Michael J. Demchik
Science Teacher Prince George's County and Virginia C.Demchik
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Bowie State CoHeae Bowie, Maryland 20715
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Size of a Mdetule-
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or What's in a Shape?
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In experiments performed in junior and senior high school on the size and mass of an oleic acid molecule (1) and molecular layers (Z), students determine the height of a unimolecular layer and assume a shape in order to determine the number of molecules of oleic acid present on the surface. In the molecular layer experiment, they are asked to determine Avagadro's number based on the assumed shape. The assumed shape is a cube and this causes an error that is 100 times that found by better methods. Although the objective in each of these experiments is to acquire some notion of the size of molecules and unimolecular layers, an alternative procedure based on the characteristics of this molecule can provide a more accurate assessment of the probable shape of this molecule and Avagadro's number. The current experiments are based on the fact that oleic acid is essentially insoluble in water. But it is a polar molecule with a hydrophobic (water hating) tail and a hydrophilic (water loving) head. The head which is a carhoxylic group (-COOH) L'dissolves" in the water while the hydrocarbon tail does not. This ensuing method provides one dimension, the length of the oleic acid molecule. If before the assumption of a cubic shape were made, we were to spread one drop of oleic acid on a very dilute hydrochloric acid solution, we could add another dimension to our molecule. "It is thought that in this circumstance the carboxyl groups cannot penetrate the aqueous layer in the same way that they can in pure water, and thus are forced to lie side by side" (3). The additional dimension will provide us with the information that oleic acid molecules are long and thin. In this way, we have eliminated both the cubic and spherical shapes. Several probable shapes for this molecule are available and include the cone, pyramid, rectangle, and cylinder. Both the cone and pyramid are included as possible shapes since "the area of the head determines the area occupied by the molecule, and the tails cannot be tightly packed" (3). If a larger number of measurements provides a consistent measure for height, subsuming experimental error, the cylinder can he utilized as the shape for further calculations. This rationale is that if the molecule is placed long side up, the point of contact from molecule to molecule along a unimolecular surface will he equal to each shape, and if as previously stated the head determines the area of the molecule, therefore a cylinder can be selected as the desired shape. The figure provides such a comparison. 770 / Journal of Chemical Education
The experimental procedure involves use of a 0.2y0 oleic acid in alcohol,' one drop (4.00 X lo-= g/cm" of which is placed on a layer of water 2-em deep covered with lycopodium powder of finely divided chalk. The drop spreads into an approximately circular layer and the average diameter is determined. Height (see the table) is determined by V = rr2/h. The same procedure is followed to determine the second dimension except in place of water a very dilute HC1 solution is used. The table provides the remaining dimensions. I n utilizing the original volume determined, a more accurate assessment of the -up number of molecules on that Strvdurol oleic ocid molecule with Surface and subsequent dervpcrimpored cylindrical model. termination of Avagadro's number can he made. Procedures for calculations follow Volume of oleic acid in one drop = number of molecules Volume of the cylinder 4'00 lo-' = number of molecules 5.07 X em5 7.89 X 10'' = number of molecules in one drop of oleic acid
Avagadro's number can be found by dividing the mass per molecule into its molecular weight (282). The mass per molecule can he determined in the followingmanner. Volume of one drop of oleic acid X density of aleic wid = mass of oleic acid 4 . 0 0 X 10- cma X 0.90 g/cmJ = mass of oleic acid 3.60 X
g = mass of oleic acid
Therefore
'Isopropyl, ethyl, or methyl alcohol or Paco burner fuel is suitable.
Condensed Data Table
Water
Medium Dilute acid solution
Average diamet,er of monolayer (cm) 14.00 Height of molecule (cm) 2.60 X 10-' Cross-sect,ional area (cms) Volume of molecule (cma) Number of molecules/ drop of oleic acid Massof the oleic acid ( g ) Mass per molecule (s/moleeule) GrLm moleeulsr weight, Avagadro's number Per cent of error
32.00 4.97 X 10F 1.95 X lo-'6
6.07 X 10-sP 7.89 X 10"
282 6.18 X 10%" 2.6%
3.60 1°-'g = mass per molecule 7.89 X 10" molecules 4.56 X
g/molecule = mass per molecule
Then gram molecular weight = number of molecules per mole mass per molecule 282 g - number of molecules per mole 4.56 X 10-la g/molecule 6.18 X 1Oa8molecules = number of molecules per mole
This procedure produces a value of 6.18 X lo2% molecules/mole which is reasonably closer (less than 3% error) to the Avagadro number of 6.02 X loz3molecules/molc than that prescribed by assuming a cube. It can be expected to find reasonably wider ranges for Avagadro's number with student data. Although values are wider, they provide a more accurate assessment of size or shape. Furthermore, students would exhibit a keen interest since the are actually determining the size of molecules. At times the abstractness of terms such as molecule leave a void when it comes down to actually envisioning what the shape of the molecule really turns out to be. It is the feeling of the writers that the accuracy sacrificed in the original experiment, at least at the high school level, need not have occurred since a more accurate value requires only a slightly more rigorous procedure, not beyond the original intended level. Literature Cited (1) "Introductory Physical Science." IPS Group, Education Development Center. Ino.. Prentiee-Hall. Ino.. 1967, pp. 163-65. (2) "Laboratory Guide for Physics." Physical Science Study Committee. D. C. Heath and Co.. 1960. o. 13. (3) n n ~ r W . A L L A C ~ 8.. JR., . . ~ ; i i o i ~ of ~ ephysical ~ hemi is try;^ ~ p p e ~ t o n Century-Croits Ino., New Ymk. 1958, pp. 236-40. (4) MOOBE,W. J., "Physical Chemiatry." (3rd ed). Prentiae-Hall Inc.. Englewood Cliffs, N. J., 1962, pp. 738-41. (5) MOYNIH*N,C o n m ~ l u aT., A N D G O L D W E ZHAROLD. ~B, J. CHEM.EDUC. 46.779 (1969).
Volume 48, Number 1 I , November 1971
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