AN APPARATUS FOR THE STUDY OF DIFFUSION IN LIQUIDS
8
GERARD KRAUS and RUSSELL TYE University of Cincinnati, Cincinnati, Ohio
THE
apparatus described in this paper has been found useful in the determination of diffusion coefficients in liquids, particularly in concentrated solutions, where large concentration gradients are encountered. Although it is not capable of the high degree of accuracy of the diaphragm diffusion cell of Gordon1 or of the more elaborate optical procedure^,^.^ it exhibits few, if any, of the experimental difficulties associated with these methods. Its simplicity of construction and ease of operation render it well suited for a laboratory experiment in physical chemistry, as well as for diffusion measurements not requiring extreme accuracy. The operation of the apparatus is based on the optical effect produced by a capillary illuminated by parallel light from a slit. The capillary forms a cylindrical lens, the focal length of which is a function of the refractive index of the liquid filling the tube. When the tube is viewed through a cathetometer telescope a bright band appears within a dark band, the aperture of the telescope acting as a stop. Since the width of the inner bright band is also a function of the refractive index of the liquid in the tube, it is readily adaptable to the measurement of concentrations along a capillary in which diffusion is taking place. The accompanying figure shows a diagrammatic view of the entire apparatus. It is not necessary to use monochromatic light; a standard household fluorescent light fixture A has been found entirely satisfactory as a light source. The diffusion capillary C is made of No. 0041 Corning clear standard thermometer tubing, the refractive index of which is 1.545. This, in effect, limits the apparatus to the investigatiod of liquids having refractive indexes below approximately 1.530, althoueh the ranee is eltsilv extended bv use of s~ecial glasses of higher refractive index. For maximum sensitivity the capillary should not be directly immersed in the water bath H. The arrangement pictured consists of a cross made of comer tubing. -, into which the diiusion tube is fastened by means of rubber stoppers, the entire assembly being submerged in the thermostat. A 32-power cathetometer G, fitted with a graduated eyepiece is used to measure band width. In conducting a determination the capillary is first filled carefully from reservoir D through the stopcock F. The diffusing liquid is then introduced into reservoir E. Reservoir E is sufficiently large to assure constancy of the concentration of the diffusing substance in the
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reservoir throughout the experiment. The liquid in the reservoir should be agitated gently by means of a reciprocating stirrer. A series of cathetometer readings along the tube is taken at several time intervals. It is essential that there be a sharp transition in diameter from the capillary to the reservoir; so that the zero point may be located with accuracy. From the data. a plot of concentration against distance and time is readily constructed. To calculate diffusion coefficients, it is necessary to solve the differential equation of diffusion, subject to the boundary conditions of the apparatus, that is, for diffusion from an infinite reservoir into a semi-iniinite tube. If the diffusion coeEcient D is assumed constant, the solution takes the
' GORDON, A. R., Ann. N. Y. A d . Sci., 46, 285 (1945).
From this relation D may be calculated. To obtain differential diffusion coefficients,the following relation must be used?
~~~~~
LONGSWORTA, L. G., Ann. N . Y . Acad. Sci., 46, 211 (1945). HARNED, H. S., Chem. Rar., 40, 461 (1947).
..
c = Concentration of the diffusing liquid in the tube at a distance z along the tube st time t ca = Concentration of the diffusing liquid in the reservoir D = "Diffi~aion -~ ~ ~aonst,nnt? . .-~ .. ~~.~ . ~ ~ -
-
A L~
,.
where
D=--- l d ( z / d i ) 2
dc
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As a rule, diffusioncoefficientscan be determined by the method described with an accuracy of a few per cent, depending on the difference in refractive index between the two liquids. The main disadvantage of the method is its inability to give high accuracy at low concentrations where the change in refractive index is small.
' CHURCHILL,R. V., "Fourier Series and Boundmy Value Problems," McGraw-Hill Company, New Yark, 1941, p. 123. 489
