Cornelius T. ~ 0 ~ n i h . n ' and Harold Goldwhite Cal~forn~a State College at 10s Angeles LOS Angeles, 90032
Determining Avogadro's Number from the Volume of a Monolayer
A
popular experiment for the general chemistry course is the one in which Avogadro's number is estimated from the volume of a monolayer on a water surface. We offer here some comments and suggestions on the conduct of the experiment and the treatment of the data. The procedure suggested in most laboratory manuals is similar to that originally proposed by King and Neilson (1). A small volume V of a solution of oleic or stearic acid in pentane or other suitable solvent is added to a prepared water surface from a calibrated pipet and the area A of the acid monolayer on the partially covered water surface is measured. The height L of the monolayer is calculated from
where C is the concentration in grams per cm3 of the acid in the solution and p the density of the pure acid. Values of L obtained by this procedure (1) are usually in the range 12-14 A, about half the actual length of the stearic or oleic acid molecule, 27 A (8). The low values of L arise because the monolayer is not under compression, and hence the bulk acid density used in calculating L is greater than the effective density in the uncompressed monolayer. Avogadro's number, N.,, may be calculated from L if one assumes a shape for the acid molecule and accepts the fact that the monolayer is one molecule thick. For instance, if the molecule is assumed to be cubical, the area occupied by one molecule is LZ, so that N,
=
used rather than a convex water surface (in a watch glass). Values of L determined via eqn. (1) for the Kokes experiment average around 24 A, in good agreement with the actual length of the acid molecule. Apparently when the water surface is completely' covered, the monolayer is under sufficient compression to insure that the molecules are packed closely with the hydrocarbon chains parallel to one another and perpendicular to the surface. Kokes and his co-workers suggest that students treat their data by first calculating the diameter of a carbon atom, d,, on the assumption that the stearic acid hydrocarbon chain has the zig-zag configuration shown in the figure. The students are then given the density of diamond (and possibly the structure) and asked to calculate Avogadro's number from this and the value of d, which they have determined. If the correct structure of diamond is used in the calculatiou, excellent values of N,, are obtained. The calculation, nonetheless, leaves much to be desired, since the density and structure of diamond are not actually determined by the students and would further be sufficient in themselves to determine Avogadro's number. We suggest, rather, the following procedure for the calculation of NA. The students are asked to assume that the relative shape and dimensions of the stearic acid hydrocarbon chain are as shown in the figure, with the carbon and hydrogen atoms having equal diameters. The tetrahedral bonding angles in the chain are easily rationalized on
MA CVL'
-
where M is the molecular weight of the acid. Values of N A calculated in this fashion tend to be low by a factor of about four (I). One can, of course, assume other shapes for the molecule until a value of Avogadro's number in good agreement with the accepted value is obtained, but this defeats the whole purpose of the experiment. Further, the shapes which lead to good values of NA give an inaccurate portrayal of the relative and actual dimensions of the molecule (1). A better version of the monolayer experiment is described by Kokes and coworkers (3, 4.) I n this version, a solution of stearic acid in benzene is added drop by drop from a micro-pipet to a clean water surface until the entire water surface is covered with a monolayer of stearic acid. We wish to amend the originator's experimental instructions in only one regard, by observing that the experiment seems to work better if a concave water surface (in a shallow dish or large beaker) is 1 Present address: ChemicalEngineeringDepartment, Catholic University, Washington, D.C. 20017.
Scale model of rtearic odd hydrocarbon chain.
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the basis of VSEPR theory (6). The equality of sizes of carbon and hydrogen is an out-and-out assumption, but in fact turns out to be rather good, since the sum of the covalent and van der Waals radii of hydrogen (0.3 A 1.2 A) is very nearly @ice the single bond covalent radius of carbon (2 X 0.77 A). Simple geometric and trigonometric calculations based on the figure give the following relative dimensions of the hydrocarbon chain
+
li;= L -
1
= 1 1 a
+ 17 sin 54.7" = 14.9
+ 17 sin 54.7'
+ 3 cos 54.7'
(2)
= 5,44
An alternative procedure, which seems to work well with students whose mathematical backgrounds are poor, is to have them determine the L / d , and L / a ratios by measuring L, d,, and a on an 8 X 11 drawing of the figure. Combination of the ratios in eqs. (2) and (3) with the experimentally determined value of L yields the diameter of the carbon atom, d,, and the thickness of the hydrocarbon chain, a. The average area occupied by a
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stearic acid molecule may be taken as aZ. Avogadro's number is calculated from N*
MA
=
where A is the ckoss-sectional area of the dish or watch glass. A set of results from a group of typical students gave L = 24 4 A, d, = 1.6 0.3 A, and N , = 8 + 4 X loi3. These results show that the experiment can be made to yield realistic values of atomic sizes and of Avogadro's number on the basis of a rather minimal number of assumptions and without the introduction of additional data not actually determined by the students.
*
*
Literature Cited (1) KING,L. C., AND NEILSON, E. K., J. CREM.EDUC.,35, 198 IlORXI. (2) MOG,'W. J., "Physical Chemistry," (3rd ed.), PrentieeHall, Inc., Englewood Cliffs,N. J., 1962, pp. 73841. M. K., AND MATEIA,T., J. CHEM. (3) KOKES,R. J., DORLMAN, EDUC., 39,18 (1962). D. H., AND KOKES,R. J., "Lshoratory Manual (4) ANDREWB, far Fundamental Chemistry," John Wiley and Sons, Inc., New York, 1962, p. 14. ( 5 ) GILLESPIE, R. J., J. CHEM.EDUC.,40. 295 (1963).
