Surface tensions of binary liquid systems. II. Mixtures of alcohols

Surface tensions of binary liquid systems. II. Mixtures of alcohols

Surface Tensions of Binary Liquid Systems II. Mixtures of Alcohols ~ G. C. BENSON A~D V. T. LAM 2 Division of Chemistry, National Research Council of ...

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Surface Tensions of Binary Liquid Systems II. Mixtures of Alcohols ~ G. C. BENSON A~D V. T. LAM 2 Division of Chemistry, National Research Council of Canada, Ottawa, Canada Received October 12, 1970; accepted July 13, 1971 Surface tensions were measured at 25°C for the ten binary liquid systems : methanol-n-deeanol, ethanol-n-decanol, n-propanol-n-decanol, n-butanol-n-decanol, nhexanol-n-decanol, isopropanol-n-decanol, methanol-n-butanol, methanol-isobutanol, methanol-see-butanol, and methanol-terg-butanol. The principle of corresponding states provides a fairly reasonable correlation between the excess surface tensions of these systems and other properties of the pure component liquids and of their binary mixtures. INTRODUCTION The excess surface tension, ~ , of a binary mixture is defined to be the amount by which the surface tension, % of the mixture exceeds the ideal value calculated from the surface tensions of the pure components, assuming additivity on a mole fraction basis. Thus, R

"y = ~' -- x1~'1 -- x~,2,

[1]

where x~ is the mole fraction of component i in the mixture, and -y~is the surface tension of pure component i. For most mixtures of nonelectrolytes ~,~ is negative, and this is generally attributed to Gibbs enrichment of the surface region by the component of lower surface tension. However, positive values of the excess surface tension have also been observed for some systems; usually these involve polar molecules. Part I of this series (1) described measurements of the surface tensions of a number of binary systems formed primarily from nonpolar molecules. As an extension of these studies, the present paper reports values of ~/ (and ~/~) for ten binary alcohol systems at 1 N R C C N o . 12302. 2 N R C C P o s t d o c t o r a t e F e l l o w 1967-1969. 1)res e n t a d d r e s s : D 6 p a r t e m e n t de Chimie, F a c u l t 6 des Sciences, U n i v e r s i t 6 de S h e r b r o o k e , S h e r b r o o k e , Canada.

25°C. Very little previous information is available about the surface tensions of binary alcohol mixtures. The meager results for methanol-ethanol mixtures (2) indicate that the surface tension for this system is very nearly ideal. Values of ~,~ for methanoln-propanol mixtures at 25°C are negative for methanol rich mixtures but become positive with increasing content of n-propanol (3). The systems we have studied were formed by mixing n-decanol (DeOH) with methanol (MeOH), ethanol (EtOH), npropanol (PrOH), isopropanol (iPrOH), n-butanol (BuOH) and n-hexanol (HxOH), and by mixing methanol with n~butanol, isobutanol (iBuOH), see-butanol (sBuOH), and tert-butanol (tBuOtt). EXPERIMENTAL Materials. The component alcohols were purified by passing them through appropriate columns in a preparative gas chromatograph. The final products were checked in a Perkin-Elmer Vapor Fractometer using several different columns, and in all cases the purity exceeded 99.8 %. Apparatus and Operational Procedure. Surface tensions of the pure liquids and of their binary mixtures were measured by the maximum bubble pressure technique in an

Journal of Colloid and Interface Science, Vol. 38, No. 2, Febrtmry 1972

294

Copyright © 1972 by Academic Press, IRe.

SURFACE TENSIONS OF BINARY LIQUID SYSTEMS apparatus similar to that used b y Quayle (4). Details of our equipment and operational procedure can be found in P a r t I. The bubbler was calibrated frequently with resegrch grade benzene (from Phillips Petroleum Company), assuming a surface tension of 28.20 dyne cm -1 for this material at 25°C (5). The temperature of the bubbler was controlled at 25.00 ± 0.01°C; values of the surface tension were generally reproduci--1 ble within =i=0.03 dyne cm Mixtures with known compositions were prepared b y weight from the pure components. Precautions were taken to mirfimize evaporation losses during the preparation and subsequent determination of the surface tension. As in Part I, values of the densities of the mixtures were estimated from their excess volumes (6-9) and densities of the pure components. RESULTS Surface tensions measured for the pure component liquids at 25°C are given in Table I, together with values from the literature (5, 10, 11) for comparison. In general, our results agree fairly well with these earlier values, bearing in mind the scatter evident in the latter. The experimental values of the surface tensions of the binary alcohol mixtures (also at 25°C) and the corresponding values of the excess surface tensions are summarized in Table II. In all cases our results for the surface tensions of the pure components were used in computing the ideal values for the mixtures; any systematic errors in the determination of V will tend to cancel in the evaluation of 7 ~. The method of least squares was used to fit each set of results for v ~ with a RedlichKister form •~

= xlx

Z

nc

p(x2 -

xl)

[2]

containing n adjustable coefficients, cp. By convention, the subscripts 1 and 2 were assigned to the two components in the order used in naming the system. The number of

295

TABLE I SURFACE T E N S I O N S (DYNE CM-1) OF COMPONENT ALCOHOLS AT 2 5 ° C Alcohol

Present Work

MeOH EtOH PrOH iPrOH BuOH iBuOH sBuOH tBuOH gxOH DeOH

22.10 21.83 23.33 20.78 24.18 22.44 23.00 20.11 25.83 28.30

Ref. (5)

22.12 21.85 23.30 20.90 24.16 22.38 23.04 20.12 24.08

Literature a Ref. (10)

22.6 22.2 23.4 21.2 24.2 22.3 23.3 20.8 25.8

Ref. (11)

24.08 27.02

a Some of t h e values were o b t a i n e d from the original d a t a b y i n t e r p o l a t i o n .

coefficients was varied for each system, and the nfinimum number needed to represent the results adequately was selected. Values of the coefficients obtained in this way are given in Table III, together with the corresponding standard errors of estimate, ~ , associated with the use of Eq. [2]. Plots of the experimental results for v E and of their Redlich-Kister representations are shown in Figs. 1 and 2. In general, the relative behavior of the excess surface tensions for the present systems parallels fairly closely the behavior of the molar excess enthalpies, H ~, of their bulk phases, as studied previously (7, 8, 12, 13). Thus, at corresponding concentrations both the excess surface tensions and the molar excess enthalpies of n-alcohol-DeOH systems decrease as the chain length of the first component increases. Also the curve for ,/E of i P r O H - D e O H mixtures lies above that of P r O H - D e 0 H mixtures and a similar pattern is observed for H ~ (7, 13, 14). In the case of the 5~[e0H-isomeric butanol systems, the parallel between the relative behavior of v E and H E is not as close. The excess surface tensions of the BuOH, £BuOH, and sBuOH systems are predominantly positive and those of the tBuOH system are negative; the excess enthalpies of the B u O H and iBuOH systems are positive, those of the sBuOH and

J o u r n a l o f Colloid a n d Interface S c i e n c e ,

Vol. 38, No. 2, Februul~y 1972

296

BENSON TABLE

EXPERIMENTAL (DYNE

CM -I)

VALUlgS OF

AT

TABLE II--continued SURFACE

7

0.1294 0.2092 0.3502 0.3952 0.4741 0.5454 0.6587 0.7744 0.9136

28.26 28.24 28.12 28.09 27.61 27.32 26.52 25.16 23.42

TENSION

7E

0.76 1.24 1.99 2.24

2.25 2.40 2.30 1.66 0.78

Xl

7

0.1637 0.2905 0.3773 0.4778 0.5474 0.6025 0.7021 0.7960 0.8944

PrOH-DeOH T

7 E

28.16 27.85 27.56 27.01 26.61 26.30 25.40 24.57 23.35

0.92 1.43 1.70 1.80 1.85 1.90 1.65 1.42 0.84

iPrOH-De0H 7 E

Xl

7

7 B

0.1569 28.09

0.57 0.1495 27.72

0.54

0.2624 0.4150 0.5015 0.5958 0.7004 0.7964 0.9003

0.96 1.16 1.23 1.22 1.14 0.95 0.46

1.13 1.37 1.42 1.39 1.29 1.09 0.62

27.95 27.40 27.04 26.56 25.96 25.29 24.28

0.2846 0.4070 0.5117 0.5930 0.6929 0.7973 0.8974

BuOH-De0H Xl

7

0.1513 0.2824 0.3982 0.5079 0.5952 0,6927 0,7913 0,8980

28.11 27.76 27.40 26.92 26.59 26.09 25.60 24.84

7

27.29 26.61 25.89 25.25 24.40 23.41 22.19 HxOH-DeOH

7E

0.43 0.62 0.74 0.71 0.75 0.65 0.57 0.24

Xl

T

0.1538 27.87 0.2780 0.3953 0.5002 0.6057 0.7083 0.7963 0.8907

MeOtt-BuOH Xl

7 E

-0.05

27.68 27.48 27.27 27.05 26.80 26.52 26.25

0.07 0,16 0.20 0.25 0.24 0.19 0.15

MeOH-sBuOH 7 E

Xl

7 E

w _ _

0.1090 0.1593 0.2180 0.3141 0.4055 0.4717 0.5098 0.6081 0.6932 0.7949 0.8997

24.00 23.99 23.99 23.81 23.63 23.48 23.45 23.14 22.97 22.71

22.38

M:eOH-tBuOH

Xl

^,

0.1472 0.2870 0.4070 0.4749 0.5751 0.6859 0.7961 0.9000

22.47 22144 22.38 22.29 22.24 22.21 22.16 22.11

7~

Xl

7

7E

EtOH-DeOtt

u

xl

MeOH-iBuOH

ALCOHOLMIXTURES

25°C

MeOH-DeOH ~1

LAM

II

OF THE

]~INARY

AND

0.05 0.1632 0.14 0.2053 0.27 0.29 0.29 0.28 0.33 0.23 0.23 0.18 0.08

0.3100 0.4094 0.5120 0.6011 0.6893 0.7889 0.8424 0.8930 0.9247

0.05 0.05 0.07 0.10 0.05 0.06 0.02 0.01 --0.01 --0.01 --0.02

0.08 0.1055 20.34 0.10 0.08 0.02 --0.01 0.00 0.01 --0.02

O.2288 0.3144 0.4020 0.5025 O.59O5 0.6888 0.7943 0.8986

20.54 20.64 20.72 2O.90 20.98 21.10 21.31 21.62

0.02 --0.03 --0.10 --0.19 --0.21 --0.31 --0.38 --0.38 --0.28

tBu0H systems are negative (8). The differences between the 7 E curves for the iBu0H and sBuOtI systems are too small to allow a meaningful comparison of their relative behavior, however the H E curves for these systems are quite distinct, even differing in sign. ANALYSES OF RESULTS Several different methods of analyzing the present surface tension results were investigated. Only one of these, a corresponding states calculation, led to a correlation which we believe is of sufficient interest to justify a detailed description. The other treatments considered were based on theories of the surface tension of mixtures due to Guggenhelm (15), Hoar and 5/[elford (16), and Shereshefsky (17). In general, reasonable representations of the experimental 7 E values were obtained with all of these thecries, provided one or two of the parameters occurring in the formulas were adjusted empirically to give a least-squares fit. However, in most cases, the resulting values of the parameters were of questionable physical significance. Thus, negative molecular surface areas were required to fit the excess surface tensions by the Guggenheim theory; in the Hoar and IVIelford treatment, values of the energy parameter obtained by fitting the experimental 7 ~ results usually differed in sign and magnitude from those estimated from the molar excess enthMpies; and finally, for a number of the systems, analysis of the results by Shereshefsky's method led

Journal of Colloid and Interface Science, Vol. 38, No. 2, February 1972

297

SURFACE TENSIONS OF BINARY LIQUID SYSTEMS TABLE I I I ~ A L U E S OF COEFFICIENTS FOR E Q . [2] DETERMINED BY THE ~V~ETtIOD OF L E A S T SQU.A-RES a System

cl

1

MeOH-DeOII

2 3 4 5 6 7 8

EtOtrI-D eOH PrOH-DeOH iPrOH-DeOH BuOH-D eOH HxOH-DeOH MeOH-BuOH MeOH-iBu0H MeOH-sBuOH MeOIt-tBuOH

9

10

c2

@'l'

c~

9.539

- I. 946

7.495 5.017 5.731 3.067 0. 852 1.168 0.166 0. 239 -0.961

- 1.472 - 0.798 -- 1.209

- 2.446

0.069

-- 1.051

-0.650

0.583 0.307 1.839

--0.750

0.044 0.044 0.053 0.038 0.019 0.039 0.022 0.018 0.023

Units: dyne cm-~. 2.5

1.5

,

j

~

i

,

,

,

I

,

~

~

i

~

~

,

f

/

i

-

/

/

i.o

\

/

\~

\

'~°~ ///////

T E

\

/

/

1.5

~

\\

/ 1.0

j

X

/%

2.0

,

0.5

\\\\\I]

- ~ -

0.5

0.0 "~'o -0.5 0.0

i,,, 0.2

0.4 ×a

0.6 (DeOH)

0.8

1.0

0.4 xf

FIG. i. Excess surface tension of DeOit mixtures at 25°C. Systems: 1, MeOtt-DeOH A; 2, Et0H-DeOH ~ ; 3, PrOI-I-DeOH O; 4, i P r 0 H DeOH Q; 5, BuOH-DeOH O; 6, I-IxOH-DeOI-t V. Solid curves are least squares representations by Eq. [2]. Broken curves were calculated from theory of corresponding states. to a thickness of t h e a d s o r b e d layer which corresponded to a n o n i n t e g r ~ l n u m b e r of molecular diameters. In Part I the principle of c o r r e s p o n d i n g states was used to calculate t h e surface t e n s i o n s of t h e p u r e c o m p o n e n t liquids a n d of t h e i r m i x t u r e s

Corresponding States Analysis.

0.2

i,,,

oj

I,,,,,,, 0.6

0.8

.0

(MeOH)

FIG. 2. Excess surface tensions of MeOH mixtures at 25°C. Systems: 7, MeOH-BuOH A , 8, MeOH-iBuOH ~ ; 9, MeOH-sBuOH O; 10, MeOH-tBuOH O. Solid curves are least squares representations by Eq. [2]. Broken curves were calculated from theory of corresponding states. from other properties of the c o m p o n e n t s a n d of t h e i r mixtures. T h i s t r e a t m e n t , which is b a s e d on the reduced surface t e n s i o n equation formulated by Patterson and Rastogi (18), a n d on t h e F l o r y t h e o r y of m i x t u r e s (19), p r o v i d e d a satisfactory correlation b e t w e e n calculated a n d e x p e r i m e n t a l excess surface tensions for a n u m b e r of b i n a r y sys-

Journal of Coltoid and Interface Science, VoL 38, No. 2, February 1972

298

BENSON AND LAM

tems composed primarily of nonpolar species. Although a similar analysis of the surface tensions of the present binary alcohol systems may be questioned on the grounds that the original development of the Flory theory specifically excluded hydrogen bonding and strong dipolar interactions (20), nevertheless an investigation of this approach is of interest, since it has been found that the molar excess enthalpies and volumes of binary n-alcohol systems can be correlated b y the Flory formalism (9). Before describing the results of this analysis, the relevant equations used in calculating the surface tension from the principle of corresponding states will be outlined briefly; further details and references to the background literature can be found in Part I. Relationships between the various thermodynamic properties of systems conforming to the principle of corresponding states can be expressed b y universal forms when the values of the properties are reduced b y the use of appropriate characteristic values. B y convention, characte~istic and reduced values will be indicated b y a superscript asterisk and tilde respectively. In the case of a van der Waals' liquid, the expressions for the

characteristic and reduced surface tensions, given b y Patterson and Rastogi (18), are 3'

$

[3]

= kllSp*213T*lla,

and ~ ( ? ) = M?-~

_

[(71]~ _

1)/?~]

In [(171:~ - 0.5)/(17 m -

1)],

[4]

where p, V, and T have the usual significance (pressure, volume, and temperature), and k is the Boltzmann constant. In our calculations we adopted a value of 0.29 for the parameter M, as recommended in (18). Flory (19) has shown t,ow the reduced equation of state for a van der Waals' liquid can be used to obtain values of the characteristic quantities p*, V*, and T* from the molar volume V, the coefficient of thermal expansion a, and the isothermal compressibility 3. Table IV summarizes the results of these calculations for the present alcohols. Theoretical values of the surface tensions calculated from the relation 3" = ~ * ~ ( ~ ) ,

[5]

using Eqs. [3] and [4] are listed in column 8. The last column of the table gives the dif-

TABLE IV CORRESPONDING STATES CALCULATION OF SURFACE TENSION OF COMPONENT ALCOHOLS AT 25~C a Component

MeOtt Et OI-I PrOH iPrOH BuOH iBuOH sBuOH tBuOI-I HxOtt DeOH

V (cm~ mole-1) 10~a (deg-1)

40.73 58.68 75.16 76.96 91.96 92.90 92.37 94.97 125.26 191.43

1.185 1.083 0.981 1.044 0.937 0.948 0.988 1.344 0.852 0.804

106f~ (arm-1) p* (J cm-a)

126.4 116.5 102.5 114.6 94.5 102.6 98.2 126.1 84.3 73.9

467.3 449.0 447.3 434.6 456.6 427.1 471.3 556.1 451.9 478.1

V* (cm~ mole-~)

T* (deg K)

31.71 46.41 60.43 61.24 74.48 75.10 74.18 72.26 102.96 158.72

4784 5011 5287 5110 5425 5390 5266 4501 5734 5939

5' Theory (dyne cra-1)

22.00 23.12 25.06 23.34 26.39 25.00 25.80 22.18 28.33 30.83

AS" (TheoryExpt) (dyne cm-1)

-- 0.10 1.29 1.73 2.56 2.21 2.56 2.80 2.07 2.50 2.53

a For n-alcohols, the values in columns 2-7 are %he same as in (9), where sources of the primary data are indicated. For the other alcohols, v~lues of ~ were obtained from densities tabulated at various temperatures in (5); adiabatic compressibilities derived from sound velocities (21) were converted to isothermal compressibilities using the values of V and a given in columns 2 and 3, combined with molar heat capacities from the following sources: iPrOtt (22), iBuOH (23), sBuOH (24), and tBuOH (25). Journal of Colloid and Interface Science, Vol. 38, No. 2, February 1972

299

S U R F A C E T E N S I O N S OF B I N A R Y L I Q U I D SYSTEMS

ferenees between these values and those observed experimentally. The excess surface tensions of binary systems is calculated from the equation

~

s~2 = ( v~*/v~*) lj3,

= (~*)~(?) - x m * ~ ( ~ ) - z~*q(?~),

[6]

assuming that the mixture is equivalent to a single component liquid with the following characteristic values: (V*) = z~V~* + z~V~*,

[7]

(p*) = ¢1p1" + ¢2p2"

IS] -

-

Values of s~2 and XI~ for the present binary systems at 25°C are given in Table V. In all eases the value of s12 was calculated from the relation

(~1(~2X12/((~2 -~- 812(J~1),

and

In Eq. [81, the quantities ¢i are volume fractions, X~2 is a parameter characterizing the difference in energy of interaction between segments of unlike molecules from the average of the interactions in the pure component liquids (19) and s~2 is the ratio of the molecular surface areas of contact (per segment) for each species. This treatment is somewhat unorthodox since it effectively ignores concentration differences occurring at the surface of the mixture.

[10]

which assumes that the molecules are approximately spherical. The values of the parameter XI2 were obtained by fitting the Flory expression for H E (19) to the smoothed experimental results (7, 8, 12, 13) as described in (9). Excess surface tensions computed from the theory of corresponding states as outlined above are shown as broken curves in Figs. 1 and 2. The standard deviations, z, between the theoretical and smoothed experimental creates are also given in Table V along with a comparison of the theoretical and experimental values of 7 E for equimoIar mixtures. DISCUSSION

The surface tensions of the pure component alcohols, estimated by the principle of corresponding states outlined previously, are of the right order of magnitude and exhibit approximately the same relative order as the experimental results. Except for 5,ieOH, the theoretical values are all high and the discrepancies for n-alcohols tend to

TABLE V CORRESPONDING STATES CALCULATION OF SURFACE TENSION OF BINARY ALCOHOL MIXTURES AT 25°C a

1 2 3 4 5 6 7 8 9 10

System

si2

X12 (J cm-~)

MeOIt-DeOH EtOIt-DeOtt PrOH-DeOH iPrOH-DeOIt BuOH-DeOIt HxOH-DeOH MeOtI-BuOH MeOH-iBuOH MeOH-sBuOH MeOH-tBuOH

1.711 1.507 1. 380 1,374 1. 287 1.155 1.329 1.333 1. 328 1. 316

35.64 19.35 12.68 15.07 8.59 3.19 14.26 14.88 -9.22 - 61.32

7~0.5) (dyne cm-1) Theory Expt 2.23 1.63 0.96 1.25 0.55 0.18 0.47 0.17 0.92 1.23

2.38 1.87 1.25 1.43 0.77 0.21 0.29 0.04 0.06 --0.24

~r (dyne cm-1)

0.27 0.19 0.21 0.13 0.16 0.07 0.13 0.09 0.66 1.22

a F o r the binary n-alcohol systems, the values of s~2 and X12 are the same as used previously in considering t h e i r molar excess volumes (9). Journal of Colloid and Interface Science, Vol. 38, No. 2, February 1972

300

BENSON AND LAM

be less than those for the other alcohols. In constrast to this behavior, the surface tensions calculated for the nonpolar molecules in P a r t I were generally low; furthermore, the magnitudes of the discrepancies between theory and experiment were somewhat smaller than those found for the present alcohols. I t is interesting to note t h a t the excess surface tensions of the binary alcohol systems are positive in most of the cases studied; again this is in contrast to the predominantly negative values of ~/s found in Part I. The principle of corresponding states reproduces the change in sign of ~s fairly satisfactorily. With the exception of the systems M e 0 H - s B u O H and M e O H - t B u O H , the calculated ~,s curves show the same pattern of relative behavior as observed experimentally, but the agreement between the theoretical and experimental curves (within about 4 times the standard error) is not as good as found in Part I. Large discrepancies occur between the theoretical and experimental values of ,ys for M e O H - s B u O t t and M e O H - t B u O H . Application of the Flory theory to both of these systems is unsatisfactory on several

and tBuOH. However, the calculations of for these alcohols do not support this view. I t is possible that steric differences between primary, secondary, and tertiary OH groups should be considered more explicitly. In conclusion, the calculations presented here illustrate the usefulness of the principle of corresponding states in estimating the excess surface tensions of binary alcohol mixtures, particularly in the case of n-alcohols. ACKNOWLEDGMENTS The authors wish to express their appreciation to Mr. C. J. Halpin and Mr. P. J. D'Arcy for technical assistance during the experimental work.

1. 2. 3. 4. 5.

counts:

(a) The fit of the molar excess enthalpies, used to determine the parameter X12, is poor. The standard deviations between the experimental and theoretical H E curves are 42 and 139 J" mole -1, respectively. (b) Estimates of the molar excess volumes, based on the same parameters as used in calculating ~ , show large errors. Thus, for equimolar mixtures, the theoretical and experimental molar excess volumes are respectively --0.106 and 0.088 cm amole -~ for M e O H - s B u O H , and --0.526 and - 0 . 0 5 0 cm3mole-* for M e O H tBuOH. The failure of the theoretical treatment of these systems m a y be due to uncertMnties in the values of the coefficients of expansion and of isothermal compressibility for sBuOH

REFERENCES LAM,V. T., ANDBENSON,G. C., Can. J. Chem., 48, 3773 (1970). MORGAN, J. L. R., AND SCiRLETT, A. 5., JR., J. Amer. Chem. Soc. 39, 2275 (1917). K~.~ANN, R., AND MEINGAST, R., Monatsh. Chem. 35, 1323 (1914). QuAYL]~,O. R., Chem. Rev. 53, 439 (1953). TIMMERMANS, J., "Physieo-chemical Constants of Pure Organic Compounds," Vols. I and II, Elsevier Press, New York (1950 and 1965). There appear to be some misprints in the "B.E." surface tension data for iPrOtt and tBuOH; see Hennaut-Roland, Mme, and Lek, M., Bull. Soc. Chim. Belg. 40, 177 (1931).

6. PFLUG, H. I)., AND BENSON, G. C., Can. J . Chem. 46, 287 (1968). 7. SINGH,J., PFLVG, H. D., AND BENSON, G. C., Can. J. Chem. 47, 543 (1969). 8. POLf~K, J., MURAKAMI, S., LAX, V. T., PFLUO, H. D., i n n BENSON,G. C., Can. J. Chem. 48,

2457 (1970). 9. BENSON, Cx. C., AND PFLUG, H. D., Or. Chem. Eng. Data 15, 382 (1970). 10. SMITH,G. W., ANDSolzG,L. V., J. Phys. Chem.

45, 671 (1941). 11. KATTI, S. S., D a t a 14, 73 12. POPE, A. E., BENSON, G.

AND PATHAK, S., J. Chem. E n g . (1969). PFLUG, H. D., nACRE, B., AND C., Can. J . Chem. 45, 2665 (1967).

13. PFI,UG, H. D., PoP~, A. E., AND B~NSON, G. C., J. Chem. Eng. Data 13,408 (1968). 14. SINGE, J., AND BENSON, G. C., Can. J. Chem. 46, 2065 (1968). 15. GUGGENHEI~,E. A., Trans. Faraday Soc. 41, 150 (1945).

Journal of Colloid and Interface ~cience, Vo]. 38, No. 2. February 1972

SURFACE TENSIONS OF BINAI%Y LIQUID SYSTEMS 16. HoAn, T. P., .~ND MELFORD, D. A., Trans. Faraday Soc. 53, 315 (1957). 17. SHERESHEFSKY, J. L . , J. Colloid Interface Sci. 24, 317 (1967). 18. PATTERSON, D., AND RASTOGI, A K . , J . Phys.

Chem. 74, 1067 (1970). 19. FLonY, P. J., J. Amer. Chem. Soc. 87, 1833 (1965). 20. FLORY, P. J., AND ABE, A., J. Amer. Chem.

Soc. 86, 3563 (1964). 21. SCHAAFFS, W., in "Molecular Accoustics," Vol. 5 of "Landolt-BSrnstein New Series

301

Group I I " (K.-H. tIellwege and A. M. Hellwege, eds.), Springer Verlag, Berlin (1967). 22. KELLEY, K. K., J. Amer. Chem. Soc. 51, 1145 (1929). 23. WILLIAms, J. W., AND DANIELS, F., J-. Amer. Chem. Soc. 46, 903 (1924). 24. PANOV, N., AND DUDNIKOV, I., Sb. Tr. Opytnogo Zavoda im. Akad. S. V. Lebedeva 1938, 36; cf. Chem. Abstr. 34, 15143 (1940). 25. ]:)A.RI~S,G. S., AND ANDERSON, C. T., J . A m e r .

Chem. Soc. 48, 1506 (1926).

Journal of Colloid and Interface Science, Vol. 38, No. 2, February 1972