The diffusion of ferri- and ferrocyanide ions in sodium hydroxide solutions has been studied by means of a platinum rotating disk electrode. Results were obtained at variable concentrations an in the range of temperature between 24 and 40°C. 
The product Dɳ/T was approximately constant and independent of temperature in the range studied. The dependence of D on the total ionic strength is mainly due to the change of viscosity at large ionic concentration.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA)Facultad de Ciencias Exacta

Arvia, Alejandro Jorge

Bazán, Julio César

Electrochimica Acta

English

El Servicio de Difusión de la Creación Intelectual

Elcctrochimica Acta. 1965. Vol. 10, pp. 1025 to 1032. Peqamon Pnm Ltd. Printed in Northern Ireland 
THE DIFFUSION OF FERRO- AND FERRICYANIDE 
IONS IN AQUEOUS SOLUTlONS OF SODIUM 
HYDROXIDE* 
J. C. BAZAN and A. J. ARVIA 
Instituto Superior de Investigaciones, Facultad de Qulmica y Farmacia, 
Universidad National de La Plata, La Plata, Argentina 
Abstract-The diffusion of feni- and ferrocyanide ions in sodium hydroxide solutions has been 
studied b 
d* 
means of a platinum rotating disk electrode. Results were obtained at variable concentra- 
tions an m the range of temperature between 24 and 40°C. 
The product Dq/Twas approximately constant and independent of temperature in the range studied. 
The dependence of D on the total ionic strength is mainly due to the change of viscosity at large ionic 
concentration. 
R&m&-On a etudie la diffusion des ions ferri- et du ferrocyanure dans des solutions d’hy- 
droxyde de sodium au moyen dune 6lectrode 51 disque toumant en platine. On a effectue les mesures ii 
differentes concentrations et a des temp&ature comprises entre 24 et 40°C. 
Dans le domaine etudie, l’expmssion Dg/T bait pratiquement constante et independente de la 
temperature. La variation de D avec la force ionique totale est due principalment au changement de 
la viscosite cause par la grande concentration ionique. 
Zusasmnenfassung-Der Diffusionskoefhzient von Ferri- und Ferrocyanid ions in Natriumhydrox- 
ydlosungen wurde mittels einer rotierenden Scheibenelektrode aus Platin untersucht. Die Messungen 
wurden bei verschiedene Konzentrationen und bei Temperaturen zwischen 24 und 40°C ausgefiihrt. 
Das Produkt Dq/T war ungefahr konstant und im untersuchten Gebiet von der Temperatur 
unabhiingig. Die Abhangigkeit von D von der gesamten Ionensttike ist hauptsiichlich auf die Ander- 
ung der Zahigkeit infolge der hohen Konzentration zurilckzuftlhren. 
INTRODUCTION 
FOR studying the mass transfer rate in electrochemical systems olutions containing 
potassium ferro- and ferricyanide and sodium hydroxide in excess have very often been 
used, because the redox reaction involved can be studied in both directions on activated 
nickel or platinum electrodes and the limiting current density related to the reaction 
under convective-diffusion control is easily determined. 
As data reported in the literature ls2 about the diffusion coefficients of potassium 
ferro- and ferricyanide are for ternary solutions where the concentration of the 
supporting electrolyte was not appreciably changed, we decided to evaluate them 
within a larger range of concentration, employing a different experimental technique. 
Electrochemical determination by means of the rotating disk electrodes was chosen. 
The rotating disk electrode has been successfully tested for this type of measurement 
by different authors especially Yuktanova. 4 Results were satisfactorily compared to 
the very accurate determinations of von Stackelberg.6 The rotating disk electrode 
offers the advantage of determining diffusion coefficients in a reasonably short time. 
In the present work the effect of the concentration of the various species in the 
solution and of the temperature on the diffusion coefficient was determined. 
EXPERIMENTAL TECHNIQUE 
Electrolysis cell and rotating disk electrode. A double wall Pyrex vessel was used as 
the electrolysis cell. It had a Lucite cover holding the reference and the counter- 
electrode. The rotating disk electrode was placed axially in the middle of the container. 
* Manuscript received 20 July 1964; as amended, 22, December 1964. 
1025 
1026 J. C. BAZAN and A. J. ARVM 
A circular platinum sheet was placed symmetrically at the bottom of the container. A 
platinum electrode arranged in a separate compartment, filled with the solution and 
ending in a capillary tip was used as a reference lectrode. 
The cell design allowed the possibility of maintaining an inert atmosphere and ,the 
bubbling of purified nitrogen prior to electrolysis. 
The working electrode was a platinum disk of O-31 cm in diameter embedded in a 
Lucite rod of 1 cm diameter and welded to it with a small amount of an inert resin. 
The piece was adjusted and centred on the end of the rotating shaft. Its apparent area 
was O-0754 cm2. 
The electrode was driven by an ac l/8 hp motor electronically regulated. The 
rotation rate could be set between 20 and 1500 rpm with a maximum relative error, at 
the lower rates, of 1%. It was measured with a Zeiss stroboscope and regularly 
checked. 
Procedure 
Aqueous solutions of potassium ferro- and ferricyanide were used; the ratio 
between the salts ranged from O-08 to 10. The supporting electrolyte was sodium 
hydroxide; its concentration ranged from 0.5 to 2-O M. The ratio between concentra- 
tion of supporting electrolyte and diffusing ions was kept at about 20 or larger. The 
concentration of each component of the solution was determined by chemical analysis. 
The viscosity and density of solutions were determined as usual. 
400 
;I’*, (rad/s )‘j2 
FIG 1 I5 us UN*. Oxidation of ferrocyanide ion. 25°C. . . 
. ch: 1’014, C, x 10’: 1.00, C, x lo*: 1.04 
+ C,,: 2.070, C8 X lOa: 9.80, CI x lOa: 244 
a Ch: 1.084, C, x lo*: 250. C, x lo*: 2.38 
0 Ch: 0.5170, Cs X 10': 0.32, C, X 10': 0.31 
x ch: 1.031, CII X lo*: 0.25, CI X lo*: 0.27 
Diffusion of Fe(CN),‘- and Fe(CN),+ in NaOHaq. 1027 
Fro. 2. I& us &. Reduction of ferricyanide ion. 25°C. 
0 Ch: 1’014, C* x 10’: 1.00, C, x 10’: 1.04 
. Ch: 0.5170, C, X lo*: 0.32, CI X 10’: 0.31 
+ Ch: 1’031, Cs x 10*: 0.50, C, x 10’: 0.53 
x Ch: 0.5195, CJ X 10’: 0.16, C, X lo*: O-16 
A Ch: 1.031, CI, X lo*: 0.25, C1 X lo*: 0.27 
Experiments were performed at temperatures between 24 and 40°C. Solutions 
were prepared with analytical reagent chemicals, ERA and MERCK. 
According to circumstances the working electrode was the anode or cathode of the 
cell. The limiting current flowing through the cell was measured as usual by means of 
conventional circuitry. 6 Current voltage curves for a chosen set of experimental 
conditions were determined at different rotation rates, from 300 to 1500 ‘pm. These 
curves show the usual behaviour of reversible reactions comprising two soluble species 
entering the electrochemical reaction. 
D@sion coefjcients 
RESULTS 
To calculate the experimental diffusion coefficients the equation deduced by 
Levich3 for limiting current density under convective-diffusion control for the rotating 
disk electrode was used, 
zF 
iL = - ciDi~/3y-l&$/~ 
1.61 
3 
where iL is the limiting current density in A/cm2, ci the concentration of the diffusing 
species in mole/cm 3, D its diffusion coefficient in cm”/s, v the kinematic viscosity of 
the solution in cmZ/s and o the rotation rate of the electrode in rads/s. 
The determination of the dependence of iL on o thus allows the calculation of D. 
In Fig. 1 and 2 some results obtained from the anodic and cathodic experiments are 
ftm J. C. BAzAN and A. J. ARVIA 
TABLE 1 
ch c* x 108 c4 x lo* t DSrl 7j x 10” Do x 10” D4 x lo6 -y X 10” T 0171 x 10’0 
M M 
cm8 
M 
ems poise cm* poise “C pi* C$ s s”K -- 
S “K 
05880 0.18 25.0 1.114 
0.5195 016 0.16 25.0 1.023 
0.5100 0.28 0.30 27.2 1.015 
0.5100 0.28 0.30 30.2 0.912 
0.5100 0.28 0.30 35.9 0.802 
0.5100 028 0.30 41.8 0.717 
05170 @32 031 25.0 1.025 
05960 0.37 0.72 25.0 1.118 
0.5001 1.18 1.23 27.6 1.016 
05001 1.18 1.23 30.5 0900 
0.5001 1.18 1.23 36.0 0.828 
0.5195 1.27 1.25 25.0 1.037 
0.5960 1.26 2.39 25.2 1.131 
0.5134 2.54 2.51 25.0 1.045 
0.5980 240 4.81 25.0 1.140 
6.74 - 
7.43 6.16 
7.51 5.83 
8.33 7.07 
9.50 7.68 
10.57 8.74 
- 6.21 
7.12 - 
7.17 6.29 
8.13 7.13 
8.99 7.47 
6<1 6.04 
- 5;5 
6.56 - 
2.52 
2.55 
2.54 
2.50 
2.47 
2.41 
- 
2.67 
2,42 
2.41 
2.41 
- 
2.62 
- 
2.51 
- 
2.11 
1.97 
2.13 
1.99 
1.99 
2.14 
2;3 
2.11 
2.00 
2.10 
2G2 
- 
DO17 ( 1 T = (2.50 f 0.17) x 10-10 q gg ; xi ( ) T = (2.06 * 0.09) x 10-m C$f_g 
shown. The slope of the best straight lines obtained from a plot of iL US oA2 were used 
in the calculations and the results are assembled in Tables 1, 2 and 3. In the same 
tables dynamic viscosity, q, in g/cm . s and also the quotient Dq/T, where T is the 
temperature in “K, were added. C,, C, and Ch are the molar concentrations of 
potassium ferricyanide, potassium ferrocyanide and sodium hydroxide, respectively. 
ECect of temperature 
The experimental diffusion coefficients fit an exponential aw with respect to 
temperature, as shown in Fig. 3. The average xperimental energy of activation from 
the Arrhenius plot is 4100 f 250 Cal/mole. 
A similar law was followed by the dependence of viscosity on temperature, as 
TABLE 2 
Ch c3 x lo* c4 x 102 t q x 10a Do x lo8 
Wi 
D, x 10” 7 x 10”’ q x 10’0 
M M M “C poise 
- 
1.087 0.12 0.12 25.5 1.152 
1.031 0.25 0.27 25.3 1.122 
1.091 0.31 0.32 25.5 1,155 
1.031 0.50 0.53 25.3 1.126 
1.014 1.00 1.04 25.0 1.109 
1.103 1.27 1.31 25.5 1.164 
1.083 2.57 2.50 25.0 1.170 
1.083 4.86 4.96 25.0 1.195 
1.014 4.84 5.10 25.0 1.158 
cm1 
s 
cm% cma poise cm2 poise 
s 
-- -- 
S “K S “K 
6.35 546 2.45 2.11 
6.65 5.51 2.50 2.07 
6.41 5.23 2.48 2.02 
6.84 5.78 2.58 2.18 
6.77 5.81 2.52 2.16 
6.30 5.00 246 1.95 
6.39 5.61 2.50 2.20 
6.54 5.55 2.62 2.22 
6.63 5.68 2.57 2.20 
DIrl ( ) T = (2.52 f 0.1) x 10-m 7 pq ; (F) = (2.12 f 0.17) x 10-10 C$ p<. 
Diffusion of Fe(CN)f and FeQQes- in NaOHaq. 1029 
TAIU 3. 
Ch c* x 10” c, x 10’ t 7x10” &xl@ 0,x10+ x 1010 9 x 1010 
M M M “C 
cma 
poise 7 
cm8 cm’ poise cm* poise 
s 
_- -_ 
9 “K s “K 
2.055 0.038 (0+-W 
2.043 
2.028 
2.065 
2.028 
1.974 
2.072 
2.072 
2.072 
2.072 
1.985 
l-985 
1.985 
1.985 
1.996 
2-130 
2.050 
2.010 
1.930 
1901 
1901 
2.110 
2.070 
2.030 
0.12 
0.49 
0.95 
2.45. 
4.85 
490 
;:g 
4.90 
9.42 
9.42 
9.42 
9.42 
9.82 
1.17 
2-37 
4.50 
10.05 
10.05 
10.05 
9.68 
9.80 
9.72 
‘0.13’ 
0.51 
0.98 
2.55 
4.96 
5.08 
5.08 
5.08 
5.08 
9.78 
9.78 
9.78 
9.78 
960 
10.03 
10.03 
9.87 
1.08 
2.07 
5.07 
(1.45) 
244 
4.85 
27.2 
25.0 
25.0 
25.9 
25.0 
25.0 
27.0 
31.3 
35.7 
40.7 
27.0 
31.0 
36.1 
40.6 
25.0 
25.0 
25.0 
25.0 
25.0 
25.0 
25.0 
25.0 
25.0 
25.0 
1.371 
l-410 
1.416 
1.420 
1.433 
1442 
1.381 
1.267 
1.153 
1.045 
1.435 
1.302 
1.191 
1.094 
1.494 
1.502 
1 a474 
1467 
1.419 
1.421 
1.431 
1.486 
1483 
1.477 
5.70 - 
5.59 4.30 
5.56 4.22 
5.34 4.56 
5.33 4.45 
5.31 4.25 
5.36 4.48 
5.95 4.84 
6.84 5.70 
7.63 6.24 
5.33 4.48 
590 4.74 
6.25 5.32 
7.16 5 1 X:E 
5.03 - 
5.14 - 
5.08 - 
- 440 
- 440 
- 4.12 
- 4.38 
- 4.37 
- 4.32 
2.58 
264 
264 
2.54 
3.56 
2.57 
2.47 
2.48 
2.55 
2.54 
2.55 
2.53 
2.41 
2.50 
2.56 
2.50 
2.54 
2.50 
- 
2.03 
2+tO 
2.17 
2.14 
2.05 
2.06 
2.01 
2.13 
2.08 
2.14 
2.03 
2.05 
2.13 
2.10 
- 
- 
- 
- 
- 
- 
- 
- 
- 
2.09 
2.10 
1.98 
2.18 
2.17 
2.14 
= (2.54 f 0.13) x lo-lo ‘$ $ ; Dlrl (y) 
FIG. 3. Arrhenius plot for the diffusion coetkients. Dotted straight lines were drawn 
with the average value of the experimental energy of activation for diEtsion. 
Ch: 0.5100, CI x 10’: 0.28, C, x 10’: 030 (Ds: 0, D,: +) 
Cs: 2.072, CI x 10’: 490, C, x 10’: 5.08 (0,: 0, D,: x) 
C,,: 1.985, Ca X lOa: 9-42, c4 X 1O8: 9.78 (Da: A, D,: A) 
1030 J. C. BAZ,&N and A. J. ARVIA 
indicated in Fig. 4, and as can be predicted, the thermal effect is opposed to that found 
for the diffusion coe%cient. The experimental energy of activation in this case equals 
3900 f 100 cal/mol. 
Concentration dependence 
The concentration of the diffusing entities was changed in order to make the 
migration term negligible compared to the convective diffusion term in the ionic mass- 
0.20 - 
FIG. 4. Arrhenius plot for dynamic viscosity. 
(1) Ch: O-5001, Cs x 108: 2.37, Cd x 10’: 2.37 
(2) CI,: O-5001, C, x lo*: l-18, C, x 10’: l-23 
(3) Ch: @5100, CI x lo*: O-28, C1 x lOa: O-30 
(4) Ch: l-985, C, x lop: 9.42, Ca x lo*: 9.78 
(5) Ch: 2072, Cs x 10’: 490, C& x lo*: 5.08 
(6) Ch: 2065, Ca X 10’: 0.95, c, X 10’: 0.98 
transfer equation. The experimental diffusion coefficient shows a slight dependence on 
the concentration of the diffusing species, tending to a very slow decrease when 
concentration is increased. 
The extrapolated diffusion coefficients at zero concentration of the diffusing 
entities are plotted in Fig. 5 against the concentration of the supporting electrolyte. 
The diffusion coefficient shown at zero ionic strength for both ferro- and ferri-cyanide 
ions were obtained from molar ionic conductivity according to the Nemst-Hartley 
equation. ‘** It is clear that the diffusion coefficient increases as the total ionic 
strength decreases. 
Diffusion of Fe(CN),4- and Fe(CN)6a- in NaOHaq 1031 
Accuracy of results 
Considering the weight of each term in equation (l), the maximum experimental 
error affecting the calculated diffusion coefficient amounts from 3 per cent for .the 
solutions of higher concentration up to 10 per cent for the more diluted ones. 
DISCUSSION 
It is evident that the electrolytic system studied in the present case is complex. 
Although our first purpose was to extend knowledge of experimental diffusion 
coefficients of ferro- and ferricyanide ions in sodiumhy droxide solutions, a brief 
discussion of the foregoing results may be of interest. 
FIG. 5. Diffusion coefficients at zero concentration versus concentration of the support- 
ing electrolyte. D,: l and D,: 0. 
One feature to emphasize is the relatively small effect of the concentration of the 
diffusing species on the experimental diffusion coefficient within the range of concentra- 
tion of this work. A second is the net effect of the total ionic strength. The facts agree 
with the general predictions of the theory of diffusion coefficients in concentrated 
solutions of strong electrolytes. n In the present case, the following simultaneous 
processes take place besides the diffusion of the reacting species to the electrode 
surface, (a) transfer of ions of the supporting electrolyte, (b) transfer of species yielded 
by the electrochemical reaction itself, (c) changes of viscous forces due to the presence 
of a large ionic concentration and (d) transfer of solvent molecules (which might be 
differently associated with the reacting ions), and all should be considered. 
Since we have a great excess of supporting electrolyte, a condition imposed by the 
very application of the measuring method used in the present case, changes of concen- 
tration of the diffusing species will not appreciably affect its mean activity coefficient, 
which depends on the total ionic strength of the solution. Therefore the diffusion 
coefficient should show only a very small dependence on the concentration of the 
diffusing entities, as found. 
As the concentration of the supporting electrolyte is changed, the change of 
1032 J. C. BAZ& and A. J. ARVIA 
viscosity with concentration is appreciable and causes a marked decrease of the 
diffusion coefficient with the increase of concentration of sodium hydroxide. 
Under the present circumstances the convective diffusion of ions occurs in the 
same way as the diffusion of neutral molecules provided that the effect of the order of 
the ratio of the concentration of the reacting ion to that of the supporting electrolyte 
is ignored.lO Therefore the ratio Dg/T, as predicted by Einstein-Stokes as well as in 
Eyring’s theories for the diffusion of non-charged particles,11 should appear as a 
constant. 
The constants reported in the Tables are in satisfactory agreement with earlier 
results of Eisenberg, Tobias and Wi1ke.s 
Curves plotted in Fig. 5 show for any fixed concentration a ratio of 1.20 f 0.12 
between the diffusion coefficients of ferro- and ferricyanide ions. This ratio is 
also found between the diffusion coefficients at infinite dilution for both ions, calcu- 
lated independently from their conductances. 
Acknowledgements-This work was in part supported with financial aid by the Consejo National de 
Investigaciones Cientificas y Tknicas of Argentina. J. C. B. thanks the Consejo for the Fellowship 
granted. 
The authors are indebted to the Department of Inorganic and Physical Chemistry of the University 
of Buenos Aires for the original drawing of the rotating disk electrode proposed by Dr. R. Parsons 
and to Prof. J. J. Newman of the University of California for his interesting comments. 
REFERENCES 
1. M. EISENBERG, C. W. Toeus and C. R. Wnxe, J. Electrochem. Sot. 101,306 (1954). 
2. M. EISENBERG, C. W. TOBIAS and G. R. WILKE, J. Electrochem. Sot. 103,413 (1956). 
3. V. LE~ICH, Physico-chemical Hydrodynamics (English edition), p. 57. Prentice-Hall, N.J. (1962). 
4. V. LEVICH, ibid, p. 325. 
5. M. VON STACKEL.BERO, M. PILGRAM and V. TOOME. 2. Elektrochem. 57,342 (1953). 
6. J. C. BAzAN and A. J. ARVIA, Electrochim. Acta 9, 17 (1964). 
7. I. M. KOLTHOFF and J. J. LINGANE, Polarogmphy, Vol. I, Second Edition, p. 52. Interscience, 
New York (1952). 
8. R. A. ROBINSON and R. H. STOKES, Electrolyte Solutions, p. 293. Butterworth, London (1955). 
9. R. A. ROBINSON and R. H. S~>KES, ibid, p. 309. (1952). 
10. V. LE~ICH, lot. cit. p. 293. (1962). 
Il. S. GLADSTONE, K. J. LADLER and H. EYRING, The 7’heory of Rate Processes, p. 480. McGraw- 
Hill, New York (1941). 


The diffusion of ferro- and ferricyanide ions in aqueous solutions of sodium hydroxide

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The diffusion of ferro- and ferricyanide ions in aqueous solutions of sodium hydroxide

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