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The Statistical Description of Precision Conductivity Data for Aqueous Sodium Chloride

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Abstract

Published precise data for NaCl in the temperature range 0–50 °C were assembled, corrected to current standards and analyzed by weighted least-squares regression. There was a notable paucity of data at 0 °C. Data were analyzed as specific conductivity to avoid violation of the statistical independence assumption. The regression model was a polynomial in \(\sqrt{c}\), with an added transcendental term. Powers of \(\sqrt{c}\) were added to published equations to extend the range of c fitted. Temperature dependency of the coefficients was individually modeled by cubic functions in the Celsius temperature. Criteria for an acceptable model included lack of bias, similarity to published theoretical equations, and extrapolation to infinite dilution consistent with literature values. The predictive equation chosen was of the form:

$$\kappa = \varLambda _{0}c - Sc^{3/2} + Ec^{2}\ln c + J_{1}c^{2} + J_{2}c^{5/2} + J_{3}c^{3} + J_{4}c^{7/2} + J_{5}c^{4} + J_{6}c^{9/2} $$

and fit the data without bias but with high precision (±0.33 μS⋅cm−1) for the full range of published concentrations (up to 5.4 mol⋅L−1), over the temperature range 0–50 °C, something not previously achieved. All coefficients but J 5 and J 6 were temperature dependent; the latter terms were required for an unbiased fit at higher concentrations (>1 mol⋅L−1). Solution of the equation for infinite dilution matched published values closely. The use of separate empirical temperature dependency for the equation coefficients may provide an independent means of validating theoretical treatments of conductivity data.

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Notes

  1. The IPTS of 1968 is the scale used for the most recent measurements and differs little from the more recent revision of 1990 in the applicable temperature range. It was not thought worthwhile to apply this further correction.

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  1. John C. Wadsworth

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    John C. Wadsworth

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Wadsworth, J.C. The Statistical Description of Precision Conductivity Data for Aqueous Sodium Chloride. J Solution Chem 41, 715–729 (2012). https://doi.org/10.1007/s10953-012-9823-6

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