Chronopotentiometry

REVIEW - ..-

-

--.

._ -

-

1.

Elctiroannl.

Chmr..

14 (1Wj)

447

474

I-.ig

2

V;u

clrctrulysis.

i.rtir3ra

(I:“).

lysis at current

of

Iu,tc-xati.ll

Ec~uitih:ium

flcnslty

i.

s.f

fr*..t

I

I

I I I

I I I

l-lc-ctrrulr:

~wtcntiai;

(E,),

xv;tIl

time

potcntinl

cl~tinfl Knlvnnmtntic non-r.tmcly St.?te of tcrt c-lcrtrodc at t)rginninF: Ot c*tfXtr(~

Galvanostatic non-steady state ckctrolysis 0cf:urs duririg chnngf: in the tollcentration of the reaf-tant at tlw ttlcctrofk from its initial value CO” to zercj valut:. The duration of this non-steafiy state t:lcct.rolysis is deGgn;~ted t. OUCX furlctions CC, tilno fIiilctic)n in terms f>f t.rnnsition Cc,(r, L) and C*r -c~c(x, L) XIX: k110w11, n Ilc3tc:nti.d. time

can

be obtained.

CHRONOPOTEXTIOIETRY

149

Therefore,thefirstprobleminthetheoryof potential-time curves in galvanostatic non-steady state electrolysis with total or partial control by diffusion, is to investigate the variation of concentration with time at the electrode. This review- is not intended to be a complete coverage of all the pertinent literature but rather a survey of basic ideas, principles and potentiaLties of the chronopotentiometric method. The mechanism of electrode processes is of particular interest to most

electrochemists

II. FUNDAMENTALS I.

OF THE

and

is,

therefore, even

thorough

treatment.

THEORY

of comzent~ation, Co(_x, t), CR(x, t), re-uersibleawd iryeveusible ekdrochenzical

Variation

A _ SiztgZe

more

ami? tramsitiox reaction.

tinze

Kinetic

scheme

I

O+ne+R

(4)

(;) R.sac.famt 0 am? $rodfzrct R aye soluble s$ecies. This part of the theory is the same for reversible and irreversible electrochemical reactions. Change in concentration of the reactant, CO, at the electrode, on switching on a constant current, was calculated by WEBER~ and S_~SD’-~ by solving the differential equation expressing Fick's law, aco(-x, t> =

5=0(x,

D

8)

0

at

(5)

a_??

where Do is the diffusion coefficient of reactant 0. The solved with the following initial and boundary conditions; Co&

o)=P,

Co@,

6) -co,

iinF=

Do

afferential

equation

was

(6-1) forx-02

aco(x,

(6.2)

t)

(6-3) > Z=O

ax

where C" is the bulk concentration of 0, i the current density and F the faradayof the Condition (6.1) expresses that, initially, before electrolysis, the concentration solution

is homogeneous

at all distances,

x, from

the electrode, equal

to the bulk

concentration of reactant 0. Theboundarycondition (6_3)followsfromthefactthat,accordingtoFaraday's law, regardless of the current-controlling factor, the cutient density at any given

time

is

by (7)

where dN/dt is the number of moles that react at the electrode in unit time and +~fi is thechargeinvolvedinthereduction of one mole of substance 0. When the current-controlling factor is the rate of diffusion of reactant to rhe electrode and when resultofelectfolysis, given by FicKslaw,

-= df

d?.m

Do

the concentration gradient at the electrode is developed as a d?V/dt is equal to the flux of the reactant at the electrode andis

acob

( - ax

t) _)

z_o

(8)

The bound:lry

condition

(11.3) results

from

(7) and (8). l‘hct result

of integration

is3

(10)

.-_---

-___

___ ‘c

-__

-.---

-r

-

--

---

--

_

1 __

I1

____>----

,>‘<_;/;

/

>A ,/ fi

/T / I.4

‘f.

C

J.

/ __I_

Efrrtroanul.

-

Chcnr..

-------

_L_-

-.--

._-.

-_ _

.*47-q7.(

-

dmtraty

(lO-“A

-3

J

Cut-vent

14 (1907)

-*L

cm-‘)

CHROSOPOTE~TIONETRY

45=

For t=t,

since Co(a, t) =o

(eqn_ (3)) it follows from eqn. (14) that,_

mFCo”Do+Jzi

tf=,xf

(16)

According to eqn. (16). 24 is proportional to the bulk concentration of the substance reacting at the electrode and inversely proportional to the current density. assuming DO independent of concentration, and for For a given system, constant current density, eqn. (16) reduces to t*=

const.xCO

(17)

Thus, ts is a linear function of C" and can be used for quantitative determinations of Co_ Equation (16). and in the simplest form (17), are the fundamental equations of chronopotentiometric

analysis_

(Zz) Product R is imolzrbk O+?ze

+

scheme:

R(insoluble)

Concentration

(i) Two

Kinetic

(4a)

change,Co(x,

t), and

t are the same

as in Case

A(i).

corrseczitzveeZectrochEmiccz2 reactioms inaolving differe~~tsztbstnlzces. Kine-

tic scheme I Ol+nle

+

RL

W)

0.7 + zce +

Rr

(19)

Reactant 01 is reduced at less cathodic potentials. electrolysis was developed by BERZISS -QTD DELAHAY"_ If ionic species

potential--'Lime curve

01 and 02 eshibits two

are reduced steps.

The theory of this type of

at sufficiently different potentials, a

For the first reduction, at potential EL, the theory of a single electrochemical reaction applies. The transition time, tI, for this first step is given by the eqn. (16). Afterthe elapse ofatimer-1,thesituation atthetestelectrodecanbe described of 0, at the electrode is as follows: (a) at the transition time ~1, the concentration equal to zero and remains equaI to zero as the electrolysis proceeds after time TV; (b) reactant

O1

continues

to diffuse towards

the electrode

where

it is immediately

reduced. Since this supply by diffusion of reactant 01 is insufficient to maintain the impressed constant current, a part of the current at the test electrode is used for chargingofthe doublelayeruntilthe potential reaches the valueEzwhenreactant0~ is reduced. Then the currentatthe working electrodeis the sum of two components correspondingtothe simultaneous reduction of substances 01and OZ. : Afterthe transitiontime ~1, thecurrentdensitythroughthecellisgivenbythe equation (analogous to the formula (6-3)). i=nFDo,

(x f)

x0,

(

ax

GO

z=O

where the time t’ is defined by the equation

i!‘=.t--& t being the time

(21) elapsed

since the_heginning

of the electrolysis_ -J_

Ele&o&d:

Chem..

14

(1967) 447-474

reactant:; 0, and It1 arc rctducxxi at sufficiently sqxuatcd curvtf r*silil>its twcb stctI)5; tilcl trcatmcnt of tilis thcx l”‘tc~rlti~l--tirn~~ treatment of the kinetic schctme with reactions (18) and (19). f;or rcac’ticln (I’lj tlie theory of a single eiec:trocllrnlic-;~

potc-?nti.?ls then is sirriilar to tilt>

If

After

time

to rcdllc-tion

~1, anti since

the test

electrock

of that intcrmcdintc K,, tlic rcsp:t to the rcactarit 01.

FVitli

conccnt (I,) I-c-actawt

(a)

:ation 0,

of 0,

at the

c.cjntiriutrs

reaches

situation

clcctrodct

tc, cliffuse

rrt tllc

at

tc,w:lrcl

71

and

II2 corrcspontiing

clcctrode

is:

after

tl IS qua1

tilcb c*lt*ct rocI*-

the

r’wc-tant

for stttp

from

that

iriit ial

tl!c:

dClK’“ClCrlt

tllc:

(25).

is a function

t:lcc:trc)dc

cone-entratiori

during of

tlx:

of

diStail(:e

first

step

rc;act;int

iri

.c

from

first

step

to zero; t 116: csltv-trcbcic*

of 01 to

that

I
c-oriccmtr;lticm

tile cicctrodc

(it is notewc,rthy

tilt:

at

;lncl

is reducccl dircctl>* to Ii:! in 3 procttss iri\roiving (x1 -+922) ciectrons. l\‘itII reslxxt to tiic reactant Rl (intctrmctiiatc in reduction (a) c-one-critration of I<, nt the c:lcx:trodct nt ;imc* ~1. i.c., initial diffusicm

aIq)iit:s.

react1011

potential

of

as a Icsult it wns

is 1iornogt:ncous

of

assmmc~

arld

in-

caf x) ;

in erme!ciiate Ii1 diffmes back towards the clwtrode; at tlw clcctrodt~, 1x1 is (25). 11 2 . 3s in cqn. I;z-act (n) collsidcarnhly coml>licatc?s the math~?m:~tic.?i treatnlc~nt of tilt l)rcasctnt

rt , duccJbt!o.

1

jra>l>lcrn

with

t’ definrtd

by eqn.

(27).

453 trmsition

The

tirw

~2 is given

5::. - (‘z z’:?D (C”):‘/+rq

by the

equation

(27)

(‘7LIZL.. + u.r”).

or c:qu;rtion.

(2s) oi,t‘airlcci

where ill

from

kt ard

C~IIS.

kh are

(16)

and

formal

(~7).

rate

constants

for the

(29). Assuming

thnt

the- diffiision

crn?fficicnt

of

fonvard

am1 backward

subsbmx5

_I. ISleclrQanoi.

0

and

Cheni.,

Y

proccsscs arc

14 (1967)

ectud, 447-474

In the prcsencc

of adsorption of an elwtroactlvc spwicts at tlw ttlrtc:trocle, the current nt the clcctrode is composed of two components accord!ng to the origin of iorls: i - i,ds, + itlfifl_. Currerlt i,*,. 01 iGirlntc:s frc~nl tllc disc:li;irp2 of tiic ions coming from the adsorption lxyttr at the ttlcctrodeH. The cliffusion current, 2’dlfr.. is detc~rmined by ttics concentration gmdicnt according: to cqn. (0.3). I‘lics surf:lc-ca cxmc-entrntion, Z’, of acisorbable icjriic slx3:ic.s ir; a furic:tion c,f tirrie, nricl ;Cads. is given l>v tlie cyu:ltion,

A plot

c,f

ir us.

x/i

yic*l(ls a straight

line with

311

intclrcq)t

xl;.l’:~nci

a sloI)ct proportional

to <:“I). the supply of ions is csclusively due to the concentration grncl+nt at the clctctrocie according to Fick’s law. until Cr..0 =o. Wtlcn the adsorbed species of 0 is less easily rcduccrd (i.e., rctiuces nt more cathodic potcsntinl) thxn the solution species. eqn. (rh) applicts to th(* first at the clcctrodc is qu‘alitatively similar to tllat of step. After ~dlff., the situation In

I/2t: st-co22d

caseb-8,

it

is

a~surncd

that

in

the

f

first

stcl),

E-:lccfvoand.

C.ehrm..

1.8 (1967)

4.47

.+74

CHROKOPOTENTIOMETRY

The

45;

theory

of a single

electrochemical

reaction

(section

IA)

applies

to the firs:

step. Treatment concentration tion

of the second

of reactant

with

step is more distance

Variation of the concentration to 0 is shown in Fig. 5.

complex

from

because

of variation

of the initia

the electrodea.

of reactant

R before

(at r) and during

reo,xida-

,

RDI

RT R,=RD,

+RT

Fig. 5. Theoretical curves for variation of the concn., CR(_Z. t), before (at r, d.e..Y=o) re-oxidation. Thenumberoneachcurveisthetimeinsecondselapsedafterreversalofcurrentatt (BERZIXS AWD DELAHXY~).

and during

Fig (5.Simplified equivalent circuit for single electrode reaction involving two consecutive steps, mass transport by diffusion and a chargetransfer. (Cnr). Double-layer capacity oftestelectrode; (Rnl), diffusion resistance; (22~). transfer resistance of electrode reaction; (RI), resistance of electrode reaction.

Transition

time

for reoxidation

t’=

{e”/(e+1’)2-@;t

The

functions

8 and

step

(54)

is4

(55) R’ are defined

by equations,

e =ifnFD~

m

R’ = i’/nFDR

(57)

Where i and i’ are the current densities in the first md second electro-chemical respectively, and DR is the diffusion coefficient of substance R. When i =i’, then 8 = A’ and i’ is given by tr=+t

when

Relationship R is insoluble rr+r

step,

(58) (58) holds when the reduced species, and remains on the electrode11

R,

is soluble.

In the

case

(59)

Relationship t’ to t provides a very useful diagnostic criterion- in electrode kinetics_ This criteridn is necessary iu the study of the irrev_ersibIe electrochemical reactions11 where the potential-time function does not provide criteria for- distinguishing between the cases with soluble and insoluble reduced forms, R.

M. PAI.INOVIC

458

(60)

0 + ~zc+-bF: Wllcn galvano+taik ing to ecln. component

allcmlating current wit11 constant nml>litude pil~e. the flus c)f tllc rcnctnnt 0 at tllc! electrode (b.3)) lly (i,.,,):‘Vll’

the

sum

of ttit: dircc:t

/fasic Lrcat~rrcrtt -4 simI)lificd trcIuivillc1lt

_-I

circuit

current

is suyetimpOscd on is cicttcrmincd (xcnrd

c-ornlx~nent

for t lit: singIt:

c:lcctrodc

(id.r.)

rtractioll

i~ncl xltcrnating

clisc:ussc:cl in tliis

diffIlsiO11 c;1I1;lC:ity, (:dlff.. is IlcgIecttxI. \Vllcli ;L c:c,nstarit, current is ;iIjplitrcI tcj tlic: sybtc:nl sliown iri (electron flo\v) i5 used forlzl.*G.

reVkV

iS ShOWI

i--i..

Fig.

6.

Tile

Fig.

wit

c:urrent

(Cl?)

and it. faradaic: c-urrcnt. of t lict tcsst cl~~ctrc)clt* at wliich a ~,roct:ss is occurring. c-ircllit in I;ig. 0 (luring non-stcacly state gxlvanostatic:

tllc? cxluivx!ent

varies

0,

t ir

i, is calxl(:itive. l‘lic~ Ix~tentinl

w-tlcvtt t,y

in

!I time

Tiirc:c (T)

xc-c-cmtillg

tirrlc:

I’imc

;L

tc,

iritcrvals

in tm-wl

t JIG CIII-V~~ givcw

can

Ix

idcntificd

111 this

(l=o-lo).

in in

Izig. the

rcJ)rcscntctcl

clcctrolysis,

2. cumc

in

the

rise

treatrrient

Fig.

3.

tirrlc

xross

tht:

circuit

ion bctwctctn t iic tc:st ctlt,c:troclc and tiict till 0: tllct l_uggin cnl)ill;lry (R,, C,,) i.i ncgltxztecl since it is IO--g sf:c or lctsslSC. The first process aft,cr alq’lying 3 current to tile system is charging tile doublcpotential, E”, up to potential El layer capacity. Cnr. in Fig. 6, from the rcversil>lc wlieri the clcctrodc rcac:tioIi bci;i~~s at tii*: rricasu12l~lc: rate. cornposcd

t,f

1‘)~ imposed

t,he

time

voltage

resistancx:

arid

ncccssnry

to

caJmc:itarice

clmrg~

the!

of

tlic

capncify

solilt

C_ in

an

UC:

circuit

to

c)c).o~~,

of thp

is

tx__O.b)OPC = 4.6 K(_ ITor example and

/_

R=

(in order

(03)

to show

the order

z Q, L, ~4.6 x IO’ 4 sec. (2) Time inicn& (Lz .L,). When

Elcdroana~.

Chmn..

14 (1907)

447-474

of the

magnitude)

the potential

taking

El is reached

CL)I,=SO the rate

~1;

cm,-’

of change

of

i

I’tic: iIiflucncc of tlic doul~lc laycx calmcity un tile sliapc of tlic yotcritial tirnc curve is gi\rcn clualltativcly in the! above discussion of E’-2 time interveals. It is obtained clu;antitntivc:ly froni tlie ccluatiori for c:liargirig of tlic cxpacitor in the h’C circuit (a sctrics circuit) l6

(W

by the capacity whicll in the function E--j(l) up to potential VC, ix., ipr~~sirrl;ztcd by ;L straight lint. tlte tangent at L-7 0, fIc>ni tllc cclu:itioI1 0f tlie taripnt (at x0, y=/‘(z~~,)x) follows (Ob)

V, = (V,/ztC)t setting

V = VC.. 011:: gets (“7)

,,-KC

If

the

capacitor

xI)prosimation (Of)) is usc
I’httreforl:. time

intcrvd

(lo

npl>rosiniatc III

merits

me:

tiic:

Cl)

is ~ivcri

time ricc:css;uy fur-thcr tiic:oIy

cmnducted

the

(05) ;irld

tiic

voltngc bc

slopr

after

;?lrllc)st

of

length

the

of tllc

time

(a-3’>:

k.-=/(1)

tirric

z-i wiy

that

11, tlw

time

nece_ss.uy

in conllxkrison with 1~’(2.C.. with tlic ‘2~; t=t~ nc~~l~tctin~ i, (SW cqn. (Oz),

the

(61)). for the

cclll.

CIIWC

int.rtrval.

to charge

transition Fig. 6).

1:-M,‘,

usillg

to rcncli t lie I)otctnti:ll Et (Fig. 31, by eclns. cjf lx>tcrltial tililc: c‘u~ vft_s it will tx ;Issur~iecl

in such

layer, can t)ct nq:lcctcd systttni will bc trc:Lted

;Il)l)roXirn;+tion.

by cqn.

tllc wc~lll
i.c.,

I Ile

(6:)) ant1 (67). tllat

the

cxlx:ri-

tfouble

tin-it-z T) :mcl tllc

rtnkrrsihlc* c,frrrroc/r~nrirmL rzc~rtt~mr. liintstic schcrrrt~ (‘1) ‘I’lic rntc of rcxxtiori is c:c~ritrc,llc:d t)y Ctiffllsion orily. (‘A11 f1t: c-;llc:lll;ltttcl (i) I\‘t:uckxnl 0 und fi:rndtcrt~ I\’ TITL*solacblc s+x:it*.s. *I’llt! pdctr1ti;1l as n function of tinie from tlw Xcrrist t-quation by using thtt tinie function, C,*o(o. 1) (14) and (I_;) in the Iogarithnlic: term. and CIr(o, 1). as givttn by cqns. II.

Siqlt-

Taking

iFto

account

~~=z~,,~_I-(I\“l’/rzz;) wit

ccln.

(T(J) for x, in cxdcr

to clirrlinntc:

!rl{r+--1’)/1+}

Co, 1; -j(t)

is given

tjy” (OS)

tl JC;,,

wI1crc

cicrits. yielcfs

-7 E”+

(J\‘7‘/rtI;)

III (/~,J,,c~//,lJ~o+)

((‘9)

is ?ilc standard potential for ttlc c:uuplc 0 13 ;mcf t tic f’s art: ;+c:tivity c:ot:ffiFor t = .) t. E 7 E r,J. Eclu;~tiorl (GR) SilclWS tllat il l)lot of tlltt Cluant it y lri{(r + -t +)/L+) 7s. Imtcrlti;ll a stlaigtit lint? wit t1 slol~ K*Zl’/?tI~‘. Act-orciinr; to ccjn. (09). I*‘_rjs is inclcrpcncic*nt of C.‘C30nncl i. i c*., J?

dfi :,.a --=” co

(70)

a iI

al5 r,J ._ cl 111-i

.-

0

(71)

ctrolvsis. K. is insohhk. Kinetic: scheme: (.4x) (ii) Prodtxt of P.?.e Wit11 that assumption that tlic: activity of the! clcposit (insoluble! product) is efju.21 to unity, k---/(t) c::m ba czklc.ul:rt.cfl losing the Nc:nist c~c~llntinrl with CC,(c), t), from crqn. (14). The r~sul t is” E=E”‘1-(RT/xF) where

E O’ is the

formal

In {?-;/~~~(nZ,“)~}+(RT/rrI=) standard

potential

of the

In conple

(T~-L?()

0-K

(72)

(7.5)

dfi _- ll.1 3 In C”

-- ml’

txtLsi=

A

plot

of

In ((T + t’) 1 - 21’4 }

Tlw rate const;mt

7~s.

Ii

yictlds

3

strni.qht

kh,tl can be calcnlattxl

c.alc3latior1 of A*,;, froIIi cqri. (7‘3) i.cz., (79). I‘hcrcfore, the current-reversal mctthod of clectrochemiczl reactions in both directions.

from

lint>

Et,..0

can lw used

witil

Slop

in an

KT/(I

w~alo~:ous

for tile study

--‘)nn’lT.

way

of tk

to the

kinetics

CHROXOPOTENTIOMETRY

the imperfections

465

of the electrode,

sional tiea is the same is equal

as the projected

to r (f= With

eqn_ (r4)

real/geometric decreasing distance

Fig. factor

be seen in Fig.

9. Schematic w-ith decrease

For these

area of the electrode

(apparent) surface from the electrode,

thickness of the diffusion layer, uneveness the real diffusional area increases; hence, Can

is valid5

conditions

the

and the roughness

diffufactor

area) _

which istantamount

of the surface the roughness

to decreasing

becomes more important and factor,f, also increases_ This

Q_

representation in thickness

of diffusion of diffusion

Ia>-er on a rough layer in the order

electrode. Increase of 1-4 (LoRE~;~~).

in roughness

When one encounters larger real diffusional areas and largerf's for the same imposedcurrent.thereis a correspondinglylowerrealcurrentdensity (iresl=I/Prerrl= ) and therefore a longer time of electrolysis. apparent IffxP One can thus expect positive deviations from constancy of the product it* of the electrode_ with increasing current density resultin g from roughr-ess (GZ) -Won-Zinearzty of the diffzbost field_ The plane indicator electrode should be designed in such a way that it provides conditions for unidirectional diffusion only along Lines that are normal to the surface. For precise measurements and precise a planar electrode should be shielded27*“8. checking of the validity of eqn. (r6), These conditions can be approLximated satisfactorily for analytical applications by the use of a platinum foil electrode positioned in such a way that the current lines are normal to the plane surface. An unshielded planar disc electrode can be used as a micro-electrode. Under certain conditions eqn. (16) may be valid for spherical electrodes and cylindricaI wire electrodes’9,3*. IThen the dimensions of an electrode are large compared with the diffusion-layer thickness, then the electrode surface referred to the diffusion layer appro_*mates an infinite plane. Deviations from the transition-time equation are very often noticed in the use of all types of electrodes mentioned including the shielded planar electrode. Diffusion to the unshielded planar electrode occurs not only in directions J.

EZectroanaL

Chcnr_.

14 (x967)

447-474

normal

to the surfxc:.

l>ut zdso

in ar’)itrar)r a planar circular

dircwtions. clcctrodct.

T11c:rc: arcI s~~lwricd

contribu

Non linedty of the diffusion field around the: ekctrocie can be a c:ausc of devi;rtions from theorcticd equations. U’hen the thickness of tlie diffusion layer is I:lrgc by com~x~riwri with tile drrIicrlsions of that electrocle. tlw diffusional field is to ttic first ap~,x.osirllatioli, linear. As tlit: tliicknctss elf tllc! dlftllrion hycr clc-crcascs, ttic? dctlmrturc: from linc*arity inc-rca-ses. tiorls

to

tile

diffllsion

to

I

__

-

1

I\‘.

,\l’l’Ll~..\

I IOH:,

IO

bb.1

I..<. I l,.lJ

l’KOI~I.l~..~l~

>I. I’AlINOVI(;

46s

The precision of the concentration determination
TIIC

c3f ~ICCtr-~W:1~~IIii~-;L1;IIIJ

kinctie

chcrnicd

rcactioIis

can

i~c studlcd

galvariostatic non-steady state elcctrolysls as shown above. A knowlwlge of ttlc kinetics enables the mechanism of clectrochcInical tions to be elucidated. I;our tiiagnostic criteria were prol)owdll : (a) A linear plot of some logaritllmic function of timct and 7 ‘us. potential, of t11at

tt1c siope

E

-’

f _ Elrcc~ounul.

q(ln

plot.

k’(L,

T)

) ;

k@{ln 1;(1, --_ t)} -. _. ._ilk-

C-hem:. , 1 , (Z’#‘7) .).$7 -47 ;

by

tlic

rc’ac-

and

tl~c

I~~~:;~rrthrn

of

ttlf* t)lllk

h¶. PIVSO\‘iC

470 ctitermn on comparison of t.he cxprirnwt;4 tical equations. (knstanc-y of tlie diffusion cxx-wentratmns

it; an auxiliary

MUKKAY

ciinK:nostic

sugg:cxtccl

i-r relationship with the stxwral coefficient. 11. over a range of

tllcorcsulutiuri

critter ion**J.

the: uhc of rilmp

CUIICIIL

(d--pL)

c 1IIorloyutcntiorlrc:try

iw CL

tclst’19.

hlURR.AY

.+X1)

portanw in rayring rrG.chnnisms. They c:lw:trodct rcacticjns

discusw
(;KOSS.‘”

tht: cxpc~rirnental

conditions

oiit mtL3surerwnts for distinguishing bctwecn wcrtf abIt: to come to definite conclusions on in the C;~SC of adsorption of l~tacl :mcI mewury(

til;lt

different

;icct of

irrl

clt:ctrodc

tlic rriwli;uiisrri of I I) on ;L r~~c:rcury

clwtrock.

1 E M .AN _+%sI) J%oCKH15z~2 calcul;ltv> dettr~ninin:: t titr quarter-tint<: ptcntials. On tile basis c)f kricnvlcclgc cjf tiic suc:ccs.sive formation constants and the rate constants for formation and dissociation uf tllc

slowest

dissotrincing

dil-;soci;ltinK

c:)nlpIcx.

c:omplcx

ion

CL cd.-> 3.J.1 calc:lllatccl

I
in tlw

the

lifetiriic: of tlic slcnvcst

setics.

llasicxlly, tllrce tyyc:s of cells CXII 1~ usedwith c>nc, two or thrc:c .xparntct cornparCmcnts. ‘I‘llc system can contain two or three electrodes. In two-clcctrode systems, the reflxenre electrode is also the auxihary electrode and in tllis case slluulti

hc of large

arca

C;IERST

growing electrode /. Ekdrooncl.

in order ANI)

mercury (1’~

to :~void p2lariz:~t ion.

jUI^IAHD1”

drop

(Y-

z,oo mmz), Chew:.;

14 (1967)

in

I mm”) in a single 447-474

Iy)5j

used

a

two-clectxwd~

as a test electrode compartment.

witI

;1 slow-

and a tarp2 rcversiblc

Systc‘IiI,

couritcr

r 71

(b)

9OV

I

4)lf -

-

-_

-Jc, T

_--

c2u2

_L 1

474

3f

I’.\lINoVIL: