Surface Tensions of Solutions: Methods

Single Solutes

• For the single solutes that make up H⁺ - NH4⁺ - Na⁺ - K⁺ - Mg²⁺ - Ca²⁺ - SO4²⁻ - NO3⁻ - Cl⁻ - Br⁻ - OH⁻ - CO3²⁻ - H2O mixtures the calculated surface tensions are based upon available measurements for temperatures from 233 K to 523.15 K. The data include surface tensions of melts (liquid electrolytes), which have been extrapolated to ambient temperatures in order to estimate surface tensions of solutions supersaturated with respect to dissolved salts.

  The model for surface tension developed in reference (1) is a modified Arrhenius mixing rule. It includes the surface tensions at the limits of salt concentration (i.e., surface tensions of water and pure liquid solutes) and fitted parameters for the concentration dependent terms.

  At low temperatures, and for concentrations above those of the saturated solutions of most solutes, surface tensions are extrapolations based upon assumptions regarding the surface tensions of supercooled water (below the lower limit of measurement of about 250 K), and those of the (hypothetical) pure liquid solutes. Full details are given by Dutcher et al. (1).

• Surface tensions of pure water above 0 °C were calculated using the equation of Vargaftik et al. (2). For temperatures below 0 °C, extrapolated to temperatures as low as 123.15 °C, surface tensions were calculated from an equation fitted to available measurements and the results of molecular dynamics simulations of supercooled water.
• Surface tensions of hypothetical pure liquid solutes were calculated using the equations of Janz (3), which were fitted to high temperature data, or predicted from ion properties using equations of Dutcher et al. (1) where no data are available.

Mixtures

• Surface tensions of aqueous or molten mixtures of electrolytes and NH3 are estimated using the model (1), based upon the properties of the individual (single) solutes.

  We note that predictions of surface tensions of mixtures can be improved when additional interaction parameters, determined from surface tensions of binary molten mixtures of electrolytes or of ternary aqueous solutions, are included in the model (see ref. (1) for details). The interaction parameters for mixtures are not used in this calculator in order to ensure the widest range of applicability of the model in terms of temperature and concentration.

• The composition of a solution containing ≥2 cations and ≥2 anions cannot, in general, be uniquely assigned in terms of individual electrolytes. We use the formula given by Clegg and Simonson (4).

References

(1)  C. S. Dutcher, A. S. Wexler, and S. L. Clegg (2010) J. Phys. Chem. A, 114, 12216-12230.

(2)  N. B. Vargaftik, B. N. Volkov, and L. D. Voljak (1983) J. Phys. Chem. Ref. Data 12, 817-820.

(3)  G. J. Janz (1988) J. Phys. Chem. Ref. Data 17 (Suppl. 2), 1-309.

(4)  S. L. Clegg and J. M. Simonson (2001) J. Chem. Thermodyn. 33, 1457-1472.