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 den- simekr. 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 inter-

facial) 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 interpret- ed 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 l l a 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 alumi- num 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 be- low. it is not necessarv to zero the balance. Next, a home- made nichrome ring (see ref 1 for details about it~construc- tion, is also hunn from the balance as is shown in the figure, - . . pa& b.

To measure surface (or interfacial) tension, the ring should be placed under the surface (or interface) to be mea- sured and the balance reading, m,, recorded. Next, the sam- ple is slowly lowered with a lab jack (we found that a pneu- matic jack works better than a mechanical one) until the ring is hanging free. The maximum reading, m,, should he re- corded; 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.

The surface tension can then be calculated from the equa- tion:

where M is the maximum reading (m,) minus the reading whenthe ring isunder the interface (rn,),gis thegravitation- al 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 (f i).

The re~roducihilitv of our measurements is within 1 mr. which is the accurac~ of the balance used. A comparison of surface tensions measured here with those reported in the literature is shown in Table 1. Temperature control ( f0 .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)]acketed beaker, and (F) pneumatic jack.

158 Journal of Chemical Education

Table 1. Experlmntal and Literature Surlace Tensions of Pure Liquids

Benzene 20 25 30 40 50

Water 20 25

svface Tension (dynelcm) Experimental Literature (8 )

19.06 18.40 16.42 17.68 17.93 17.37 16.80 16.35 15.81 15.33 14.73 14.31

25.36 25.24 24.65 24.65 24.15 24.06 22.80 22.87 21.60 21.68 20.40 20.49

22.00 21.62 21.50 21.14 20.90 20.67 20.08 19.72 16.66 18.77 17.97 17.81

24.17 23.83 23.60 23.87 23.11 22.91 22.18 21.99 21.66 21.07 20.23 20.15 29.02 28.85 28.32 28.20 27.61 27.56 26.19 26.26 24.91 24.97 23.49 23.62

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 i t 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 1 mg 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 neces- sary 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

Table 2. Experlrnenbl and Literature Densltles o( Pure Llqulds and NaCl Brlnes at 25 ' C

T(%) 20 25 30 40 60 60

b a n e Exp. 0.66977 0.65816 0.65428 0.64009 0.63493 0.62718 Lit. (8) 0.65925 0.65471 0.65015 0.64009 0.6315 0.622

CyclDhexane Exp. 0.78204 0.77430 0.76656 0.75623 0.74849 0.73588 Lh.(8) 0.7786 0.77385' 0.7693 0.7598 0.7501 0.7405

Octane Exp. 0.70461 0.69816 0.69429 0.68396 0.67680 0.67106 Lit.(@ 0.70267 0.69862 0.69454 0.6863 0.6780 0.6697

Decane Exp. 0.73042 0.73755 0.72268 0.71494 0.70719 0.69945 Lit.(@ 0.73012 0.72635 0.72257 0.7150 0.7073 0.6996

Benzene Exp. 0.87883 0.87109 0.86593 0.85497 0.84657 0.63360 Lit.(B) 0.8790 0.8737 0.8684 0.8577 0.8469 0.8359

Water Exp 100659 099885 099627 099110 098852 098594 LIt (8 ) 0 99823 0 99707 0 99566 0 99225 0 98807 0 98324

NaCl Brlne Exp. Lit. (91 (M%) (glee) WCC)

1 1.00788 1.00409 2 1.01433 1.01112 4 1.02466 1.02530 8 1.05434 1.05412

12 1.08531 1.06365 16 1.11757 1.11401

hoUow glass rod with a small handle by which to hang i t 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 mea- surement. Next, weigh the glass rod while immersed in the test liquid, W,,L From Archimedes's principle:

The formula to calculate the test liquid density, p ~ , is then obtained from eqs 4 and 5:

I t is important to notice that a dece of the wire used to hang the rod is also immersed during measurements. There- fore, a correction for the volume of liquid displaced by the immersed piece of wire must he taken into account for accu- rate 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 follow- ing 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 i t can he im- proved by using a better temperature control and a more sensitive halance.

Volume 6.3 Number 2 February 1991 159

The accuracy of the density determinations can be esti- mated 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, calculat- ed from its weight in air (623 mg) and eq 4, is 1.719 glcc, then:

(1)(*.719' = 0,0,,7,,3 APL 1- 622

Evidently, the accuracy of the measurement, A ~ L , can be improved by increasing the balance sensitivity or by de- creasing the density of the rod.

Conclusions In this work we have descrihed how to convert an analvti-

cal 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-

cially available ring tensiometers. The precision of the densi- ty 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 tensi- ometer, and a densimeter for a cost much lower than that of the three separate instruments.

LICrature Clted 1, S6nchez-Rnhi0, M.: Gordillo, B.: Rushforth, D. S. J. Chem. Edue. 1983,60,7&71. 2. Adamsom. A. W. Physical Chemistry ofSur/ocea; Wilv: New York, 1982. 3. Hiemone,P. C. Plin~pieaofColloidondSur/ace Chemisfry;Dekker: New York, 1977. 4. ASTM D-I331 Mothad. Surfme and InLsr/aciol Tension of Solutions of Surfoee-

Act& &mta. 5. Harkina, W. D.; Jordan, H. F. J. Am. Chem Soe. 1930,52,1751. 6. Freud, B.H.:Rsud,H. 2. J.Am. Chem.Soc. 1930,52,1772. 7. Warren, M. L. hlrnductoryPhy8ics: W. H. Freeman: San Francisco, 1979: p 193. 8. American PeUoleum Institute Research Pmjed 44, Selected Prop~rfiea of Hydiydrocor

bona and Related Compounds; 1966: Vol. 11. 9. We8t.R. C. CRCHondbookoiChamzstryondPhysiea. SOthed.;TheChemicalRubber

Co.: Cleveland, 1970. 10. Perry. R. H.: Chilton, C. H. Chemical Enainmring H a n d h d , 5th ad.; McGrsw-Hill:

New York. 1973.

180 Journal of Chemical Education