Sub-microgram-scale analysis by coulometry at controlled potential

ANALYTICA

456

CHIMICA

ACTA

VOL.

SUB-MICROGRAM-SCALE ANALYSIS BY COULOMETRY CONTROLLED POTENTIAL LOUIS Dcfxwlmcrzl

of

Chcrnislvy,

Polyleclmic

20 (195’9)

AT

33EIT1.3

Inslitrtie

of L3rootdyn.

f_irooltly?r, N. Y. (U.S.A.)

The utility of coulomctry at controlled potential in analyses at the decigram to milligram lcvcl is now well established, but the practical problems involved insecuring accurate current integrations at that lcvcl liavc been solved too recently to permit any concern with the further problems that may bc cxpcctcd to arise in dealing with much smaller amounts of material. 1Meanwhilc many successful applications of coulomctry at controlled current to microgram-scale analyses have been described. These facts have led to a general belief that the controlled-current tcclmiquc is the more useful of tile two in trace analyses. This belief has been held dcspitc the demonstration by I,OICII, O’NEIIL, AND ROGEI~S~ that cvcn rnillimicrogram amounts of silver can bc determined with good accuracy by a procedure which, though quite diffcrcnt in apparatus and mcthoclology, conforms to any operational definition of coulomctry at controlled potential. More recently, using more conventional proccdurcs, UOOMAN, 'l-Ic~L131~ooxc, ANI) k151N2 have succccdcd in determining 7.5 ,ug of uraniuln with a standard deviation of j= 2.2O/c,, while MEITES~ was able to obtain a mean clcviation of & I.o”/~ in the determination of 5.2 pg of chromium. The present paper dcscribcs the results of an attempt to extend coulomctry at controlled potential to its cxtrcmc lower limit, using a chemical system which was believed to be ideally suited to that purpose togcthcr with conventional apparatus and techniques for current integration. This attempt was made, partly in pursuance of the considerations described above, and partly in the hope of casting new light on the sources of error which afflict all analyses by coulomctry at controlled potential and on the techniques by which these errors can bc cl’minatcd. EXPERIMENTAL The Analytical lnstrumcnts, Inc. (Uristol, Corm.) potoutiostat and clcctromcchanical wcrc carried out in current intcgrntor cmploycd have been clcscribcd elscwl~crc~. All clcctrolyscs a double-diaphragm ~~114, using a well-stirrccl mercury pool working elcctroclc having an arca of fitcr-type saturatctl calomcl rcfcrcncc clcctrodc, and a helical platinum 47 cm? a commercial wire auxilinry clcctrodc. A few drops of suturntcd hydrazinc diliydrocl~loriclc wcrc added to the supporting clcctrolytc solution in the auxiliary clectrotlc compartment of the ccl1 to prevent anodic attack of the platinum. A x.5-V dry ccl1 in series with the auxiliary elcctrodc was used to permit the potcntiostnt to maintain control throughout each electrolysis in which the working clcctrodc was anodics. Whcrc ncccssnry, a dccadc rcsistancc box in series with the bias battery was employed to limit the initial current to a value just smaller than the rated maximum value for the integrator input resistor employed. This unusual step was prompted by the extremely Refsrs?rces p.

462

VOL.

20 (1959)

COULOMETRS

AT

CONTROLLED

POTENTIAL

457

rapid decrc.ase of the clcctrolysis current: had an input resistor becn used which was small enough to bring about accurate integration of the initial current, too few counts would often have been secured to permit the maximum precision to bc attained. Mcasurcments of the electrolysis current were made with a multi-range milliammetcr in the electrolysis circuit. Oxygen was cxcludcd from the working electrode compartment of the ccl1 by a very rapid stream of prcpurificd nitrogen which had been passed through two efficient gas-washing bottles containing o. I F chromous chloride, I F hydrochloric acid, and cxccss heavily nmalgamatcd zinc, then through a similar bottle containing water, and finally through still another bottle containing the ammoniacal supporting clcctrolytc used. The first and second of these bottles scrvcd to rcmovc the tract of oxygen prcscnt in the nitrogen 3, the third to trap droplets of chromous chloride that might have been sprayccl over, and the fourth to prcvcnt cxccssivc volatilization of ammonia from the solution being elcctrolyzcd. A stock o.05M solution of zinc ion in o.zF hydrochloric acid was prcparcd detcrminatcly from pure metallic zinc. hlorc tlilutc zinc solutions wcrc prcparcd from this by dilution with 0.2 F hydrochloric acid, using carefully calibrated volumetric glassware. Other chcmicnls used were ordinary rcagcnt grade. “Vacumctal” mercury (Mctalsalts Corp., llawthornc, N. J.) w.as usccl without further purification in all determination involving as much as 0.5 mg of zinc, but the ammonia and ammonium monohytlrogcn citrate usccl to prcparc the supporting clcctrolytc containctl enough zinc to cause a dctcctnblc error cvcn at the 5-mg lcvcl. Hcncc the supporting clcctrolytc was usually frcctl from zinc immcdiatcly bcforc use by an electrolysis at --I .50 V tls. S.C.E. ; tlw zinc amalgam formed in this step was drained out of the ccl1 nncl rcplacctl by fresh mercury before the actual analysis was commcncetl. For tlctcrminations of less than 0.5 mg of zinc, mercury was used which had been previously purified by anutlic strippir,g into purifictl ammoniacal citrate at -.-0.50 V vs. S.C.E. . DATA

ASI)

DISCUSSIOS

sensitivity of coulomctry at controlled potential is ultimately limited by the magnitude of the correction that must bc made for the lx~.ckground cluantity of electricity, i.e., the cluantity of clcctricity which is consumccl at the working electrode by processes other than the one of intcrcst. Five components of this background quantity of clcctricity have been distinguishccl by I’V~ITES ANI) &~oRoS~, but only three arc rclcvant to the clctcrmination of izinc by the prcscnt method. ‘I’hcsc are the “charging” or “condenser” c!uantity of clcctricity, QE, rccluircd to charge the working clcctrodc and the clcctrical double layer at its surface up to the control potential; the “faradaic impurity” quantity of clcctricity, QI.,, rccluircd to osidizc or reduce impurities in the mercury and the supporting electrolyte; and the “continuous faradaic” quantity of electricity, QI,~, which results from the reduction of hydrogen ion, water, ammonium ion, or some other constituent of the supporting clcctrolytc whose concentration remains substantially uncllangcd throughout the clcctrolysis. When the working clcctroclc arca is about 50 cm 2, as was the case in this invcstigaIt iS tion, Qc could hardly cscccd TO m/t 1:,., as pointcc! out by h~EITlss AND Monos. thcrcforc significant only at or below the microgram lcvcl. The value of Q/J has no such natural limit, but it can be made negligibly small by appropriate preliminary purification of the mercury and the supporting electrolyte. When this is done, Qc can bc mcasurcd clirectly by the proccdurc illustrated by Fig. T (a). To minimize difficulties that might otherwise bc caused by traces of surface-active materials which affect the capacity of the double layer, it is preferable to determine QC immediately bcforc the addition of the sample, using the same mercury and supporting clcctrolyte that will be used in the later analysis. The values of QC thus obtained differ appreciably from one run to the nest, but the fact that an absolute error of & 0.2 m/Aequiv. could bc achieved in the dctcrmination of zinc indicates that each individual value of QC is probably meaningful to within a few o/O. Whereas Qc is essentially completely accumulated within a second or two after the ‘Iluz

Kefcremes

p. 4Ga

49

VOL.

20 (1959)

of the clcctrolysis *.Q.a and Q/J approaches a constant value in accordance with J,rNc;r~:\;15’s equation’, (3,.= incrcascs linearly wit11 time and thus rcprcsents an error which incrcascs virtually indcfinitcly as the electrolysis is prolonged. This error can, it is true, be climinatccl by making periodic measurements of QM,,~, the total quantity

start

03 0

200 Time,

600

400 seconds

of Q’tolnl witll clcctrolvsix tirnc tlurinK ty])icill clcctrcApcs CJ~ (;L) 65 Fib’. I. Variation citr;Itc with 2.5 ml of clcctrolytically clcctrC~1ytici~1l~ purifictl 2 I; iLlllnlollii~- I P :~tiitnonillni &xl kIK. nntl (II) SiLTllC -t_ 0.007Noz pcquiv, (0.2jjs y) of zinc. ‘I’IIC C.liltZr wcw sccurccl :lt -0.50 S.C.lS. ilniilctliatcly after aI1 clcctrolysiu irt --I .,)o \’ 0s. S.C:.l<.

of clcctricity accum!llatccl, at times so long that reaction is complctc, ancl cStrapolntiIlg Q tnl,,l to zero clurc WiLS givan by hlEl*rllS AND MC)I
by

this

unless

tlic

cstrapolation

continuous

bccomcs

fardnic

cuncnt

intolerably is wry

\’

VS.

tllc clcsirctl working clcctrodc An c.SiUnplC of tllis procc-

tinw.

llowcvcr,

Inrgc small

IllI of puri-

or

on tlic

the the

uncertainty

intro-

submicrogram

scale

cstrapolation

very

short.

is obvious that tlic best sensitivity and accuracy will bc sccurcd when the final current intcgriLtiot1 is lxxformccl during an clcctrolysis wliich proceeds very rapidly and which involves only a very small continuous faruclaic currcn t . ‘flw first of these dcsiclcrnta is rather difficult to acIIicvc when tllc SuhSti~nCl! being This is bCCiluX! tllc rate of tllc clcctrotlctcrminccl is initially in tlw solution plwsc. lysis then depends, accorcling to LINCIANIS’S cquation~, on tlic cliffusion coefficient of thcionor n~olcculc being rcducccl, on the ratio of clcctroclc ;LTC;Lto solution volume, and on the thickness of the Ncrnst diffusion layer. l3y using a large cfficicntly stirred working clcctroclc and the minimum possible volume of solution, it is gcncrally possible to acllicvc gqq’)o completion in about 15 min. But a further substantial incrcasc From

thcsc

consiclcrations

it

* This is not trw when the initial current is linlitctl I)y the insertion of a scrics resistor into the clectrol~siu circuit, as wts somctiuws tlow in this work, LXC;~USC tlw working clcctrotlc ptcntial then drifts with tirnc up to tlic control ptcntkil, so that tlrc accumi~lation of QC bccianws cornplctc only whcii tlic clcctrolvsis current Ixgins to fall Ixlow tlic ikrtificinlly imposctl limit. This, liowcvcr, has no cffcct on tlic Ilnnl value of QC. l
p. 4G2

VOL.

20

COULOMETRS

(Ir)pJ)

AT

COSTROLLED

POTESTIAL

459

in this rate can be cffectcd only by increasing the diffusion coefficient of the species being determined. This could he done by raising the tcmperaturc, but this approach is neither practical nor useful. Taking the ordinary tcmperaturc coefficient of the diffusion cocffifrom 25O to 95” during an cknt as -j-z;.{, per degree, increasing the tempcraturc electrolysis would barely quaclruplc the clcctrolysis rate. To be sure, this might be a profitable approach for the routine analytical laboratory which is desirous of obtaining the greatest possible use from its instrument. On the other hand, it is usclcss in submicrogram analysis, because i/.l:increases with increasing temperature, and in the cstrapolation to zero time this introduces an increased unccrtaint_v which more than counterbalances tllc acl\*antagc derived from increasing the rate of the clcctrolysis. I n the prcscnt work, aclvnntagc was taken of the fact that the diffusion coefficient of a metal dissolved in mercury is often considerably larger than that of a metal ion diffusion in aqueous solutionn. Thus, from I~rsc,~sr~‘s data on the polarographic current constant of zinc( 1 I) in ammoniacal ammonium chloridc0, the diffusion coefficient of this ion at 25O is cnlculatcd from the ilkovic equation to be ~,cyro-O cm~/scc. ‘1’1~ diffusion cocfficicnt of zinc in mercury has been measured by I~ISYISI~~~,VOX WOGAU”, \vIsIsClIlilnx.‘“, ancl I~l;R;\li\X ASD CooP121<‘~; from the concordant results of WICISCIIEDISI, and I;u~tz~ns ASD COOPI:.R, one estimates that in very dilute amalgams the diffusion coefficient of zinc is approsimatcly 1.7.ro-fi cm’/scc. ‘lkrcforc tllc anotlic stripping of zinc sl~oulcl proceed almost twice as rapidly as the cathodic deposition of zinc ion if the volumes of solution and mercury arc iclcntical and if the Ncrnst diffusion layer thickncsscs arc the same for tllc anoclic ant1 cathodic processes. In fact, howcvcr, it is easy to carry out an clcctrolysis with only one-half toonc-fourth as much mercury as solution, and in addition it appears that the Ncrnst diffusion layer tllickness for the anodic process is appreciably smaller than for the cathodic

0

100

200 t, seconds

300

400

I;iK. 2. Cllrrcnt-time curves c~htainctl for (a) the rctluction c,f Ho pcqlliv. of zinc from 50 ml of z 1: ilIntlloni:r- I I: ammonium citrntc at ---.I ,.+s V vs. S.C:.LS., illId for (I)) the subscqucnt rcoxidation of the Same quantity of zinc from ttlc .2g-ml iIlIl;~l~;~~Ilctcctrotlc iLt -0.70 V Vs. S.C.E.

process. ‘I’hc actual rates of thcsc two proccsscs in a typical cxperimcnt arc indicated by Fig. 2, which shows that the stripping is 9c,.9’yo complete within about 3 min. The estreme rapidity of the stripping process permits the correction for if,= to be made by means of a very short extrapolation, and in addition it is a simple matter l~cfcrc~rces

p.

462

L.

460

MEITES

VOL.

20 (1959)

to carry out the stripping at a potential where if, c is very small. As was pointed out above, these conditions arc essential to the success of controlled-potential coulometric analyses on the submicrogram level. An ammoniacal ammonium citrate supporting electrolyte was selected for this work on the basis of polarographic data secured by KAIZP AND MEITES~~~~~, which indicated that such a medium should bc well suited to the determination of zinc in the presence of other elements commonly encountered in non-ferrous alloys. A “2 1; ammonia-r I; ammonium citrate” solution (3 molts of ammonia and one mole of diammonium hydrogen citrate per liter) was used to minimize the ccl1 resistance and to enable substantial concentrations of metal ions to be handled. Fig. 3 shows typical

-60 -

.

-0.3 Fig.

-0.7

Ewe.’

-1.1 v vs.

-1.5

-1.9

S.C.E.

curves for (a) o.G m&I zinc (I I) in 2 F ammonia- I IT ammonium and (1)) the amalgam clcctrodc prcpnrctl by the quantitative rctlrlction of 50 ml of tllc solution of curve ~bwith 15 ml of mercury at -1.45 V vs. S.C.15.

3. Current-potential

citrate,

current-potential curves of zinc(I1) and zinc amalgam in this medium. From these curves it is apparent that zinc(I1) can be quantitatively rcduccd at any potential V zrs. S.C.E., and that zinc can bc quantitatively more negative than about -1.35 stripped out of the amalgam at any potential more positive than about -1.20 V ZJS. S.C.E. To avoid any formation of ammonium amalgam, which would lead to a high and erratic consumption of electricity in the stripping step, it is preferable to carry out the deposition at -1.40 or -1.45 V ‘us. S.C.E. In dealing with substantial amounts (0.1 mg or more) of zinc, good results can be secured by carrying out the stripping at -1.00 V even if the continuous faradaic current is ncglccted. However, the correction for i~,~ at such negative potentials becomes undesirably large when smaller quantities of zinc arc involved, and hence for maximum sensitivity it is preferable to carry out the rcoxidation at about -0.50 V. Attention may be called to the fact that the amalgam clcctrodc at the completion of the deposition step is at a potential where if, c is by no means negligible. If the amalgam is then allowed to stand with the electrolysis current off, the zinc will rcentcr the solution at a rate which is proportional to this value of i,,c. Especially when dealing with small amounts of zinc, therefore, it is essential to begin the stripping as rapidly as possible after the reduction is completed. Refevmccs

p. 462

VOL.

20 (1959)

COULOMETRY

AT CONTROLLED TARLE

COULOMETRIC

1986.8

(65

POTENTIAL

461

I

DETERMINATION

OF

ZXNC

1988.6

mid 4 4

99X.2

398.1

+ 0.09

99X.6 397.7

+ -

0.04 0. IO

f f f

0.03% o.ozoy?,

-+

0.0x

-

0.02

o.o7Ok,

-

0.09

f f f

0 ooq/,

-I_

0.01

oJw”/o 0.05%

+

0.05

0.7857

7.858 2.3700 0.7852

-

0.06

0.2352

0.2356

-I- “0.;7

0.07724 0.0=359

f f f

0.149.b

0.07791 0.02346

0*34%, 0.5 O/o

5014

0.00767 0.0021g

f f

x59.8?

Isg.85 59.28

59.27 19.734

19.75a

7.857 2.3689

0.007802 0.002298

to.07

Ptid

i

2.8 ‘0.3

% O/o

-

1.7

-5

Table I shows the results obtained when the method just dcscribcd was applied to solutions containing known amounts of zinc. With quantities of zinc exceeding about IO peg, an accuracy and precision of -& o. r o/0arc easily attainable. Even r clg of zinc can bc dctermincd with an accuracy and precision of & 1% or better; this is comparable with what has been achieved by coulomctric titrations under equally favorable conditions. As little as 0.07 ,ug of zinc can be determined with an accuracy and precision of about -& IO%, which corresponds to an uncertainty of about 0.2 rnp FY. This last value represents about 2% of the value of Qc under thcsc conditions. It is therefore apparent that the ultimate sensitivity of controlled-potential coulometric analysis is governed primarily by the accuracy with which the necessary correction for QC can be determined. A significant improvement in the relative error involved in this determination appears somewhat improbable, and hence it seems safe to say that the further extension of controlled-potential analysis into the millimicrogram range will be possible only if QC can be reduced well below its value under these conditions. In principle this can be achieved in three ways. One is by considerably decreasing the area of the working clectrodc, which will cause a proportional decrease in the value ‘of Qc; this must be accompanied by a roughly proportional change of solution volume if clcctrolyses* arc not to be unduly prolonged. This involves some difficulties, though by no means insuperable ones, in ccl1 design. Another is to decrease the extent to which the working clectrodc potential is altcrcd during the electrolysis: hcrc this was 0.9 V, and this corresponds much more nearly to a maximum than to a minimum change. This, howcvcr, is not a truly general solution, for the potential change during any particular proccclurc is governed partly by the + Including,

for cxamplc,

Refereuces p. 46a

the deposition

step in the present procedure.

I.. SXlc1TI:S

462 clcctrochemistry minimizing

of

cxpcrimcnter’s

substance the

control.

capillary-active

A

clccreasc

‘I’l’c ccmsiclcr~rtio’is

final

of the

wl’icli

detcrminecl

electrolysis, possibility

wl~osc

tlctcr’ninc

thcsc

would at

layer

and

and

adsorption

double

lCVCl MC: diSCllSSd

Sll~Jli~iCr~J~r;~li~

being

final

substance

a considcrablc

the

the

il.= during

VOL. 20 (x()59) partly arc

involve

the

by

the

matters

aclcling

clectroclc

necessity

outside

to

the

surface

of

of

the

solution

would

a

lead

to

capacity.

tlic si’cccss of

, and it is sliown

controllctl-l,‘Jtcnti;rl

tllat

the “ltin’atc

coi’lumctric

analysts

sensitivity

on

of the mcll’otl

is ~ovcrnctl by tl~c ;l.ctlrr;lcy with which the rccl”isitc Imckgro”ntl corrections, cspccially that for Llic Cl’irrKi’lg qii;mtity of clcctricity, ciii’ 1x2 tlutcrrninc:cl. r\ mctlirxl for tl’c cc~“lo’nctric tlctcrn’ini~tic,” of zinc Imsctl 011 tl,cnc coiisitlcr;~tioiin issllcJwn tcJ C0lltilill ;~li’niti’iC: ‘lnccrti’int~ of f 0.2 ‘n/41;,, iw 0.07 pK of zinc CiLll 1x2 tlctcrriiinccl witliiti alJo1’t -1. lo’,‘;,, wl’ilc qiiontitics of SO tllirt ilS littl?: ir’lll pxXiSi~Jn ‘Jf f 0. I’,!<, Or zinc cxccctling abo1lL lo/lg call Ilc tlctcrn~iiictl wiLlI ill1 ilCCllrilC> IJcttcr.

into

I’cJssilJlc

tl’c

0’1

CXi~lllillC:

Its

Lriclucs !r l~utcril_icl ildtcrriiinc!r jiisclii’li dc

zinc

for t.hc furtl’cr arc briefly

tccl’nic~“cS

“iiIIi”iicro~r~r’ii

Clb~~ilSSiL’lt

ritllgc

pg

d’iin

tloSilj+!

1% wcrclcn die I:;rktorctl “ntcrsiwht, wclcl’c tlic trullicrlcnl I’otc~~t.i;~l bci S”1~‘~~ikr~J~r:~t’~“~-~~~~n~:C’~

13r~cl”‘issc

van %ink, untcr I3criicksicl’tigt’nK tlicscr Faktorcn, Gc’muigkcit untl Mengcn von ‘nchr nls IO pg ‘nit f

’ S. S. LORD, 1X. C. O’NKILI. 2

G.

I..

Ij00MAN.

\v.

,\N’>

IS. Ilol.lllcoo’c

I,.

Kor~TOa’

AnlStcrtli~lll,

7 J. J.

AND

J, 0’31.

1953, 1). 36 I

IJNGANII,

I30c1;1c1s,

I\Idyscn

(‘q=j’)) CJ/

Ckttt.,

/IJlftl.

f~ICCl~o~~tctl)~liccll

C/trttti.sfry,

1.1 ( I!,SZ) roe). ‘2zg (1957) r1cJ.

23.

i~lccfrac:/tc~tttisfry,

15lswicr

lntcrscicncc

I’~rl~lislwrs,

Inc.,

AND t\‘. C’. ~oo~w~, ./. .dttt. Chttt. .%_!., 74 (I()~L) 0183. ” J. J. hNGANI<, I,td. f
30

(lc)SQ)

ko’l-

C/tC?Jl.,

I’iil~lisl’iriy

.

pp. lC)Z-195. ” N. I-1. f~ulcn1A.u

Cltitt1. rfcfa,

Init

coi’lo’nctriscl’c 13cstini”iung his 211 0.07 ccg ‘nit ca f IO’!{, o. I’X, ~\hvcicl”‘ny ZII crfnsscn.

J. IS. REIN,

‘I’e.r/Ooo/r

ClJllkNTlCtriSC~ler

Ijic IJccinflusscn. crla’ibt Xlcripci~

13. ROGI~M. Aittrl. ANIJ

3 I,. Misrr’ss, /I Jld. Chittr. .4c/u. IH (lC)_=p) 36). CiiCJtl., “7 (‘().pg I 116. 4 I.. i\l’3*r’ss , .d tttlt. fi I,. hlluTILS AS’J s. A. hlOI
irnirlysis

11

d’il~~p~iC;iti’Jll,

I,‘css;ri

ccJlltr~Jl&.

0.07

co’ilo’nctric

I’&~IIcIIc IiItri~tilicrcJcllitiiiclu(:, ClCS RliirlYSCS COll~lJ”l~c011lo1m?tric~i1c clc ziiic fll’Jiit.rC cl”‘il cst PlJSSilJlC tic cl’crrcrir. tanclis flue clcs (l’ii~lltitlh /CR tic ccl. hhcnt iL\‘CC CIlVir(Jli AZ ‘o’~;, ~Jc’lvcllt Ctro ‘IodcS iLVc’C I’m pdcision tic h 0. I’jiJ (011 nicmc n’cillcurc).

ClJllditiO’iS

lo

cxtcnsion of ccJntrc,llctl-l)c’tcntiill tliscr’ssccl.

New

York,

L.

i\lIClTJCS,

Co.,

1953,

rlttd.

397.

kccivccl

Scptcmbcr

Gth,

1958