,Agq ,sat'd

Rei

^{reFerence'electrode. . ,.}

" In ;~~lr;I-~': ~::;;'~~+;F.';;, ^an?

^H,O/O,

^{e cup!es b elore}

",.ivol'no;"

•whetJ the 'DlulionI" we!fltirred,-themixed-potentialwillshirt fothe right insteadof to.

the,

len..

Be~atise :ti~ring;

^decre.ases

th~ tbic~ness ,~r'

^{'thedi'lfusionIs; ;;}60

'~l;ld jncr~aS~

^the

surrac~' coIi.ce~trat~~_C~~·'ix=O),~EllliiI· ~bifts'to

^{,morepoSitive}

val~-es

:a.s>obse;,·ed.

TbOi~mu

shift is shown

~~~litaiiV~lY

^{inFig.3.8. .}

Fi~~~'

^3:8

o~ n'~t ~~ge.';

..

Considerj~g ^!hernixed

poi,entlais

inF~g. 3.~:,E~is m~~e Posi;i~~

^than

'E~I thu~ ~E

.~. E~dj.t1ri.·:'"^Erllll>',0;"!ber,8t; ,p~sitiveIY;si~ed..'_:·The dp,tll~~Ta~.Ie'3.3.(a~e

_ ', ': :, .' ,-_."I

taken'from different'meaSuFem~nts. :~e,y,areabout0.2ndadd,ed,titrantbey~nd ~be'

end.p~i~_i

^in'

ea:e~

^{·case. _-.;-('1,(}

" ,

. .

'..Ta,'b,1.\"

,~'.,'.:1 . ~at~::Sh~Wing- ^the -~~~ ~~!~t ~ '~~r~'

^PosiUve'

':~l,fte~,"Mt~~

^theEnd·

, point1ort~eCouple Ce3+jCe^H(r~om'several setsofcbeervatione]..

,1072, 1057

<

'1'!13

mixedpote,ntiabberor e.~nd a.rte~equivalence._Putti,ngall~h

. c;lrV~(orre'Z+'/fe~+, Ce3+/C.e.~ ~nd

0'2/H20.:couples

·~gethe.:; "I, I,av!" b"f""'" ,,,,

.ShO,:,,", Din,F:jS:~~~.'Tak^...e,nt~etber wi.tb:~ig.3.~^and3.8·1be.diag r~~s rills,cancau7eEmilb toshift to lesspositive pctenlialssothat .t:t.. #=

:

~co~e~;~e~~tive. '.~~ey al~o s'h~W_ t ~ha~ st.ir:~ >~:~II~~hirt '~mix,

^"to

.~te.~ ti llls:soth!-t~E=,E.t_i~~n_~^-f;.i,iU,b,ecomes.·~ive., , _W1!.

,between,the.twomixedpoten t ia1syste_~,~be-ecncent ratjonsof b-th F e2+'and...c.e4+

..

a~e' ~~ S~'::~ta~lisli','~ ,~~~. ~?t.~D~ial: ^- The·~ii~·atio~.

^;111

^{b .}

^{,thi tof}

~.i,~;·3.,1(

'inwhicht'be-limitbtgcu~;e~ts^{ror Fe2+}oiidation'andCeH reduct! n arediminished

~·'Iieglf~i-b.le\.alue~~ '

^{." " ?,"}

/

.

. " :'), ,' , "I

Figllres·3.~an d'3JO0,0nextpage.

From

Fig,'3:~O, t,b~;~.oint ~~'1,O~HP

^{istheonlyzerocurrentpoint.T}is is-thestt ue-.

. ~;;n o r• 'in~le ~n~I~" ^{"I Uilibrinm:} ~ilh ':i>ol" li'li~d'Pe;d'';1 n\;li'~i~g. ^{Tb, ·}

~2/H2~,co:uple._I!l1g~~t,control

th:

pot e,ntlal t[ lf.s.:xchan!!:e curren t~e.~e r~enough, Comp etition2::'0uld,-~~,,:~v~r.eXIstbe!w eeD thiseouple'.,a~d~~he,maln edcxoouP~~. Fc2+/Fe^3tand.Ce^H

teeH,.

con t rolling the potentialin°the clas sicalN rDsHan'way

,; ',' £!;"F~:'" + ·£&.1+·c,... , ' . .' . ..

(~,q~i~.".nct= ".',' :2.' ..', ,). C~ICIl~~tion:Of ~he.eqpivalence~o ceDtratio~s of

f';~+.~n~,.C~4t

^·is.

p~i.b~e i~m l~~llilibri~mcon5tant 0 ;

(3 02;2)

~.

^{d,since the:}

·rate'

c'on~{n,~ts

^?r

t~~ ,

^two

~~~X"~_OUPI,es'(F~+

^:...

~'e~ ^-+

^,e-.'ana

C~(Di! .

e~)"'are Ii~ely

^to'

~~

'ls cger than-'tlilli

'o~

^the:

J;/H

20

ooupi~,

^;he

exch&D~

lb~:'~~ili:ns ~l.y""".Hh:t-Of.:'b;I,"er b;.I:,g.",,,g;~:It ;, , ;;o1,d,di~

. laler:,e~lio; 'b :;,t 'b ,:N orn/, ",e'b~;~';' .'lb': j t me;ho~;,}n

^0/,;,

"1i,1;.ni,;1

,(,qU;"o'!W{ : .~.~(: ^{-. . . ..} _ ·~<-A : . .: . . . . ... .

3.4',9Ullotilllt iveTreatmenti-:"

(d).aelore

EqUiJ~lenee: '

^,')

..:h e

mixe! potenti aldiscussed.qualitativel yabovemay alsobetreat ed quant ita- tively.Letusbeginwiththesituat ion.belore equivale nceina'P?tentiomet~ic'redox titrlltion .

,Thehe,at'ment01the systembaving amixedpotentialisb~ed⁰⁰the'currents,

\i_{mil ,,,,}andimit ,tit;'bebalancedat

t.~e

^mixed

poten~ial,·E~i:.-' Il.nd:the oc~rrespon~in.g

^\

r~tions

^arethe

a~,?d.ic

roadi op"

~

^{- .}

(3.4.1)

andthecat hodicreaction

~ O

2

,,+

4H+

+ 4e~ ~: 2 "20

^(3.4.2)

.. .. . ' I '.

!The r.cll.·dion,,(3.4,l )~iye~^the~urrent, ;~b.",,"whieh'^islIPpr~ximat.~llpropcrfica al.to

ihe.coneentrlL~ib~:~i8'~~,~ne.e .

^Cre,.-:

CF.(~~O), '~here

^{Cr••:~!s.thebulk}

,e~oe~ni~ati~~.

^.

Il.~d cre.,~=o)istheelectrodesurfaceconcentr~,tlon,or Fe2+,.mr....I~themass

•translerocotridentand!-

.

is the electrode surracearea

.

';~.

⁼

~r.1+ (C;.t:'~-

^CFe....(x:;::::O)JI

., ' , ~ ~ ' .,

Combini~,g^equlltion(?.4.a)~ith(3.2.3)inthela5t's(!~lion,.we·l..a.v~with 0=1and

"'npproprintc substitutions

. [C

r ".-

^Gr,'·(x=O)

I

~'. . ^{Crt': " '}

, . .\ . ' .';" -:~5 - ^{. ... - ' . . '}

whereC~e':"(x=O)is,the concentr ation

o r

^Fe3+ncartheelectrode eurteee..There ls..

•another

rel~tion'i~p

^between

Cfe~ ( x=~)

^and

Cr:~~ (x~O) whi~h

^ls

us~rul

^in'

thi~

Thecurrentimix,. canalso be expressedintermsorthec.oncenti'lltiongmd icnt or Fe³+as:'

(3.'1.6) Combiningit with(3.4.;J),

V

pote ntial"change and.the

ro~at~~D. s.peed we;~ r~c~rded ~i~ult~neou~ty

^'\v.illt.

a .X~~

^•

recorder-jedtherotation.speede~~Dgedfromzeroto ebout2500.rPl1\ wi~~.in'''IO

_s~c6nd~. , _ _. . . ' .

With,therot ating

_,

_.dis:electrode,_. ~ the'Levich"equation ea'u- ,be!?-PP),icd'0

eqllatio~ "

^•

{3.4.~).Equation(3.2.5) would.be~om.e

. z .1 J

r "

il,..

=

FAD:~~,~^/I,8

, C i••

J!:i,2· ^.j .where Dro'"isthediffusioncoefficientorFe1'+ions,11isthe kinematic'

wate rand,Wisth~rotation.

speed'in'

redlenaper,second..Equation'

Em;,= RT.F

I".!.

2

+

.

~~I"[

F '

'~

C;~I"

.T. ^)Ei...

," ^,,,.":+

. .!

^),

[5!!--l

^CFel+

~: " ~~I'.I"+ t . ^.

^'2

^{. ,;,}

^_-

"~'r

1 ' .".!

· lt]

:

• -.' •

~ FOf~~"

^{/I,S C; .H.w2•'',_}

.''T he.measuredpotentialEm;zdecreasedwithincrease or'rotat ioIlSpeed.Inorder to

find _~

simp:le ,relat ionship .rrom• "

·equation

-'. .

·(3.4.~)

• ^further.

a.pproxi~ali~~

1 . ^has•^to'b. ^e'.

.madeb'yc?m_~aring th~v~lue_s^ofi~~·.term.^{in the}squar~^root'and";ea n anginl CT-,IE"..

~.

^{".-:. ;_ . . . - ,"\•}

Replace.Dre

g

+e' ,. I by b andsubstituteII,.back ap.drearr ange!~.4"3S.)togl.ve~ ;

. .. . , .~ ^{... ··1 · . :} I ,. ' ; ''''''I.!.\ · '·

Emlx .~

^RT

In'l. ~+ ".!IT..Jn'

^{b+ b2+}

"4iat:~· : ' . ~, . ;

F. ~~. ..F _ ' '.'~. . .

oCarot ating diseelectrode.

potential decreased

.

^{' ., .'} ~tb'i~creaseoCrotatinJ.speed, Fur

^.

^{. . "} bermo~,^{" plotting'. -the'curve..'" '..} ..of Fig.3.12as Iogaritbn:a

o r

rotationspeed, a !airly linearrelationisCoundIn

Fig,~:13,^givin.r;expe~mental s~fport~^the\beo~etic (3.<'43)

p,ooi,,, i. n.;.'i~;

^elopenftho

~'vi 'I~ ~ pi

' ." . -

,

.

~b~ .~a~.ue~,,~, y

^per

ti~i,t in~re~~~_t

" In·w.:

~'e

icperimentnl.!J2pe

(~.:n

^Fig,w

'3.13i.-OJ1OSYwhieh"quit.good '' 'ee mont .'<. .:\

. . ^"'..

I~order'totre~l.:the'titrati~Dafterequival~nee.tb' formal potentialforthe'.coll-

"pie:

. 0

2:

+ 4H~ ⁺

^4e-

~

^2H'20,

need~ · . to b~ d~U"~~

^"

Tb~ ~~asurement. or

^the'

staitdard'-~ientialoftheOJH₂0eo~pleh~a long s ylG.T-he standardp~ieniiai•

;;Co: 'thisc.oupie

~u c~leul:ted 'C~m ~hermodlna~ic"

^d

t~

^it

~hou~d- ~'~-1 :22g-'y v~"

SHE but nobodyobta ined thisvalue~nADeleetroehejncalsystemunt ilrecent years beeeusetbesol~tionusedin themeasurementbad

to

beextremel, pure, Instead,

,

.

^{, "}

-

^{.~ . ,}

'.

the_ fo~,niai ~qUmb~i~'.::potenii~1 Ot..0Jj'20 eoupl ~~1! lu:II , ' ~bs~rv.~d,,~ be.a~:t· .

^;

1.06V,withoutspecial preparation. Underourexprri.e.ntal'conditibns, the-reagentl . .,'and waterwere'

·~~t'. sl?efi~I1~ ' ~repa'red ;0 . '

thatthe'

;~nn~I' poi~ntiai

^is.

~~~en

^to

be '

, , L~OV; ^{T h ee} qn l,mb:~;:::::n:l :O~:h: :oO~;:: ~~:':Op:: 25 ~G~ -,

:]: