Langmuir 1992,8, 2644-2648
2644
Surface Tension Measurements of Benzyl Benzoate Using the Sugden Maximum Bubble Pressure Method James L. Ross, W. D. Bruce, and William S.Janna* Department of Mechanical Engineering, Memphis State University, Memphis, Tennessee 38152 Received May 15,1992. In Final Form: August 13, 1992
The surface tension of benzyl benzoate in air was measured by Sugden’s maximum bubble pressure method. Data were obtained with several test liquids in order to assess the accuracy of the method. The liquids used were distilled water, isopropyl alcohol, benzyl benzoate, and methyl salicylate. In all cases, the greatest discrepancy between our results and published data occurred for benzyl benzoate. Percent errors in the benzyl benzoate data averaged 8%, while for the other fluids the average percent error was less than 1% . Consequently, a need exists for presenting improved data on the surface tension of benzyl benzoate. Extended surface tension data were measured using the Sugden maximum bubble pressure method. Results are presented here and compared to values found in the literature.
Introduction New experiments are constantly being sought for the traditional undergraduate fluid mechanics laboratory. Recently, surface tension experiments were devised and introduced. While the methodswere being calibrated with various liquids of known surface tension, it was discovered that the published values for surface tension of benzyl benzoate might need improvement. Thus, this study was undertaken in order to present the new data. Theory Molecules at the surface of a liquid are subjected to strong attractiveforces exerted by other molecules in their vicinity. The resultant of these attractive forces acta in a plane which is tangent to the surface at a particular point. The magnitude of this resultant force acting perpendicular to a line of unit length in the surface is known as the surface tension. The surface at which the surface tension exists is between the liquid phase and its saturated vapor in air.l A more physically appealing definitionof surface tension exists.2 Consider that a certain amount of energy is required to reach below the free surface of a liquid and pull molecules upward to the surface to form a new area. The energy required per unit area formed is defined as the surface tension. There are several methods for measuringsurfacetension. The familiar ones are (1)the capillary rise method, (2) the ring method, and (3) Sugden’s maximum bubble pressure method. In the capillary rise method, a capillary tube with axis vertical is partially submerged in the liquid. Due to surface tension effects, the liquid will rise inside the tube to a height which is a function of the surface tension. A discussion of improvements or corrections to the basic method are given by Adam.3 The Du Nouy ring detachment method is a quick and reasonably accurate method for determining the surface tension of .a liquid. A platinum-iridium ring is submerged just below the free surface of a liquid. The ring is suspended from the end of a lever arm which lifts the ring up and out of the liquid.
* To whom correspondence should be addressed.
(1) Daniels, F.; et al. Erperimental Physical Chemistry, 7th ed.; McGraw-Hik New York, 1970; pp 359-365. (2) Janna, W. S. Introduction to Fluid Mechanics; PWS Publishers: Boston, 1983; pp 13-15, 27, 28. (3) Adam, N. K. The Physics and Chemiatry of Surfaces;Dover: New York. 1968.
The ring eventually becomes *caughtnin the surface and ultimately breaks free. The force required to detach the platinum-iridium ring from the surface is thus measured. On the basis of elementary theory, the force should be equal to twice the perimeter (inside circumference plus outside circumference) of the ring times the surfaca tension. To obtain an accurate result with a real ring, however, the force must be multiplied by a correction factor that varies from 0.76 to 1.1. An excellent description of the ring method including factors that affect the accuracy of measurementa is presented by Harkins and Alexander.’ TheSugden maximum bubble pressure method isasimple but accurate method of determining the surface tension of a liquid. It is necessary in this method to form bubbles at the tip of large- and small-diameter tubes while they are submerged in the test liquid. As bubbles are formed by either tube, a manometer is used to precisely measure the correspondingpressure in the flow line. The difference in the pressures is then related to the surface tension. Determiningsurface tension by measuring the pressure required to form bubbles from the submerged tip of a single vertical tube was first suggested by Simon.6 Jaege+l7 developed and extensively used the method for determining the surfacetension of a large number of substances. Canto# gave the theory of the method and also used it to obtain surface tension data. The bubble pressure method in the above-mentioned studiesk8 involved the use of a single submerged tube to obtain data. Sugden9Joadvanced the use of two tubes. A single tube gives data which are a function of the radius of the tube which can lead to appreciable error. Sugden suggested that two tubes be used and immersed to the same depth. The pressure required to liberate bubbles from each partially submerged tube is then measured, and the pressure differenceis related to the surface tension. Errors introduced by the use of each tube cancel when the pressure difference is determined. Figure 1 is a sketch of the (4) Harkins, W. D.; Alexander, A. E. In Technique of Organic Chemistry, vol. 1, Physical Methods of Organic Chemistry, 3rd ed.; Weiseberger, A., Ed.;Interscience: New York, 1959; Part 1, Chapter 14, pp 786-797. (5) Simon. Ann. Chim. Phys. 1861,32 (iii), 5. (6) Jaeger, F. M. Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. XI.,Abt. 2A 1891,100, 246, 493. (7) Jaeger, F. M. 2.Anorg. Chem. 1917, 101, 1. (8) Cantor, Wied Ann. 1892,47, 399. (9) Sugden, S. J. Chem. SOC.1922,121,122,858-868. (IO)Sugden, 5.J. Chem. SOC.1924,126, 27-41.
0743-7463/92/2408-2644$03.00/00 1992 American Chemical Society
Langmuir, Vol. 8, No. 11, 1992 2645
Surface Tension Measurements of Benzyl Benzoate
hcad tank
1
indincd manometer
hemispherical. The accuracycan be further improvedwith the use of a second tube9J0which results in avoiding the need to determine the immersion depth d of the tube. The larger diameter tube is used as a reference pressure tube and should be immersed to exactly the same depth as the measurement tube. When pressure is measured for both tubes, we write
pressure tank
Pmml- P A
= 2glr1+ pgd - p g d
~ " 2 - PA
= 2gIr2 + pgd- P&
and Designatingsubscript 2 as the larger tube, we subtract the second equation from the first to get Pmml-
pm-2 = 2gIr1- 2gIr2
Solving for surface tension gives Ap (2) 2(1lr1- 11r2) Working with the above equation is not difficult except for measuring the inside radius of the smaller tube rl. Results obtained with eq 2 can be improved, however, the objective beingto measure surfacetension with the greatest accuracy possible. So SugdenlO incorporatedrefinements to developan empiricalrelationshipwhich allows the liquid surface tension to be estimated to within 0.3%. The Sugden equation is u=
Figure 1. Schematic of the components needed for Sugden's maximum bubble pressure method (drawing not to scale).
Figure 2. Schematic of an air bubble being formed a t the submerged tip of a capillary tube.
apparatus used in this study for measuring surface tension with the Sugden method. Analysis Consider a bubble being formed at the end of a partially submerged tube as shown in Figure 2. The tube radius is R, and it is submerged to a depth d . The bubble is identified as ABC and its bottom-most point is B. The liquid density is p , and the vapor density is pv. When a gas bubble is formed at the end of a tube that extends below the surface of a liquid, the pressure inside the bubble must be greater than the pressure outside the bubble. The pressure within the bubble increases to a maximum, correspondingto a hemispherical bubble, and then decreases as the bubble breaks away from the tip of the tube. The maximum pressure that will exist at the tip of the tube is Pmm. The pressure at the submerged end of the tube is PA. The difference between these pressures is (1) = pgd - p& + 2gIr Equation 1 can be used for a single submerged tube which is the basis of the Jaeger m e t h ~ d . ~Continuing ~' only with eq 1 and working toward measuring surface tension is difficult because accurately determining the depth of submergence d is cumbersome. For more accurate results, the method should be refined to account for the departure of bubble shape from Pmm - P A
The constant C is determined by calibratingthe apparatus with a liquid of known surface tension. The inside radius of the larger tube r2 remains in the equation because the pressure obtained with this tube is the reference pressure. The apparatus used in the Sugden method (Figure 1) was fabricated at Memphis State Universityusing standard chemistry laboratory equipment. The outer vessel containing the tubes is an Erlenmeyer flask with a vent open to the atmosphere. The rubber stopper in the flask holds the two glass tubes in position. The smaller tube has an inside diameter that is less than 0.2 mm. The larger tube inside diameter is 2.10 mm. Allother flasksand connecting tubing are readily available. Constant-Temperature Bath A constant-temperature bath was used in the experiments to maintain liquid samplesat constant temperature. The bath (ColeParmer Model No. 1266-02)could maintain sampleswithin f0.02 "C of the set point in the temperature range of 5-150 "C. Experimental Rssults and Discussion The Sugden method was used to measure the surface tension of distilled water, isopropyl alcohol, methyl salicylate, and benzyl benzoate. These preliminary data were compared to those found in Lange's Handbook of Chemistry.ll For distilled water at 10 "C, the percent error was 0.56% ;for isopropyl alcohol also at 10 "C,the error was 0.42 % . For methyl salicylate at 50 "C,the error averaged 0.29%. For benzyl benzoate at 50 "C and at 60 "C, the error in seven measurementsaveraged 8.1 % .In all cases, the greatest percent error was for benzyl benzoate. It should be mentioned that chemicalsof fairly high purity (11) Dean, J. A. Lunge's Handbook of Chemistry, 12th ed.; McGrawHilk New York, 1979.
2646 Langmuir, Vol. 8,No. 11,1992
Ross et al.
Table I. Density and Specific Gravity Data of Benzyl Benzoate specific specific T/"C p/(kg/m3) gravity0 T/OC p/(kg/m3) gravity0 10.1 1126.7 1.1287 82.5 1067.0 1.0689 22.0 1117.1 1.1191 82.9 1066.7 1.0686 34.7 1105.9 1.1079 89.7 1063.3 1.0652 58.7 1088.5 1.0905 118.0 1040.4 1.0423 73.9 1075.5 1.0774 ~~
(I
Specific gravity based on water density of 998.20 kg/m3.
data available in the literature on the surface tension of benzyl benzoate needed updating. Therefore, the Sugden maximum bubble pressure method was used to obtain improved and extensive data of the surface tension of benzyl benzoate. In order to use eq 3 to find surfacetension, it is necessary to have data on the density of benzyl benzoate. Data were obtained in this study using a standard Westphal balance, and are shown in Table I. The density and specificgravity of benzyl benzoate are reported as a function of temperature. Figure 3 shows a graph of density versus temperature. A least-squares fit of the data yielded p/(kg/m3) = 1134.5- 0.8029(T/OC) valid over the temperature range
(4)
283 I TI 391 K with
0
20
40
60
80
100
120
T/T
Figure 3. Density of benzyl benzoate as a function of temperature; data obtained in this study.
were used for the present work. The benzyl benzoate purity was at least 99% according to the manufacturer. On the basis of experience with the method and the comparative results obtained, it was concluded that the
r2 = 0.9990 Lange's Handbook of Chemistry" gives the density of benzyl benzoate at 25 "C as 1112.1 kg/m3. The above equation predicts the density of benzyl benzoate at 25 OC as 1114.5 kg/m3. The percent error is calculated as 0.22%. Table I1 provides updated data on the surface tension of benzyl benzoate obtained in this study using the Sugden maximum bubble pressure method. Column 1 is temperature (K).Column 3 is the measured pressure required to liberate an air bubble from the submerged tip of the smaller tube. Column 4 is the measured pressure developed when a bubble is liberated from the tip of the larger tube. Column 5 shows the pressure difference. The data are divided into groups accordingto temperature. Several trials were made for each temperature, and an average surface tension was calculated. Column 6 is the surface
Table 11. Surface Tension Data for Benzyl Benzoate Using the Sugden Maximum Bubble Pressure Method. p,&(in. 283.2 283.2 283.2 283.2 283.2 290.2 290.2 290.2 290.2 290.2 295.2 295.2 295.2 295.2 295.2 308.2 308.2 308.2 308.2 308.2 323.2 323.2 323.2 323.2 323.2 333.2 333.2 333.2 333.2 333.2 348.2 348.2 (I
0.993 672 0.0450 0.0448 348.2 3.22 1074.3 0.985 3.23 0.998 666 0.0446 348.2 1074.3 0.984 3.21 1.OOO 671 0.0449 348.2 1074.3 0.986 0.995 672 0.0449 358.2 3.17 1.010 1066.3 0.996 3.18 669 0.0448 358.2 1066.3 1.020 3.17 LOO0 1.OOO 658 0.0440 0.0435 358.2 1066.3 3.15 1.020 358.3 1.030 646 0.0432 1066.2 3.17 0.0437 1.030 358.3 1.OOO 653 1066.2 3.18 1.030 1.020 0.0432 358.3 646 1066.2 3.17 1.020 1.010 358.3 646 0.0432 1066.2 3.18 1.030 0.985 650 0.0435 0.0434 358.3 1066.2 3.12 1061.5 0.999 364.2 0.983 650 0.0435 3.12 1061.5 0.995 364.2 0.985 650 0.0435 3.11 0.995 364.2 0.985 650 0.0435 1061.5 3.11 1061.5 0.995 364.2 0.983 648 0.0433 3.12 0.992 1061.5 0.995 625 0.0419 0.0418 364.2 2.95 0.995 622 0.0417 1038.2 393.2 0.998 0.995 0.0418 2.95 1038.2 393.2 0.997 625 2.95 1038.2 393.2 0.997 0.993 625 0.0418 2.95 0.996 0.993 0.0417 623 1038.2 393.2 0.987 0.0401 0.0401 393.2 2.95 1038.2 0.996 599 2.78 0.988 599 0.0401 1014.1 1.OOO 423.2 2.78 1.010 423.2 0.990 599 0.0401 1014.1 0.990 2.78 1014.1 1.OOO 423.2 0.0401 599 2.78 0.991 1014.1 0.999 423.2 598 0.0401 0.992 2.78 1.OOO 581 0.0389 0.0389 423.2 1014.1 2.79 1.050 0.992 0.0389 581 1014.1 423.2 0.988 2.79 1014.1 1.040 423.2 579 0.0388 0.989 2.78 1014.1 1.040 423.2 579 0.0388 2.79 1.030 423.2 0.988 0.0390 582 1014.1 0.987 2.79 1014.1 1.040 0.0372 0.0372 423.2 555 0.990 554 0.0371 10-6 m;g = 9.797 37 m/s2;r2 = 1.05 X m; temperature of benzyl benzoate is shown.
1126.5 1126.5 1126.5 1126.5 1126.5 1120.9 1120.9 1120.9 1120.9 1120.9 1116.9 1116.9 1116.9 1116.9 1116.9 1106.4 1106.4 1106.4 1106.4 1106.4 1094.4 1094.4 1094.4 1094.4 1094.4 1086.4 1086.4 1086.4 1086.4 1086.4 1074.3 1074.3
C = 6.61 X
3.70 3.68 3.70 3.70 3.69 3.65 3.63 3.63 3.62 3.62 3.60 3.60 3.60 3.60 3.59 3.51 3.50 3.51 3.51 3.50 3.40 3.40 3.40 3.40 3.40 3.33 3.33 3.32 3.32 3.33 3.22 3.22
of H20)
o/(N/m) 555 558 552 537 537 539 529 532 534 537 534 527 528 525 525 528 485 485 485 485 485 442 440 442 442 442 432 435 432 437 435
0.0372 0.0374 0.0370 0.0360 0.0360 0.0361 0.0355 0.0356 0.0358 0.0360 0.0358 0.0353 0.0354 0.0352 0.0352 0.0354 0.0325 0.0326 0.0326 0.0326 0.0326 0.0297 0.0295 0.0297 0.0297 0.0297 0.0290 0.0292 0.0290 0.0294 0.0292
0.0360 0.0357
0.0353
0.0326
0.0294
Surface Tension Measurements of Benzyl Benzoate Table 111.
Langmuir, Vol. 8, No. 11,1992 2647
A Comparison of the Results of This Study to
01)5
Literature Values
1
1
u/(N/m)
283.2 290.2 293.2 295.0 295.2 308.2 313.2 323.2 333.2 348.2 353.2 358.2 358.3 364.0 364.2 373.2 383.2 393.2 403.2 413.2 423.2 433.2 443.2 463.2 473.2 483.7
0.0448 0.0435 0.045 9 0.0474 0.0434 0.0418 0.043 81 0.0401 0.0389 0.0372
0.041 68 0.039 55 0.021 ' 250
0.0360 0.0357
'
..
'
I
300
0.0358
'
I
'
'
.
'
350
8
'
'
'
.
400
I
450
'
'
'
1
I 500
T/K
0.0353
Figure 4. Surface tension of benzyl benzoate aa a function of temperature for all data: (a) this study; ( 0 )ref 13; (A)ref 14;
0.037 42 0.0337 0.0326
. .
( 0 ) capillary tube.
0.035 29 0.0313 0.033 16
0.0294 0.03103 0.029 96 0.02783 0.026 77
0.0266
tension as calculated using eq 3, while column 7 is the average value for each group. Data in column 6 (this study) are accurate to within *0.0006, as calculated with the method outlined by Moffatt,12which is discussed later. Constants for the apparatus are provided as notes at the end of the table. Table I11 provides a comparison of the surface tension data of this study to surface tension data found in the l i t e r a t ~ r e . ' ~All J ~ are listed as a function of temperature which is given in column 1. Column 2 is a summary of the Table I1 data obtained by using the Sugden method with a calculated accuracy of *O.o006 N/m. Column 3 is data found in the International Critical Tables,13 with a reported accuracy of h0.002 N/m. Column 4 is data collected by Jasper,14 accurate to a reported value of &0.00190. The Jasper treatise14 was published in 1967, but data contained therein were obtained in 1917 by use of the Jaeger method, Le., using a single submerged tube. (Another collection of Jasper's data are provided in ref 15.) As a further check of our results, the capillary rise method was used to obtain average surface tension values at two other temperatures. Column 5 of Table I11 is data obtained using the capillary rise method. Figure 4 is a graph of surface tension versus temperature, with all data from Table I11 plotted. Figure 5 is a graph of surfacetension versus temperature for the data of this study, using the Sugden maximum bubble pressure method. A least-squares analysis performed for these data yields the linear relationship u/(N/m) = 0.07567- 0.0001102(T/K) valid over the temperature range 283 IT I423 K with (12) Moffatt, R. J. Exp. Therm. Fluid Sci. 1988, 1, 3-17.
(5)
(13) Washburn,E. W., Ed.ZnternationaZCritical TabZesofNumericaZ Data, Physics, Chemistry and Technology; McGraw-Hilk New York, 1928; Vol. 4. (14) Jasper, J. J. In Treatise on Analytical Chemistry; Kolthoff, I. M., Elving, P. J., Ede.; Interscience: New York, 1967; Vol. 7, p 4612. (15) J . Phys. Chem. Ref. Data 1972,1, 841-1010.
0.M
250
300
3%
400
450
TJK
Figure 5. Surface tension of benzyl benzoate aa a function of temperature measured using the Sugden maximum bubble pressure technique.
r2 = 0.9968 Also considered was fitting the data with a quadratic equation. An analysis performed for the data of Figure 5 gave the result a/(N/m) = 0.08770- 0.0001803(T/K)+
O.OOOOO01008(?a/K)(6) valid over the temperature range
283 5 T I423 K with
r2 = 0.998 Error Analysis An analvsis was Derformed in order to determine the accuracy of the results displayed in Table 11. The measurementsof significancewere the pressuresp-1 and p-2, and the temperature of the samples, T.The smallest scale division on the readout device for each of these parameters is shown in Table IV. Pressures and temperature were allowed to vary by 1/2 of the smallest scale division, and the calculations were repeated. The effect of each variation was determined, and the overall variation was obtained by adding the individual ones. This wae
Ross et ai.
2648 Langmuir, Vol. 8,No. 11, 1992 Table IV. Scale Divisions of Manometer and Thermometer (Bath Temperature) for Error Analysis quantity measd for each run p-1 p w
T total
small?.$ scale divlsion 0.05 in. of water 0.01 in. of water 0.1 OC up to 101 OC 1 O C above 101 OC
effect on surface tension 0.0005 N/m 0.0001 N/m negligible negligible +O.o006 N/m
max % error 1.57%(at 150 O C ) 0.44% (at 150 "C) 2.01 %
done according to the method outlined by Moffatt,12to determine the maximum error in the surface tension measurements. The maximum variation in surface tension was found to be *0.0006 N/m, or 12.01%.
Conclusions It was evident that the Sugden maximum bubble pressure method is a convenient and accurate way of measuring surfacetension. The method was used to obtain extensive data on the surface tension of benzyl benzoate. In the course of this study, the density of benzyl benzoate was measured. It was found that the density of benzyl benzoate can be predicted with eq 4. The surface tension of benzyl benzoate can be predicted with eq 5 or 6. The error in the surface tension measurement is f0.0006N/m. The variability in the data of this study is slight, but the variability in the data reported by Jasper14is also slight.
The data obtained here are consistently about 0.002 N/m less than those obtained by Jasper. Another check on these results would be preferable.
Nomenclature C = apparatus constant d = depth of submergence of tube
F = correction factor, dimensionless g = local acceleration due to gravity h = distance from bottom of tube to lowest part of bubble p-1 = pressure required to form bubbles at the smaller diameter tube ~ m - 2 = pressure required to form bubbles at the larger diameter tube Pmm = maximum bubble pressure AP P m s l l - Pmslz p = density of liquid sample pv = density of vapor R = inside radius of tube r = correlation coefficient, dimensionless rl = inside radius of smaller tube r2 = inside radius of larger diameter tube u = surface tension of liquid ua = apparent surfacetension read from device, using ring method T = temperature V = volume of liquid raised in capillary tube
