Anal. Chem. 1999, 71, 1469-1473
Infinite-Dilution Diffusion Coefficients of Complex Ions from Solution Conductivity Data David A. Dudek and Peter S. Fedkiw*
Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905
A technique is presented for determining infinite-dilution diffusion coefficients of complex ions from solution conductivity data. The method involves measuring the conductivities of dilute solutions in which the distribution of complex ions is systematically varied and statistically regressing the data to an equation that effectively relates individual ion diffusion coefficients to solution conductivity. The procedure is simple and requires no specialized equipment to perform. Unlike methods that require a concentration gradient, the solution composition is homogeneous and at equilibrium during measurements, which is a significant advantage when labile complexes are being studied. In this paper, diffusion coefficients of cuprous cyanide complexes are determined. Statistical analysis yields the infinite-dilution diffusion coefficients of Cu(CN)2-, Cu(CN)32-, and Cu(CN)43- at 25 °C as 1.43 × 10-5 ( 9%, 1.08 × 10-5 ( 9%, and 6.21 × 10-6 ( 22% cm2/s, respectively. As computers that are capable of solving multicomponent transport problems become increasingly accessible to scientists, the need for physical constants on which to base these models grows. Transport models of systems involving complexation chemistry require diffusivities for individual complexes, and workers are often forced to assume that diffusion coefficients for several species are equivalent1,2 or to estimate unknown values.3 It is not possible to measure directly the individual diffusion coefficients of complex ions in equilibrium solutions containing mixtures of labile complexes. It is therefore desirable to develop a method of extracting these values from experiments conducted on mixtures. Most methods of measuring diffusion coefficients, including the diaphragm cell and optical, electrochemical, radioactive tracer and Taylor dispersion techniques require either the establishment of a concentration gradient or otherwise disturbing the solution from equilibrium.4 In mixtures of labile complexes, the distribution of species may change across a concentration gradient, and the composition of the mixture varies in a typically unknown manner with position. In contrast, the solution composi* Corresponding author: (e-mail)
[email protected]; (fax) (919)5153465. (1) Mathias, M. F.; Chapman, T. W. J. Electrochem. Soc. 1990, 137, 102-110. (2) Katagiri, A.; Inoue, H.; Ogure, N. J. Appl. Electrochem. 1997, 27, 529538. (3) Podlaha, E. J.; Bonhoˆte, Ch.; Landolt, D. Electrochim. Acta 1994, 39, 26492657. (4) Tyrrell, H. J. V.; Harris, K. R. Diffusion in Liquids; Butterworth and Co.: London, 1984; Chapters 5, 6, and 8. 10.1021/ac981054i CCC: $18.00 Published on Web 02/18/1999
© 1999 American Chemical Society
tion is homogeneous and at equilibrium during a conductivity measurement. Knowledge of the complexation equilibrium constants allows calculation of the solution composition. If the diffusion coefficients of the noncomplex ions are known, the portion of solution conductivity due to the motion of complex ions can be calculated and subtracted from the measured value. Statistical regression of this residual conductivity for dilute solutions in which the distribution of complex ions is systematically varied allows determination of diffusion coefficients of individual complex species. The conductivity κ of a homogeneous solution described by dilute-solution theory is given by5
∑z u c
2 i i i
κ ) F2
(1)
i
where F is Faraday’s constant and zi, ui, and ci are the charge number, mobility, and concentration of species i. The mobility ui and ionic equivalent conductivity λi are related by5
λi ) |zi|F2ui
(2)
Ionic conductivities are strong functions of ionic strength I4,6,7
I)
1 2
∑z c
2 i i
(3)
i
At low ionic strengths (
