Liquids in Solution

(13) jest, w., “ ~ i f f ~ ~ i ~ ~ and chemisehe Reaktion in Featell Stoffe. (14) Michel, A,, Bbnard, J., and Chaudron, G., Bull. SOC. chim., [5]. (...
0 downloads 0 Views 523KB Size
Download PDF
INDUSTRIAL AND ENGINEERING CHEMISTRY

M a r c h 1951

LITERATURE CITED

(1) Bbnard, J., Bull. soc. chim.France, 1949,73--87. (2) BQnard,J., J . chim.phys., 44,266-8 (1947). (3) BQnard, and Chollet-Coquello, 0.9 Rev. mdt.9 43,113 (1945). (4) Chaudron, G., B u l l . SOC. chim. belo.. 44,339 (1935). (5) Chaudron, G., Mdtauz & corrosion, 17,37,155 (1942). (6) Chaudron, G., “Proceedings of Pittsburgh International Conference on Surface Reactions,” Pittsburgh Corrosion Publishing Co., 1948. (7) Chipman, J., and Murphy, J. W., IND. ENG.CKEM.,25, 319-27 (1933). (8) Goldschmidt, H.J., J . I r o n Steel Inst., 146, 157-80 (1942). (9) Gulbransen, E.A., J . Applied Phys., 16,718-24 (1945). (10) Gulbransen, E. A., Rev. Sci. Instruments, 18,546-50 (1947). (11) Gulbransen, E.A., and Hickman, J. W., Metals Technol., 13,NO. J.9

a

703

7; Am. Inst. Engrs., Iust. Metals Div., Tech. P u b . 2068 (1946). (12)Jackson, R.,and Quarrell, A. Q., Iron and Steel Inst., Spec. R e p t . 24,65-104 (1939). (13)jest, w., “ ~ i f fand ~ chemisehe ~ i ~ ~ Reaktion in Featell Stoffe 1937,”pp. 166-8,Ann Arbor, Mich., Edwards Bros., 1943. (14) Michel, A,, Bbnard, J., and Chaudron, G., B u l l . SOC. chim.,[5] 11,175(1944). (15) Pfeil, L. B., J . I r o n SteelInst., 119,501-47 (1929). (16) Ibid., 123,237-55 (1931). (17) Tesche, 0. A., Am. Soc. for Metals, Preprint 12, Fall Meeting (1949). (18) Valensi, G., “Proceedings of Pittsburgh International Conference on Surface Reactions,” pp. 156-65, Pittsburgh Corrosion Publishing Co., 1948. R E C ~ I Y EApril D 25, 1950. Scientific Paper 1514.

Diffusion Coefficients of Organic Liquids in Solution FROM SURFACE TENSION MEASUREMENTS R. L. OLSON1 AND J. S. WALTON, Oregon State College, Corvallis, Ore.

* *

There is no general theoretical method for predicting liquid diffusion coefficients and a method for estimating them would be useful for many engineering purposes where experimental data do not cover the system in question. A method is proposed using surface tension measurements for the estimation of diffusion coefficients of organic liquids in water solution. The proposed correlation fits

the available data with an average accuracy of 25%. Approximate methods are suggested to allow for the variation of diffusivity with temperature and for the variations encountered in different solvents. Included in the discussion is a brief treatment of a theoretical equation for the diffusivity of electrolytes in dilute solution. The methods of estimating diffusion coefficients should be useful in engineering design and in research.

L

A method for the estimation of liquid diffusion coefficients has been developed by Wilke (9). The group T/qD is plotted aa a function of the solute molal volume with different curves for different solvents. The method has a u average accuracy of 10% and can be used for a wide variety of solutes. The relationship presented here is limited t o organic liquids in dilute water solutions, but it correlates the known experimental data used in formulating i t with about 2% average deviation. Approximate methods are given to extend the relationship to solvents other than water. Inasmuch as neither the proposed method nor others mentioned here give satisfactory results for the diffusivity of electrolytes in solution, a later section of this paper discusses briefly the applicability of a previously published theoretical equation for electrolytes.

IQUID diffusion coefficients are used in calculations related to diffusional operations such a s absorption and extraction. The state of development of the kinetic theory of liquids does not permit the use of general theoretical equations for liquid diffusion coefficients. Because the experimental determination of these coefficients requires much tinie and great care, the literature contains few data on the subject, and more often than not the data for the system or the conditions at hand are not available. In such circumstances a reasonably accurate estimation of the diffusion coefficient would be useful. Theoretical equations for the diffusion coefficients of electrolytes in dilute solution and of colloidal particles in solution have been derived. However, for other solutions semitheoretical or empirical correlations must be employed. These should express the diffusivities as a function of some easily determined variables. Several such methods are available in the literature for the prediction of liquid diffusion coefficients in the absence of experimental data. An early empirical equation by Thovert (8) expressed the diffusivity a s a function of the viscosity of the aolvent and the molecular weight of the solute.

D ? d % = constant

(1)

This equation, while easy t o use, gives only a rough approximation. Arnold (1)presented an equation based on a modification of the kinetic theory of gases. While this equation has a theoretical basis and gives satisfactory results, it is difficult to use because of the amount of data required. 1

Present address, General Electric Go., Hanford Works, Richland, Wash.

DISCUSSION

I n water solutions of organic liquids the surface tension ia observed t o be lower than would be expected, considering the surface tension of the pure liquids and their concentrations. For example, a 1% by weight solution of n-butyl alcohol in water st 20” C. has a surface tension of 53.0dynes per cm. At the same temperature water and *butyl alcohol have surface tensions of 72.7 and 24.6 dynes per cm., respectively. This greater than expec,kd surface tension lowering may be explained b y the fact $ha% the alcohol concentrates at the surface to lower the surface energy of the system. It is postulated t h a t the entire surface is not alcohol and the surface energy not a mipimum Because diffusion opposes the concentration of the alcohol a t the surface. This leads t o the hypothesis that the lowering of the surface tbnsion of water solutions by organic liquids is related to the

704

INDUSTRIAL AND ENGINEERING CHEMISTRY

Figure 1. Correlation of Diffusion Coefficients for Organic Liquids in Water Solutions with Surface Tension Data D (sq. om. per second), diffusion coefficient, is a t 1.5' C. y (dynes per cm.), sur-

face tension of pure organic liquid, is a t 20" C. Ay/Ca (dynes-liter per em.mole), slope of surface tension lowering-concentration curve a t low concentraion8,is a t 15' C., b u t is nearly independent of temperature. Small numbers by each point indicate surface tension of pure organic liquid.

ability of the solute to diffuse through water; and that a t the same concentration those solutes with lorn ability to diffuse should lo~versurface tensions of their solutions more than solutes with higher diffusivities, even though the solutes themselves have the same surface tensions. The diffusion coefficient for liquids is usually defined by the equation for the steady-state diffusion of a solute through a stagnant solvent ( 7 ) .

thirteen additional points with estimated diffusion coefficients obtained by using the correlation of Wilke (9) substantiate the position of t,he curves. While the hypothesis used here to explain the behavior of the surface tension of aqueous solutions of organic liquids is supported by the correlation obtained, the primary purpose of this paper is to present a useful method, and not necessarily to demonstrate the validity of the hypothesis. Another theory or other theories may also fit the facts. Effect of Temperature. The effect of temperature on diffusion coefficients of liquids has been correlated by the group Dv/l' which is essentially independent of temperature, as has been shown by Wilke (9). This relationship is based on the well known StokeE-Einstein equation for the diff usion coefficient of large spheres diffusing through a niedium of small particles, such as colloidal particles through a liquid. The StokesEinstein equat,ion is (4)

This equation gives good results for colloidal particles, and the group Dq/T is seen to be constant for a given colloid. Although the equation is not rigidly valid for molecular diffusion, the fact that the group DvlT is approximatply constant for molecules is useful. (See Table I.) By plotting DvIT in place of D,the graph may be used for obtaining diffusivities for any temperature. This is done in Figure 2. As an alternative method, D from Figure 1, a t 15" C., may be converted to the desired temperature by thc relationship =

Because CA, the concentration of the solute, is usually small compared to CB, the concentration of the solvent, the equation is often simplified. (3)

Because the diffusion coefficient is a measure of the ability of the solute t.0 diffuse through the solvent, it should be related t o the lowering of the surface tension for the case of organic liquids in n-at,ersolutions according to the hypothesis used here. A majority of the diffusion coefficients in the literature have been determined for very dilut'e solutions; so the surface tension Ion-erings should be compared a t some Io\\- concentration. In very dilute solutions the surface tension varies linearly with concentration ( 6 ) . The surface tension lowering a t a specific low concentration is then given by the product of the slope of the surface tension lowering-concentration curve and t,he cmcentration. The concenbrat'ion being constant, the multiplication may be omitted and the slopes used as the variable. Another variable t o be considered in correlat,ing diffusivities is the surface tension of the pure orgsnic liquid. Two organic liquids with different surface tensions will not lom-er the surface tension of a water solution the same amount, even if their concentrations and diffusivities are the same. When diffusion coefficients, as obtained from the literature, are plotted against the slope of surface tension lowering-concentrstion curves a t low concentrations, a family of curves is obtained for variations in the surface tension of pure organic liquids as in Figure 1. The curves for y = 50 and y = 60 are based on only one point and the shape and spacing of the other curves. They were included not only t o extend the range of the correlation but a,lso to show t h a t glycerol does not, contradict the hypothesis. I n all, only ten points based on previously published avzilable experimentally determined data are used; however,

Vol. 43, No. 3

constant

(5)

Prediction of Surface Tensions of Solutions. Surface tensions of the pure organic liquids a t 20" C . are used for both Figures 1 and 2. These data are available in handbooks, International Critical Tables, and other published sources. The data, to construct a surface tension-concentration curve are not as plentiful; hoxever, a relationship has been worked out by Langmuir ( 6 ) which makes it possible to predict the slope concentrations from the molecular formula of the organic liquid. By applying LIaxuweIl's distribution lam, t h r Gibbsequationfor the excess of the solute a t the surface of the solution, and a representative thickness of the surface layer, Langmuir -as able to calculate

W

Figure 2. Correlation of D q / T for Organic Liquids in Water Solutions with Surface Tension Data Qrnuu Dn/T (sa. cm.-centiDoises uer second. K.). ia essenLiallv indeDeiident of y (dynes per ern.), surface t.ension of pure organic liquid, is at 20' C. Ay/Ca (dynes-liter per cm.-mole), slope of surface tension lowering-concentration curve a t low concentrations, is a t 1.5' C.. b u t is nearly independent of temperature.

March 1951

INDUSTRIAL AND ENGINEERING CHEMISTRY

the difference in potential energy t h a t must exist between the surface layer and the main body of the solution for the different concentrations to remain in equilibrium. The potential energies were found to be additive for each additional CH2 group, and the potential energy for any compound could then be found by the equation E = Eo 625%

+

705

TABLE I. EFFECT OF TEMPERATURE ON DIFFUSION COEFFICIENT OF

Temp.,

O

C.

ACETICACIDIN WATER

D x 105, Sq. Cm./Sec.

Cent%oises

9.0 12.5

17.0 18.0

Langmuir's final equation for calculating E is

(7) and this equation is useful because A ~ / C is A the slope of the surface tension lowering-concentration curve a t low concentrations. Solving for the slope, 7?

i.

TABLE 11. VALUESOF EO Type Tertiary alcohol Normal alcohol Amine Ester Acid Ketone

c

EO 210

- 510

-700 -400 - 800

TABLE 111. ESTIMATED DIFFUSIONCOEFFICIEKTS FROM FIGURE 1 The sloDe can now be calculated by means of Equation 8, the value of E D X 10: y(200 C.) C A (Obsd.) c 9 (Calcd.) (Obsd.Ia (Est.) Solute being determined from Equation 6 with 22.6 11.0 10.3 1.28 1.26 Methyl alcohol the aid of Table 11. With A ~ / C Athus 33.9 22.3 E t h y l alcohol 33.4 1.00 1.04 98.0 23.8 0.87 102.0 0.87 n-Propyl alcohol determined, or obtained from actual 22.8 310 0.77 312 0.77 Isobutyl alcohol data when available, and y a t 20" C. for 23.8 910 0.68 Isoamyl alcohol 910 0.69 8.0 7.8 37.6 0.99 1.04 Formic acid the pure organic liquid readily available 27.0 27.7 0.97 26.1 0.97 Acetic acid 3.8 46.7& 0.91 3.8 0.96 Acetamide in the literature, the diffusion coefficient ... 0.74 128.0 0.71 40.9 Phenol a t 15' C. can be estimated from Figure 46.0 0.90 50.0 25.8 0.93 Allyl alcohol 0.28 . . . 0.72 63.4 0.75 Glycerol 1, or from the group D q / T , which is esa All diffusion coefficients are in very dilute solutions except acetic acid, which is for 0.01 IM. sentially independent of temperature, F r o m extrapolation of surface tension d a t a t o 20' C. from Figure 2. The values of A ~ / C A from Equation 7 and on Figures 1 and 2 are a t 15" C. However, this term The results of this method are seen to be in fair agreement is nearly independent of temperature, at least over the range with the observed diffusivities and can be used when no better of 15' to 35" c . method is available or where an approximate value is sufficient. Results of Correlation. The results of this method of estimatAnother less satisfactory approximate method of estimating ing liquid diffusion coefficients are given in Table 111, together diffusivities in different solvents is to assume t h a t the group with observed values (4). Values of A ~ / C Afrom actual data D q / T is constant for all solvents. This is a n application of were used in the estimation, and the calculated values are listed Thovert's (8) empirical equation (Equation 1). T h a t this is only for comparison. a rough approximation is seen from Table V. All estimated values are seen to be in good agreement with Effect of Concentration. The scarcity of data makes a study of the observed results. the effect of concentration on liquid diffusion coefficients difficult. The surface tension approach to diffusion coefficients is most The available data indicate that these coefficients do not vary applicable to organic liquids-water solution, and would not be greatly with concentration in dilute solutions, but that there is a expected to give as good results for other systems. Because of slight decrease with concentration increase for organic liquids in the large differences between the surface tensions of most organic water. For acetic acid D X 106 changes from 0.99 to 0.89 as liquids and water, the surface tension lowering in these solutions the concentration varies from 0.01 to 0.10 M. is pronounced and is therefore relatively easy to measure. When the surface tensions of the solute and solvent are nearly the same, the concentrating a t the surface of the component with the PREDICTION OF DIFFUSION COEFFICIENTS FOR lower surface tension is slight. ELECTROLYTES Solid Solutes and Other Solvents. Surface tensions t o be used As indicated previously, theoretical equations exist for the with Figures 1 and 2 for substances that are solid at 20" C., yet prediction of diffusivities of electrolytes in dilute solutions and of soluble in water, may be estimated by extrapolating the surface colloidal particles in solution. The well known Stokes-Einstein tension data down to 20" C.-for example, the surface tension of equation for the diffusivity of a colloidal particle has already been acetamide a t 20' C. by extrapolation is 46.7 dynes per em. discussed (Equation 4). A theoretical equation for the diffusion The estimated diffusivity is within about 5y0 of the observed coefficients of electrolytes in dilute solution, which has received value a s shown in Table 111. little attention in recent reference works, has been derived by While correlations such as these of Figures 1 and 2 cannot be Nernst (6). This equation for 1to 1electrolytes is constructed for other solvents, the diffusion coefficient of organic liquids in other solvents can be estimated if the diffusivity of one .substance in the solvent is known. The ratio of the unknown to the known coefficient in the solvent is approximately equal to the ratio of the coefficients of the same compounds in water (9). The equation for the general case has been published by Has(9) kell ($).

ar

4

(Calories per gram per mole) EO Type 950 Aldehyde 575 Amide 600 Dibasic acid or 470 alcohol 437 Double bond 295 OH on acid

Examples of the accuracy of the method are shown in Table IV.

INDUSTRIAL AND ENGINEERING CHEMISTRY

706

TABLE IV. ESTIMATION OF DIFFUSIOIV COEFFICIENTSIN ORGANIC SOLVENTS

D x

Solute

105

Solvent (Obsd.) Methyl alcohol 1.80a Allyl alcohol Methyl alcohol 1.40 Phenol Methyl alcohol 1.62> Propionic acid 1.920 Acetic acid Benzene 1.48 Iso-amyl alcohol Benzene 1.60 Propyl alcohol Benzene a Taken as known diffusivity for methyl alcohol. b Taken as known diffusivity for benzene.

D x 105 (Est.) 1 32 1 65

...

1.34 1.68

Vol. 43, No. 3

Nernst’s equation for the calculation of the diffusivities of electrolytes includes the temperature not only as the absolute temperature but also in the equivalent ionic conductances, which vary with temperature. However, a s the equivalent ionic conductances may not be available a t the desired temperature, a method of predicting the change in diffusivity with temperature would be useful. The group Dq/T is essentially independent of temperature and may be used for this prediction as a reasonably satisfactory approximation. CONCLUSIO~S

OF SOLVENT ON DIFFUSION COEFFICIENT TABLE V, EFFECT

(Solute, isoamyl alcohol, T = 288’ K.) Solvent Water Methyl alcohol Benzene

7,

Centipoises

1.145 0.642 0.701

$x

D X IO5 0.69 1.34 1.48

108

2.74 2.99 3.61

The equation is more easily used if written

D = 1.785 X 10-9

+ i] u + v [‘ u UV

~

T

where D is in square centimeters per second, U and V are in square centimeters per ohm-equivalent, and T i s in O K. It is seen that when Equation 11 is used, the calculated values are greater than the observed values in all cases. This may be explained by the fact that the observed values are a t a finite concentration while the values calculated by the equation are a t infinite dilution. The diffusion coefficients are observed (4) to decrease with increasing concentration a t low concentration and then increase a t high concentrations. Insufficient data and inadequate theory make a complete analysis of the effect of concentration difficult. Because the diffusivities of electrolytes in solution vary with concentration, the calculated values a t infinite dilution are approximations for most cases, but should be fairly satisfactory for most dilute solutions. For concentrated solutions the variations may be greater.

A reasonably accurate estimate of the diffusion coefficient of an organic liquid in dilute aqueous solutions can be made from surface tension measurements. As a working hj.pothesis the relationship is assumed to exist because of a balance between the tendency for minimum surface energy and the tendency for diffusion to oppow a concentration gradient. The surface tension approach t o diffusion coefficients is most applicable to organic liquids in water because of the usually large differences between the surface tensions of organic liquids and water. The temperature variations of liquid diffusion coefficients can be correlated by the group Dq/T, which is essentially independent of temperature. An estimation of the diffusivity of organic solutes in a solvent other than mater can be made if one coefficient is known in the other solvent, inasmuch as diffusion coefficients in one solvent are nearly directly proportional t o those in another solvent. A theoretical equation by Sernst can be used for the estimation of diffusion coefficients of electrolytes in solutions. NOMENCLATURE

CIA = concentration of solute, moles per liter C(, = concentration of solute, moles per ml. (2; = concentration of solvent, moles per ml. D = diffusion coefficient or diffusivity, sq. em. per second E = potential energy difference between surface layer and main body of solution, calories per mole Eo = potential energy contribution of chemical type, calories per mole M = molecular weight n = number of carbon atoms in molecular formula N = Avogadro’s number ;VA = rate of diffusion of solute, moles per second-sq. cm T = radius of colloidal particle, em. R = gas constant ’1’ = absolute temperature, IC. u = valence of cation U = equivalent ionic conductance of cation at infinite dilution, sq. em. per ohm-equivalent TABLEVI. EQUIVALENT IONICCONDUCTANCE AT INFINITE v = valence of anion DILUTION, 18”C. (9) V = equivalent ionic conductance of anion a t infinite dilution, Cations u Anions v sq. em. per ohm-equivalent x = distance in direction of diffusion, em. X = subscript denoting solvent other than water y = surface tension, dynes per em. A y = lowering of surface tension, dynes per cm. 7 = viscosity of solution, centipoises ACKNOWLEDGMENT

TABLEVII. DIFFUSIONCOEFFICIENTSOF ELECTROLYTES IN WATER,18” C. ( 4 ) Electrolyte

Concn., M

D X 106 (Obsd.) D X 105 (Calcd.)

Grateful acknowledgment is made for the financial aid from the Oregon State College Engineering Experiment Station whleh permitted this investigation t o be conducted. LITERATURE CITED

O F TEMPERATURE ON DIFFCSION TABLE VIII. EFFECT COEFFICIENT OF SODIUM CHLORIDE (0.05 M )

Temp.,

C.

9. Centipoises

D X los

(1) Arnold, J. H., J . Am. Chem. SOC.,52, 3937 (1930). (2) Haskell, R., Phys. Rev., 27, 145 (1908). (3) Hodgman, C. D., and Holmes, H, N., “Handbook of Chemistry and Physics,” p. 1972, Cleveland, Chemical Rubber Publishing Co., 1947. (4) International Critical Tables, Vol. 5, New York, McGraw-Hi11 Book Co., 1929. (5) Langmuir, I., J . Am. Chem. Soc., 39,1883 (1917). (6) Nernst, W., “Theoretical Chemistry,” p. 430, London, Macmillan Co., 1923. (7) Sherwood, T. K., “Absorption and Extraction,” pp. 22-4, S e w York, MoGraw-Hill Book Co., 1937. (8) Thovert, G., Compt. rend., 150, 270 (1910). (9) Wilke, C. R., Chem. Eng. Progress, 45, 218 (1949). RECEIVED December 27, 1949