Chemistry and Chemical Biology ETDs

Publication Date

5-24-1973

Abstract

The previously existing method of determining diffusion coefficients (D values) by diffusion from capillaries is critically reviewed. A differential error analysis of the method is given, and a formula is derived for the upper error bound on D as a function of capillary length, time span of the experiment, and ratio of final to initial diffusant concentrations. It is concluded that when the initial concentration and capillary length are not corrected for convective loss of diffusant solution from the capillary, the errors in concentration and length are additive and can significantly affect the accuracy of D. A new method (the tube method) for determining D values is proposed. This method is related to the capillary procedure but uses tubes of several millimeters in diameter in place of capillaries. Convective loss is used to advantage to form hydrodynamically forced boundaries between stationary and moving columns of fluid. A method of calculating D is developed which accounts for convective loss, and it is shown how the experimental procedure may be optimized so as to minimize the maximum error in D. The tube method was tested by determining D values for anthracene, p-nitroaniline, and dinitroazobenzene in acetonitrile, and for ferricyanide and plumbic ions in aqueous potassium chloride solution. It is concluded that the tube method should furnish essentially the same information as the older capillary method but give greater accuracy in D because convective loss is taken into account, and be more widely applicable because of the much greater amount of material that can be diffused. The diaphragm cell method is also reviewed as an alternative means of obtaining D values. Diffusion in a diaphragm cell is simulated by the finite difference method, and the resulting data used to verify the correctness of a previously published exact mathematical solution for diffusion in a diaphragm cell. It is concluded that use of the exact solution should make it possible to eliminate one step in the usual diaphragm cell procedure. Particular attention is paid to the possible application in electroanalytical chemistry of D values determined by the capillary and tube procedures, and equations are derived which show how an error in D affects the value of n (the number of electrons transferred) calculated from any one of the several commonly used equations describing diffusion controlled electrode processes. As an introduction to the above studies, diffusive transport phenomena are reviewed from a thermodynamic standpoint, and there is considerable discussion of the influence of such factors as concentration, viscosity, and ionic strength on diffusion rate.

Project Sponsors

The National Defense Education Act and the National Science Foundation

Language

English

Document Type

Dissertation

Degree Name

Chemistry

Level of Degree

Doctoral

Department Name

Department of Chemistry and Chemical Biology

First Committee Member (Chair)

Roy Dudley Caton Jr.

Second Committee Member

Nicholas Ernest Vanderborgh

Third Committee Member

William Morris Litchman

Fourth Committee Member

Guido Herman Daub

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