Comparative Methods for Gas Diffusivity and Solubility Determination

Amanda C. Garcia , Alberto Diaz Herrera , Edson A. Ticianelli , Marian Chatenet , Christiane Poinsignon. Journal of The Electrochemical Society 2011 1...
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Ind. Eng. Chem. Res. 2000, 39, 3083-3089

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Comparative Methods for Gas Diffusivity and Solubility Determination in Extreme Media: Application to Molecular Oxygen in an Industrial Chlorine-Soda Electrolyte Marian Chatenet, Marc Aurousseau,* and Robert Durand Laboratoire d’Electrochimie et de Physicochimie des Mate´ riaux et des Interfaces, ENSEEG-INPG, 1130 rue de la piscine, BP 75, 38402 Saint Martin d’He` res Cedex, France

Low-solubility-gas mass-transfer parameter determination has been achieved using conventional, and nonconventional, electrochemical, or predictive calculation methods. The methods have been compared for the oxygen diffusivity and solubility determination in alkaline media. Their validation has been fulfilled in the case of 1 M NaOH at 25 °C. Their use for membrane chlorinesoda process industrial electrolytes, 11.1 M (33 wt %) NaOH at 25 and 80 °C, has then been undertaken, leading to DO2(80 °C) ) 2.54 × 10-9 m2 s-1 and He-1(80 °C) ) 1.17 × 10-7 mol m-3 Pa-1, which is 72 times lower than that in 1 M NaOH at 25 °C. Introduction

conditions, 33 wt % NaOH at 80 °C, are compared and discussed.

Numerical model elaboration for an air cathode in the brine electrolysis process requires the knowledge of the oxygen mass transport coefficients in very concentrated soda at rather high temperature: 33 wt % ()11.1 M) NaOH solution at 80 °C. Unfortunately, such information is not available in the literature, except at low temperature and concentration1 or partially for potassium hydroxide solutions2 whose characteristics are close to those of soda. Moreover, direct volumetric methods, i.e., measurement of the volume variation induced by the gas solubilization into the solution, performed from a mercury pointer moving in a gauged capillary, appeared unsuccessful. Indeed, the dissolved oxygen amount was too small to be determined with enough accuracy, and the cell gastightness was not easy to realize. Consequently, the goal of this study is to test and compare various electrochemical methods, allowing these parameter determinations. A classical method has first been attempted: chronoamperometry coupled with quasi-steady-state voltammetry, as described by Levich.3 A nonclassical method, which coupled two electrochemical techniques, was also undertaken: oxygen diffusivity (diffusion coefficient) transient determination on a platinum rotating ring-disk electrode (RRDE), suggested both by Gan and Chin4 and Lozar et al.5 according to the Bruckenstein and Feldman method,6 and limiting current measurement in quasi-steady-state oxygen reduction voltammetry on a platinum rotating disk electrode (RDE). Besides, because no literature reference values are available, a predictive method has been applied: numerical estimations from correlations7 were calculated and used as reference values. The experimental and numerical methods validation has been done with literature data for a 1 M NaOH solution at 25 °C1,8,9 and for NaOH solutions in the range 0.5-6.4 M at various temperatures,1,8-11 respectively. The experimental or numerical results obtained for industrial chlorine-soda electrolyte at operating * Corresponding author. E-mail: [email protected]. Tel: (33) 4 76 82 65 90. Fax: (33) 4 76 82 67 77.

Theoretical Basis for Electrochemical Methods All of the considered methods are detailed with molecular oxygen, O2, as the reactant but could be generalized to other gases. Classical Method. The classical method combines chronoamperometry and voltammetry techniques. In the first transient method, a potential step is applied at the disk of a nonrotating RDE to electrochemically reduce oxygen. With the RDE rotation rate being zero, it can be considered that the diffusion layer has an infinite thickness. In the case of a reversible charge transfer with identical mass transfer for both reactant and product, the resulting current I is given by Cottrell’s equation3

I ) IL*(πt)-1/2V(E)

(1)

IL* ) -nFSCO2DO21/2 in A s1/2

(2)

with

and

V(E) ) [1 + exp{nF(E - E0)/(RT)}]-1 ) 1 with our potential values (3) from which the product CO2DO21/2 can be determined. The quasi-steady-state voltammetry experiments lead to limiting diffusion-convection current densities iL (A m-2), according to Levich’s equation3

iL ) -0.621nFDO22/3ν-1/6ω1/2CO2

(4)

and consequently to the product CO2DO22/3. Finally, once CO2DO21/2 and CO2DO22/3 are both known, the gas diffusivity and solubility can be determined. DO21/6 is first isolated and then DO2. This value is afterward introduced in one of the previous products, leading to CO2 determination.

10.1021/ie000044g CCC: $19.00 © 2000 American Chemical Society Published on Web 06/29/2000

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Nonclassical Method. In this second transient method, a potential step is applied on the disk of a RRDE to electrochemically reduce oxygen, whereas the ring is maintained at an oxygen reduction potential. The final potential value has to be sufficiently low to yield quickly to a diffusion limitation and therefore to a large oxygen concentration decrease. The induced lack of oxygen in the solution, created at the disk, reaches the ring after a certain transit time ts (s), given by4,5 1/3

-1

ts ) K(ν/DO2) ω

(5)

where dimensionless parameter K only depends on the electrode geometry. For an ideal RRDE, with absolutely concentric ring and disk electrodes and a perfectly smooth surface, K is given by4-6

K ) 4.51(log[r2/r1])2/3

(6)

The graph showing ts variations versus Kω-1 results in a straight line crossing the origin, whose slope allows the oxygen diffusivity determination. The oxygen solubility is then determined from the product CO2DO22/3 obtained by voltammetry, as previously described. Number of Electrons Exchanged per O2 Molecule (n) Determination. All of the methods previously described require the knowledge of the number n of electrons exchanged per O2 molecule during its reduction. This number is equal to four on platinum in acidic media and in low concentrated alkaline media. Appleby and Savy12 and Yeager13 both proposed a mechanism involving, according to three different pathways, four electrons per O2 molecule and only leading to hydroxide ion formation. In concentrated NaOH, no published data are available. Consequently, n was determined in such media on a Pt-Pt RRDE. The principle of the method is to make oxygen reduction voltammograms on the disk, whereas the eventual peroxides produced in a two-electron reaction are oxidized on the ring. The ring IR and disk ID currents are simultaneously recorded as a function of the disk potential ED. n is then determined from charge (7) and mass (9) balances, taking into account relation (8) that expresses the two-electron reduction current I2e on the disk:

ID ) I2e + I4e

(7)

I2e ) IR/N

(8)

with

where N is the collection efficiency depending only on the electrode geometry.14 Besides,

ID/n ) I4e/4 + I2e/2

(9)

n ) 4ID/[ID + IR/N]

(10)

Finally

Experimental Procedures and Error Estimations Apparatus and Solutions. The RRDE (Pine Instrument AFDT 136 Pt-Pt) consists of two platinum electroactive surfaces: a central disk (r1 ) 2.5 × 10-3 m)

Table 1. Viscosities of the Different Electrolyte Solutions from Reference 15 1 M NaOH, 11.1 M NaOH, 11.1 M NaOH, 25 °C 25 °C 80 °C dynamic viscosity 1.23 × 10-3 η (Pa s) kinematic viscosity 1.19 × 10-6 ν (m2 s-1)

15.7 × 10-3

2.73 × 10-3

11.6 × 10-6

2.07 × 10-6

Table 2. Experimental and Estimated Oxygen Solubilities CO2 (mol m-3) and Henry Constant Inverse He-1 (mol m-3 Pa-1) in Various Electrolytes

PO2 (Pa) CO2,experimental He-1experimental CO2,Onda20 CO2,Weisenberger21b CO2,tabulated9

1 M NaOH, 25 °C

11.1 M NaOH, 25 °C

11.1 M NaOH, 80 °C

9.82 × 104 8.35 × 10-1 8.50 × 10-6 8.10 × 10-1 7.77 × 10-1 8.80 × 10-1

9.99 × 104 8.58 × 10-3 8.59 × 10-8 1.25 × 10-2 7.86 × 10-3

7.95 × 104 9.30 × 10-3 1.17 × 10-7 1.20 × 10-2 9.95 × 10-3

and a concentric ring (r2 ) 3.75 × 10-3 m and r3 ) 4.25 × 10-3 m). The surface of the electrode was smoothed by diamond paste polishing, down to 1 µm. This electrode surface preparation led to an experimental value of 1.379 for the parameter K of eq 5, determined using the Fe(CN)63-/Fe(CN)64- redox couple in a 1 M NaOH solution. This value is in agreement with the theoretical value, 1.417, calculated with eq 6 for an ideal RRDE. The organic solvents of the diamond paste were eliminated by three 15 min ultrasonic washes in acetone, ethanol, and water successively. The NaOH solutions (1 M from Prolabo Normapur pellets diluted with Millipore water and 11.1 M (33 wt %) from ELFATOCHEM) were saturated with pure oxygen or argon (Air Liquide, purity N45 and U, respectively), and their temperature was controlled by thermostated-water circulation. The various viscosities of these solutions determined from published data15 are given in Table 1. For the RRDE experiments, two potentiostats were used: a PGP 201 (Radiometer Analytical) connected to Hg-HgO in a 1 M soda reference electrode (E ) +0.1 V/NHE at 25 °C) via a Luggin capillary and a platinum grid counter electrode for the disk and a PAR 263A (Princeton Applied Research, EG&G) with another HgHgO reference and another platinum grid counter electrode for the ring. In the RDE experiments, the PAR was connected to the disk. The cell volume was approximately 10-3 m3, and the total pressure of the gas phase was maintained constant at 1.013 × 105 Pa. The correction by the saturated vapor was made for all electrolytic solutions at all temperatures to determine the oxygen partial pressure in the cell (Table 2). Before each set of measurements, the solution is deaerated by argon bubbling for 30 min, ensuring a complete degassing, at the end of which both electrodes are cycled between +0.300 and -0.880 V/Hg-HgO at 2 × 10-2 V s-1 in order to clean their surfaces. The surface is considered clean when the hydrogen adsorption voltammogram under an inert gas has the conventional shape. Then, the solution is saturated with pure oxygen by means of a 30 min bubbling, with the disk and ring electrodes being kept at the open circuit potential. Finally, in these experiments, the electrode surface is controlled before and after each set of measurements by voltammetry under an inert gas: no evolution has been found during the measurements. At last, the amount of oxygen reactant involved in the reaction has

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Figure 1. Example of a iL-ω1/2 curve for corrected oxygen reduction voltammograms in 11.1 M soda at 80 °C.

always been smaller than 5% of the initial amount in the solutions. Nevertheless, a permanent bubbling in the concentrated solutions ensured a total compensation of the oxygen consumption on the working electrode: the bulk concentration could be considered constant during the entire experiment. n Determination on RRDE. The quasi-stationary oxygen reduction voltammograms are obtained at 10-3 V s-1 on the disk electrode in oxygen-saturated 1 M soda between +0.100 and -0.600 V/Hg-HgO or in 11.1 M soda between +0.040 and -0.600 V/Hg-HgO. IR is simultaneously recorded as a function of ED for various rotational speeds, with the ring being held at +0.350 V/Hg-HgO, a potential where the hydrogen peroxide oxidation occurs. This oxidation reaction involves 2 electrons/peroxide molecule.16-18 n is then determined from IR and ID using eq 10, with N being experimentally determined using the Fe(CN)63-/Fe(CN)64- redox couple; it does not significantly differ from the manufacturer value of 0.2249 (Pine Instrument Co.), which is consequently chosen. However, the method is not that simple to use in the case of concentrated electrolytes. Indeed, the stationary measure of CO2 requires different procedures according to the various electrolyte concentrations. The weak oxygen reduction current in 11.1 M soda, because of the very small molecular oxygen solubility, has in such solutions the same order of magnitude as the reduction current of the oxygenated species adsorbed on the platinum surface (depending on the scan rate). The limiting current is therefore considered as the sum of the molecular oxygen reduction limiting current and the one which corresponds to the reduction of the electrode surface. The real limiting current is then determined by subtracting the voltammogram under an inert gas (reduction of the oxygenated species) from the voltammogram under oxygen. The corrected voltammograms give limiting currents in agreement with Levich’s equation (Figure 1). Once again, the main problem of the method is caused by the weak current values, increasing the noise/signal ratio and therefore making difficult the limiting current determination. Chronoamperometry. The chronoamperometry experiments are made on the disk Pt electrode in the various NaOH solutions, saturated with pure oxygen. A step is applied to the disk, from the open circuit potential to -0.300 V/Hg-HgO, where the oxygen reduction reaction is only diffusion-controlled. Meanwhile, the disk current is monitored versus time. CO2 Determination. The procedure is the same as that for n determination, except that only the disk

Figure 2. Ring current IR vs time (normal view and zoom of the ts determination region) during the potential step imposition on the disk in 1 M soda at 25 °C, ω ) 83.8 rad s-1.

current is monitored. The total error can be determined from derived eq 4:

∆CO2/CO2 ) ∆n/n + (2/3)∆DO2/DO2 + (1/6)∆ν/ν + (1/2)∆ω/ω + ∆iL/iL (11) Considering ∆n/n ) (10%, ∆DO2/DO2 ) (45.5%, ∆ν/ν ) (5%, ∆ω/ω ) (0.5%, and ∆iL/iL ) 5%, the error in CO2 determination increases up to 46%. DO2 Determination on RRDE. For each rotation speed, the ring is put at -0.600 V/Hg-HgO, with the disk being maintained at its open circuit potential. After 5 min a potential step is applied to the disk, from the open circuit potential to -0.600 V/Hg-HgO, a potential involving a pure diffusion control5 for the oxygen reduction reaction. Meanwhile, the ring current IR is monitored on a numerical potentiostat. The IR-t curve in response to this potential step allows the graphical determination of the transit time ts, as represented on Figure 2. The simultaneous recording of the disk potential and the ring current on a two-channel oscilloscope (Tektronix TDS 210) shows that the sharp pulse on the ring current is synchronous with the potential step at the disk, as stated by Gan and Chin4; it is due to the electronic measurement hardware (potentiostat) and is used as the transit time origin.4,5 The transit time is then determined by the intersection of the base steady ring current line and the fast attenuated ring current line as shown on Figure 2. This procedure is repeated for each rotation speed in the range 41.9-209 rad s-1, and the collected data permit the plotting of the transit time vs Kω-1 straight line whose slope gives the oxygen diffusivity in the considered solution, as shown on Figure 3. The main difficulty in concentrated soda comes from the low oxygen solubility and, therefore, from the weak oxygen reduction current, which increases the electric noise influence on the IR-t curves, making more hazardous ts determination. Considering the logarithmic derivative of eq 5, the error can be maximized as follows:

∆DO2/DO2 ) 3∆K/K + ∆ν/ν + 3∆ω/ω + 3∆ts/ts (12)

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However, for concentrated electrolytes, whose viscosity is typically larger than 2 × 10-3 Pa s, the modified eq 14b is generally admitted:19

Dηa/T ) cte

Figure 3. Example of transit time vs rotational speed inverse curves in various NaOH solutions: [, 1 M at 25 °C; 2, 11.1 M at 25 °C; 0, 11.1 M at 80 °C. Table 3. Experimental and Estimation from Various Correlations (from Reference 7) for Oxygen Diffusion Coefficients DO2 (m2 s-1) in Various Soda Solutions

modified Wilke and Chang (a ) 0.5) Wilke and Chang (a ) 1) Scheibel Reddy and Doraiswamy tabulated9 experimental

1M NaOH, 25 °C

11.1 M NaOH, 25 °C

11.1 M NaOH, 80 °C

1.65 × 10-9

4.62 × 10-10

1.31 × 10-9

1.65 × 10-9

1.29 × 10-10

8.80 × 10-10

1.77 × 10-9 1.35 × 10-9

1.34 × 10-10 1.19 × 10-10

9.22 × 10-10 8.06 × 10-10

1.65 × 10-9 1.56 × 10-9

3.10 × 10-10

2.54 × 10-9

Taking into account ∆K/K ) (3%, ∆ω/ω ) (0.5%, ∆ν/ν ) (5%, and ∆ts/ts ) (10%, the error ∆DO2/DO2 in the estimation of the oxygen diffusivity reaches 45.5%. This relatively wide error interval is similar to the error range generally admitted for oxygen diffusion coefficients, with the value of 20% being admitted in pure water;11 it mainly comes from the difficulty in ts determination and could be reduced by widening the diskring gap, so that the transit time would be longer.

PO2 ) He°CO2°

(15)

The oxygen partial pressure PO2 is here the total pressure, 1.013 × 105 Pa, corrected by subtracting the equilibrium vapor pressure11 over the considered solution, water or soda. For example, at 25 °C, the oxygen solubility in pure water under an oxygen atmosphere is11 1.23 mol m-3. For the electrolytic effect (or salt effect), two relations are available:19

log [He/He°] ) hI ) (h+ + h- + hG)I

These estimations are important in our case because they provide a reference range of values for the different oxygen transport parameters in the various soda solutions, with no published data being available for very concentrated soda (10 M NaOH solutions and upper) at high temperatures. Oxygen Diffusivity in 11.1 M Soda. Several correlations are available: classical ones based on the equivalent conductivities and others used for nonaqueous solvents but also usable in the case where the dissolved gas has a low solubility (such as oxygen in concentrated soda solutions).7 For example, the well-known Wilke and Chang equation is

(13)

Other correlations exist; they give similar values for DO2 as shown in Table 3, assuming the Stokes-Einstein equation validity:

Dη/T ) cte

The exponent a compensates for the large viscosity of the solution.19 It typically varies between 0.5 and 1; the value of 0.5 which can appear as a lower limit case is chosen in the so-called modified Wilke and Chang equation; the results might then be compared to those from the conventional case where a ) 1 in eq 13. The interaction coefficient Φ can be calibrated with a known value of diffusivity. For example, in 1 M soda at 25 °C the generally admitted value9 is DO2 ) 1.65 × 10-9 m2 s-1. Taking into account M ) 18.4 × 10-3 kg mol-1 for 1 M soda, we obtain Φ ) 2.26 and 1840 for a ) 1 and 0.5, respectively; the first value is in agreement with those proposed by Hayduk and Laudie for aqueous solutions.7 However, in more concentrated solutions, we chose to keep the product ΦM constant according to eq 14a,b. The results of these numerical estimations are presented in Table 3. Oxygen Solubility in 11.1 M Soda. Gas solubility in a concentrated solution can be estimated for a given experimental condition, i.e., temperature and partial pressure, from that of the same gas in a reference electrolyte. In the present case the reference solvent is water, for which oxygen solubility is calculated considering Henry’s law:

Van Krevelen and Hoftijzer’s equation

Numerical Estimation from Correlations: Predictive Method

DO2 ) 5.86 × 10-17(ΦM)1/2Tη-1VO2-0.6

(14b)

(14a)

(16)

Onda et al.20 determined these coefficients, whose values lead to h ) 1.80 × 10-4 m3 mol-1; then, for 11.1 M soda at 25 °C, log [He/He°] ) 2.00.

Schumpe et al. relation, adapted to the case of several salts7 log [He/He°] )

∑HiIi

(17)

Schumpe et al.21a values lead to log [He/He°] ) 2.08 in 11.1 M NaOH at 25 °C. In a more recent paper,21b Weisenberger and Schumpe have calculated the temperature effect on hG in the range 273-363 K for solution concentrations up to 5 M. The opportunity to use this correlation for more concentrated solutions will be further discussed. Results and Discussion n Determination. In 1 M NaOH at 25 °C, the number of electrons per O2 molecule, n, varied between 3.8 and 4 in the limiting diffusion-convection current

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Figure 4. Example of a n-ED curve for corrected oxygen reduction voltammograms in 11.1 M soda at 80 °C.

potential zone. This cannot be attributed to a quantitative hydrogen peroxide formation during the oxygen reduction on the disk. As a consequence it will be assumed that n ) 4 in 1 M NaOH at 25 °C, as predicted by Yeager.13 On the contrary, in more concentrated NaOH, hydrogen peroxide formation is not negligible in the limiting current zone, whatever the medium temperature is. One example among our various trials in 33 wt % NaOH at 80 °C presented on Figure 4 shows that n is, in this case, closer to 3 electrons/O2 molecule, which implies a partial peroxide formation. Indeed, the mean value (from several experiments) of 3 electrons exchanged/O2 molecule during the oxygen reduction on platinum in 33 wt % NaOH is found and assumed. DO2 and CO2 Determination Using the Classical Method. The chronoamperometry experiments did not give reproducible results in concentrated soda: more than 100% irreproducibility was found. This might be due to the fact that the oxygen reduction reaction does not fit the method-required hypothesis, e.g., reversible charge transfer with identical mass transport for both reactant and product. All the more, the results coupled with quasi-steady-state voltammetry yield an exponent 6 in the oxygen diffusivity determination resulting from the values of CO2DO21/2 and CO2DO22/3 determined with each technique, respectively. This dramatically increases the experimental error, already important in concentrated NaOH because of the weak CO2 value. This method is therefore not suitable for utilization in concentrated soda. DO2 and CO2 Determination Using the Nonclassical Method. (a) DO2 Determination. The transit times ts are determined from the ring chronoamperograms as shown in the example of Figure 2. Examples of corresponding straight lines, whose slopes allow the oxygen diffusivity calculation for the considered electrolyte, are plotted on Figure 3 for the various NaOH solutions. The experimental results of oxygen diffusivities calculated for several experiments can be seen in Table 3, with the estimated values. Considering a ) 1, no major differences are observed between the various predictive values, showing a good homogeneity among the proposed correlations. Moreover, for 1 M NaOH at 25 °C, they differ from the tabulated value with a relative error lower than 18%, which validates their use. The same conclusions can be given for the experimental method: our value is about 5% lower than the tabulated one. In 11.1 M NaOH at 25 °C, the oxygen experimental diffusivity is always in agreement with the numerical estimations from modified or unmodified Wilke and

Figure 5. Parity plot for calculated20,21b vs tabulated1,8-11 or experimental oxygen He-1 in various NaOH solutions.

Chang correlations. The oxygen diffusivity is included between the two limit case values and would correspond to a ) 0.65: the large viscosity encountered for this solution made it predictable. For 11.1 M NaOH at 80 °C, the experimental value is about twice as high as the estimated ones. However, the relative error with the predicted value from the modified Wilke and Chang correlation (a ) 0.5) does not exceed 49%, which is close to the experimental one, estimated by relation (12). Then, considering both the experimental (45.5%) and predictive (20-30% classically) relative errors, the adherence value ranges show a large shared area, which completely validates the method. (b) CO2 Determination. Oxygen diffusivity previously calculated, coupled with oxygen reduction voltammetry data, allows the determination of its solubility. The oxygen reduction voltammograms made on the disk give reproducible values for CO2DO22/3. The deducted solubilities are presented in Table 2, with the estimated values from the considered correlations. As previously noted, no data are available for concentrated soda at high temperature; the only references in 11.1 M soda at 25 or 80 °C are therefore the calculated solubilities. To validate all of these correlations’ use, a parity plot for literature and estimated He-1 values is shown on Figure 5. The considered solubility data10,11 (about 30 points) recovered NaOH solution concentrations up to 6.4 M at room temperature or around 1 M solutions in the range 15-100 °C. In 1 M soda, the relative error between the experimental and tabulated values is around 5%, and it reaches 12% between the calculated and tabulated ones. Such differences could appear nonnegligible for thermodynamic parameters, but the different oxygen solubility values in 1 M soda at PO2 ) 1.013 × 105 Pa in the literature are not in agreement either: CO2 ) 8.8 × 10-1, 1.1, and 6.92 × 10-1 mol m-3 from refs 9, 8, and 22, respectively. That reveals the difficulty in the determination of this solubility, with the main reason being its small value, and allows the validation of the methods. The estimations from ref 20 are less accurate, probably because the h coefficients used in this method do not completely take into account the temperature variation. On the contrary, those from ref 21b are close to the experimental values within 8%. This might show the correlation usability in the case of very concentrated

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solutions (more than 5 M) as expected from Figure 5. All the more they confirm the oxygen solubility inversion with a temperature increase observed experimentally and noted in KOH solutions;2 this is shown in Table 2 on either the solubility or the Henry constant inverse (solubility per unit of partial pressure) parameter to be considered for the comparison as far as it does not depend on the oxygen partial pressure. This temperature effect on the oxygen solubility is then double. For a given temperature increase, the higher the NaOH solution concentration, the more important is the He/ He° ratio decrease. At the same time, (He°)-1 also decreases. Then, when the first variation becomes predominant, the solubility increases with the temperature: this happens for NaOH solutions over 6 M considering a 25-80 °C temperature step. This effect may be related to the important viscosity decrease with a temperature increase in very concentrated solutions. Conclusion The oxygen solubility and diffusivity in concentrated industrial NaOH solutions (33 wt % at 25 or 80 °C) have been determined, which is interesting because no data were available in the literature for these types of solutions. The classical electrochemical method (chronoamperometry coupled with steady-state voltammetry) cannot be applied with enough accuracy in such electrolytes. On the contrary, the nonclassical methods (diffusivity transient determination on RRDE coupled with steady-state voltammetry) and the numerical correlations predictive method have led to results in agreement. This validates their use for concentrated electrolytes in the case of low-solubility gas. The oxygen solubility is 72 times lower in 11.1 M soda at 80 °C than in 1 M soda at 25 °C. Acknowledgment This work was supported by ELF-ATOCHEM Research Centre (Centre de Recherche Rhoˆne-Alpes, PierreBe´nite, France) and the French Environmental Agency (ADEME). Notations CO2 ) oxygen solubility, mol m-3 CO2° ) oxygen solubility in water, mol m-3 DO2 ) oxygen diffusivity, m2 s-1 E ) electrode potential, V E° ) standard potential for a O2/OH- redox couple ) +0.301 V/Hg-HgO at 25 °C E - E° ) electrode overpotential, V ED ) RRDE disk potential, V F ) Faraday constant ) 96 485 C mol-1 h ) Setchenow coefficients, m3 mol-1 (+, -, and G subscripts for cation, anion, and gas, respectively) Hi ) specific coefficient for the ion i, from the Setchenow coefficient, depending on the gas and the temperature, m3 mol-1 He° ) Henry constant for oxygen in water, Pa m3 mol-1 He ) Henry constant for oxygen in soda, Pa m3 mol-1 i ) current density, A m-2 I ) current, A I ) (1/2)∑zi2Ci ) ionic strength equal to the NaOH molar concentration, mol m-3 Ii ) partial ionic strength for the single ion i, mol m-3 M ) soda solution molar mass, kg mol-1

N ) collection efficiency (species reacting on the ring/ species produced on the disk) n ) number of electrons involved in the oxygen reduction reaction PO2 ) oxygen partial pressure in the considered conditions, Pa R ) ideal gas constant ) 8.314 J mol-1 K-1 RDE ) rotating disk electrode RRDE ) rotating ring disk electrode r1, r2, r3 ) RRDE disk, inside ring, and outside ring radii, respectively, m S ) electrode geometric area, m2 t ) time, s ts ) transit time, s T ) absolute temperature, K V(E) ) potential step numerical representation ) 1 in this study VO2 ) oxygen molar volume at its normal boiling temperature7 ) 25.6 × 10-6 m3 mol-1 Φ ) interaction coefficient involved in eq 13 ν ) solution kinematic viscosity, m2 s-1 η ) solution dynamic viscosity, Pa s ω ) RDE or RRDE rotating speed, rad s-1

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Received for review January 11, 2000 Revised manuscript received April 27, 2000 Accepted May 10, 2000 IE000044G