ESTIMATION OF AVOGADRO'S NUMBER An Experiment for General Chemistry Laboratory L. CARROLL KING and E. K. NEILSEN1 Northwestern University, Evanston, Illinois
IN
INTRODUC,TORY courses in college chemistry the concept of molecular weight and atomic weight can be illustrated by well-eshblished laboratory experiments or classroom demonstrations. After demonstration or laboratory work with the properties of gases it is not difficult to introduce the first postulate of the atomic molecular theory, "Matter is composed of small partirles called molecules." A natural qnest,ion rvhich follows this postulate is, "What is the siae of a molecule?" For the mature chemist this question has been answered by study of the various ways for estimation of Avogadro's numher. For the beginning student, however, the size of molecules and the magnitude of Avogadro's number is usually presented as something to he accepted now and justified later. It seemed to us that the estimation of Avogadro's number and molecular siae was of sufficient interest to the beginniug student to be incorporated in the laboratory of the first year college course. With this in mind an experiment for determination of the thickness of a monomolecular film was adapted for use by beginning students in the laboratory. The data obtained from this experiment were used to estimate Avogadro's number.
DIRECTION GIVEN TO STUDENT3 In this experiment a direct measurement of the size of s. molecule is made. To do this a known volume of oleic acid is spread o n a water surface and the area of the surface film is measured. From tho area of the surface film and the volume of the oleie aeid in the film it is ponsihle to cslculste the thickness of the film. It will he evident that the film (if it e n i a t ~must ) he at least one molecule thick. From the film thickness, the molecular weight, and donaity of the oleic acid in the film it is possible to calculate Avogadro's number "N," if one assumes Rome reasanahle shape for the molecule and that the film is one molecule thick.
Figure
198
I.
Tray with Monomolecular Film i n Place
Apparatus
The nppwntus for measurement of the film area is a shallom black-hottomed tray 15 X 35 rm., suppmted or, l~velingscres-s F i g 1 The t,ray is coated wit,h h x d paraffin and filled vith clean nater until t,hc lcwl is ahovc the edge of the tray. The tra?is provided with a 17- x 3- r I-rm. Iwite harrier for cleaning hhr WB~,PI.surfaw.
Procedure (1) Oht,ain a sample of aleie arid and meanure its density. To do this plnee 2.0 ml. in a graduat,e cylindev and weigh it. (21 Determine the molenilar weirht of the oleie acid. To do t h k w i a h a sample, alxnrt 0.400 g:, dissolve it in slrohol 2nd titrste bo a phenolphthalein end paint nsing standard sodium hydroxide solution. (Assome the romhining weight. obtained to be the moleculsr weight far oleio acid.) (3) I'lnce two drops, about 50 mg., of olcic mid in R clean beaker, and determine the maet weight of the aeid. Dissolve the ol& acid in pentsne, tmnsfrr qunntit,at,ively to a 500-ml. volum~tricflask and make n p to 500 ml. with pentane. , the ~ u r f a r eof the watcr on the (4) Cring the b ~ r r i e r ~36511 measuring tray,2 cover the snrfarr with oxidized piston oil8.' and dust with lycopodium (5) Using a graduakd pipd, plarr rsactly 0.10 ml. of the solut.ian of oleie acid in pentme on the surface of the tray, allow
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Kraft Foods Company, Glenview, Illinois. % F o r this operation some individual instrurt,ion is usually necesmry. After the surface has l,em saept clean the harrier is left in position and used for adinsting the eolor of the &on oil film. A droplet of oxidized oil may be transferred to the water surface by touching it with a 0.5-mm. glass rod previously dipped in the piston oil preparation. Piston oil is added or the harrier is moved until the color of the ail film is green. Such s. film has been shown to have a tension of ahout 20 dyneslem. 6 The piston ail is prepared from s. good grade of lubrication oil heated to 300°C. for 8 hours or until it spread5 as a. monolayer. See BLODGETT,K. B., J . Am. Chenr. Soe., 56, 495 (1934); also 57, 1007 (1935). Available a t most drugstores. The lyropodium powder is not nhsalut,el~rnecessary hut it makes the sorfaeo rnsily visihle.
Figure 2.
Method for Outlining Film Area on a GI-
Plate
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Figun 3. Method for Estimating Area of the Monomolecular Film
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observed a thickness of 1.3 + 0.3 X lo-' em. for the oleic acid film with most of the values falling within the range 1.2 and 1.4 X lo-' cm. The over-all picture of results obtained using this experiment is perhaps best illustrated by a display of the data recorded by a good student. Dala
(1) the pentane to evaporate, and determine the area of the residual oleie acid film. The oleic acid film is easily visible since it will push haok the oridiaed p i ~ t a noil and lycopodium powder and form an approximately ci~cnlararea on the tray. The area. of the oleie aeid film may ho conveniently measured by outlining the film on s g h s platc, transferring the outline to a piece of graph paper graduated in millimeters, and counting the quar re^.' Calculations a n d Interpretations (1) Calculate the mass (weight) of oleic acid in the film. (2) Calculate the volume of oleio acid in the film. For the olcic acid, assume that the d e n ~ i t yin bulk and the density in the film are identical. (3) Calculat,e the thickness of the oleic mid in the film. (4) Calculate the volume of ono molecule of aleic mid. To do thfs $0" will have to assume t h s t the oleic acid film is one molecule t,hiek, and you will have to assume some shape far the molecule. The simplest assumption will be that the oleic mid is 3,cube. (5) From the denaity and molecular weight of oleic acid in bulk calculate t,ho volume of 1.0 mole of oleic acid. (6) Calculate Avogadro's number "N." (7) Compare your value for "N" with the accepted value. List all sources of error in the above experiment, consider all assumptions used in the calculation, and try to account for the difference between your value and the accepted value for "X." (8) Now assume thst the oleic scid molecule is shaped like a rectangular solid twice as long as it is wide. Calculate the volume of one molee~deof the oleic acid and from this Avogadro's number "N." ( 9 ) O p t i m a l . Repent t,he above calculations assuming the oleic soid molecule is a, cylinder of length four times the radius and that thc molecules in the film are close-paoked.
STUDENT RESULTS
When conducting this experiment in the laboratory the student was provided with a good grade of oleic acid.' Values reported for the density measured by t,be method suggested varied from 0.863 g./ml.0.949 g./ml. a t room temperature vith most of them in the range 0.88 g./ml.-O.SO g./ml. This variation is of little consequence in the final determination. Values reported for the combining weight (molecular weight) of the oleir acid varied from 272-294. Occasionally values of 282, the theoretical, were reported. I n item (3) of the procedure the student was told to weigh accurately two drops of oleic acid. This is both possible and practical on the equipment available in this laboratory. Where less precise equipment must he used, the student might weigh a larger amount and adjust the concentration by proper dilution. I n any event the mass of oleic arid used for formation of the film should be about 1 X g. The transfer of 0.10 ml. of the solution of oleic aeid in pentane to the film was easily accomplished by the students after instruction on the use of graduated pipets. Csing the above techniques, some of the students U numher of workers have used a technique very similar t o this for estimating micro quantities of lipids in biologicalpreparations: OORTNER, E.. AND F. J. GRENDEL, J. E z p . B i d , 41, 439 (1925); JONES, K. K., Science, 111, 9 (1950); BERQUIST,D. H., AND F. WELLS.Food Technol... 10. .48 119561. . . 'Purified olke acid from Fisher Scientific Company.
VOLUME 35, NO. 4, APRIL, 1958
Weight of graduate and 2 ml. of oleic acid Weight of graduate . . . . . . . . . . . . . . . . . . Weight of 2 ml. of oleic acid.. . . . . . . . . . . Density of oleic acid.. . . . . . . . . . . . . . . . . .
27.276 g. 25.531 g. 1.745 g. 0.873 g./ml.
45.202 g. ( 2 ) Weight of heaker and oleic acid.. . . . . . . . 44.750 g. Weightofheaker . . . . . . . . . . . . . . . . . . . . . . Weight of oleic acid. . . . . . . . . . . . . . . . . . . . 0 452 g. Burette reading after titration. . . . . . . . . . . 1 6 . 3 ml. Burette reading before titration. . . . . . . . . 0.6 ml. 1 5 . 7 ml. Vohme of 0.101 M NaOH solution. . . . . . Moles of NaOH solution.. . . . . . . . . . . . . . 0.00158 "Molecular weight" of oleic acid. . . . . . . . 286 (3) Weight of beaker and oleic acid.. . . . . . . . Weight of beaker. . . . . . . . . . . . . . . . . . . . . Weight of oleic acid. . . . . . . . . . . . . . . . . . . .
44.791 g. 44.747 g. 0.044 g.
Volume of pentitne solution of oleic acid. Volume of pentane solution on tray. . . . .4rea of oleic acid film. . . . . . . . . . . . . . . . .
500 ml. 0.10 ml. 75 cm.%
(4)
M a s s of oleic aeid in the film m = 0.014 g. X 0.10 m1./500 ml. = 8.8
X 10-6 g. Volume of oleio acid in the film V = 8.8 X 10-'g./0.873 g . / ~ m .=~ 1.01 X 10-6cm.a Thickness of the oleic acid film h = 1.01 X 10-%c./75 cm.2 = 1.35 X 10'em. Volume of one molecule of oleic acid, assuming the molecule is a cube V = (1.35 X lo-' cm.)* = 2.46 X 10-21 em.= Volume of 1 mole of oleie aeid V = 286 g./0.873 g./em.' = 327 Avogadro's number N = 327 ~ m . ~ / 2 . 4X6 cm.* = 1.33 X lo2' The numher I found was 1.33 X loZ: as compared to the actual number 6.023 X 1025. Errors in weighing8 and messurements will account for some of the error. There a h was probably more or less than 0.1 ml. of the pentsne solution of oleic acid dropped onto the surface of the water. The measurement of the ares. of the film is difficult to determine ac~:m-atelyand would account for some error. Also you are only assuming that the shape of the oleie acid molecule is a cube. If it is not, bhe volume of the molecule would be eonsiderahly different, as would the number determined for Avogadro's number. Calculation of Avogadro's number sssuming the oleic acid molecule is a rectangular solid twice as long as it is wide IV = 4 X 327 ~ m . ~ / 2 . 4X6 ~ m =. 5.32 ~ X loZS Calculation of Avogadro's numher amuming the oleic scid molecule is s cylinder of length four times the radius and that the molecules are elose-packed in the film N = 4 X 2/1.73 X 327 ~ m . ~ / 2 . 4X6 cm." 6.15 X loP"
The instructions given to the students mere written in a general manner with the hope that the student would be forced to think through each operation before doing it. The lack of detailed instructions elicited numerous questions on the proredure and on the assumptions made in connection with the calculations. Some questions most frequently asked mere: Horn do we know that the film is only one molecule thick? How do you know the density of the oleic acid in the film is the same as the density in bulk? How do you know the combining weight and molecular weight of oleic acid are the same?
Why do we assume that the oleic acid molecule is a cube or a rod? Why not assume it is a sphere:' Why do we get all answer closer to the accepted value when we assume the oleic acid molecule is a rod? All such questions were answered with a discussion on the nature of theory, an argument for the soundness of the assumptions involved, by reference to a good source of information on surface films8 and by reference to a scale model of the oleic acid molecule. The principal virtue of the experiment as described
herein is the preparation of a readily visible monomolecular film with clearly defined edges. This experiment has been pedormed successfully in our freshman laboratories for the past three years. The student response to it has always been enthusiastic. Various modifications have been used for demonstration purposes. $ADAM,N. K., "The Physics and Chemistry of Sudaces," Oxford University Press, London, 1941.
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