The Diffusion Coefficient of Ferricyanide Ions in Aqueous Potassium ...

The Diffusion Coefficient of Ferricyanide Ions in Aqueous PotassiumChloride Solutions with and without Polyethylene Oxide AdditionBruin Roffel" and Jan J. van de GraafChemica! Engineering Research Group, Council for Scientific and Industrial Research, Pretoria 000 1, South AfricaThe diffusion coefficient of ferricyanide ions in aqueouspotassium chloride solutions containing up to 1000 ppm ofpolyox has been determined using the rotating diskelectrode. Correlations for viscosity and density as afunction of temperature are given and results are discussedin terms of the Einstein-Stokes ratio.Diffusion controlled mass transfer rates in flow systems mayconveniently be studied by determining current densities atconcentration polarized electrodes imbedded in the transfersurfaces (4). Such electrolytic systems find increasing applicationin determining local transfer rates in complicatedgeometries and are used as mass transfer analogues in the studyof heat transfer problems.A commonly used electrolyte is a dilute equimolar solutionof potassium ferri- and ferrocyanide in a 1 or 2 M solution ofsodium hydroxide (4). The sodium hydroxide acts as a carrierelectrolyte; at the potentials used, the currents are determinedsolely by the diffusion rate of ferricyanide to the cathode andferrocyanide to the anode.To convert the measured currents to significant transfernumbers it is essential to have reliable data for the physicalproperties-diffusion coefficient, viscosity and density-of theelectrolyte solution. A considerable amount of data has beenpublished for the ferro-ferricyanide-sodium hydroxide system(4).It is sometimes desirable to use a carrier electrolyte other thansodium hydroxide. Thus, although it is corrosive, potassiumchloride may be used, if a neutral pH is required; it requires fewersafety precautions than sodium hydroxide. For instance, if masstransfer rates are to be determined in the presence of drag reducingpolymers, potassium chloride is preferred because manypolymers are degraded by sodium hydroxide (2).Experimental TechniqueFor the rotating disk electrode an electrode to disk diameterratio of 1 to 3 was selected. The electrode diameter was 3 mm.The electrical contact to the spinning electrode was made byusing a mercury/platinum contact: a graphite brush was unsatisfactoryas a change in resistance with time was recorded. Therotation speed of the disk was constant at 750 rpm f0.2%.All solutions were stored in black painted glass vessels toexclude light, which slowly degrades the ferricyanide ion. Solutionswere prepared using Merck analytical grade reagents,dissolved in deionized water ( 7). The solutions were purged withnitrogen for 1 h and during measurement they were kept undera nitrogen pressure blanket with a bleeding valve. The nitrogenwas first bubbled through distilled water for saturation, becauseotherwise a change in concentration of ferricyanide was foundduring a day's measurements.Temperature was controlled to within 0.1 OC by using athermostat bath, covering a temperature range from 20 to 35OC.Platinum foil, with a surface area far in excess of that of thedisk electrode, and a saturated calomel electrode were used asanode and reference electrode, respectively.Before each run the disk electrode was cleaned with softpaper.The potential was increased continuously at a rate of - 1 mVs-' until -500 mV to the calomel reference electrode wasreached.The concentration of ferricyanide was determined by potentiometrictitration (2) using isonicotinic acid hydrazide (isoniazid).The average ferro-ferricyanide concentration was in the orderof 5 mol m-3.The apparent viscosity of the solutions was determined withan Ostwald type viscometer, the density by using a pycnometer.The average molecular weight of the polyethylene oxide, asgiven by the supplier, was 4 X lo6.ResultsThe diffusion coefficients were obtained from Levich'sequation (3):For the meaning of the symbols the reader is referred to theglossary.The viscosity and density of the solutions may be calculatedfromand@ = (CY, - In t)/n2 kg m-ls-l (2)p = ($, - In t)/& kg m-3 (3)where N and 0 are given in Tables I and II for the various solutions.The concentration of potassium chloride is indicated byC,; the concentration of polyethylene oxide with Cp and thetemperature t is expressed in degrees Celsius.In Tables 111 and IV and Figures 1 to 3, the results are given interms of Einstein-Stokes ratios.In order to compare this work with the results of Arvia et al.( I), three different ratios are calculated: R1, R2, and R3, definedby eq 4-6Table 1. Constants for Correlation of Viscosity Data0.51 .o2.01 .o1 .o1.01 .o1 .o1.01 .o1.01 .o1 .o1 .o0001025507510014020035050075010005.12435.13555.23885.08215.02974.94404.95374.99515.03915.17664.88425.01044.72614.53472123.072134.502215.372049.861965.151829.101810.531829.101774.501770.101340.881280.85885.05646.370.150.040.100.110.060.060.040.110.250.290.100.300.190.33300 Journal of Chemical and Engineering Data, Vd. 22, No. 3, 7977

Table II. Constants for Correlation of Density Datacc 1 e,kmol m-3 dl 32 YO05 117 483 0 1049 010 02 $210 122 648 0 114320 138 279 0 1321 0 01&p= 30Table 111. The Dp/ T Ratio for Various Solutions and Temperatures inthe Range from 20 to 35 OCc, cp, ioi5 R ~ , 1015 R~ 1015 R~ 1kmol m-3 ppm kg m s-* K-’ kg m sC2 K-’ kg m s - K-’ ~-ftI5200 PPM140PpMLP TO IOOPPM05 0 2 29610 0 2 259J28 3620 0 2 256‘ernperoture “C10 10 2 187 2 156 2 16310 25 2 290 2 228 2 241 Figure 1. Einstein-Stokes ratio as a function of temperature1.0 50 2.220 2.092 2.1171 .o 75 2.345 2.174 2.2071.0 100 2.262 2.072 2.1061.0 140 2.456 2.086 2.1161.0 200 2.700 2.087 2.1931.0 350 2.955 1.994 2.158although we would prefer the use of R, only.Arvia et al. ( I) relate the different ratios to the average radiusof a solvodynamic unit.The viscosity pels stands for the real viscosity of the solutionwith polymer; the viscosity pc stands for the viscosity of the samesolution without polymer.The diffusion coefficient D, is calculated from eq 1 by usingthe kinematic viscosity and current for the solution with polymer;the diffusion coefficient D,, however, is calculated by using thekinematic viscosity for the solution without polymer and thecurrent for the same solution with polymer.For polymer solutions up to 350 ppm the Einstein-Stokesratios R1, RP, and R3 are constant over the whole temperaturerange from 20 to 35 OC, as can be seen from Table 111.From Table IV it can be seen that at higher polymer concen-10 100 1000ppm po0ror -Figure 2. Einstein-Stokes ratio as a function of the polyethylene oxideconcentration.trations these ratios are temperature dependent.In Figure 1, R, is given as a function of temperature for differentpolymer concentrations.The dependence of R on the polymer concentration can beseen from Table 111 and Figures 2 and 3.Up to 100 ppm the ratio R1 is independent of the polyoxTable IV. The Dp/T Ratio for High Concentrated Polyox Solutions, at a Potassium Chloride Concentration of 1.0 kmol m-3Cf. CP . T, 1, 10” D,. 10” D, 10’5 R’, 1015 R2, 10’’ R3.mol m-3 ppm OC PA m2 s-’ m2 s-l kg m s - ~ K-’ kg m s - ~ K-’ kg m s-’ K-’4.69 500 20.8 1244.69 500 23.7 1324.69 500 24.4 1334.69 500 26.6 1404.69 500 28.0 1434.69 500 31.2 1524.69 500 33.8 1604.69 750 18.6 1114.69 750 21.0 1164.69 750 24.8 1234.69 750 26.8 1264.69 750 29.5 1314.69 750 35.0 1414.56 1000 17.0 1004.56 1000 199 1044.56 1000 23.4 1104.56 1000 27.0 1144.56 1000 30.4 1204.56 1000 35.0 1246.5187.0477.0907.5817.7648.3478.8755.9276.2236.6236.7787.0647.6275.6345.8336.1766.3416.6806.7865.8306.3046.3546.7846.9537.5048.0095.0055.2745.6425.7915.5386.5964.5074.6985.0135.1935.5165.6743.4203.4243.3923.4313.3873.3353.3004.1404.0223.8073.6733.5333.2755.1154.7574.4544.0513.8163.3381.9541.9621.9461.9691.9511.9591.9791.7791.7571.7081.6711.6431.5851.67716111.5711.4921.4661.3642 1852 1952 1711968195119592 1902 1062 0732 0051956191618332 0962 0001935182116121632Journal of Chemical and Engineering Data, Vol. 22, No. 3, 1977301

10 I00 1000ppm POIYOXFigure 3. Einstein-Stokes ratio for different polyox solutionsconcentration; the ratios R2 and R3 are independent up to 350ppm. The results can be summarized by: for 20 < t < 35 OC, Cp5 100 ppm:DsFslT = (2.27 f 0.09)10-15 kg m sT2 K-'for 20 < t < 35 OC, Cp < 350 pprn:andDcyclT = (2.1 1 f 0.12)10-i5 kg m s-* K-lD,p,l T = (2.16 f 0.08)10-15 kg s - ~ K-'c(7)For higher polymer concentrations the Einstein-Stokes ratiobecomes temperature and concentration dependent, and mustbe obtained from the results presented in the tables and figures.DiscussionThe value of the Einstein-Stokes ratio for aqueous potassiumchloride solutions without polymer addition is, according to TableIll, found to be (2.28 f 0.08)10-15 kg m s - ~ K-'. Arvia et al. ( 7)found in this case a value of (2.00 f 0.12)10-15 kg m K-l,hence a difference of about 14%. One explanation for this differencemay be the fact that Arvia et al. used an electrode to diskdiameter ratio of about 1 to 1.15, although a ratio of at least 1to 2.4 is recommended (4). In our study we used a 1 to 3 ratio.For the diffusion coefficient in carboxymethyl cellulose solutionsArvia et al. found that the value of R3 was constant for the wholerange of polymer solutions between 0.2 and 1.6% CMC, at (2.13f. 0.31)10-'5 kg m s-* K-I. In our investigation we found aconstant value of R3 equal to (2.16 f 0.08)10-15 kg m K-l,(8)(9)only when the polyethylene oxide concentration was below 350ppm. For more concentrated polymer solutions the ratio R3became temperature and concentration dependent.Although the accuracy of the determination of the diffusioncoefficient by Arvia is within 15 %, our data are accurate within6%.The measured diffusion coefficients are not the true binarydiffusion coefficients (n2 diffusion coefficients are required todescribe isothermal diffusion in a system with n solute components)but they are the correct ones to be used in the evaluationof the results of electrochemical studies of transfer problems.Besides, as the concentration gradients of the shared counterions(K') and the coions (GI-), both present in large excess arenegligible or zero, respectively (only the ferricyanide ions producedat the electrode would cause a gradient for this coion),we consider it reasonable to treat the system as if binary diffusionwere occurring.GlossaryA area, m26 constantC concentration, kmol m-3D diffusion coefficient, m2 s-lF Faraday constant, C kmol-Ii current, AR ratio Dp/ T, kg m s-~K-It temperature, OCT temperature, OK(Y constant in eq 2P constant in eq 3t errorP viscosity, kg m-l s-'U kinematic viscosity, m2 s-lP density, kg m-30 angular velocity, rad s-'SubscriptsCflimPSLiterature Citedsolution without polymerferricyanidelimitingpolymersolution with polymer(1) Arvia, A. J. et al., Electrochim. Acta, 13, 81 (1968).(2) Hicks, R. E., Pagotto, N., CSlR Rep., (Pretoria), CENG M-024, Feb 1974.(3) Levich, V. G., "Physico-chemical hydrodynamics", Prentice Hall, EnglewoodCliffs, N.J., 1962.(4) Opekar, F., Beran, P. J. f/ecfroana/. Chem., 69, 37 (1976).Received for review October 11, 1976. Accepted March 21, 1977302 Journal of Chemical and Engineering Data, Vol. 22, No. 3, 7977