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592 P I N C H A NG A ND C. R. WILKE Vol. 59values for both nickel surfaces are compared inFig. 4. These values were one to two entropyunits lower for the unreduced surface and supportedthe content ion based on previous da ta tha t thi sunreduced surface was he most heterogeneous ofth e two t ,ypes studied. Furtherm ore, the con-figurational entropies fo r both surfaces tendedtoward zero as 0+ 0, a fact already deduced fromth e shapes of th e integral entropy curves at low 0.

The calculated Sc curves increased with in-creasing coverage and eventually exceeded themaximum possible configurational entropy, S,.F or th e reduced sample, this took place at 0 - .2and undoubtedly was evidence for the onset ofadsorbate interact ions at unusual ly low coverages.The equat ions developed by Hil l2 to t reat adsorp-tion on a h eterogeneous surface with nea rest neigh-

bor interact ion were too complex to t reat mat 'he-maticall y even if a proper dis tributio n function hadbeen avai lable. Th us i t was l ike ly tha t a mod el oflocalized adsorption on a heterogeneous surfacewithout adsorbate interact ion was not val idbeyond 0 = 0.2 and 0 = 0.5 for the reduced andunreduced surfaces, respectively.In th e presence of in teraction s a division into anon-configurational an d configurational- entr opybecomes arbi t rary. Thus, i t is difficult to interpretthe essent ial ly constant entropy values at highercoverages. These values are very near the entropyof liquid argon for both samples.Acknowledgment.-The authors gratefully ac-knowledge the financial support provided by theOffice of N av al Research , Pro ject NR -057-18 6,Con tract N8onr-74300.

SOME MEASURE,MENTS O F D I F F U S I O N I N L I Q U I D SB Y P I N C H A N G . 4ND c. R . ~ ~ I L K E

Division of Chemical Engineering, University of Calijornia, Berkeley , Calif.Rece ived No vemb er 26, 954

Diffusion coefficients for iodine and toluene in a series of satur ated hydrocarbons and for benzoic, acet,ic and formicacids in a number of organic solvents are reported. Da ta were obtained by the diaphragm cell method.Introduct ionAt the present t ime diffusion in l iquids is notful ly understood. Besides inadequ ate theoret icaldescri ption of t he liquid st at e, insufficiency ofexperimental data has const i tuted one maii idifficulty in its inves tiga t ion. Not a l l the da ta inth e l i tera ture are sufficient ly accurate, and somepertain to relat ively high concentrat ions of thesolute thereby requiring a knowledge of activitycoefficients for interpretat ion . In addit ion therehas been more extensive study of the diffusion ofvarious solutes in a given solven t tha n of a singlesolute in various solvents. Th e lat ter is desirablefor considerat ion of the role of solvent properties.This inves t iga t ion was under taken to provideaddit ional data for di lute solut ions to serve as apossible basis for th e development of im provedcorrelations of liquid diffusion.ExperimentalSolvents Used.-All solvents except normal hydro-carbons were of C. P. grade and were used without furthe rA .purification.The normal hydrocarbons were first passed through asilica gel column, and then distilled. The portion of dis-tillate having a boiling point within one degree of the boilingpoint of the pure substance was recovered for use in thediffusion studies . The viscosities of the normal hydro-carbons were measured with an Ostwald viscosimeter.Their viscosities are compared with those reported inTimmermans' as follows.

SolventViscosity ofViscosity of pure solvents atsolvent used 25O reported inat 25 ' , (2.1). Timmermans

n-Decane 0,8 60 0.853n-Dodecane 1.416 1.3 53n-Heptane 0.384 0.389%-Hexane 0.3 04 0.2 94n-Octane 0,5 09 0.508n-Tetradecane 2.12 . . .

Compounds," Elsevier Publishing Co., Inc., N ew Y o r k , N . Y.(1) T. T i m m e r m a n s , "Pliysico-chemical Constants of Pure Organic

I t is seen tha t except for n-dodecane and n-hexane viscosityvalues agree very closely with those reported in the litera-ture.B . Apparatus.-The diaphragm cell method was usedfo r measurement and its principles and technique havebeen described previouslg.2 The diaphragms had a porediameter of two t o five microns so that stirring had nodetectable effect on the transport within the diaphragms.Each of the cells consisted of a vertical glass diaphragmapproximately 3 mm. in thickness and 5 cm. in diameterseparating the cell into two compart ments having a volumeof 80-100 ml. each. Short iron rods encased in glass wereplaced in each compartment to be operated as magneticstirrers. Magnets were located suitably beneath the cellson pulleys which were rotated by a variable speed beltdrive. This arrangement provided adequate stirring t omaintain uniform concentrations in each compartment. Theentire apparatus was built in to an air-bath containing eightrotating magnets capable of simultaneous operation of fourcells. Bath temperature was controlled to f.0.1'.C . Procedure.-In treating the diffusion experiment tht,standard equation2 was used

wherep' = the cell constantDi = the integral diffusion coefficienttACi and ACr = the initial and final concentration dif-Equation 1 is based on the assumption of concentration-independent diffusion coefficients and quasi steady-stateconditions. Therefore th e diffusion coefficient obtaine!is an integral diffusion coefficient. The cell constant, p ,has to be determined with a standard substance whose diffu-sion coefficient is known as a function of concentration.For this purpose, 0.1 N KCl aqueous solution was used.For the diffusion of 0.1 N KCl solution in water until con-centrations in the two compartments are, respectively,0.075 and 0.025 N the integral diffusion coefficient is 1.870X cm.Z/sec. at 2503 and 2.093 X cm.2/sec.at 30". The value at 30' is based on diffusion da ta ob-tained partly from Harned and Nuttall3 and part ly from theextrapolation by theory of Onsager and F u ~ s s . ~ince

= time during an experimentferences

(2) A . R. Gordon, N . Y . Acad . S c i . , 46, 285 (1915).(3 ) H. .Harned an d R. L. Nuttall, i b i d . , 61,781 (19491.

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July, 1953 MEASUREMENTSF DIFFUSIONSLIQCIDS 593diffusion data 01 IiCl up to 0.1 A' solution at 4 and 25" andthe existing data at 30" agree well with the theory, thevalues obtained by extrapolation were e\pected to becorrect within their experimental error. This was evi-denced by agreement between the values of cell constantobtained at 25 ant1 30 " .For a nieasurcment, the solutions weie kept at constanttemperature in a water-bath. Either concentrated ordilute solution was charged into one compartment andapplication of vacuum t o the other comp:wtment enabledthe solution to wet and f i l l ul , the glass diaphragm com-pletely. This compsrtment \vas then filled. The othercompartment was similarly filled with the other solution,and preliminary diffusion started in order to obtain acontinuous concentration gradient of solu te across thediaphragm. For estimating the time necessary t o do so thefollowing rule2was used

-t = 1.2L2where

1 = time requiredD = diffusion coefficient of the soluteL = effective length of the diaphragmAfter sufficient tinip hnd elapsed, th c solution in each com-partment was replaced by fresh solutions and the normaldiffusion period s twted. The noi,mnl diffusion periodusually required a few days . At the end of the experiments,samples were nithdrrtnw f rom each compaitment for anal-ysis. Gen eid practice byas to run the experiment longenough so as to malie log, ( A C i ) / ( A C f ) larger than 1.2.In this case 1 % error in titration would give about 470 errorin diffusion coefficient.D. Analyses.-The analyses of solute concentrationswere pe,rfornied by t,itration with a microburet, graduated to0.02 ml. Standard solution of sodium thiosulfate of con-ceiitration 0.05 N was used for analysis of iodine, and 0.1 Nstandard solution of sodium hydroxide was used for theanalysis of the acids with phenolphtha lein as indicator.The reproducibility of this titr ation was usually =t0.15%.For th e dcterminatioii of potassium chloride concentration,standard silver nitrate solution was used. The error in thevalue of t he diffusion coefficient introduced by the ti trationwas found to depend on the time of the experiment.. I t wnsimportant to titrate solutions in one run with the samestandard solution so that the error i n stand:irtlization of thesolution, if a ny, would be cancelled out , producing noeffect on the value of diffusion coefficients.The analysis for toluene in normal hydrocarbons wasmade by means of D Beckman spectrophotometer. Theextinction coefficients were determined and found to obeyBeer's law. However, these extinction coefficients may notbe those for the pure substances, for although the solventshad been refined, there was no proof that they were chemi-cally pure. The diffusion coefficient was considered to beindependent of the extinction coefficients as long as Beer'slaw was obeyed. Values of extinction coefficients for thesolvents used are shown in Table I. The reproducibilit,yof the iipect,rophotometric reading is within 1.5%.

TABLEHYDROCARBONSEXTINCTIONOEFFICIENTS O F TOLUESE:S NORRIAL

SolventWave Mo l a lTemp., length, extinctionOC. A . coefficient

n. Hexane 23 .5 26002620

n-Heptane 23 .5 2GOO2620n-Decane 23.5 2GOO

2620n. Dodecane 23 .5 2600

2G20

185.0f . 82 0 G . 8 3 ~ 71 0 9 . i f . 11 1 2 , S f .21 0 5 . 2 f .41 0 6 . 3 f . 11 4 8 . 2 2 ~ 51 6 6 , 4 f . 6

E. Reliability of the Method for Measu rements Used inThis Investigation.-The reliability of the present method ofmeasurement was examined by the following measures:Calibrat,ion of the diaphragm cells at 25 and 30,using data of Harned and Nuttal13 for potassium chloride,1.

gives reproducible cell constaii ts. Further inore, themeasurement of diffusion coefficient of potassium chlorideat 50.9" gave a value of 3.18 X cm.2/sec. i n agreementwit11 the estr apolated value from the da ta of Harned andKuttall a t 25 and 30" Table 11).TABLE1

DIFFUSIONF 0.1 ATICC1 I N T O WATERT e p p . ,C . D X 105, ciii.?/sec.25 1.870 (Haimed and Sut,tall)30 2.093 (Harned and Nuttall)50 .0 3. 18 (This refiearch)50.9 3.2 0 (Estrapolnted v:~Iiic)

2. Measurement of the diffusion copfic4ent of hydro-chloric acid a t initial concentrat ions of 0.07 1V and zero at80" yielded a value of 3.40 X cm.*/sec. Interpolationof data of James and Gordon4at 25 and 35" gave a value of3.30 X 10-6 cm.2/sec. On the other hand, Fdinski'sdatum6 of 0.1 N HC1 diffusing into water at 16" is alsohigher tha n the interpolated value from Gordon's dntn(Table 111).T . 4 B L E 111

DIFFUSIONF 0.07 A \ HC I ISTO WATERDiffusion coefficient, D X IO $ D I I I . ~ / I S PC ,Inter-polationTemp., This froni

O C . rcsearcli Gordon Falinsk30 3 .40 3.30 , . .IG . . . 2.39 2.523. 1Ieasurement of diffusion corKcic:iit of iodine i t ibromobenzene at 30" yielded 1.394 X 10-6 cni.z/sec. whilethe ext,rltpolated value from RIillcr's data6 cnnir out to be1.39 X 10-5 cin.2/sec.-in rsorllent :tgrceinent. Diffusionof iodine i n carbon tetrachloride was also inpasured a t 30"and compared with Rliller's da ta . Table I V shows that thepresent values a t mean concentrattioils of 0.0501 and 0.0921

i at 30" are, respectively, 1.58 X l o + and 1.51 X 10-jcm.Z/sec. compared with a n extra pol at, ~d :tlue of 1.53 X10-5 cni.*/sec. from RIillei,'s da ta for diffusion from 0.095N to zero conceiit,ration in his apparatuw. Since? Millerused a different method of measurement, this integralcoefficient would not correspond exactly to one obtainedin this study with initial concentmtions of 0.005 A' andzero.TABLEV

DIFFIWOSF IODINE N CCI,A I'x 10 i rlii.?/nec.Temp. , This concn.,"C . I enenrch Niller !V

30 1.58 , . .I .5 0 , . .

0.05010.09211 5: 3 0 .048

ResultsD a t a fo r diffusion of benzoic acid, acetic acid,formic acid, cinnamic acid, toluene and iodine aretabulated in Tables V through X. The repro-ducibility of data depended upoti the durat ion ofthe experiment and the technique of t i t rat ion.The acids and iodine were t i t rated by standardsolut ions with a microburet cal ibrated to 0.02 of amilliliter. Usually three milliliters of standardsolut ions were required t o t i t rate a sample of largervolume, and i t was possible to read the buret to0.01 milliliter. Th e reproducibility was thereforewithin 0.3y0. For the diffusion measurement , th evalues of A C i / A C f were usually around 1.4. Sincethe diffusion coefficients depended 011 the logarith-

(4 ) W . A . James and A. R. Gordon, J . C hem. P h y s . , 7 , 9G3 (1439).(5 ) AT . Falinski, Cor n pl . rend . , 218, 754 (1944).(6 ) C . C. hliller, P roc . Rou. Soc. ( L o n d o n ) ,106, 724 (1024).

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59 4 PIX HAR'GX D C. R. W I LK E T'ol. 59

9011en tCarbon

tetra-chloride

Benzene

Toluene

.dicetone

Ethyleneglycol

TABLE.'DIFFUSIONF BENZOICkC'ID

Viscosity Init ial cellD X lo', of solvent coinliartnient concn.,cin.2/sec. q X 102, poise g. mole/l.14.8 0.7825.0 0.914 0 . 5 1.1715.0 1.1725.0 1.8840.0 1.7616.0 1.2925.0 1.4940.0 I .8513.2 2.3725.0 2 .6240.0 3.0550.0 0 .18 (+lo% )25.0 0 . 0 4 3 (f 0%)

TABLEIDIFFUSIONF ACETICACID^

Diffusion Viscositycoefficient of solventTemp. , D X 105, 7) X ,102, D q / T XSolvent OC. crn.z/s ec. poise 1010Carbon 6 . 5 1.15 1.201 4.94tetra- 14.8 1.27 1.052 4.63

chloride 25.0 1.49 0,907 4.5340.0 1.78 ,736 4.18

Benzene 25.0 2.09 ,603 4.225 . 9 1.58 ,817 4.62

Toluene 25.0 2.26 ,552 4.1915.0 1 90 ,620 4.106 . 8 1.66 . i o1 4 . 1 6

Acetone 40.0 4.04 ,268 3 . 4 525.0 3 .31 ,312 3.4615.0 2.92 .337 3.41

Ethylene 15.0 0.039(&lo%) 26.09 3.5glycol 25.0 0 .13 (&lo%) 17.33 7 .4

30.0 0.20 (kklO%) 13.35 8 . 85 Initial cell compartment concentrations approximately0.003 and 0 mole fraction.

TABLEI1DIFFUSIONF CINNAIUC CID

D X Viscosity Initial cell105 of solvent compartmentTeinp., crn.i/ q X, 102, concn., D v / TSolvent '(2, see. poise g. mole/l. X 1010Carbon tetra-

chloride 25 0.70 0.907 0.03501 0 2.30Benzene 25 1.12 ,599 .03922 0 2 . 2 5Toluene 25 1. 18 .552 ,03230 0 2.18Acetone 25 2 .4 1 ,312 ,04915 0 2.52

TABLEI11DIFFUSIONF TOLUENE

Viscosityof sol\-entTenip., D X 105, v X,102. D q / T XSolrent "C. C I I I . ~ / S ~ C . poise 10'0n-Hexane 25 .0 4.2 1 0.304 4.13n-Heptane 25.0 3.72 0.3 84 4.80n-Decane 25.0 2.09 0.8 60 0.04n-Dodecane 25.0 1.38 1.416 6 .54n-Tetra-

decane 25. 0 1.02 2.120 7.23n-Hept ane G . 9 2.05 0.469 4 . 9 4

40.0 4.33 0.333 4.60

1,0480,907

,732.696.503,497,620,552.471.342,312,268

17.336.62

0.07389 0,07227 0,07218 0,090GO 0.00061 0,09052 0,03195 0.OR195 0,03018 0,05089 0.05099 0.05088 0,05933 0,00048 0

TABLEXDIFFUSIONF FORMICCID"

D v l T X10'02.822.762.742.832.792.782.762.772.782.822.752.732.493.77

Diffusion Viscositycoefficient of solventTemp., D X 106, q X,102, D q / T XSolvent OC. cm.2/sec. pome 10'0Carbon 8 . 5 1 .6 1 1.163 (3.05tetra- 25.0 1.89 0,907 5.74

chloride 15.0 1 67 1.048 6.08Benzene 6. 2 1.9 9 0.815 5.81

13.9 2.31 .712 5.7 225.0 2. 28 ,603 5.21

Toluene 6. 2 2.28 ,706 5.7 714. 1 2.46 .G35 5. 4425.0 2.65 ,552 4.90

Acetone 2 5.0 3 .77 ,312 3.9 413.5 3.27 ,346 3.956. 5 3.13 .370 4.14

Ethylene 25.0 0.094 (& lo %) 17.33 5 . 5glycol 50.0 0.22 (=!= lO%) 6.62 4. 4

a Initial cell compartmen t concentrat'ions approximately0.003 and 0 mole fraction.TABLE

DIFFUSIONF IODINEN VARIOUS ORGANICSOLVENTSD X Viscosity Init ial cell105, of solvent compartmentTemp., cm.z/ q X.102, concn., D v / TSolvent O C . sea. poise g. mole/g. X lo io

n-Tetra- 25 0.96 2.120 0.007745 0 6 .81%-Octane 15 2.43 0.579 0.04220 0 4.89

25 2. 76 0,5 08 ,04210 0 4.7140 3. 22 0.417 ,04231 0 4.29

n-Hexane 25 4.24 0.304 .05600 0 4.31Cyclo- 15 1.54 1.050 ,06389 0 5.65hexane 30 1. 92 0.820 ,06334 0 5.2140 2.3 0 0.703 ,06383 0 5.17

hZet,hylcg- 40 2.71 0.549 .04422 0 4.74clohexane 30 2.30 0.639 ,04421 0 4.86Et,hj,l 40 1.77 0,821 ,1164 0 4.65alcohol 25 1.32 1.065 ,1105 0 4.71

Broino- 30 1.30 0.085 ,03043 0 4.53benzene

Carbon 30 1. 63 0.83 9 ,01450" 4. 57tetra- 1. 61 ,03622"chloride 1. 58 05005"

,09205"

decane

Q Average concentration over both compartments duringthe diffusion measurement.

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J u ly , 1955 ME.4SlTREMENTS O F DIFFLTSIOSN LIQUIDS 59 5mi c v alu es of ACi/ AC f, a reproducibility within1.5% frequently was obtained, in fact , wi th inlYc i n man y measurements.F o r diffusion in very viscous solutions, forexam ple th e diffusion of ac ids in ethy lene glyco l,the data , were not espe cted to be accu rate becauseof the slon diffusioii rate and resulting small con-tration changes during an experimeiit . Theywere expecbed to be good wit'liiii 20:7,, however.T he diffusion of toluene at 23" in varioiis normalhydrocarbons was tudied. -1nalyses by the Beck-man spectrophotomet'er were reproducible to mith-i n 1.5%. W ith a value of ACi/ACf equal to 1.5,t,liis repro duci bility shou ld g5ve an accu racy of*2y0 for the diffusion coefficient. No duplicater u n s were made in normal hydrocarbons becauseof t8h e imited am ou nt of solve nts.

DiscussionData \ \ .e re ta lmi a t var ious temperatures formost of th e system s. It was of particular interestto examine the group D q / T which according t'obot8h he Stokes-Einstein equation and the Eyringtheory should be essentially independent of

t'emperature.T h e D q / T groups fo r benzoic acid diffusion incarbon tetrachloride, benzene, toluene and acetonedo not vary by more than .57, over a fairly widerange of temperature. Benzoic acid has ananomalous behavior in ethylene glycol, as showiiby the appreciable c,hange of D q l T with tempera-t 'ure (Table TT) . This does not seem to be a t -tr ibutable t o inaccuracy of th e results a s mentionedin th e preceding section. However, it is not sur-prising i n view of the complicated hydrogen bond-ing s tructure in ethylene glycol which may changei n character wi th temperature .Es ce pt fo r the syst'ems of ace tic acid in acetoneand toluene and formic acid in acetone, formic acidand acetic acid do not give constant values ofD v / T . This is possilily due to some complicat.ionfro m mole cular a'ssociatjon of formic an d aceticacids.In an adjunct paper8 the au thors l ia\ ,e esamineda large body of data and proposed an empiricaleq ua tio n for estimatio n of diffusion coefficientswhere

D = diffusion coefficient, cm.Z/sec.T = temperature, "I

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59 6 K . BRIL,S. BRILA N D P. K R U M H O L Z Vol. 59Hilde brand and previously suggested to be a factorin iodine diffusion by Hammond and Stokes.12From the foregoing discussion i t is evident th ata further theoret ical approach is needed whichadequately accounts for specific interactions ofsolvent and solute molecules to serve as a basis forimprov ement of emp irical relations such as equa-

(11) H. .4. Bcnesi and J. H. Hildebrand, J . A m . C h e m . SOC., 1,(12) H. R . Hsinmond and R. H. Stokes, Trans . Faraday Soc., 49 ,

2703-2707 (1040).886 (1953).

tion 2. Although not entirely satisfactory, theassumption of c ons tanr y in D v / T appears to pro-vide a fair representation of the t empera ture de-pendence. Equat ion 2 is considered to be usefulas a first approximation for engineering design andcertain other purposes for u-hioh moderate pre-cision ma y be sufficient.Acknow ledgment.-Assistance of Research Co r-poration through a grant-in-aid is gratefullyacknowledged.

THE KINETICS O F DISPLACEME,R;T REACTIONS INVOLVING METALCOMPLEXES O F ETHILENEDIAMINETETRAACETIC ACID

BY I