Effect of solvent viscosity on boundary layer in electrode processes

Effect of solvent viscosity on boundary layer in electrode processes

458 E L E C T R O A N A L Y T I C A L CHEMISTRY A N D I N T E R F A C I A L E L E C T R O C H E M I S T R Y Elsevier S e q u o i a S.A., L a u s a n ...

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E L E C T R O A N A L Y T I C A L CHEMISTRY A N D I N T E R F A C I A L E L E C T R O C H E M I S T R Y Elsevier S e q u o i a S.A., L a u s a n n e - P r i n t e d in The N e t h e r l a n d s

Effect of solvent viscosity on boundary layer in electrode processes

Introduction In connection with the use of electrochemical separation to determine reaction rates, limiting currents for the electrode reaction, A g + I - ~ A g I + e - , had to be established in a variety of solvents covering a broad viscosity range, viz. from 0.3 to 16 cP*. Since we think that the observed dependence of the limiting current density on the viscosity of the electrolyte may be of importance in polarography with solid microelectrodes, it is reported in the present communication. Experimental Limiting currents in sodium iodide solutions without any supporting electrolyte were determined by a radiochemical method previously described 1 using a cell of 50 ml volume. The electrolyte was agitated at 400 rev. m i n - 1. The circular silver anode, with an area of approx. 0.5 cm 2, was placed vertically in the cell. Results A summary of the data obtained is given in Table 1 in which t is the temperature, TABLE 1 LIMITING CURRENT DENSITIES IN VARIOUS SOLVENTS FOR THE ELECTRODE REACTION, m g + I - "--)AgI + e - , AT A SODIUM IODIDE CONCENTRATION OF 1.0 X l 0 - 4 M

Solvent

t/°C

q/cP

it/#A cm- 2

D x lOS/cm 2 s- 1

Acetone Methanol Methanol Ethanol Propanol Iso-propanol Butanol E t h y l e n e glycol E t h y l e n e glycol

25 55 25 25 25 25 25 55 25

0.32" 0.388 0.55 ~ 1.08 c 2.00 a 2.1 b 2.6 b 5.7 b 16.3 b

> 5700 1200 78 51 32 28 22 20 7.7

2.5 1.7 1.2 0.51 e 0.24 y 0.21 / 0.18: 0.19 0.065:

" Ref. 2. b Figures o b t a i n e d from s e m i l o g g r a p h s of q (refs. 2-4) vs. 1/(t + 273.15). c Ref. 3. a Ref. 4. e Ref. 9. : Ref. 8.

r/ the viscosity of the solvent, il the limiting current density, and D the diffusion coefficient of the salt. All limiting current densities quoted, the uncertainties of which are estimated to be less than + 1 0 ~ , refer to a sodium iodide concentration of 1.0 x 10-4 M. The diffusion coefficient of sodium iodide in acetone was estimated from the equation 5,

* 1 cP=10 -3kgm

-1 s -1

J. Electroanal. Chem., 27 (1970) 458-460

459

SHORT COMMUNICATIONS

where the symbols have their usual meaning, using limiting equivalent conductances for Na + and I - given in ref. 6. Diffusion coefficients in methanol at 25° and 55° were obtained from the value v, D = 1.0 x 10-5 cm 2 s- 1, at 14° assuming Dr/= const., which was also employed to estimate the 55° diffusion coefficient in ethylene glycol from the 25° value 8, D=0.065 x 10 -5 cm 2 s -1, in this solvent. Calculations below involve transport numbers, t_, of the iodide ion. For most of the alcohols studied this quantity is not available. Anion transport numbers in acetone, methanol, and ethanol, obtained from limiting equivalent conductances of Na ÷ and I - are t_ =0.586, 0.58 l°, and 0.571°, respectively. The value, t_ =0.6, was used for the other alcohols. A graphic representation of the dependence of the limiting current density on the viscosity of the solvent is shown in Fig. 1. For convenience logarithmic scales have

# 1°3 O

. ~ 102

t lo I, 0.2

I 0.5

/ 1

I 2

I 5

I 10

I 20

•r/ cp

Fig. 1. Limiting current density as a function of viscosity of electrolyte.

been used. As can be seen there is an abrupt change in the curve at ~/"~0.5 cP. For lower viscosities there is a very rapid increase in the limiting current density, and hence in the rate of transport of electroactive species to the anode surface, with decreasing viscosity of the electrolytic solution. In unajzitated solution, the transport of electroactive species to an electrode surface is generally purely diffusion controlled. In agitated solution, as in the present investigation, the transport is governed by convection and diffusion. To give a correct picture of the boundary layer through which the rate determining transport of electroactive species to the electrode surface occurs is not a straightforward matter 11, especially for agitated solutions, and hardly possible at all under the non-ideal conditions in the present investigation. Nevertheless it might be of interest to have some kind of measure of the "thickness" of the boundary layer adjacent to the anode surface. To that end we shall adopt the highly idealized Nernst diffusion layer modeP 2, which assumes purely diffusion controlled mass transport through a layer of thickness, 6, in which the concentration of electroactive species increases linearly with the distance from the electrode surface. With this model, and with the actual experimental conditions, the limiting current density is given by the equation, J. Electroanal. Chem., 27 (1970) 458-460

460

SHORT COMMUNICATIONS

il = FDc/(1 - t_)6

(2)

where c is the concentration of sodium iodide (1 × 10- ¢ M). This equation has been used to calculate the thickness, 6, for the various solvents studied. A graphic representation of 6 vs. the viscosity of the solvent is shown in Fig. 2. For q _~0.5 cP, where

0

E

ir I

I

t

I

0 I

I

10- 4

I I

I

I

I

/

I

I

0.2

0.5

1

2

5

10

20

~T/Cp

Fig. 2. Boundary layer "thickness", 6, as a function of solvent viscosity.

we observed a sudden change in the limiting current density vs. viscosity curve (Fig. 1), there is an abrupt change in the boundary layer thickness as defined by eqn. (2). For higher viscosities, 6 is remarkably constant and approximately 2 × 10-3 cm. Below t/=0.5 cP there is a rapid decrease in 6. Thus, when going from methanol at 25 ° (q = 0.55 cP) to acetone (q =0.32 cP) 6 decreases to below 1 x 10 -4 cm, i.e. by a factor of 20 or more.

Acknowledgements The author thanks Dr. Michael Sharp for linguistic revision of the manuscript and the Swedish Natural Science Research Council for financial support. Division o f Physical Chemistry, University o f Umed, S-901 87 Umed (Sweden)

P. Beronius

1 P. BERONIUS,Acta Chem. Scand., 15 (1961) 1151. 2 R. C. WEAST(Ed.), Handbook of Chemistry and Physics, The Chemical Rubber Co., Cleveland, Ohio, 49th ed., 1968-1969. 3 J. TIMMERMANS,Physieo-Chemical Constants of Pure Organic Compounds, Vol. I, Elsevier Publishing Co., Inc., New York, 1950. 4 A. WE1SSBERGER(Ed.), Technique of Organic Chemistry, Vol. VII, Interscience Publishers, Inc., New York, 2nd ed., 1955. 5 I. M. KOLTHOFF AND J. J. LINGANE, Polarography, Interscience Publishers, Inc., New York 1952, pp. 53-56. 6 C. W. DAVIES, The Conductivity of Solutions, Chapman and Hall, Ltd., London, 1933, p. 208. 7 InternationalCritical Tables V, p. 72. 8 P. BERONIUSAND R. ENBERG, Z. Physik. Chem. (Frankfurt), 46 (1965) 373. 9 S. ASUNMAA,Ann. Acad. Sci. Fennicae, A 53 (1940) No. 11. 10 P. BERONIUS, G. WIKANDER AND A.-M. NILSSON, Z. Physik. Chem. (Franl(furt), 70 (1970) 52. il K.J. VEXTER,EleetroehemicalKineties, Academic Press, New York, 1967, chap. 2B. 12 W. NERNST, Z. Physik. Chem., 47 (1904) 52.

Received March 25th, 1970 J. Electroanal. Chem., 27 (1970)458-460