42
JOSEPHA. NEFF AND JAMESB. HICKMAN
t h e present range is necessary to complete the vapor pressure curve. Acknowledgment.-The authors wish to acknowledge the advice and aid given by Dr. L. F. Epstein,
VOl. 59
Knolls Atomic Power Laboratory, General Electric Company, Schenectady, New York, and the sponsorship by the United States Atomic Energy Commission under contract AT(30-1) 1101.
TOTAL PRESSURE OVER CERTAIN BINARY LIQUID MIXTURES BY JOSEPHA. NEFF’ AND JAMESB . RICKMAN Contributionfrom the Department of Chemistry, West Virginia University Received July 2.8, 1964
Measurementa of total pressure over binary liquid mixtures of perfluoroheptane with heptane and 3-methylheptane, titanium( IV) chloride with heptane, and tetrachloromethane with 3-methylheptane a t two or more temperatures, in the range 25-80’ are reported. The data substantiate the conclusion that the solubility behavior of the non-regular solutions of hydrocarbons in other non-polar liquids is adequate1 represented by the Hildebrand equations, using an empirical solubility parameter for the hydrocarbon. The HildebranJequations are used as a means of reducing the total pressure measurements to more usable form.
Introduction Studies by Hildebrand2f3and others4J on binary liquid mixtures of hydrocarbons with other nonpolar substances have established that the criteria of regular solution formation are not met by such mixtures, and hence that the equations describing the behavior of regular solutions are not applicable to them. It has further been suggested3 however, that for the group of binary non-polar mixtures containing a hydrocarbon and a non-hydrocarbon the regular solution equations can be made applicable by use of a suitable empirical solubility parameter for the hydrocarbon. This suggestion implies two consequences that have not been tested thoroughly by experiment: (1) that hydrocarbons should be better solvents for materials of high solubility parameter, and poorer solvents for materials of low solubility parameter, than their calculated solubility parameters indicate (only the latter has been well established), and (2) that the regular solution equations represent correctly the form of behavior of hydrocarbon-non-hydrocarbon mixtures, provided an empirical solubility parameter be used for the hydrocarbon. It is here proposed to study these two conclusions on the basis of data from experimental determination of total pressure above binary liquid mixtures. This method of experimentation offers the advantages of simplicity of operation and avoidance of the possibilities of systematic error inherent in the determination of partial pressures. It is superior to the much simpler determination of critical solution temperatures in that it may be used with systems that remain homogeneous throughout the liquid range, and in that it can provide data for a wide range of temperatures and compositions. An advantage of total pressure measurement over determination of liquid-vapor equilibrium data is that total pressure is readily determined isother(1) Based in part on a dissertation submitted by Joseph A. Neff for the degree, Doctor of Philosophy, West Virginia University, May, 1954. (2) J. H. Hildebrand, J . Chem. Phys., 18, 1337 (1950). (3) J. H. Hildebrand, B. B. Fisher and H. A. Benesi, J . A m . Chem. b‘oc., 78, 4348 (1950). (4) J. H. Simons and R . D. Dunlap, J . Chem. Phye., 18, 335 (1950). (5) D. N. Campbell and J. B. Hickman, J . A m . Chem. &e., 76, 2878 (1958).
mally, providing information more susceptible to comparison with the predictions of the regular solution equations than are the isopiestic data of the liquid-vapor equilibrium method. Because of the limited nature of the questions asked in this research, concerning a restricted group of substances, the outstanding disadvantage of the total pressure method, absence of any wholly satisfactory method of reduction of the data6 is largely avoided. Experimental Apparatus.-The apparatus used was essentially that described by Sanderson,’ combining the essential features of his simplified high-vacuum apparatus-manometer, condensation traps and McLeod gage, illustrated in his Fig. 37 with his vapor pressure apparatus-air surge chamber, differential manometer, and sample chamber diagrammed in his Fig. 27. A Pirani hot-wire gage, calibrated against the McLeod gage, also was provided for rapid checking of the pressure during experiments, and as an aid in the detection of leaks. The sample was introduced into the system by distillation under vacuum, and degassed by distillation From one condensation trap to another, freeaing and pumping. The thoroughness of degassing was indicated by constancy of pressure with time, and by the agreement of measured vapor pressures of pure substances with the best literature values. The liquid sample was constantly stirred during a determination by means of an iron bar sealed in glass, kept in motion by an external horseshoe magnet moved by a reciprocating stirrer. Since the vapor pressure was determined by finding what external pressure had to be applied just to balance the pressure developed by the vapors above the liquid, and since the volume available for occupancy by the vapors of the liquid was small (less than 10 cm.*), there was no appreciable change in composition of the liquid during an actual determination. A careful check was made to determine whether changes in composition might result from the degassing process. Although such changes were found, by analysis of samples before and after degassing, to amount to 2% or less, they were essentially eliminated by determining the composition of the sample at the end of each experiment, following a one-step distillation out of the system. The temperature of the sample was measured by means of a copper-constantan thermocouple in a thermocouple well in the Rample chamber. The thermocouple had been calibrated against a platinum resistance thermometer whose temperature-resistance characteristics had been determined by the U. s. National Bureau of Standards. (6) G. Scatchard in G. K. Rollefson (ad.), “Annual Review of Physical Chemistry,” Vol. 111, Annual Reviews. Inc., Stanford, Calif. 1952, p. 269. (7) R. T. Sanderson, “Vacuum Manipulation of Volatile Compounds,” John Wiley and Sons, Inc., New York, N. Y., 1948, pp. 78105.
Jan., 1955
TOTAL PRESSURE OVER CERTAIN BINARY LIQUIDMIXTURES
43
TABLE I PURIFICATION AND PURITY MEASUREMENT FOR SUBSTANCES USED Substance and source
Still efficiency, theo. plates
Rp., OC.,
cor. to 760 mm.
B.p. O C 760 .‘mm:’ Ilt.
Mole .%
F.&
impurity
24 80. 12b.c 80.Oc Benzene, Eastman5 5.34 0.18 Tetrachloromethane, J. T. Baker 24 76. gd 76.7’ 22.9 0.07 24 98.3” 98.428’ - 91.025 0.07 Heptane, Eastman 24 117.7’ 118.9O - 122 2.0 3-Methylheptane, synthesized Perfluoroheptane, Carbide and Carbon 100 81.5’ 82 5’ 76 3.6 Titanium(1V) chloride, National Lead 5 134. 135.8’ - 24.51 0.34 a All commercial chemicals best grade of the manufacturer. Literature references for this column give source of d t l d p F. D. Rossini, et al., “Selected Values of Properties of Hydrocarbons,” (Circular C461) value used in correcting b.p. U. S. Govt. Printing Office, Washington, D. C., 1943, pp. 483. Ref. 10. e F. D. Rossini, et al., “Selected Values of Chemical Thermodynamic Properties,” (Circular C 500), U. S. Govt. Printing Office, Washington D. c., 1952 pp. 588, 716. R. D. Fowler, et al., I n d . Eng. Chem., 39, 375 (1947). L. L. Quill (ed.), “Chemistry and hetallurgy oi Miscellaneous Materials,” McGraw-Hill Book Co., New York, N. Y . , 1950, pp. 193-275.
-
-
I
The sample chamber and intermediate differential manometer were thermostated in a large Dewar flask, the leveling of the mercury in the arms of the differential manometer being attained by matching a horizontal scratch on a previously leveled mirror contained in the Dewar flask. The manometer measuring the applied pressure was read by means of a cathetometer. Materials.-Standard methods of preparation and purification, as summarized in Table I, were used for the substances employed. Purities were determined by f.p. according to the methods of Rossini and co-workers,* the f.p. and purity determination for titanium(1V) chloride being carried out in a closed, magnetically stirred f.p. tube9 into which the sample could be introduced by distillation under vacuum. The validity of results obtained by using this tube was indicated by obtaining identical purities within f-0.1 mole % for identical samples by use of the closed tube and the conventional Rossini apparatus (a non-hygroscopic sample being used for this test). Analysis .-All mixtures except those involving titanium(IV) chloride or perfluoroheptane were analyzed by refractive index on the basis of refractive index-composition curves determined in the laboratory. Because of the hygroscopic nature of titanium( IV) chloride, mixtures containing it were analyzed by rapid hydrolysis in ice-water, followed by dilution to 500.0 ml. and titration of an aliquot with standardized sodium hydroxide, using brom thymol blue as an indicator. Analysis of known mixtures by this method gave results accurate to f-1.5% of the titanium( IV) chloride content. Mixtures involving perfluoroheptane could not be analyzed by refractive index because of the low index of refraction of the fluorocarbon. The composition of these samples was determined by the Victor Meyer vapor density method, which was especially well suited to this determination because of the similar volatility and greatly differing molecular weights of the components. The error was *l.O% in composition, as found by comparison with known samplea of mixtures of the same materials.
Results and Discussion The experimentally determined total pressure values are given in Fig. 1 (the significance of the dotted line in Fig. 1 is discussed below) and Tables 11. 111 and IV. Total pressure data were also determined for the system tetrachloromethanebenzene, not given, as a check on apparatus and procedure. Results for this system were reproducible within f 1 mm. for different samples of the same composition, and deviated not more than f-3 mm. from the literature values.lO*ii ( 8 ) A. R. Glaegow, Jr., A. J. Streiff and F. D. Rossini, J . Research Nall. Bur. Slandarda, 86, 355 (1945), and references there cited. (9) D. N. Campbell, J. A. Neff, R. F. Stewart and J. B. Hickman,
Proc. Weal Va. Acad. Sei.. in press. (10) F. A. H. Sohreinemakers, Z . phyaik. Chem.. 47, 445 (1904). (11) C. P. Smyth and E. W. Engel, J . Am. Chem. SOC.,6 1 , 2636 (1929).
200
150
100
50
I 0 0
23 50 75 TIcptniie, mole %. Fig. 1.-Total pressure in the system: titanium(1V) chloride-heptane (for significance of dotted lines, see text).
T u r n I1 TOTAL PRESSURE, SYSTEM:PERFLUOROHEPTANE3-METHYLHEPTANE Perfluoroheptane mole fraction
60’
0.00 .0912 .314 .722 .755 .914 1.000
10.2 31.1 38.2 38.1 38.6 38.2 34.3
Pressure, om. at 6b0 70°
12.5 37.3 45.5 45.5 45.9 45.6 41.1
15.3 43.1 53.8 54.6 55.1 54.6 49.5
80 ‘
22.1
50.0 73.8 76.0 76.8 76.2 69.6
TABLE I11 TOTAL PRESSURB, SYSTEM:PERFLUOROHEPTANE%-HEPTANE
Perfluoroheptane mole fraotion
0.000 .128 .394 .732 .856 1.000
50’
14.1 31.9 32.3 32.8 31.8 23.7
Pressure, om. at 550
60°
17.3 37.9 38.8 39.4 38.0 28.9
21.0 44.9 46.3 47.3 45.5 34.9
JOSEPHA. NEFFAND JAMESB. HICKMAN
44
Vol. 59
TABLE IV stances with solubility parameters lower than their own. PRESSURE, SYSTEX:TETRACHLORO~VETHANEAnalysis of Total Pressure Data.-In order to 3-METHYLHEPTANE Tetraolilororeduce the total pressure data to a form more methane, readily available for comparison purposes, the mole Pressure, om. a t fraction 250 380 50' 60' following equation could be solved for 2, the solu0.000 1.95 3.29 6.68 10.2 bility parameter difference, (a1 - 62) TOTAL
,330 ,511 .742 ,930 1.000
5.14 7.13 9.39 11.4 11.4
8.22 11.7 14.2 17.1 17.6
14.7 19.6 25.1 30.1 31.7
21.3 28.2 35.7 42.7 45.1
P T= ~ PIO(~Z/VI
+
VZ)
+
exp [0.25v~z~/RT] v2) exp [ 0 . 2 5 ~ ~ z ~ / R 1(3) ']
pno(vl/vl
+
PT, being the measured total pressure when the volume fractions of the two components are equal (for which nl = v2/(v1 v2), etc.), x being identical' The dotted lines in Fig. 1 represent the total pres- for the two right-hand terms of equation 3. Use of equation 3 implies that solutions of hydrosure for the system titanium(1V) chloride-heptane carbons follow the regular solution equations procalculated by the regular-solution relationship vided that an empirical parameter difference be PT = p l 0 m exp [@&(61 - ~ Z ) ~ / R T I used. This is suggested, but not proved, by the pzon2 exp [@1~v2(61- 6d2/RTI (1) fact that solutions of a hydrocarbon with a subin which PT is the total pressure, pol and p02 the re- stance of high parameter are more nearly ideal, spective vapor pressures of the two components in solutions of a hydrocarbon with a substance of low the pure state a t the temperature of investigation, solubility parameter more highly deviating from nl and n2 the mole fractions of the two components, ideality, than the regular solution equations predict. a1and % the respective volume fractions, a.g., A closer examination of the suitability of the equals nlvl/(nlvl n2vz)(vl and v2 being the respec- form of the regular solution equations, using an tive molar volumes of the pure components.) 61 empirical solubility parameter difference, has been and S2 are the calculated solubility paramet,ers of made by analysis of the published experimental t,he pure components, 6 = ( A E V / v ) o . sthe , values of data of Simons and Dunlap4 for the system penA E , (increase in internal energy of vaporization tane-perfluoropentane. This system provides a upon vaporization of one mole) and IJ being calcu- sensitive test for the applicability of equation 3, lated for the temperature, T , a t which the computa- since the apparent parameter difference between the tion was being made. components is large-if it were small, the spread Equation 1 follows directly from the Hildebrand between the prediction of the regular solution equaequation tions, the actual behavior of the system, and ideality would be so small that no firm judgment could RT In yl = @z2v1(6, - &)2 (2) be made. and the definition of the activity coefficient, y , as As a test of equation 3, the values of p / p O nwere approximately equal to p/pOn. calculated directly from Simons and Dunlap's exIt will readily be observed in Fig. 1 that the perimental values of pressure of the pure substances actual total pressure of the system is less than that and mixtures, and compared with values computed computed by equation 1 by an a,mount well exceed- using equation 3 as follows (use of the method of ing the experimental error (the use of AE, and v a t Schultze12as a means of obtaining partial pressures .the temperature of investigation rather than a t 25" proved entirely inadequate for these data) : x was is a refinement probably unnecessary in view of the calculated a t the composition corresponding t o stated approximations involved in derivation of the equality of volume fractions of the components Hildebrand equations, but this was done to mini- according to equation 3, and the value of x inserted mize any deliberate exaggeration of the difference in equation 2, rewritten for ease in computation as between the two curves). This provides experip l / p l o n l = exp [ ~ ? U I X ~ / R T I (4) mental verification of the implication of Hildebrand'ss work that the hydrocarbons are better Table V compares the values obtained. solvents for materials of solubility parameter higher TABLE V than their own, than would be inferred from the COMPARlSON OF VALUES4 OF p / p o n OBTAINED B Y DIRECT calculated solubility parameters. COMPUTATION AND BY EQUATION 3 Table I V reports total pressure data for the sysTemp., p / p % , CaFir p / p % CsHir tem 3-methylheptane-tetrachloromethane,likewise OIL Directb Eq. 3 Directb Eq. 3 illustrating an entirely similar instance of behavior 1.95 1.89 1.48 1.51 292.9 more nearly ideal than predicted. However, it does 288.2 1.91 1.90 1.59 1.52 not constitute as sensitive a test as to the solvent 1.55 1.54 283.1 1.91 1.93 power of the hydrocarbon because of the fact that 1,55 1.95 1.49 278.6 1.98 the two parameters concerned have so nearly the 1.57 262.4 2.03 1.98 1.53 same value. a For the composition, n CaFll = 0.393, at which a1 = Tables I1 and 111 present data showing the well- @z. From the data of ref. 4. established large positive deviations from regular Evidence having been offered as to the correctsolution behavior for mixtures of hydrocarbons and fluorocarbons. Such deviations indicate that hy- ness of the two implications inherent in the applicaclrocarbons are poorer solvents (than would be ex- tion of the regular solution equations (using an pected from the Hildebrand equations) for sub(12) W. Sohultee, 2. p h y s i k . Chern., 198, 314 (1951).
+
+
+
MOBILITY OF MICELLE OF SODIUM LAURYL SULFATE
Jan., 1955
45
In Table VI, column 5 represents an arbitrary and empirical solubility parameter for the hydrocarbon-ascribing all the effect of deviation to the alteration of the parameter of the hydrocarbon. It is considered significant that essentially the same TABLE VI numerical value of the parameter is obtained for COMPARISON OF VALUES OF (6, - &)' etc., FROM COMPONENTSeach hydrocarbon, whether it is derived from calculations based on the behavior of mixtures with subA N D SOLUTIONS PROPERTIES stances of higher, or of lower parameter. 1 2 3 4 5 (81 - 62) from GilpnarPnt, Acknowledgments.-The director of this work properties of Hydrocarbon, Temp., Pure cornSoluB. H.) gratefully acknowledges the assistance of System ponents tions" + (14A E-v / u31) o J a(J.grant from the National Science Foundation, a 1.901 1.110 7.89 TiC14-C7Hls 323.2 part of the time made available by which was spent 1.798 1.098 7.54 333.2 on this work; the authors acknowledge the assistCClr-CsH18 323.2 1.271 1,000 8.24 ance of the Atomic Energy Commission (as repre1.000 8.11 333.2 1.218 sented by Carbide and Carbon Chemical's Co.), the 2.65 7.75 C ~ F I ~ C I H I 333.2 ~ 1.56 Minnesota Mining and Manufacturing Co., and C~FigCgH18 333.2 1.73 2.77 8.05 the National Lead Co. in making samples of materials available free or at special prices. a Calculated by equation 3.
empirical parameter) to the non-regular mixtures of a hydrocarbon and a non-hydrocarbon, some derived results of experimental determinations are given in Table VI.
OK.
TRACER ELECTROPHORESIS. 11. THE MOBILITY OF THE MICELLE OF SODIUM LAURYL SULFATE AND ITS INTERPRETATION IN TERMS OF ZETA POTENTIAL AND CHARGE1 BY D. STIGTER~ AND K. J. MYSELS Contribution from the Department of Chemistry, University of Southern California Received July 89, 1864
Measurements of electrophoretic mobility of micelles of sodium lauryl sulfate in water and salt solution a t finite concentration of micelles are extrapolated to infinite dilution of micelles. Corresponding zeta potentials and charges a t the shear surface of the micelle are calculated according to several theories including new modifications of Booth's approach. The great effect of the curvature of the double layer and of relaxation effects is thus established for these systems which are far from ideal even a t the ChlC. A comparison of the zeta potential with that calculated from the charge of the lauryl sulfate ions forming a smooth micelle with a diffuse double layer leads to a large discrepancy. A "roughness" of the surface of the micelle is therefore suggested. The calculations involved required the computation of charge-potential and of potentialdistance relations for double curved layers at high potential. These general problems are dealt with in appendixes.
The size, charge and shape of a micelle, besides their intrinsic interest, provide experimental tests for any theory of association colloids, yet they are still a matter of uncertainty. In the present paper we shall present accurate measurements of the electrophoretic mobility of micelles of pure sodium lauryl sulfate (NaLS) obtained by the tagging technique suggested by H ~ y e r . This ~ mobility is obviously related to the charge, size and shape of the micelle and to the composition of the solution. These relations are not yet fully elucidated but it is shown that they lead already to a reasonably accurate estimate of the f potential and of the charge of the micelle. The f potential is quite high: 65-100 mv. and the charge corresponds to 25-30% ionization, which is not readily explainable by the conventional picture of a smooth micelle surface. Since the experimental accuracy greatly exceeds that of the interpretation, the present data should be capable of yielding more accurate estimates of charge as the theories are developed further. (1) Presented in part at the J. W. MoBain Memorial Symposium of the Division of Colloid Chemistry at the American Chemical Society meeting, Chicago, September, 1953. (2) Bristol Myers Company Fellow, 1952-1953. Present address, Shell Research Laboratories, Amsterdam, The Netherlands. (3) H. W. Hoyer and K. J. Mysels, THISJOURNAL,64,966 (1950).
Experimental Methods and Materials.-The open tube method of measuring electrophoretic mobilities4 and the sodium lauryl sulfate6 and orange OT tracer6 used have all been described previously. Oil red N-1700 obtained from the American Cyanamid Co. was purified by solution in acetone and precipitation with water repeated twice and followed by double recrystallization from ethanol-benzene. Validity of the Method.-Three questions may be raised concerning the validity of our measurements. Is the mobility of the tracer accurate? Does introduction of the tracer dye modify the micelle? Does the mobility of the tracer equal that of the micelle? The first question has already been discussed in the first paper of this ~ e r i e s . ~The second question, about the disturbing effect of the dye, has been partially answered reviouslya but we can add the following: ( a ) Dr. H . W. koyer has found7 that two different dyes, Sudan IV and Nile black, give the same mobilities (3.52 and 3.51 X cm.2 v.-l aec.-l, respectively) for the micelle of 5y0 otassium laurate solutions and we have found that orange 8 T and oil red N-1700 in 3.5% solutions of sodium lauryl sulfate give the same mobilities (3.70, 3.75 and 3.74, 3.73 X cm.2 v.-1 sec.-I, respectively). It would be quite a coincidence if the disturbing effect of different dyes were significant and yet the same. (b) The fact that orange OT in saturated solution does not affect measurably the critical micelle concentration of sodium (4) H. W. Hoyer, K. J. Mysels and D. Stigter, ibid., 68, 385 (19541. (5) R . J. Williams, J. N. Phillips and K. J. Mysels, Trans. Faradny Soc., submitted. (6) K. J. Mysels and D. Stigter, THISJOURNAL, 67, 104 (1953). (7) Ph.D. Dissertation, 1951, University of Southern California.
