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Potentiometric Cells with Liquid Junctions: A Combined Analytical and Computational Study

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Abstract

It is known that the electromotive force (emf) of cells with transference is dependent on an integral involving electrical transport numbers, t i , and chemical potentials. However, the origin of this integral, the conditions under which it is valid, its properties and utility are not well understood. This article aims to clarify such aspects. A general emf equation is derived in a manner in which the integral arises from the entropy production due to diffusion. Five important properties of the equation are recognized: (1) invariance with respect to the reference frame for t i measurements, (2) redundancy of single-ion activities, (3) lack of a potential function for the integral when the number of independent t i is greater than 1, (4) irrelevance of any metric on the junction 3-D space, and (5) invariance with respect to the free-diffusion time. As an application, the emf equation is tested for calibration of cells with dissimilar electrodes and junctions between the saturated potassium chloride solution and hydrogen chloride solutions in a range of concentration. It is found that (1) the standard emf can be estimated with a precision of about 0.1 mV for accurate enough data sets, and (2) the free-diffusion model is more appropriate for the flowing junctions than the continuous mixture model, although the difference between the two models is slight. In similar systems with less concentrated potassium chloride solutions, the free-diffusion mass density profiles are found to bear a sign of convective instability, because of which previously reported steady emfs for such cells may pertain to a changed solution composition in one of the two half-cells.

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Notes

  1. Any such is a curve the tangent vector to which at each point is the vector of the field at the point.

  2. For discussion of curvilinear coordinates see [26] or e.g. [27].

  3. For the topic of differential forms see, e.g. [40–44].

  4. In this connection, note the IUPAC recommendation to use the term cell potential difference instead of emf [45].

  5. In fact, the D i,m were calculated both by Miller's method and that of Leaist et al., as described, e.g., in [60]. However, we report here only on systems and concentration ranges where the latter has no advantage over the former as judged by experiment or makes only negligible difference in the calculated emf.

  6. That equation was derived specifically for a cell with a single electrolyte in a single component solvent and gave the emf in terms of the Hittorf transport number, the vapor pressure and concentration of the solution.

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    Dmitri P. Zarubin

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Zarubin, D.P. Potentiometric Cells with Liquid Junctions: A Combined Analytical and Computational Study. J Solution Chem 45, 591–623 (2016). https://doi.org/10.1007/s10953-016-0460-3

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