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edited hv .. JAMES 0 . SCHRECK UNIVERSITY OF NDRTYERN COLORADO GREELEY. CO 80638
An Analytical Balance as Tensiometer and Densimeter Manuel Sanchez-Rubio Gerencia de Planeacion industrial, Subgerencia de Planeaci6n de Refinerias. Petroieos Mexicanos, Mexico. D.F. 11320 J d R. Castellanos-Ortega and Jorge E. Puig Facultad de Ciencias Quimicas, Universidad de Guadalajara, Guadalajara. Jal. 44430, Mexico Earlier ( I ) we described a very simple and inexpensive Du Noiiy tensiometer that requires a plastic drinking straw, a rinn stand. a cork. a needle. a homemade nichrome rinn, and labjacks. Here we show how to convert a common laho~atory analvtical balance into an accurate ring tensiometer or densimekr. Using a balance with an accuracy of 1 mg, surface and interfacial tensions can be measured with an accuracy better than 0.1 dynelcm, whereas liquid densities can he measured with an accuracy better than 0.003 glcc. The Balance a s a Tenslometer From a thermodynamic point of view (2),surface (or interfacial) tension is the surface excess free energy defined by
where y is the surface tension; G, the Gihbs free energy; and A, the interfacial area. Surface tension can he also interpreted as the stress (force per unit length) that acts on the surface and operates perpendicular and inward from the boundaries of the surface, tending to decrease the interfacial area (3). .. Surface tension can be determined by measurin~the force reouired to DUN a solid ohiect (such as a wire rind through a s&ce; this is the basis of the Du Noiiy tensio%eter. ?his technique is described in the ASTM-D 1331 method (4), where a torsion wire is used to measure the force required to ~ u lal rinn through the surface (or interface). '1'0 convert an'malytical balance into a tensiometer, it is required to replace the balance pan with a counterweight of equal or slightly larger weight: In our case, the p& of a Mettler balance model H3 weighs about 30 g. So an aluminum wire (chosen because its ductility) weighing 30 g is coiled as shown in the figure, part a, and hung from the balance instead of the pan. Since only differences in weight are needed to calculate the surface tension, as detailed below. it is not necessarv to zero the balance. Next, a homemade nichrome ring (see ref 1 for details about it~construction, is also hunn- from the balance as is shown in the figure, . . pa& b. T o measure surface (or interfacial) tension, the ring should be placed under the surface (or interface) to be measured and the balance reading, m,, recorded. Next, the sample is slowly lowered with a lab jack (we found that a pneumatic jack works better than a mechanical one) until the ring is hanging free. The maximum reading, m,, should he recorded; usually this value occurs just before the ring breaks loose from the interface. This procedure is repeated several times to determine the reproducibility of the measurements. 158
Journal of Chemical Education
The surface tension can then be calculated from the equation:
where M is the maximum reading (m,) minus the reading whenthe ring isunder the interface (rn,),gis thegravitational constant, R is the radius of the ring, and f is a correction factor. In the case of liquid/air interfaces, this correction factor, which is provided in tabular form in the literature (51, depends on the ratio MlAp (where Ap is the difference in density of the two phases) apd on the ratio of the radius of the ring to the radius of the wire, Rlr. In the case of liquid1 liquid interfaces, an experimentally determined equation can be used:
with c = 0.04534 - 1.679(rlR). . . . and a = 0.7250 and b = 0.0009075 as universal constants for all rinm (fi). The re~roducihilitvof our measurements is within 1 mr. which is the a c c u r a c ~of the balance used. A comparison of surface tensions measured here with those reported in the literature is shown in Table 1. Temperature control ( f 0 . 1
Deslgn of the tenslometer. (a) Coiled aluminum counterweight (b) sketch of tensiometer and sample: (A) balance. (6)counterweight. (C)ring support. (0) ring. (E)]acketedbeaker, and (F) pneumatic jack.
Table 1.
Experlmntal and Literature Surlace Tensions of Pure Liquids
Table 2.
Experlrnenbl and Literature Densltles o( Pure Llqulds and NaCl Brlnes at 25 ' C T(%)
25
30
40
60
60
Exp. 0.66977 Lit. (8) 0.65925 CyclDhexane Exp. 0.78204 Lh.(8) 0.7786
0.65816 0.65471 0.77430 0.77385'
0.65428 0.65015 0.76656 0.7693
0.64009 0.64009 0.75623 0.7598
0.63493 0.6315 0.74849 0.7501
0.62718 0.622 0.73588 0.7405
Exp. 0.70461 Lit.(@ 0.70267 Exp. 0.73042 Lit.(@ 0.73012 Exp. 0.87883 Lit.(B) 0.8790
0.69816 0.69862 0.73755 0.72635 0.87109 0.8737
0.69429 0.69454 0.72268 0.72257 0.86593 0.8684
0.68396 0.6863 0.71494 0.7150 0.85497 0.8577
0.67680 0.6780 0.70719 0.7073 0.84657 0.8469
0.67106 0.6697 0.69945 0.6996 0.63360 0.8359
svface Tension (dynelcm) Experimental Literature ( 8 )
20
bane
Benzene
19.06 16.42 17.93 16.80 15.81 14.73 25.36 24.65 24.15 22.80 21.60 20.40 22.00 21.50 20.90 20.08 16.66 17.97 24.17 23.60 23.11 22.18 21.66 20.23 29.02 28.32 27.61 26.19 24.91 23.49
20 25 30 40 50
Water
18.40 17.68 17.37 16.35 15.33 14.31 25.24 24.65 24.06 22.87 21.68 20.49 21.62 21.14 20.67 19.72 18.77 17.81 23.83 23.87 22.91 21.99 21.07 20.15 28.85 28.20 27.56 26.26 24.97 23.62
20 25
OC) was provided by circulating thermostated water through a jacketed beaker made in our glass shop. The major sources of error were found to be the cleanliness of the ring and the determination of the ring diameter. Cleaning the ring with hoiling detergent solution (we used sodium dodecylsulfate from Merck), rinsing it well, and flaming it with a Bunsen burner immediately before using it gave excellent results. When determining the diameter of the ring (this can be done with a cathetometer), one must avoid deforming the ring. The value of the ring diameter used here was the average of several measurements taken a t different positions. Using a balance with sensitivity of 1mg and a ring with a 1-cm radius, the accuracy of the measurement, Ay, can he estimated by substituting these values in eq 2: Ay
s (0.00U(980) = 0.08 dyne,m 2*
me Balance a s a Danslmetw I t is well known (7)that fluid densities can he determined by measuring the buoyancy force exerted on a solid object of known volume or density immersed in the fluid. Hence, any balance can be used to measured liquid densities using chimedes's principle. To convert the balance into a densimeter, it is again necessary to replace the balance pan with the coiled aluminum counterweight and substitute the ring with a solid rod. This solid material must he inert to and denser than the liquid whose density is being measured. We recommend using a
Octane
Decane Benzene
Exp 100659 099885 099627 099110 098852 098594 LIt ( 8 ) 0 99823 0 99707 0 99566 0 99225 0 98807 0 98324
Water
(M%)
Exp. (glee)
Lit. (91 WCC)
1 2 4 8 12 16
1.00788 1.01433 1.02466 1.05434 1.08531 1.11757
1.00409 1.01112 1.02530 1.05412 1.06365 1.11401
NaCl Brlne
hoUow glass rod with a small handle by which t o hang it for low-density liquids. To measure liouid densities. first weieh the elass rod in air, W,.;then weigh the rod while submeyged in bater, W,,,. Using the well-known equation of Archimedes's principle (n,solve for the volume of liquid displaced by the glass rod (which is equal to the volume of the rod, V,I:
where P, is the density of water a t the temperature of measurement. Next, weigh the glass rod while immersed in the test liquid, W,,L From Archimedes's principle:
The formula t o calculate the test liquid density, p ~ is, then obtained from eqs 4 and 5:
I t is important to notice that a d e c e of the wire used to hang the rod is also immersed during measurements. Therefore, a correction for the volume of liquid displaced by the immersed piece of wire must he taken into account for accurate measurements. We recommend first weighing the rod in air with a piece of wire of equivalent length and diameter of that immersed during the measurement, Wjg,., and then usine this value in eo 6 instead of W.. We also recommend to use a thin nichroke or platinum &e. An alternative is to utilize a thin nvlon strine whose weieht can be neelected so that W,, w',,;however, this stringmust he replaced after each measurement to minimize contamination of the following sample. Experimental densities and literature values are reported in Table 2. Temperature was controlled within 0.1 'C using a iacketed beaker. The agreement is good and it can he improved by using a better temperature control and a more sensitive halance.
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Volume 6.3 Number 2 February 1991
159
The accuracy of the density determinations can be estimated as follows: the difference between W , , and W g ,is~ limited by the sensitivity of the balance: in our case, W E , W g ,2~1 mg. Since the density of theglassrod used, calculated from its weight in air (623mg) and eq 4, is 1.719 glcc, then:
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(1)(*.719' = 0,0,7,3 APL 1- 622
Evidently, the accuracy of the measurement, A ~ Lcan , be improved by increasing the balance sensitivity or by decreasing the density of the rod. Conclusions
In this work we have descrihed how to convert an analvtical balance into an accurate ring tensiometer or densimeter. The surface tension values obtained here are com~arable with those measured with much more expensive commer-
180
Journal of Chemical Education
cially available ring tensiometers. The precision of the density measurements can be improved by using a more sensitive balance (0.1 mg or better) and more accurate temperature
control. With this scheme, one can have a halance, a tensiometer, and a densimeter for a cost much lower than that of the three separate instruments. LICrature Clted 1, 2. 3. 4. 5. 6. 7. 8. 9. 10.
S6nchez-Rnhi0, M.: Gordillo, B.: Rushforth, D. S. J. Chem. Edue. 1983,60,7&71. Adamsom. A. W. Physical Chemistry ofSur/ocea; W i l v : New York, 1982. Hiemone,P. C. Plin~pieaofColloidondSur/ace Chemisfry;Dekker: New York,1977. ASTM D-I331 Mothad. Surfme and InLsr/aciol Tension of Solutions of SurfoeeAct& &mta. Harkina, W. D.; Jordan, H. F. J. Am. Chem Soe. 1930,52,1751. Freud, B.H.:Rsud,H. 2. J.Am. Chem.Soc. 1930,52,1772. Warren, M. L. hlrnductoryPhy8ics: W. H. Freeman: San Francisco, 1979: p 193. American PeUoleum Institute Research Pmjed 44, Selected Prop~rfieaof Hydiydrocor bona and Related Compounds; 1966: Vol. 11. We8t.R. C. CRCHondbookoiChamzstryondPhysiea. SOthed.;TheChemicalRubber Co.: Cleveland, 1970. Perry. R. H.: Chilton, C. H. Chemical Enainmring H a n d h d , 5th ad.; McGrsw-Hill: New York. 1973.
