POUI
S. Henry
Princeton Universitv Princeton, New Jersey
I I
Evaluation of Avogadro'r Number A general chemistry experiment
T h e method of J. Perrin for evaluating Avogadro's number, N, can be simplified by making use of suspensions of latex spherules produced by the Dow Chemical Company. The particles are accurately measured in sizes down to a few tenths of a micron diameter. They are available from most electron microscopy labs, or directly from Dow, Midland, ~ichigan. The central problem of the experiment is the determination of the averaEe oooulation of articles in a suspension as a function of height. This can he done either by taking a vertical cross section of the entire suspension, or several horizontal sections a t various levels. Both approaches have been successfully used in the general chemistry laboratory. W. H. Slabaughl has recently performed the experiment with vertical cross sections; a description of the alternative method is presented below. The so-called sedimentation equation is the theoretical foundation of the exoeriment:
- ..
nJni
=
exp [-4rrag(d, - d,)(hj - h i ) / 3 k T ]
The average particle populations a t levels h, and ht are n, and n,. These particles have a density d,, while that of the suspension medium is dm. The volume of each particle is 4m3/3, g is the gravitational acceleration, k is Boltzmann's constant, and T is the absolute temperature. Perrin's experiment allowed him to determine k, from which he evaluated N by the relation SLABAU~E, W. H., J. CHEM. EDUC., 42,471 (1965).
where R is the gas constant. This procedure is straightforward, but it requires information about the particle density d,, and although the bulk density of the particle material may he known, it is not clear that this is the density of the particles themselves. Surface effects may be significant in the small spherules used in the experiment. To eliminate this uncertainty, the experiment can be performed twice using the same particles in two different suspension media. If the height interval, h,-hl = Ah, is the same in both cases,
The ratio of the two concentration gradients does not involved.. I n our experiment the two suspension media were water (dl, = 0.998 g/cm3) and an ethanol-water sohtion (&, = 0.990 dcm3). The sus~endedarticles had radii 1.02 X 1014ern: The suspension was observed through a vertical 300X microscope, whose depth of focus defined a horizontal plane about 5 microns thick in which the spherules could be seen in focus. At the focal plane of the eyepiece was an opaque disk with an off-center pinhole in it. The view seen by the observer was a black field with a small area of light in which a half dozen or so particles were visible. By rotating the eyepiece, another section of the level could be sampled. A total count of 100 particles per level was enough to determine the average population. The process was then repeated a t a different height. A
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typical series of measurements is shown below; in this case the suspension medium was water. Height (microns)
Relative particle count
The concentration gradients for the water and ethanol suspensions were computed. It was found that in water the average particle count was reduced by onehalf for each 14-micron rise in height, while in the ethanol the necessary distance was 9 microns. Using
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the expressions given above, we found The error estimate is based on the scatter of our data. It does not take account of the systematic error that caused the significant departure of our value from the accepted one of 6 X loZa. Smaller suspension particles (not available a t the time of the experiment) would have resulted in an improved estimate of N. They would have "stretched" the concentration gradient, making the depth of focus of the microscope a smaller fraction of the range of levels observed. Changes in average population would then be more apparent.
