I
HORACE R. CRAWFORD and MATTHEW VAN WINKLE University of Texas, Austin, Tex.
Composition Determines
Surface Tension and Density of Ternary Systems at Their Normal Boiling Point A correlation has been developed which will enable prediction of multicomponent system surface tension at the boiling point of the mixture as a function of composition well within the generally accepted engineering degree of accuracy. This should be extremely useful in design work, where it is necessary to predict the surface tension of mixtures to determine transfer rates, properties, etc.
MAX,
investigations have been conducted to determine the effect of temperature on surface tension and the effect of composition on surface tension a t constant temperature. Weinaug and Katz (23) and Ling (73) have investigated surface tension of binary mixtures at their boiling points. The investigation was initiated to determine surface tensions of ternary systems a t their boiling points and to develop correlations for predicting surface tension of multicomponent mixtures from single component or binary data. Theory. A fundamental property of liquid surfaces is to contract to a minimum area if gravity effects are negligible. The surface molecules have a net attraction inward and perpendicular to the surface. This net force inward causes a maximum number of molecules to migrate to the body of the liquid and hence causes a minimum surface area. For each molecule brought from the interior to the surface, a definite quantity of work must be performed against the attractive force inwards. This means there is a “free energy” associated with the surface. This property is more generally known as surface tension. which is the mathematical equivalent to the surface free energy. The dimensions of surface free energy are energy/area which are the same as those of surface tension which are force/length. T h e capillary rise method offers the simplest theory of any experimental method for determining surface tension. The equation for determining surface tension from capillary rise measurements is Present address, T h e Western Co., Dallas, Tex.
For mixtures, also, the free surface energy strives for a minimum. In a mixture, the component with the lower surface tension concentrates at the surface. Therefore, a small amount of solute of low surface tension added to a solvent of high surface tension will cause appreciable decrease in surface tension. Also if a solute of high surface tension is added to a solvent of low surface tension the solute concentrates in the bulk and the surface tension increases only slightly (8). Appreciable increases in surface tension caused by adding small amounts of solute are unknown. These same forces which cause solutes to be incompletely soluble in a solvent also probably cause a concentration of solute a t the surface. If the solution is one like 1-butanol in water the molecules of 1-butanol at the surface are probably oriented so that the hydroxyl groups are pointing toward the solution and the hydrocarbon groups are aligned in the direction of the vapor. Van der Waals (22) suggested this equation to represent the variation of surface tension with temperature u = A(1
-
T,)”
(2)
where n = universal constant 1.234, and T , = TIT,. The van der Waals equation is better than any other equation for the temperature dependence of surface tension, although n is not a universal constant. For nonassociated liquids, with A and n evaluated for each liquid, Equation 2 is satisfactory for the surface tension over the entire liquid range from melting
point to critical point. Ferguson (7) used Equation 2 to estimate critical temperatures from surface tension measurements. On 14 compounds reported the average deviation was 0.54’C.
Experimental Apparatus. The apparatus used in determining surface tension and density at the boiling point consists mainly of borosilicate glass parts connected by standard-taper ground joints and balland-socket ground joints. No stopcock lubricants were used so as to prevent contaminating materials being tested. The main part of the apparatus was continued in a 60-mm. borosilicate test tube about 33 cm. long and equippcd with a female 60/40 standard-taper joint. Fitted into this joint was a cap equipprd with a 12/5, 18/9. and a 28/15 ballground joint, as well as a 10/30 standardtaper joint. A Friedrichs condenser was connected to the 28/15 ball joint. A Liebig condenser. through which the thermocouple was introduced, was connected to the 18/9 ball joint. From the 12/5 ball joint a 4-mm. borosilicate tubing sampling line extended to within 8 cm. of the bottom of the test tube. A Cottrell-type liquid pump was placed inside the test tube. Sealed to this pump was a glass dish, 35 mm. in diameter and 12 mm. deep, and a large glass rod which served as a weight to keep the pump from bouncing during boiling. Suspended from the pump by an 18-gage Nichrome wire was an aluminum foil funnel, 55 mm. in diameter, with an internal angle of l 5 Z o , a wall about 2 mm. high, and a hole in the bottom slightly larger than the capillary tube. The capillary tube was inserted VOL. 51, NO. 4
APRIL 1959
601
through this hole and about 4 mm. deep into the glass dish. A 24-gage copperconstantan thermocouple was located a t the outlet of the Cottrell pump. The pump outlet was arranged so that the liquid from the pump impinged upon the capillary tube about 10 cm. above the top of the glass dish and fell down into the funnel and ran into the glass dish with a minimum of disturbance of the liquid surface in the dish. All glass joints were individually ground to ensure close fits. Procedure. T h e draft gage was 6-mm. glass tubing and a 14-inch inside diameter aluminum pan connected by Tygon tubing and metallic fittings. The glass tubing was inclined such that a distance of 9.75 inches along the tubing was equivalent to 1-inch vertical distance. Distilled water with 750 p.p.m. sodium chromate was used in the draft gage. Six grams of Aerosol OT 75y0 aqueous wetting agent was added to the water to reduce surface tension effects in the draft gage. A pressure difference of 0.001 inch of water could be detected with this gage. The pressure in the capillary was regulated by a mercury leveling bottle n i t h a screw adjustment. A stationary mercury bottle was connected between the leveling bottle and the capillary to act as a surge volume. A three-way stopcock was connected to the 12/5 socket a t the end of the capillary tube. One outlet of this stopcock went to the pressure regulating system and draft gage. The other was open to the atmosphere through a glass fiber-calcium chloride filter tube. The stopcocks and socket joint in the pressure regulating system were lubri-
cated with Dow Corning silicone stopcock grease. The temperature was determined with a 24-gage copper-constantan thermocouple connected through an ice junction to a Leeds & Northrup Type K potentiometer which could be read to 0 . 0 2 O c. The thermocouple was calibrated at 40°, 80", 155", and 190" C., against an NBS calibrated platinum resistance thermometer. The test tube, heated with a 550-watt heater, had a n uneven opening so that hot air would flow up around the test tube. Two concentric borosilicate glass cylinders (100 and 80 mm.) irere placed about the test tube to reduce heat loss. The apparatus was illuminated with one "trouble" light and one adjustable fluorescent lamp covered with thin white paper. The refractive index was determined by a Bausch Br Lomb Precision refractometer a t 30" C. using a sodium D line light source. The density data were determined a t 30" C. by calibrated pycnometers. The composition data from refractive index determinations are accurate to hO.1 mole 7 0 . T o determine surface tension, samples were charged into the 60-mm. test tube, along with a few '/d-inch ceramic Berl saddles as boiling chips. The samples were heated to the boiling point and a minimum of 15 minutes was allowed for equilibrium after the potentiometer reading became constant. The capillary was inserted into the test tube and some of the vapor sucked into it. The levels of the meniscus in the capillary and the top surface of the liquid in the dish were determined
with a Gaertner scientific cathetometer. The sample in the capillary was expelled orally by tubing through a drying filter tube and the three-way stopcock. A new sample was sucked into the capillary and allowed to seek its level. These levels were determined again. This capillary rise, varying from 2.3 over 7 cm., was determined three times for each sample and the average capillary rise was used in subsequent calculations. T o determine the surface tension both the capillary rise and the density of the sample a t the boiling point need to be evaluated. The surface tension was calculated by Equation 1. Density Determination at Boiling Point. To determine the density of the sample the capillary was connected to the draft gage b\- rhe three-way stopcock. About 1 inch of \rater vacuum was applied to the system by the mercury leveling bulb. The meniscus level in the capillary, the draft gage reading, and room temperature were determined and recorded. A positive pressure was then applied to the capillary and draft gage and their
Density and Refractive Index at 30" C.
Table I.
(Toluene-n-Octane-Ethylcyclohexane)
Mole % Toluene
PZO.
ny
G.ihI1.
Toluene-n-Octane 0.6943 0.7195 0.7504 0.7829 0.8138 0.8575
0 22.54 45.49 65.31 81.39 100
1.39302 1.40780 1.42613 1.44560 1.46462 1.49129
Toluene-Ethylcyclohexane +COOLING
WATER I N
100 88.00 78.16 72.85 59.67 45.30 36.11 26.56 11.76
0.8575 0.8440 0.8342 0.8292 0.8181 0.8071 0.8008 0.7947 0.7863 0.7804
0
1.49129 1.48062 1.47263 1.46864 1.45950 1.45066 1.44554 1.44059 1.43373 1.42865
n-Octane-Ethylcyclohexane
n-Octane 0.6943
100 82.71 59.26 35.25 20.08 0
0.7077 0.7267 0.7476 0.7614 0.7804
1.39302 1.39868 1.40653 1.41510 1.42081 1.42865
Tolu ene-n-Octane-Ethylcyclohexane
Toluene %-Octane 100 65.37 45.93 27.88
0 DRAFT GAGE
Surface tension and density at the boiling point are measured in this apparatus
602
INDUSTRIAL A N D ENGINEERING CHEMISTRY
46.40 30.53 26.82
0
0 16.88 34.33 51.92 100 18.47 31.30 16.82 0
0.8575 0.8027 0.7707 0.7443 0.6943 0.7876 0.7652 0.7776 0.7804
1.49129 1.45442 1.43497 1.41932 1.39302 1,44237 1.42882 1.43327 1.42865
P R E D I C T I O N OF SURFACE T E N S I O N
Table
II.
Density and Refractive Index a t 30" C.
(Methanol-Water-Ethylene Glycol) Mole % PlO. hIet hanol G./Ml. ny Methanol-Water 0.9957 0.962 1 0.9314 0.9009 0.8428 0.8172 0.7818
0 12.88 25.71 39.11 66.63 79.92 100
1.33213 1.33679 1.33967 1.33980 1.33492 1.33128 1.3241
Methanol-Ethylene Glycol 100 86.82 72.46 48.34 21.97 18.26 9.57 0
Table 111.
1.3241 1.34622 1.36609 1.39208 1.41437 1.41712 1.42307 1.42917
0.7818 0.8459 0.9054 0.9875 1.0584 1.0671 1.0865 1.1064
u =
fl A1
+ A I ~ Z I Z+Z
(4)
22
-A2
Constants Used in Correlation of Data Density, G./Ml. at T e , ' K. A T,' C.
Compound n 1.22 Toluene 1.22 %-Octane 1.22 Ethylcyclohexane 0.9 Methanol Water 0.9 0.9 Ethylene glycol 5 Estimated from surface tension
Water-Ethylene Glycol
Correlations, With knowledge of the surface tension properties of mixtures and the experimental evidence that surface tension is dependent on volume fraction, the authors developed this equation to correlate the surface tension data as a function of composition and temperature for a binary system. (1 - T p-~ '
The boiling point was determined and corrected to 760 mm. by the correction given by Dreisbach ( 6 ) . T h e maximum correction was 1.0" C. A temperature correction was made to the surface tension to change it from the barometric boiling point to the boiling point a t 760-mm. pressure, assuming that the surface tension varied linearly with temperature. Maximum correction was about 0.1 dyne per cm.
594.0 569.4 605.9" 513.2 647.4 775"
65.01 52.72 57.31 48.11 127.44 72.81
(12) (11)
(If) (21)
0.775 0.617 0.708 0.704 0.9584 1.050
120 120 100 100 100 100
data.
Water 0.9957 1.0284 1.0521 1.0798 1.0939 1.1005 1.1064
100 90.81 81.25 61.61 40.96 23.94 0
1.33213 1.35695 1.37548 1.39955 1.41378 1.42165 1.42917
Table IV.
Toluene-n-Octane-Ethylcyclohexane
Methanol-Water-Ethylene Glycol hlethanol Kater 100 61.03 39.44 21.38 0 41.69 23.11 22.83 0
0 20.28 41.13 58.70 100 19.35 38.92 18.70 0
0.7818 0.9079 0.9555 0.9994 0.9957 0.9843 1.0234 1.0440 1.1064
Mole % Toluene
N.B.P.,
0 22.4 45.3 65.0 81.3 100
125.7 120.5 116.1 113.5 112.0 110.6
100 88.0 78.1 72.8 45.2 36.0 26.4
110.6 112.1 113.3 114.0 118.6 120.8 123.3 127.7 131.7
-
Pa)
= hl(PL
-
P Y )
c.
'N . B . P . .
~N.B.P.,
G./M1.
Dynes/Cm
Residual Pure comD. Correlationo correlationb
Toluene-n-Octane
1.3241 1.36107 1.36884 1.37425 1.33213 1.38600 1.39189 1.40528 1.42917
11.7 0
12.1 13.0 14.0 15.0 16.3 18.3
0 0.0 0.0 0.1 0.0 0
0 0.2
0 0.0 -0.1 0.0 0.0 0.0
0 0.3 0.3 0.4 0.4 0.4 0.3 0.2 0
0.4 0.6 0.4 0
0.786 0.768 0.760 0.755 0.734 0.722 0.716 0.706 0.699
18.3
17.6 17.3 17.0 16.2 15.9 15.6 15.2 14.9
0.0
0.0 0
n-Octane-Ethylcyclohexane
n-Octane 125.7 126.7 128.0 129.4 130.4 131.7
100 82.7 59.2 35.2 20.0
(3)
where h, = difference in draft gage readings, and hl = difference in levels of menisci in capillary. 'The quantities p a and p t , both small, were determined from the perfect gas law. T h e difference in draft gage readings, h,, varied from 2 to 3 . 5 inches of water depending on the density and surface tension of the sample. Density of the liquid was corrected to temperature correspondinq to 760 mm. A small density correction was made to the capillary rise. h, since the vapor column in the condenser extended about 10 cm. higher than the point where the capillary was inserted into the test tube. T h e gas in the capillary above the test tube was assumed to be air,
0.614 0.641 0.675 0.706 0.742 0.786
Toluene-Ethylcyclohexane
levels were recorded. This gave the height of a water column equivalent to a known height of sample. These two heights at about the same levrls were determined at least three times and the density of the liquid sample, pL. was determined from hw(Pu
Normal Boiling Points, Densities, Surface Tensions, and Residuals from Correlation a t the Normal Boiling Point
0
0.614 0.626 0.643 0.664 0.678 0.699
12.1 12.5 12.9 13.6 14.0 14.9
0 -0.1 0.0 0.0 0.1
0
0 0.0 0.2 0.2 0.2 0
Toluene-n-Octane-Ethylcyclohexane
Toluene 100 65.3 45.8 27.8 0 40.3 30.4 26.7
0
n-Octane 0 16.9 34.4 52.0 100 20.3 31.3 16.8 0
Residuals from Equation 7.
110.6 114.4 117.1 120.1 125.7 118.9 120.5 122.3 131.7
0.786 0.727 0.695 0.667 0.614 0.708 0.688 0.700 0.699
18.3 15.8 14.7 13.9 12.1 15.2 14.4 15.0 14.9
Average absolute deviation Residuals from Equation 9.
VOL. 51, NO. 4
0 0.1 -0.1 -0.1 0 0.0 0.1 0
0 0.5 0.4 0.2 0 0.4 0.4 0.4 0
0.03
0.28
0.0
APRIL 1959
603
Table V.
Normal Boiling Points, Densities, Surface Tensions, and Residuals from Correlation a t the Normal Boiling Points (Methanol-Water-Ethylene Glycol) Residual from Mole % S.B.P., PH.B.P, CS.B.P.. Pure comp. Methanol O c. G./Ml. Dynes/Cm. Correlationa correlation*
binary interaction constant, n’ = zlnl f zznz = 2 t i n i , Tr’ = T/T,’, and T,’ = Z I T ~ I t2Tcz = Z ( 2 i T C i ) . For a ternary system the equation developed is
+
Methanol-Water
u =
0
12.8 25.5 38.9 66.5 79.8 100
where n’ = 2ztnt, T,’ = ZziTCi,and A123 = ternary interaction constant. Equation 5 is similar to Wohl s 3suffix equation (24)for excess free energy, which also contains volume fractions. Wohl’s equation is basically a polynomial whereas Equations 4 and 5 with all interaction constants equal to zero relate surface tension as a hyperbolic function of composition. Equation 4 was fitted to the binary data of this work, as follows: 1. The exponent, n, was estimated for each component by the method of Simkin (78), who plots n us. the entropy change upon vaporization. 2. I n the case of ethylcyclohexane and ethylene glycol the critical temperature was estimated by the van der Waals Equation 2 and two surface tension points, one at 30” C. and one at the boiling point. 3. Constant A i was determined by Equation 2 for each pure component from the surface tension at boiling point. 4. A comparison temperature was selected as a basis for volume fraction calculations. The densities of the pure components at this temperature were recorded if known or estimated by the method of Hougen and Watson (9) if literature values were not available. 5 . The constant A%,was determined for each binary by a method of least squares, with the aid of an IBM card programmed computer.
Using the densities and critical temperatures (Table 111) for system methanol-water-ethylene glycol (components 1, 2, and 3, respectively), Equation 5 is u = 21
48.11
87.2 74.5 61.1 33.5 20.2 0
0.958 0.917 0.884 0.861 0.802 0.783 0.750
64.7 68.2 72.3 82.7 107.3 140.6 197.4
86.6 72.2 47.9 21.4 9.1 0
0.750 0.809 0.865 0.943 0.993 1.000 0.972
0 1.0 0.1 -0.9 -1.3 -0.9 0
0 0.4 -0.3 -1.2 -1.4 - 1.0 0
18.3 20.8 23.6 28.4 34.3 35.2 31.4
0 0.3 0.5 0.7 -0.6 -1.1 0
0 0.9 1.5 1.8 0.1 -0.8 0
0 1.5 -0.3 -0.6
0 0.8
Water-Ethylene Glycol
Water 100 90.6 80.8 61.2 40.6 23.6
100 102.8 106.0 114.4 128.0 145.3 197.4
0
0.958 0.989 1.005 1.025 1.018 1.012 0.972
58.8 51.2 49.0 44.3 40.7 37.8 31.4
-1.1 -1.2 - 1.0 -0.8 0
-0.7 -0.6 0
Methanol-Water-Ethylene Glycol
Methanol
Water
IO0
64.7 73.7 78.7 85.8 100.0 82.1 90.0 97.3 197.4
0
60.8 39.3 21.2 0 41.4 22.9 22.5
20.4 41.2 58.8 100 19.4 38.9 18.7
0
0
0.750 0.868 0.913 0.953 0.958 0.943 0.972 0.984 0.972
18.3 24.7 29.0 34.7 58.8 29.4 34.3 34.2 31.4
0 0.2 0.0 0.1 0 0.2 0.2 0.3
Average absolute deviation a
Residuals from Equation 6 .
Equation 7 should be reliable to 3% or 0.3 dyne per cm., whichever is greater, over the entire range (from freezing to critical temperatures) a t any concentration. In Equations 6 and 7 the binary and ternary interaction constants are all 19 Z ~ Z ? Z ~ 10,000
6.3
22
+-
10,000
(6)
small, indicating that the basic form of Equation 5 can be used to predict surface tensions of mixtures from those of pure
Equations 6 and 7 together with the densities and critical temperatures given in Table I11 summarize the surface tension data taken in this work. Also these equations provide a logical means for obtaining surface tensions at temperatures far removed from those of the normal boiling point. For the ternary hydrocarbon system,
components without appreciable error. If all interaction constants are set equal to zero, Equation 6 becomes
INDUSTRIAL A N b ENGINEERING CHEMISTRY
(1 -
u = 21
T,’)0.9
22
0
0.8
0.7 0.6 0 1.2 0.6 0.6
0
0
0.05
0.78
* Residuals from Equation 8.
Similarly for system toluene-n-octaneethylcyclohexane (components 1, and 2, 3, respectively), Equation 5 becomes
604
58.8 39.7 32.2 28.1 22.9 20.9 18.3
Methanol-Ethylene Glycol
100
(1 - T,’)0.9 8.2 2 1 2 2 28.3 2123 127.44 + %% - 10,l000 + 10,000
+-
100
2 3
48.11 + 127.44 + 72.81 Similarly Equation 7 becomes
(8)
( 1 - T?’)’.??
u = 21
2 3
(9)
Tables I V and V present the surface tension data and the residuals from Equations 6 and 7 and residuals predicted from the pure component data only from Equations 8 and 3. Table I V shows that the absolute average deviation of the experimental surface tension from that calculated by Equation 9 for the hydrocarbon ternary system is 0.03 dyne per cm. The absolute average deviation from that which would have been predicted using pure component data only is 0.28 dyne per cm. with the maximum being 0.6 dyne per cm. or 4.0%. The absolute average deviation of calculated data from experimental surface tension for the polar ternary system is 0.50 dyne per cm. from Equation 8 and 0.78 from the pure component correlation (Table V). The maximum deviation using pure component data only is 1.8 dynes per cm. or 6.370.
P R E D I C T I O N OF SURFACE T E N S I O N Limitation. T o establish the limitations on the correlation it is convenient to examine it Ivith statistical mechanics theory. -Maxwell and Boltzmann derived the relation
For the two ternary systems investigated the following equation is adequate for engineering purposes: u =
(1 - T,')%
(10)
XI' t
Ai
Figure 1 shows the experimental surface tension data plotted as points \rith the curves predicted from pure component data only using Equation 10: as well as the curves obtained from Equations 8 and 9. Accuracy. Estimates of the accuracy of the data are based on plots of the data and reproducibility of experimental points:
where n , = number of molecules of energy, e,, and T = temperature, K. Equation 11 was developed to determine the number of molecules of a given energy level in a given volume a t a fixed temperature for the case where attraction or repulsion forces \irere negligible. Let us assume that Equation 11 also predicts the ncmber of molecules of a given surface energy in the surface of a liquid mixture. If a l is the area, in square centimeters, per molecule of component 1 in the surface layer, then U I U I = ergs per molecule of component 1, and Equation 11 may be written for components 1 and 2 as
.kccuracy
Density, g./ml. At 30' C. At N.B.P. Refractive index at 30° C. N.B.P., C. Surface tension at N.B.P., dynes/ cm. Polar ternary system Nonpolar ternary system Composition, Mole yo 30' C. data Boiling point data
10.0001 10.005 =kO.O001 10.1 10.5 10.2 10.01 1 0 .1
MOLE % METHANOL
MOLE % METHANOL
MOLE % WATER
CORRELATION
40
60
60 10010
MOLE % n-OCTENE
20
40
60
80
MOLE 70TOLUENE
1000
20
40
60
80
100
MOLE Yo TOLUENE
B Figure 1. Surface tension at the normal boiling point is shown b y these curves when predicted from pure component data using Equations 8, 9, and 10 A.
Polar system.
8.
All other things being equal, the ratio (ni'n.Js would be proportional to (nl 'n?)*, the ratio of nl to n? in the bulk. Hence C1/C? is replaced bv ( n 'n2)b ~ and the result is
The constant, r . can be regarded as an empirical one depending upon the nature of components 1 and 2. However, as a first approximation, r may be the ratio of solvent-phobic groups to solventphilic groups possessed by the solute. Thus, for water solutions of methanol, ethanol, propanol, etc., the ratio 7 Lvould be 1, 2, 3, etc. For ethylene glycol-water it would be 2 2 = 1 , Equation 16 is similar to that propospd by Tamura and others ( 2 0 ) ; by substituting appropriate numbers into Equation 16 it will predict Traube's rule as a first approximation. Although Equation 16 is not theoretically rigorous, it does predict qualitatively a large amount of data. Csing the ratio, I , i n Equation 16 the follolring limitation is predicted :
0 -EXPERIMENTAL
20
where nl,, n2, are the molecules of components 1 and 2>respectiveIy, in a given surface area. Dividing Equation 12 by Equation 13 gives
If. in addition to the surface energies. some forces tend to cause incomplete miscibilitv, then another factor. 7 , should be added. This results in the equation
A
0
and
Nonpolar hydrocurbon system
1. If r is one or less, equation Lcith all interaction constants zero-i.e., Equation 10-will predict the surface tension of mixtures. 2. If r = 2 Equation 5 with binary interaction constants included will predict surface tensions within general engineering accuracy-e.g.. loyo. 3. If r is greater than 2: Equation 5 is unsatisfactory for predicting surface tensions of mixtures and recourse must be made to experimental data or some other correlation. VOL. 5 1 , NO. 4
APRIL 1959
605
4. If chemical combination of the components takes place, Equation 5 is unsatisfactory for predicting surface tensions of mixtures. For example, hydrazine and water mixtures, known to combine chemically, exhibit a maximum surface tension (7).
Table VI. Maximum Residuals from Correlation for Surface Tension o f Binary Mixtures at 30” C.
Data of Ling ( I S ) Max. Res. from
(1 - T,’)n’
u = 21
117.98 -b 78.47
+ 0.00717
(17)
+
(1 - T?’)%’ 21
t?
(18) 2 3
m+64.47+44.3; where components 1, 2, and 3 refer to ethyl acetate, toluene, and 1-butanol. respectively, n‘ = 1.1 z1 1.22 z z 0.8 23, and T,’ = 523.3 ti f 594.3 2 2 561 t 3 . The maximum deviation for this system was 0.42 dyne per cm. or 1.6%. T h e 25” C. densities (in g./ml.) were 0.8933, 0.8075, and 0.8599 for components 1, 2, and 3, respectively. I n Table V I the data of Ling ( 7 3 )
+
+
606
cm.
18.87 0.32 0.25
tion
72 1.4 1.1
+
SUBSCRIPTS 1, 2 = components = air b = bulk c = critical condition i, j , X- = components in a mixture L = liquid 7 = reduced condition s = surface v = vapor ~ e ’ = water
3.30
10.8
0.27 0.91
1.2 3.5
Acknowledgment
0.88
3.0
The authors acknowledge the assistance of the National Science Foundation for support of this investigation.
Predicted from pure component data.
References are compared to the values predicted by the pure component correlation, giving a maximum deviation 10.870 for the system benzene-2-chloroethanol, where r = 2 ’2. With this one exception, however, the correlation is satisfactory (within the limitations stated).
Conclusions
Z~Z?
where components 1 and 2 refer to water and 1,4.-dioxane, respectively, n’ = 0.8 z1 1.22 t 2 and T,’= 647.4 21 f 585 22. T h e maxiinum deviation a t any temperature is 1.56 dynes per cm. or 4%. Therefore, the binary interaction constants are essentially independent of temperature, and Equation 17 summarizes, for practical purposes, all of the surface tension data of Hovorka, Schaefer, and Driesbach. Equation 17 also gives a logical means of extrapolating their data. For checking the correlation of a multicomponent mixture, the data of Litkenhous, van Arsdall, and Hutchinson (74) on the system ethyl acetate-tcluene1-butanol were selected. Since the ratio, r, of solvent-phobic to solventphilic groups is less than 2 for all of these systems, the pure component correlation Equation 10 should give u =
% Dynes,‘ DeviaSystem I-Propanol-water Toluene-n-octane Acetone-1-butanol Benzene-2-chloroethanol Carbon tetrachloride-lpropanol Ethanol-l,4-dioxane Methanol-1,4-dioxane
= density, grams per ml. = surface tension
a
Values5 Comparison with Literature Data. T o show that the interaction constants were independent of temperature, good data were needed over a range of temperatures for a mixture with a n appreciable interaction constant. T h e data of Hovorka, Schaefer, and Dreisbach (70) on 1,4-dioxane-water from 10” to 80” C. were selected. T h e exponents for the van der Waals equation were estimated by Simkin’s (78) method. T h e pure component constants were evaluated a t 30” C. and the binary interaction constant was evaluated from the datum point a t 30°C. a t the composition, 0.1916 mole fraction dioxane. T h e 30” C. densities were used to calculate volume fractions. (The 19 mole Yo corresponds to 53 volume %.) The equation for the surface tension of the system water-l,4-dioxane is
p u
A simple correlation, Equation 10, relates surface tension to composition and temperature for a multicomponent mixture. T h e only experimental surface tension necessary is one point for each pure component a t any temperature, if 7, the ratio of solvent-phobic to solventphilic groups possessed by the solute, is 1 or less. This correlation can be used when experimental surface tension data are completely lacking by using the method of Tripathi (75, 27) to estimate the surface tension of the pure components. T h e correlation with binary constant3 is adequate for systems in which r is 2 or less. Nomenclature A a
= constant peculiar to each liquid = activity, or, area/molecule in
B
= constant
g
= acceleration of gravity = enthalpy = height of capillary rise
surface layer
H h
I = constant [PI = parachor [R]= molecular refraction T k n nD r
= temperature = Boltzmann constant
= constant = refractive index = radius of capillary, or, ratio of
x
=
t
=
A
= =
7
INDUSTRIAL AND ENGINEERING CHEMISTRY
solvent-phobic to solven t-philic groups mole fraction in liquid phase volume fraction a difference viscosity
(1) Baker, N. B., Gilbert, E. C., J . A m . Chem. Soc. 62, 2479 (1940). (2) Biron, E. J., J. Russ. Phys. Chem. SOC. 44, 1264 (1912). (3) Carbide and Carbon Chemicals Corp., New York, “Ethylene Glycol,” Bull. F 8327A (September 1956). (4) Carbide and Carbon Chemicals Corp., New York, “Methanol,” Bull. F 8141A, (January 1955). (5) Davis, D. S., IND.ENC. CHEM.34, 1231 (1942). (6) Dreisbach, R. R., “Physical Properties of Chemical Substances,” The Dow Chemical Co., Midland, Mich., 1953. (7) Ferguson, Allan, Phil. M a g . 31, 37 (1916). (8) Glasstone, Samuel, “Textbook of PhysicaI Chemistry,” pp. 1205-9, Van N o s trand, New York, 1946. (9iCHougen, 0. A,, Watson, K. M., Chemical Process Principles,” Part 11, pp. 502-4, Wiley, New York, 1947. (10) Hovorka, F., Schaefer, R. A., Dreisbach, D., J. Am. Chem. SOC. 58, 2264 (1936). (11) Kobe, K. A., Lynn, R. E., Chem. Revs. 52, 117 (1953). (12) Lange, N. A., “Handbook of Chemistrv.” 8th ed.. Handbook Publishers, Ini.,’ Sandusky,’Ohio, 1952. (13) Ling, T. D., IND.ENC. CHEM.,Chem. Eng. D a t a Series 3, 82 (1958). (14) Litkenhous, E. E., van Arsdall, J. D., Hutchinson, I. W., J . Phys. Chem. 44, 377 (1940). (15) Meissner, H. P., Michaels, A. S., IND.ENG.CHEM.41, 2782 (1949). (16) Quayle, 0. R., Chem. Rem. 53, 439 (1953). (17) Rossini, F. D., others, “Selected Values of Properties of Hydrocarbons,” A.P.I. Research Project 44, Carnegie Press, Pittsburgh, Pa., 1953. (18) Simkin, D. J., National Meetinq, Am. Inst. Chem. Engrs., Seattle, Wash., June 1957. (19) Souders, Mott, Jr., J . A m . Chem. SOC. 60, 154 (1938). (20) Tamura, M., Kurata, M., Odani, H., Busseiron Kenkyd (Researches on Chem. Phys.) 57, 1 - 8 (1952). (21) Tripathi, R . C., J . Indian Chem. soc. 18,411 (1941). (22) van der Waals. J. D.,, Z . .bhys. - Chem. ( h i p z i p ) 13, 716 (1894). (23) Weinaug, C. F., Katz, D. L., IND. F.No. :HEY. 35. 239 (1943). (24) Wohl, K., Trans. Am. Inst. Chem. Eng. 42, 215-49 (1946). ~
RECEIVED for review August 4, 1958 ACCEPTED December 15, 1958
