Analytical chemical studies on electrode processes by column coulometry

Electroanalytical Chemistry and Interfacial Electrochemistry, 45 (1973) 31~14

3t

© Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

ANALYTICAL C H E M I C A L STUDIES ON E L E C T R O D E PROCESSES BY COLUMN COULOMETRY I. BASIC STUDIES ON THE C O L U M N E L E C T R O D E

SORIN KIHARA

Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken (Japan) (Received 6th December 1972; in revised form 2nd January 1973)

INTRODUCTION

Several rapid and quantitative electrolytic methods using column electrode have been reported. The idea of these interesting developments consists in flowing a solution through a column filled with a packing of conductive material, to which electric potential is applied. Silver grains 1-3, amalgamated nickel particles 4, amalgamated platinum 5, porous platinum-grid 6' 7, graphite powder 8' 9, glassy carbon grains 1°-13 and carbon fiber 1~' 15 have been employed as column packings which act as working electrodes. Blaedel and Strohl 5 studied the distribution of metallic ions between the electrode and the flowing solution. Fujinaga in his reviews 16' ~7 discussed the rapidity of the column electrolysis and the attenuation constant of an electrolytic current. Physicochemical characteristics of the electrolysis in a flowing solution have been obtained by several investigators, utilizing mainly the work of Levich 18. Blaedel and Klatt studied reversible ~9 and quasi-reversible and irreversible 2° charge transfer at a tubular electrode. Sioda examined the relation between the limiting current and the flow-rate of carrier solution 7' 9. Column electrodes offer many practical uses, e.9., chromatographic separation of metal ions using gradient potentiaP °'ix and uniform potential column electrodes 5,15, coulometric determination 3' 23, 24 and preparation of desirable solutions 13, 21 In a previous paper ~3, the two-step flow-coulometric column electrode was proposed. The first cell, which is the preparatory column, acts as a pretreatment apparatus to remove interfering elements and as a smoothing apparatus to make the oxidation state of the sample uniform. The second cell acts as a detector column. This two-step flow-coulometric system is especially effective when the reaction products are unstable or oxidizable in air. In the present work, basic characteristics of the column electrode are investigated and charge transfer processes at the carbon electrode are studied by using the two-step column electrode. Electrode reaction mechanisms of copper in a chloride solution are studied and the results agree well w i t h the polarographic data obtained by using ring-disk electrodes.

32

s. KIHARA

EXPERIMENTAL

Apparatus and reagents Column electrode. The two-step column electrode is shown in Fig. 1 and is essentially the same as that described previously 13-15. A working electrode packed in a porcelain cylinder is composed of carbon fibers of 10 to 12 /~m in diameter. The width of a slit among carbon fibers is confirmed by microscopic observation to be 25 to 30 #m. As a counter electrode, the same carbon fiber was wound around the outside of the porcelain cylinder. The carbon fiber (Nippon Kayaku Co. Ltd.) was produced from lignin and polyvinyl alcohol and heat-treated at 1500 to 2000°C. The saturated KC1-AgC1/Ag electrode (SSE) is used as the reference electrode. 2

3

3

2

lOmm

1 '

1

~5-2_~v'//t//-'/,1///_~-ySJ A ~"

,--

6

c

-

ill

f

,

E-I~ E-]I~

Fig. 1. Two-step column electrode. (1) Working electrode; (2) auxiliary electrode; (3) reference electrode (SSE); (4) porcelain cylinder; (5) satd. KC1 soln.; (6) sample inlet.

It is difficult to consider the potential distribution in the column electrode strictly. An approximate estimation of this problem, however, has been made by using 11°mAg or 64Cu as a tracer (10 -6 mole of silver or copper is used as a sample); relations between the amount and the position of electrodeposited silver or copper in the column and the volume of carrier solution passed through the column are studied at various electrode potentials. Because the distribution data of metal ions between electrode and carrier solution presented in the tracer study and data shown in the previous paper 15, show a good agreement with the theoretical treatment 5, the neglect of potential distribution in the column electrode is considered to be permissible. However, when a large amount of ionic species is used as a sample theoretical or instrumental corrections for potential distribution may be necessary. Apparatus for potential control, current recording and sample injection and the procedure for pretreatment of working electrode are the same as those already described12,14. The supporting electrolyte solution was flowed by a Furue Science Co. Ltd. Model Roller Pump and the flow-rate was controlled to within _+5~. The current integration was made with a Kimura Denshi Co. Ltd. Model E-2Bo electronic integrator. A Yanagimoto Co. Ltd. Model P8 polarograph was used. All experiments were carried out at 25_+0.5°C.

33

COLUMN COULOMETRY. I

Reagents. Reagent grade potassium ferricyanide (K3Fe(CN)6), ferric ammonium sulphate (Fe2(SO,)a(NH4)2SO4' 24 H20) and cupric chloride (CuCt2" 2 H 2 0 ) were used as standard materials. All other reagents used were of reagent grade. Procedure

The schematic arrangement of apparatus is shown in Fig. 2.

1 ~

Cyrmder

<"Nz gos Pump

I ~

~

~iution Reservoir

25°C Fig. 2. Schematic arrangement of apparatus.

The deaerated carrier solution containing supporting electrolyte flows continuously through the preparatory column (E-I) and the detector column electrode (E-II). A definite amount of sample solution, usually 10 #1, is injected into the stream. The desirable ion is prepared at E-I of which working electrode potential is E 1 and flows into E-II. The time required to transfer from E-I to E-II is 0.01 to 1 s depending on the flow-rate of the carrier solution. At E-II of potential E2, the prepared ion is detected and the electrolytic current is recorded. From the relation between E1 and the quantity of electricity (Q2) flowed at E I I or between E z and Q2, redox processes of the ion are studied. RESULTS A N D D I S C U S S I O N

The reversibility of the charge (Q)-potenfial (E) curve is investigated as functions of standard rate constant of an electrode reaction (ks), transfer coefficient (ct), flow-rate of supporting electrolyte solution ( f ) and the length of a column (l). It is well-known that the rate of an electrode process is controlled by the velocity of mass transfer, Vmt, and the velocity of charge transfer, V,. Assuming that the diffusion is the only component of mass transports, then we express Vmt as eqn. (1) using the diffusion coefficient (D; cm 2 s -x) and the thickness of the diffusion layer (6; cm). gmt =

O/(~

(1)

In the case of the column electrode used in the present work, the radius of

34

s. KIHARA

solution path (d) among carbon fibers used as the working electrode is very narrow and nearly the same as 6. Then, instead of eqn. (1), eqn. (2) can be used as a simple and practical criterion to characterize electrode processes V~t = Old

(2)

Using D = 10 -5 cm 2 s -1 and d = 1.5 x 10 -3 cm, one has V~t =6.7 x 10 -3 cm s -1 as an upper limit. Under such experimental conditions one expects that electrochemical systems having charge transfer rate constants smaller than about 10 -3 cm s -* will show Q-E curves of definite by irreversible character. Conversely, the Q-E curves for systems with charge transfer rate constants greater than about 10 -2 cm s -1 will be controlled predominantly by mass transport (ordinarily called diffusion controlled or reversible) and the electrochemical equilibrium at the electrode surface will be established immediately. The Q-E curve for a reversible reaction involving single soluble product and reactant species; 0 + n e ~ R (3) A quantity of electricity-poten'tial curve (Q-E curve ) obtained for the reaction (3) by the column electrode electrolysis is investigated on the basis of the work of Levich 18 and Blaedel and Klatt 19. Assuming a solution path as a tube of circular cross section, with radius d, the velocity profile of a solution stream is of the form of parabola in a tube with laminar flow as mentioned by Levich. If the tube is very thin, the velocity profile can be approximated by Vx = 2V~y/d

(4)

Considering the reversible reduction (3) of an oxidized species O to a reduced species R at a tubular electrode, the following' eqns. are given for mass transport of chemical species, O and R 2y Va ~3Co ~2eo d Ox =D° Oy2

(5)

2y Va Ocr ~2cr d Ox =Dr t~y 2

(6)

with boundary conditions : y---~ o 0 :

Co~ c * Cr

(7)

C r*

(8)

y---~0 :

Do(OCo/O.y) q- Or(~Cr/Oy) =

y~O:

0 = Co/Cr = exp [ ( n F / R T ) ( E - E ° ) ]

0

(9)

(10)

x and y are the distance parallel to the stream and the distance from the electrode surface; Va is the axial linear velocity; co and cr are the molar concentrations of substances O and R at the electrode surface; c* and c* are the bulk molar concentrations; DO and D r a r e the diffusion coefficients; n is the number of

35

COLUMN COULOMETRY. I

electrons; E ° is the formal electrode potential; and R, T and F have their usual thermodynamic significance. The electrolytic current i due to the cathodic reaction (3) is expressed as eqn. (11) by the flux of the substance O obtained from the solution of eqns. (5) to (10) i = nf (2rid)

f x DO(0¢o o

\~Y/~=o

dx

= K n t D o f ~ (Co-C;"~

(11)

\1+go/

where k is (Do/Dr)~; X is the effective length of tube for the substance O; f is the volume flow-rate of solution; and K is a constant. When C° mole of substance O is injected to the column electrode as a sample and has a volume of u in column electrode, O is consumed by the electrode reaction depending on the diffusion controlled charge transfer rate during the time passing through the column electrode. Then, the current it, at time t after the beginning of the electrode reaction, can be written by eqn. (13) as an approximation using

2 = KD~f~/u it = nf2¢

0

(12)

e-~t--0(1-e-Z') 1 +kO

(13)

By integrating eqn. (13) with respect to t from 0 to t, the eqn. for the quantity of electricity at time t, Qt, can be obtained Qt = o

itdt=nFc ° (l+O)(1-e-Zt)--O2t 1 + kO

(14)

Quantities of electricity, Qdct and Qdat, at the cathodic and anodic diffusion controlled limiting current regions are obtained by substituting for the 0 to 0 and oe respectively, 0 = 0; Qdct= nFc°o(1-e-zt) 0 = 00" Qdat =

(nFc°o/k)(1 - e - Z t - 2 t )

(15) (16)

The relation between the quantity of electricity and the potential is obtained from eqn. (14) by substituting for the exponential form of eqn. (10) and rearranging by using eqns. (15) and (16)

E = E o _ RT

In

(~f

RT Qa¢t-Qt + ~ff- In Qt- Qdat

(17)

The first two terms on the right side of eqn. (17) correspond to the half-charge potential similar to the polarographic half-wave potential

E½ = E o - ( R T / n F ) I n (Do~Dr)~

(18)

As the total quantity of electricity, Q_o, for c° mol of substance O is

nFc° in eqn. (15), the following eqn. can be obtained for the electrolytic efficiency, e, of the column electrode with diffusion controlled electrode reaction

36

s. KIHARA = 1-e -a

(19)

The time (t) in which substance O passes through the c o l u m n electrode can be expressed by using the length of c o l u m n (1), the volume flow-rate ( f ) and the effective cross section of solution path (S) t = Sl/f

(20)

Finally, the relation between a and f with diffusion controlled electrode reaction is written by eqns. (21) and (22) in l a m i n a r flow regime log 1/(1 - e) = f - ~ ' u / K ' S I D o

(21)

log ( - log (1 - e)) = - 2 log f - log K SlO~/u

(22)

where K ' is a constant. As a typical system for the diffusion controlled electrode reaction, a ferricyanide/ferrocyanide system in 1.0 M p o t a s s i u m chloride is investigated and the results are shown in Fig. 3. 1.0. 1.o

ooooo ~ e

eii ~ • • A A A m ® ~

A Q

• A m

,~

~t 0

0.5-

/~ (11

0.5

/ -I

g ,6

° 0.0

' ~

E/V I

"6

~ ~

ID--O

0.5

0.4

0.2

I

I

0.3

0 e o

~

vs. SSE I

I

O.l

0.0

-zl I -I

g

0

0.5

0.5

,z, ( t/' /. N

1.o

~.o

~

~

~

5 ° A

t t t~'~

Fig. 3. Charge--potential curves of [Fe(CN)6] 3 -/[Fe(CN)6] 4- system in 1.0 M KC1 with various flow-rates. Sample: 10 -2 M K3Fe(CN)6 , 10/~1 (1.00 x 10 7 mol); potential control: (1) E 1= +0.5 V, E 2 variable, (2) E z =0.0 V, E2 variable; column 2 cm; ( - - - ) log analysis. Flow rates: (C)) 5.2, (O) 24.0, (•) 33.8, (rv]) 43.7, (--) 5.2 ml min -z. In this connection, the standard rate constant, ks, and the transfer coefficient, 0t, for this reaction at a c a r b o n electrode are o b t a i n e d as 7.4 x 10 -3 c m s - I and 0.5 respectively by using r o t a t i n g c a r b o n disk electrode ( R C D E ) z2. The c a r b o n used for R C D E was p r o d u c e d from the same materials a n d has the same crystallographic characteristics as the c a r b o n fiber used in c o l u m n electrode. The half-charge potential E~ does not change by changing flow-rate f, and the slope of the log analysis of the Q - E curve is a b o u t 60 m V as shown by

COLUMN COULOMETRY. I

37

broken line in Fig. 3. At the flow-rate of 5.2 ml min-1, the electrolytic efficiency is nearly equal to 100~o, but at the faster f, e decreases. The relation between e and f i s analysed by using eqns. (21) and (22) and the result is shown in Fig. 4. F r o m the slope of the double logarithmic analysis in this figure, the value - 0.62 to - 0.79 is obtained as an index number, 7, o f f in eqn. (21). These values are close to the value of - ~ for the diffusion controlled electrode reaction in laminar flow regime as shown by Levich is for convective diffusion. Figure 4 indicates that f must be less than about 13 ml rain -1 to make e more than 99~ (log { 1 / ( I - e ) } >2). 10g f 1.0

1.5

2,0

~" tr = - 0 . 7 9

2D

= -0.62

:).5

3.0 . . . . . .

I,o -O.5

"r

IO

20

30

40

0

f (mL Imin)

Fig. 4. Relation between electrolytic efficiency(e) and flow-rate (f). Sample: 10-2 M K3Fe(CN)6, 10 #1 (1.00x 10 - 7 mol); supporting electrolyte: 1.0 M KC1;column 2 cm. The Q-E curve for a totally irreversible reaction involving single soluble product and reactant species; 0 + n e ~ R (23) The irreversible reduction (23) occurring at a columh electrode is investigated under the conditions that the backward reaction is negligibly small. For the irreversible reaction (23), the electrolytic current, i, can be expressed as a function of the concentration of the oxidized substance O, Co, the heterogeneous rate constant at the given potential, k~, and the effective surface area of electrode, A

(24)

i=nFkcAc o

When c° mol of the substance O is injected to the column electrode as a sample and the sample has a volume u in column electrode, the substance O is consumed by the electrode reaction depending on the heterogeneous rate constant kc during the time passing through the column electrode. Then, the current it, at time t after the beginning of tile electrode reaction, can be written by eqn. (25) it =

nFkcc* = (nFkca/u) c° e x p ( - k c A t / u )

(25)

Integrating this eqn. with respect to t from 0 to t, eqn. (26) is obtained for the quantity of electricity, Qt, at time t:

Qt=

f' itdt = nFc2 {1-exp (-kcAt/u)} 0

= eo { 1 - e x p ( - k c A t / u ) }

(26)

38

s. KIHARA

where Qo(= nFc°o)is the total quantity of electricity for c° mol of substance O. Here, kc, the rate constant for a cathodic reaction, is given by kc =ks exp { -

(anF/RT) ( E - E o )

}

(27)

where ks is the standard rate constant at the formal potential Eo and a is the transfer coefficient. Substituting eqns. (20) and (27) for eqn. (26), eqn. (28) is obtained as a relation between the electrode potential E, the quantity of electricity Qt, the column length l and the flow-rate f for the cathodic reaction E=Eo

~

n

+ln

\

Qo-Q,/J

(28)

Similarly, the rate constant for an anodic reaction, ka, is given by ka = ks exp {[(1 - ~)nF/gT]

(E- Eo) }

(29)

Then, the irreversible anodic reaction is expressed by eqn. (30) E=E0+

(1-~)nF

n

+ In In

(30)

The potential at Qt=½ Qo is defined as half-charge potential, E~, of the irreversible Q-E curve. Substituting ½ Qo for Qt in eqns. (28) and (30), the double logarithmic terms of these eqns. become a numerical constant, c, and the half-charge potentials for the cathodic and anodic Q - E curves are given as follows E~ (cathodic) = E o - ~

In ~

E~ (anodic)= Eo + (1 -a)n~

+ c

n

+

(32)

It is evident that the transfer coefficient, c~, is obtainable from eqn. (31) or (32) by varying the volume flow-rate, f, or the length of column, I. If a standard substance of which ks and a are known is used, ks of the other substance may be obtained relatively by using eqns. (31) and (32). As a typical system for the charge transfer rate controlled electrode reaction, ferric/ferrous system in 1.0 M sulphuric acid is investigated and the results are shown in Fig. 5. The values of ks and c~ of this system obtained by RCDE are 4.8 x 10-5 cm s- 1 and 0.43 respectively. As shown in Fig. 5, Q-E curves shift depending on f and a. The relation among E~, f and l are shown in Fig. 6. Lines a and b show the cathodic and anodic processes, respectively, but the sign of the ordinate is taken inversely in line a. As the slopes of lines a and b are 142 mV and 101 mV respectively, transfer coefficients are given as 0.42 and 0.58 for the cathodic and anodic processes by using a 2-cm column. These values are nearly equal to those obtained by RCDE. In Fig. 7, the relation between the electrode potential and the double logarithm of Qo/(Qo - Qt) is plotted according to eqns. (28) and (30) at a constant v o l u m e flow-rate. In the region, the ratio of Q.o/Qo-Qt) is large, the double logarithm plots show straight lines and the slopes give transfer coefficients similar to the values obtained by flow-rate analysis.

39

COLUMN COULOMETRY. I

1.0 x

•

~ m • A m e

A&

&

x e

x

,•0.5

0.5

x •

x • Xo x

xo ,

-- '~

0.7

06 ."

•

•

,,

o z

o"

•

"0.5

0.5

•

• •

e ~ o ~

&D ~

e

I m°

•

e •

•

t~e

•

A m e

•

tJ °

• ^ | I ~ ~

~,

m

•

-

A

x

0.4

o~

0.3

~2

-

E/V

0.1

vs. SSE

• ×

• x "

(2)

:i °::"

1.0-

5. Charge-potential curves of Fe(III)/Fe(lI) system in 1.0 M H2SO4 with various flow-rates. Sample: 5.00 x 10 -3 M Fe2(SO4)3(NH4)2SO 4, 10 #1 (5.00 x 10 -s mol); potential control: (1) E1 = + 1.0 V, E 2 variable, (2) E I ~ - 0 . 2 V, E 2 variable; column 2 cm. Flow rates: ( x ) 1.01, ( 0 ) 1.93, (~x) 4.08, (I-q) 4.93, ((3) 8.06, ( A ) 16.4 ml min -1. Fig.

0.0

2.0

b

A

Q "O

1.0

d

A

v

0.5

1o -1.0

I.C

0.0

e ~a & e e o e e ~ ~ ~ e

-0.5

, L

0.7

i

0.6

l

0.5

l

0.4

l

O~

l

0.2

0.0

,°°

e e

To°°I °

, -2.0

o.r

o.e

o.5

o.4

0.3

o.z

Potential / V vs, SSE EQ,/2 / V vs. SSE Fig. 6. Effects of flow-rate and column length on electrode potential at Qt=½Qo (E½). Sample: 5.00× 10 3 M Fez(SO4)3(NH4)2SO4, 10 #1 (5.00 × 10 -s mol); supporting electrolyte: 1.0 M HzSO4; potential control: (a) E l = +1.0 V, E z variable, (b) E 1 = - 0 . 2 V. E2 variable; column: ( Q ) 2 cm, ( 0 ) 4 cm.

Fig. 7. Analysis of charge-potential curve. Sample: 5.00×10 -3 M Fe2(SO4)3(NH4)2SO 4, 10 #1 (5.00 x 10 -8 mol); supporting electrolyte: 1.0 M H2SO4; potential control: (a,a') E l = +1.0 V, E 2 variable, (b,b') E x = - 0 . 2 V, E 2 variable; column 2 cm; flow-rate 4.08 ml/min.

40

s. KIHARA

The Q-E curve for a quasi-reversible reaction involving single soluble product and reactant species As a quasi-reversible system, ferricyanide/ferrocyanide system in 0.1 M potassium chloride is investigated. Q - E curves for this system with various volume flow-rates are shown in Fig. 8. The values of ks and ~ of this system are give n as 1.3 x 10 -3 cm s -1 and 0.5 by using the RCDE. Shapes of Q-E curves change slightly depending on fi but the theoretical treatment is now under investigation. 1.0-

-1.0

o •

® ® xx x

® x

x o "-)

0.5- ~0~

~ x

ex

[I}

® x

%

x x

.~ o.o OL.5

E/V

"6

0.2

I e9 0.4

I

O

0.5-

.

,L

0.1

0,0

i

L

v.s. SSE x • ®

Z

g

I

0.3

(2)

-0.5

x ® • ),c

x x

e

•

®

x

1.0"

1.0

x

x

xll

Fig. 8. Charge-potential curvesof [Fe(CN)6]3-/[Fe(CN)6] 4- systemin 0.1 M KC1with various flow-rates. Sample: 10-2 M K3Fe(CN)6, 10 #I (1.00 x 10-v mol); (1) E 1= +0.6 V, E 2 variable, (2) E1 =-0.2 V, E2 variable; column 2 cm. Flow rates: (0) 1.42, (G) 3.46, (x) 7.10 ml min -1.

A study of electrode processes of an electrode intermediate at the carbon electrode by two-step column electrode; Cu(II)/Cu(I)/Cu(O) system in chloride media To investigate eIectrode processes of electrode intermediates, several methods have been proposed, such as polarography using the ring-disk electrodes 23 and polarography with the attenuated total reflection method 2¢. In the present work, the column electrode is used. The polarographic curves of C u ( I I ) / C u ( I ) / C u ( O ) system in 0.1 M hydrochloric a c i d ~ . 9 M potassium chloride solution obtained by the method of N a p p et al. 23 using a rotating carbon ring-disk electrode ( R C R D E ) are shown in Fig. 9. The Q-E curves of the same system obtained by using the two-step column electrode are shown in Fig. 10. Curve 1 shows the reduction of cupric ion. The quantity of electricity Q1 is measured at a definite potential E~ with a definite a m o u n t (10 -7 mol; 10 -2 M, 10 #l) of cupric ion using E-I. The measurements of Q1 are made at various potentials E1 and the charge/potential ( Q 1 - E 1 ) curve similar to the polarographic current/potential curve is obtained. Curve 2 in Fig. 10 is the Q2-E2

COLUMN COULOMETRY. I

41 40

IO0

2o

5C

i1)

g

g

g

~

0 ¢v,

50

2o

Fig. 9. Current-potential curves of 10 3 M Cu(II) a{ RCRDE in 0.1 M HCI~).9 M KC1; electrode: disk radius 3.08 mm, ring inside radius 3.38 mm, ring outside radius 3.67 mm; 800 rev/min. ( 1 ) idisk--Edisk; ( 2 ) iring-Erlng, Edisk = - - 0 . 1 5 V ; ( 3 ) iring--Edisk, Ering = + 0 . 6 0

2.0

esOOo 1'

• •

1.0

o

oOo o o ooooo~o'~o°

o

el ~

% °A~&&&"

1.0

a 0.0

0.0

E / V vs. SSE X

13 o

X

1.0'

.=--

.o

&

2 ~'

!

o

21 •

o 0.0

- Z.O

o

1

o

o

V.

3

1.0

Fig. 10. Charge~otential curves of copper in 0.1 M HC14).9 M KCI. Sample: 10 -2 M CuCI2, 10 #l (1.00 x 10-~ mol); flow-rate 5.0 ml/min; column 2 cm; potential control: (L G), (1',O) E1 = +0.5-V, E 2 variable, (2,A), (2',&) El=0.0 V, E 2 variable, (3,73) E 1 variable, E2= +0.5 V, (4, x) E l = - 0 . 5 V~ variable, E2 = +0.5 V; (O,A) measured after copper-plated. curve of the p r o d u c t p r e p a r e d at E - I of w h i c h e l e c t r o d e p o t e n t i a l ( E l ) is k e p t at 0.0 V vs. SSE. C u r v e 3 is the Q2 - E l curve, which is o b t a i n e d b y the m e a s u r e m e n t of Q2 a t E z = + 0 . 5 V vs. SSE a g a i n s t v a r i o u s p o t e n t i a l s E I of E - I . As s h o w n in curve 1 (Fig. 10), the r e d u c t i o n o f cupric ion p r o c e e d s b y two steps. B o t h steps c o r r e s p o n d to o n e - e l e c t r o n reductions, and, therefore, the first wave is the r e d u c t i o n to the c u p r o u s state a n d the s e c o n d wave to the metal. C u r v e 2 clearly d e m o n s t r a t e s that the cupric ion is r e d u c e d to the c u p r o u s state in E - I

42

s. KIHARA

with the potential ranging from + 0.15 to -0.25 V, the cuprous ion is then oxidized to the cupric state in E-II reversibly showing the one-electron oxidation current at more positive potential than + 0.175 V vs. SSE. As shown in curve 3 (Fig. 10), at more positive potential than + 0.35 V, the cupric ion is not reduced and, at more negative potential than -0.35 V, all cupric ions are reduced further to the metallic state at E-I, therefore in both regions no oxidation current due to cuprous ions flows at E-II. Curves 1' and 2' in Fig. 10 show the reduction of the cuprous ion at a column electrode of which the working electrode was copper-plated previously. It is obvious that, when the copper-plated electrode is used, the cuprous ion shows a reversible Q-E curve, but at carbon electrode, the curve is very steep and the half-charge potential shifts to negative. These differences may be explained by the difference in the crystallization energy, that is, the deposition of copper on the carbon electrode requires more energy than the deposition on the metallic copper electrode. Consequently, when copper is plated, even if slightly, the reduction of cuprous ion is accelerated and the Q-E curve becomes steep. The oxidation mechanism of copper metal is investigated by using Q2-E1 curve as shown in curve 4 (Fig. 10). After the copper metal is deposited at E-I of E l = - 0 . 5 V, E~ is changed to a more positive potential to oxidize copper metal and the eluted ion from E-I within one min is detected at E-II of E 2 = +0.5 V. Q2 is plotted against various E~ and Q2-E~ curve is obtained. As shown in curve 4, at the potential range of E 1 from - 0 . 3 to +0.2 V copper metal is oxidized to the cuprous ion and then the cuprous ion is oxidized to cupric ion at E-II of E2= +0.5 V. At the potential more positive than E1 = +0.35 V copper metal is Oxidized to the cupric ion, more oxidation current cannot be obtained at E-II of E2= +0.5 V. Here, as the elution rate of copper metal involves the distribution and geometrical complexity, we must take different rate-consideration for curve 4 from curves 1, 2 and 3 in Fig. 10 as reported in the previous paper ~5. For the electrode reaction of the cupric/cuprous system, the rate-consideration is made by varying the flow-rate of supporting electrolyte solution and the result has confirmed that the reaction belongs to the charge transfer at a carbon electrode (Fig. 11). These experimental results obtained by the proposed method show good agreements with the results obtained by the ring-disk polarography. The column electrolysis has the following disadvantages compared with the ring-disk system: because of a high background current due to a large electrode surface area, a sample of higher concentration, usually 13 higher than 10 -5 M, is required for the column electrolysis than the ring-disk system; because it is difficult to obtain the bulk concentration, effective surface area and linear flow velocity of carrier solution in the column electrode, these values used in the theoretical treatment are relative values; because substance contacts with the electrode surface for a relatively longer time in column electrolysis than in ring-disk system, more attention is required to the electrode reaction involving following chemical reactions in column electrolysis; because it is difficult to prepare fibers of other materials than carbon fiber at the present time, theoretical treatments of electrode reactions in column electrolysis are difficult in other cases than carbon fiber electrode. On the other hand, as the column electrolysis with carbon fiber has such merits as large hydrogen overvoltages, rapidity of overall electrode reaction, ease

COLUMN COULOMETRY. I

43

1.0

I~O

Q~

).5 ~ .

0.O

0.4

E/V

8

0,3 vs.

ql,i

I

o.,

o!o

~.o ~-

SSE ~5

E 0.5 0

2

1.0

o,,oelt~

eS .0

Fig. 11. Effect of flow-rate on charge-potential curve of Cu(II)/Cu(I) system in 0.1'M HCI~?.9 M KC1. Sample: 10 -2 M CuC12, I0 ttl (1.00 × 10 -7 mol); potential control: (1) E 1 = +0.5 V, E2 variable, (2) E1 =0.0 V, E 2 variable; column 2 cm. Flow rate: (O) 1.01, ( x ) 2.32, ( 0 ) 7.89 ml min 1.

of quantitative treatments of the results and small sample size, wide applications to kinetic studies are expected. ACKNOWLEDGEMENTS

The author wishes to thank Prof. T. Fujinaga, Dr. K. Motojima, and Dr. H. Onishi for helpful discussions. SUMMARY

The basic characteristics of the column electrode have been investigated to elucidate mechanisms of electrode reactions by using this method. Carbon fiber of about 10 #m in diameter was used for the working electrode. When the ~electrode rate constant is faster than 10 -2 cm -1 s the electrode process shows reversible characteristics and when the constant is slower than 10-3 cm s- 1 the process shows irreversible characteristics. The transfer coefficient of an electrode reaction can be obtained by changing the flow-rate of the supporting electrolyte solution. The rate constant of an electrode reaction can also be obtained relatively. By using the proposed method, electrode processes of copper have been investigated and results similar to those of the ring-disk electrode polarography were obtained. REFERENCES 1 2 3 4

T. Fujinaga, T. Nagai, S. Okazaki and C. Takagi, Nippon Kagaku Zasshi, 84 (1963) 941. T. Fujinaga, C. Takagi and S. Okazaki, Kogyo Kagaku Zasshi, 67 (1964) 1798. E. L. Eckfeldt and E. W. Shaffer, Jr., Anal. Chem., 36 (1964) 2008. D. K. Roe, Anal. Chem., 36 (1964) 2371.

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5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

W. J. Blaedel and J. H. Strohl, Anal. Chem., 37 (1965) 64. R. E. Sioda, J. Electrochim. Acta, 13 (1968) 375. R. E. Sioda, J. Electrochim. Acta, 15 (1970) 783. W. J. Blaedel and J. H. Strohl, Anal. Chem., 36 (1964) 1245. R. E. Sioda, Electrochim. Acta, 15 (1970) 1559. T. Fujinaga, K. Izutsu and S. Okazaki, Rev. Polarogr. (Kyoto), 14 (1967) 164. T. Fujinaga, K. Izutsu, M. Koyama, S. Okazaki and K. Tsuji, Nippon Kagaku Zasshi, 89 (1968) 673. S. Kihara, T. Yamamoto, K. Motojima and T. Fujinaga, Talanta, 19 (1972) 329. S. Kihara, T. Yamamoto, K. Motojima and T. Fujinaga, Talanta, 19 (1972) 657. S. Kihara, T. Yamamoto, K. Motojima and T. Fujinaga, Bunseki Kagaku, 21 (1972) 496. S. Kihara, K. Motojima and T. Fujinaga, Bunseki Kagaku, 21 (1972) 883. T. Fujinaga, Bunseki Kagaku, 17 (1968) 651. T. Fujinaga, Pure Appl. Chem., 25(1971) 709. V. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J., 1962. W. J. Blaedel and L. N. Klatt, Anal. Chem., 38 (1966) 879. L. N. Klatt and W. J. Blaedel, Anal. Chem., 39 (1967) 1065. R. E. Sioda, J. Phys. Chem., 72 (1968) 2322. Z. Galus and R. E. Adams, J. Phys. Chem., 67 (1963) 866. D. T. Napp, D. C. Johnson and S. Bruckenstein,.Anal. Chem., 39 (1967) 481. W. N. Hansen, R. A. Osteryoung and T. Kuwana, J. Amer. Chem. Soc., 88 (1966) 1062.