Densities of Electrolytes: Methods

Single Solutes

• For the nine single solutes that make up the H⁺ - NH4⁺ - Na⁺ - SO4²⁻ - NO3⁻ - Cl⁻ - H2O mixture, the calculated volume properties are based upon an extensive critical review of the available data for temperatures up to 50 °C. These include densities of supersaturated solutions and melts (liquid electrolytes) from electrodynamic balance experiments.

  The fitting equations used for apparent molar volumes ( V^φ) over the normal 0 - 50 °C temperature range include a Debye-Huckel term in order to most accurately predict the values at infinite dilution in water, V^φ∞. This property of the solutes is additive in terms of the individual ions so that, for example, V^φ∞(NaCl) = V^φ∞(Na⁺) + V^φ∞(Cl^-). The model is consistent with this relationship to within about 0.1 cm³ mol⁻¹ or better at 25 °C. Note that values of V^φ∞ for single ions are based upon the convention that V^φ∞(H⁺) = 0.0 at all temperatures. At infinite dilution, the partial and apparent molar volumes of the solutes are the same.

  At temperatures below 0 °C, and for concentrations above that of the saturated solution, volume properties are derived from extrapolations based upon assumptions regarding the density of the (hypothetical) pure liquid melt, and the density of a chosen reference concentration which is likely to vary in a near linear way across a very wide range of temperatures.

  Full details are given in the references at the bottom of main density page.

• Volume properties of NH4HSO4 - H2O, NaHSO4 - H2O, and NH3 - H2O at 298.15 K are each represented using individually fitted equations. The expression for apparent molar volume that is used is the same as for the other single electrolytes, with this exception: for the two acid sulphates the Debye-Huckel term was omitted from the equations and V^φ at very low concentration represented empirically. The values of V^φ that were fitted were derived either from the Pitzer model fit to the acid sulphate system (NH4HSO4) or measurements (NaHSO4), and at infinite dilution are consistent with the values obtained for the other single solutes.
• Densities of pure water were calculated from the equation of Kell (1) to −30 °C, and at lower temperatures from an equation fitted to densities of supercooled water shown in Figure 2 of Mallamace et al. (2).

Mixtures

• Volume properties of the H⁺ - NH4⁺ - Na⁺ - SO4²⁻ - NO3⁻ - Cl⁻ - H2O mixture are predicted from the densities or apparent molar volumes of the component single electrolyte solutions using one of four simple models, which are summarised on the inputs page. Note that the composition of a solution containing ≥2 cations and ≥2 anions cannot, in general, be uniquely assigned in terms of single salts and acids. We use the formula given by Clegg and Simonson (3).
• Properties of the acid sulphate mixture H⁺ - NH4⁺ - HSO4⁻ - SO4²⁻ - H2O are modelled differently, and employ a Pitzer ion-interaction model based upon the work of Clegg et al. (4) to take account of the strong influence of bisulphate dissociation on apparent molar volumes as a function of both concentration and chemical composition.

References

(1)  G. S. Kell (1975) J. Chem. Eng. Data 20, 97-105.

(2)  F. Mallamace, C. Branca, M. Broccio, C. Corsaro, C.-Y. Mou, S.-Y. Chen (2007) PNAS 104, 18387-18391.

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

(4)  S. L. Clegg, S. Milioto, and D. A. Palmer (1996) J. Chem. Eng. Data. 41, 455-467.