Chronopotentiometry of mixtures

ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY Elsevier Sequoia S.A., Lausanne Printed in The Netherlands

475

CHRONOPOTENTIOMETRY OF MIXTURES II. OXIDATION FROM MERCURY-POOL AND MERCURY-FILM ELECTRODES

P. BOS

Department of Analytical Chemistry, Free University, Amsterdam (The Netherlands) (Received 30th June 1971)

INTRODUCTION

The reduction of mixtures at mercury-pool and mercury-film electrodes was discussed in a previous publication ~. General concentration equations were given from which the oxidation of mixtures from mercury electrodes (e.9. in "chronopotentiometric stripping") can also be investigated. In this paper chronopotentiograms are calculated for various conditions. The influence exerted by a possible onset of oxidation of the second component during that of the first, has been taken into account. OXIDATION OF MIXTURES FROM A MERCURY FILM

The mercury film contains two substances, Redt and Red2, as amalgams; the initial concentrations are c° and co and the diffusion coefficients Dal and DR2. Through the transition of nl electrons Redl is transformed into Ox t which is soluble in the solution; the diffusion coefficient of Oxl is Dot. A similar transition of n2 electrons transforms Redz into Ox2 with diffusion Coefficient 0 0 2 . The intial concentrations of Oxt and Ox2 are zero. The polarographic half-wave potentials are E_~,I and E~,z. The following dimensionless parameters are defined: C01(O,t)(Ool~ ½

tot -

c°~1 \ D~-R~] Co2(O,t)

(1)

(Do2)

(2)

(0, 0

7R1 --

c0

(3)

~R2 ~---

cO

(4)

Substitution into the Nernst equation

RT ln(yoffYRi)=E~,2 + ~IF RT In (~O2/~R2) E=E¢,a + ~1F

(5)

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results in : 701 (7R2~ ha/n2

7R, \7~2/

=~

(6)

with nlF ~ = e x p { ~ - (E~, 1 - E½,2)}

(7)

With regard to the initial flux qo of the first reacting substance, the same supposition is made as in the previous publication (see eqns. ~15) and (16) in ref. 1). The equations for the transition times z ° and z °, obtained if the total applied current is used for the oxidation of Red~ or Red2 respectively, are 2 : "co = nl F lc° /io = lc° / qo (8) "co = n2 Flc° /io = (n2/nl)(lc° /qo) where I is the thickness of the mercury layer. The ratio of z ° and z ° is o o = nlCl/n2c o o2 a = "cl/z2

(9) (10)

Oxl and Ox 2 diffuse from the interface into the aqueous solution (layer thickness infinitely large); the distribution in the solution is independent of the thickness of the mercury layer but depends only on the fluxes q and q' of the two substances and on the values of the diffusion coefficients and the duration of the electrolysis. For the surface concentrations of Oxl and Ox2 the general equation for semiinfinite diffusion (eqn. (1) of ref. 1, with c o = 0) is applicable. Application of the method of Huber for the solution of the integrals (see eqn. (1) of ref. 1), transformation of the flux q' of OX 2 into the flux of Ox 1 with q'= (n~/n2)(qo- q) and application of eqn. (10), finally introducing the film parameters h 1 and h 2 (see eqn. (29), ref. 1), results in the following equations for ?Ol and ?o2: 2h ~ ?ol - (rrN)~ (j~-~Aj)

(11)

hE z ° Aj 7oa = ~-(~zN)~ .co

(12)

with

J

{(q)k-l--q)k)[(J - k + 1)3 / 2 - (]-k)3/2]) (13) k=l and j = 0 , 1, 2 .... ; ( t = j z ° / N ) . For Red1 and Red2 the general eqn. (4) of the previous publication 1 holds. By application of the method of Huber (here eqn. (9) of ref. 1) and further deduction along the same lines as above, one finds for 7R1 and 7R2 : Aj :

2

?R1 = 1

Bj

~'RI = 1 -

~o~

(14)

N

z°J

z° J B.

+ ~o s

J. Electroanal. Chem., 34 (1972)

(15)

477

CHRONOPOTENTIOMETRY OF MIXTURES. II J

with

Bj-2--! ~0j+ Z ~0k

(16)

k=l

Substitution of eqns. (11), (12), (14) and (15)into eqn. (6)produces:

2h~~(j2-TAj) .~- 2 ( i - ~aj+ ~Bj a ),1/,~= O ( ~1 )(nN)

{4_ I7 ~ h~ aA

j),,/,2 (17)

Assuming q0j=o= 1, the successive values of q0j can be calculated, starting with q0j=1. The values of Aj and Bj can then be calculated and finally the chronopotentiograms can be plotted with the aid of eqn. (5). OXIDATION OF MIXTURES FROM A MERCURY POOL

The oxidation of mixtures from a mercury pool is analogous to the reduction from an aqueous solution at a mercury-pool electrode. In this case the appropriate equations can be deduced by changing Ox and Red in the corresponding equations of the previous publication 1. NUMERICAL CALCULATIONS AND RESULTS

For T=25°C and N = 250, chronopotentiograms have been calculated with a digital computer for several values of nl, hE, a (or cJc2), ~ (or E~,I-E~,2) and h. It was assumed that hi =h2=h, thus DRI=DRz . TABLE 1 OXIDATION OF MIXTURES

Calculated values of zl/'c °, for different values of n 1, n z, cl/c 2, AE~ and h. N o value for z l / z ° is given for chronopotentiograms in which the deflection point could not be observed; where the difference between zl and z ° was found to be smaller than 1/4~, the value of 1 is given.

na

nz

cl/c 2

1

1

1

2

2

1

1

1

1/3

2

2

1/3

1

1

3

2

2

3

1

2

1

2

1

1

AE~,/mV

100 200 100 200 100 200 100 200 100 200 100 200 100 200 100 200

zx/'c ° h~ (pool)

h = 1 0 -2 (film)

h = 1 0 -4 (film)

-1 1 1

1.030 ! 1 1

1.030 1 1 1

--

1

1

0.982 0.982 1 1.098 1 1 1 0.666 0.982 1.126 1.010

1 1 1 1.026 1 1 1 0.970 1 1.090 1

1 1 1 1.026 1 1 1 0.986 1 -1.010

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478

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0.8

I

AE½=100mV OA

£~El=200rnV

0.2

3O(

I AE~- =200mV=

tl'r'°

fill

T 20C Lu 10C 10-2 /

~

. i~.4

c -loe

-,~""

AEI =100mY

-20£ t/'r,?

~,

Fig. 1. Chronopotentiograms (below), calcd, for the const, current oxidation of mixtures by using the following data: nt = rt2 = 1; c 1 = c2; two values of AE~ (as indicated); electrodes: mercury pool ( h ~ oo) or mercury film (two values of h=12/DRtz ° = 12~DR2 z°, viz. 10 -2 and 10-4). A b o v e : t h e course of il/i with time for the two different values of AE~ and for (a) h ~ , (b) h = 10 -4.

~Z~E½

=200mV

~

I!5

T o.oE 0.2

d5

2

30C

AEt=200mv ~t,,,

10£ ,iO-2

>

E

~

£

10 2.~.._ "

_ _

10 - 4

.....

-10(; AE½=IOOmV

-20£

tlr.O

:.

Fig. 2. Chronopotentiograms as in Fig. 1 for mixtures with n 1 = n 2 = 1 and cl =½ c2. J. Electroanal. Chem., 34 (1972)

479

C H R O N O P O T E N T I O M E T R Y OF M I X T U R E S . II

T

0.(

AE~=IOOmV

O.z

o'.5

~.'5 tlx!

.

~ I

AE1 =2OOmV

1o~ .,/

,,.......

AE½ = l O O m V

~OC I

o.~

~

{~

fix? Fig. 3. C h r o n o p o t e n t i o g r a m s as in Fig. 1 f o r m i x t u r e s w i t h n 1 = n 2 = 1 a n d c l = 3 c 2.

O~

AE1 =lOOmV

T 0.6 0.4 0.2 I

"

05 tl~?

300

-

iiiiii AE'~=2OOmV

2001 t.u

•

~oc

>

E

".;5::~-

. . . .

C

.--~-_____--~_,o-

_ ......

-1OC -2OC I

0.5

I

I

1

t l'~?

1.5

I

2

.

Fig. 4. C h r o n o p o t e n t i o g r a m s as in Fig. 1 f o r m i x t u r e s w i t h n t = 1, n2 = 2 a n d c l = c2.

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480

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A g½=100 mV 0.6 0.4 0.2 ~,, I

I

0.5

300 I 200

I

o 1.5 t/T 1

AE, =200mY

2 =-

/

I

45

)

J[

10-2 ...",

u4

100

>

E

0

t.u

-10o -200

tl"C? Fig. 5. C h r o n o p o t e n t i o g r a m s

,,

as in Fig. 1 for m i x t u r e s w i t h n 1 = 2, nl = 1 a n d cl = oz.

The results are shown in Fig. 1-5. The values of'cl/'C° are given in Table 1 ; ~1 is the transition time of the first substance to be oxidized ; in the calculated chronopotentiograms this value represents the time-lapse between the onset of electrolysis and the occurrence of the deflection between the two waves. F o r the Figures and the Table calculations were made with combinations of variables similar to those used in the case of reduction 1. The chronopotentiograms for A E { = [E~,~-E½,21 = 500 mV have been omitted here; in this case the separation of the oxidation waves was excellent for any combination and z~/Zo was equal to 1 for any combination of the parameters. CONCLUSIONS

There is no difference between the chronopotentiograms of oxidation from a mercury pool and reduction at a mercury pool; it should be noted only that D o may differ from D a for the same substance, but there is a great difference between the chronopotentiograms of oxidation from a mercury pool and from a mercury film. At a mercury pool the first substance to be oxidized also reacts after ~1 as a result of the continued diffusion ; consequently the second wave is lengthened, but this is not the case with oxidation from a mercury film (see the course of il/i in the Figures). When AE~ is large (e.g. 500 mV) i~/i = 1 until t = z °, thereafter i~/i = 0. After ~1 the second substance is oxidized just as would occur in the absence of a preceding substance (omitted in the Figures). With smaller values of AE{, oxidation of the second substance occurs during oxidation of the first substance (i~/i < 1 before t = ~ x), but the eventual oxidation J. Electroanall Chem., 34 (1972)

481

C H R O N O P O T E N T I O M E T R Y OF MIXTURES. II

of the first substance after t = z 1 is equal to the oxidation of the second substance before t=zl ; thus the final duration of electrolysis equals the sum of the oxidation times needed for each component separately. A thin mercury film is free of both components at the m o m e n t z2, irrespective of the distribution of the current over the two components. With regard to the possibility of distinguishing between the two waves and to the correctness of the first transition time, the following conclusions can be drawn.

1. Influence of n 1 and n2 As in the case of reductions, the determination is much better in mixtures with

n t = n 2 = 2 than with n l = n z = 1. With oxidation from a mercury film the potential transitions at zl are more pronounced then with oxidation from a mercury pool, but differences between zl and z ° still occur, especially when the two waves are unequal in length and form. The deviations are smaller than those obtained with reduction at a mercury film; this can be seen by comparing the Figures and Tables related to oxidation with those related to reduction x.

2. Influence of the concentration ratios Excess of the second component interferes less with the measurement of zx in oxidation from a mercury film than in reduction at a film, because the second wave is not enlarged in this case. F o r c2 ~< Cl and small AE~ it appears that the measured value of the first transition time is too large. This is more evident in the chronopotentiograms calculated for n ~ - n 2 = 1 [Figs. 1 and 2) than in the Table: with c~ = c z and AE~= 100 mV the second wave seems to be much smaller on superficial inspection than the first wave.

3. Influence of the thickness of the mercury film The differences between oxidation from a film and from a pool have already

-20C

o

fl

o

j

e

-400

1

/

-600 4s

4s

8s

-800 ~ ...--------.~

Fig. 6. E x p e r i m e n t a l c h r o n o p o t e n t i o g r a m s for o x i d a t i o n of m i x t u r e s with c o n s t a n t current from a mercuryfilm electrode with thickness 13.9 #m. (a) with i = 20/~A, after r e d u c t i o n d u r i n g 90 s at a r o t a t i n g electrode at - 7 5 0 m V vs. SCE of 3.13 x 10 -6 M C d 2+ and 2.95 x 10 _6 M Pb 2+ ; (b) with i = 12 FA, after r e d u c t i o n d u r i n g 60 s at a r o t a t i n g electrode at - 7 5 0 m V vs. SCE of 3 ] 2 x 10-6 M C d z + a n d 8.85 x 10 6 M P b z ÷ ; (c) with i = 10 #A, after r e d u c t i o n d u r i n g 180 s at a r o t a t i n g electrode at - 7 5 0 m V vs. S C E of 3.15 x 10 . 6 M Cd 2+ a n d 2.13 x 10 . 6 M T1 +. J, Electroanal. Chem., 34 (1972)

482

P. BOS

been discussed. With decreasing thickness of the film (more accurate: decreasing value of h) the wave shifts in a negative potential direction (see Figs. 1-3); the displacement depends on the value of n. Unequal displacement of the first and second wave when nl #n2, sometimes results in a somewhat too small value for the first transition time when nx < n2 and a somewhat too large value when n 1 > n2. Deviations of the first transition time at a mercury film increase with nl > n2 and decrease with n 1 < n2, whilst the reverse situation is found with reduction ; this contrast is caused by a difference in the position of the second waves with regard to the first waves (the potential shift is in a negative direction for both oxidation and reduction processes but with oxidation the second wave lies positive with respect to the first). Some of these conclusions are illustrated in the experimental chronopotentiograms of Fig. 6 : in general the distinction between the two waves is good (Fig. 6a) but becomes less so when the concentrations are unequal (Fig. 6b) or with n2 < nl (Fig. 6c). DISCUSSION

F o r the first time chronopotentiograms have been calculated for the oxidation of mixtures at mercury-pool and at mercury-film electrodes, in which the oxidation of the second component during that of the first has been taken into account. The mathematical method used here is essentially the same as that employed for the reduction of mixtures1, but differs from the method formerly used for the oxidation of single substances at mercury films 2. However, in the last case the approximations for thin films and mercury pools, starting from general equations, were similar. Consequently the limiting values of h for which (with a certain accuracy) the conditions are fulfilled for the validity of the equations derived for films and pools, can be obtained from Table 2 in the work of Bos and Van Dalen 2 (the values of h = 12/DRZ~ as used in the Table must be converted into the values of h = 12/DRz° as used in the present paper, with z~/z °= 1/21 and the values of 21 for h ~ 0 ; eqn. (42) of ref. 2). The calculations for oxidation from a film are of importance for the technique of "chronopotentiometric stripping ''3- 7 used in trace analysis. The current density must be chosen in such a way that for a given film thickness the conditions for h (mentioned above) are fulfilled, otherwise deviations from the calculated form of the waves will occur as well as an unpredictable lengthening of these waves. ACKNOWLEDGEMENTS

The author thanks Prof. Dr. E. Van Dalen for his stimulating interest, Dr. W. T. De Vries for his valuable suggestions, Drs. J. K o k for his aid in programming the computers X1 and X8 of the Mathematical Centre in Amsterdam and Mr. J. D. Van Oord for carrying out the experiments. SUMMARY

Chronopotentiograms have been calculated for constant current oxidation of mixtures from mercury-pool and from mercury-film electrodes. The influence of the following variables has been studied : the value of n, the ratio of the concentrations, J. Electroanal. Chem., 34 (1972)

483

CHRONOPOTENTIOMETRY OF MIXTURES. II

the thickness of the film and the difference between the polarographic half-wave potentials. The importance of the calculations for the technique of"chronopotentiometric stripping" has been emphasized. REFERENCES 1 2 3 4 5 6 7

P. Bos, J. ElectroanaL Chem., 33 (1971) 379. P. Bos AND E. VAN DALEN,Jr. Electroanal. Chem., 17 (1968) 21. G. MAMANTOV,G. PAPOFFAND P. DELAHAY,J. Amer. Chem. Soc., 79 (1957) 4034. R. H. JOHNS, Thesis, University of North Carolina, 1958. W. H. REINMUTH, Anal. Chem., 33 (1961) 185. R. H. NEEB, Z. Anal. Chem., 190 (1962) 98. A. R. NISBET AND A. J. BARD, J. Electroanal. Chem., 6 (1963) 332.

J. Electroanal. Chem., 34 (1972)