Densities of Electrolytes: Inputs

First, the required model is selected on the input page. The input data are then entered in a series of fields, and options are set using radio buttons.

• Temperature: enter an absolute temperature (in Kelvin) that is between the specified limits. The only model that calculates volume properties over a range of temperatures is the H⁺ - NH4⁺ - Na⁺ - SO4²⁻ - NO3⁻ - Cl⁻ - H2O model that is the default choice. The other models that can be selected are for 298.15 K only, and temperature does not need to be entered.
• Choice of estimation method for mixtures: this option is only offered for the multi-ion model. There are four methods, all of which predict the volume properties of the mixture based upon the density, specific volume, or apparent molar volumes of the individual electrolytes of which it is composed. The methods are summarised below:
  1. Density (ρ): the density of the mixture is equal to the sum of the densities of solutions of the individual eletrolyte components, each at the total mass fraction (or weight percent) of solutes in the mixture. The density contribution of each electrolyte is weighted according to its mass fraction in the total solute. This approach is due to Van Dingenen and Raes (1), as generalised by Semmler et al. (2) in their equation 10.
  2. Specific volume (1/ρ): the specific volume of the mixture is equal to the sum of the specific volumes of solutions of the individual eletrolyte components, each at the total mass fraction (or weight percent) of solutes in the mixture. The contribution of each electrolyte is weighted according to its mass fraction in the total solute. This approach was suggested by Tang (3), and generalised by Semmler et al. (2) in their equation 12.
  3. Apparent molar volume (V^φ): the apparent molar volume of the total solute in the mixture is equal to the sum of the apparent molar volumes of the individual eletrolyte components, each at the total molal ionic strength of the mixture. The contribution of each electrolyte is weighted according to its equivalent fraction in the solution. This "Young's Rule" approach is one of several examined by Miller (4), and corresponds to his equation 57.
  4. Apparent molar volume (V^φ): the same as (3) above, but for apparent molar volumes at the total mole fraction ionic strength of the mixture. Note that this method cannot always be applied for concentrations approaching the pure melt (100 weight percent of solute). This is because the mole fraction ionic strength of a pure liquid 2:1 or 1:2 electrolyte is 1.0, but is only 0.5 for a liquid 1:1 electrolyte. Thus, the mole fraction ionic strength of some extremely concentrated mixtures may not be attainable in pure solutions of some of the electrolytes of which it is composed. However, for the great majority of calculations this is unlikely to be a limitation.

  Which of (1-4) above should be used? Young's rules of mixing have been quite extensively applied and tested for dilute solutions and for concentrations up to saturation. So methods (3) and (4) are a good choice for this part of the concentration range. The results of Tang (3) for densities of very concentrated mixtures, obtained using an electrodynamic balance, show that method (2) yields satisfactory estimates for supersaturated solutions.

• Concentration unit: the concentrations of the ions or salts can be entered as their weight percentages in the solution, as molalities, or as molarities. Note that molality is moles per kg of water, and not moles per kg of solution. Molality tends to infinity as the melt composition is approached, so weight percent or molarity are better choices for systems at extreme concentration.
• Concentration: enter the concentration of electrolyte or ions in the selected unit. In the latter case (i.e., ion concentrations) the charge balance will be checked by the system.

  For the model of acid ammonium sulphate (H⁺ - NH4⁺ - HSO4⁻ - SO4²⁻ - H2O) the total concentration must be entered. This is equal to the sum of the values (molalities, molarities, or weight percentages) of the two solute components H2SO4 and (NH4)2SO4. The entry for the mole fraction of acid in the solute – used to specify the relative concentrations of H2SO4 and (NH4)2SO4 – is described in the notes to that model beneath the data entry boxes on the input page. The quantity is equal to nH2SO4/(nH2SO₄ + n(NH4)2SO4), where prefix n denotes the number of moles.

References

(1)  R. Van Dingenen and F. Raes (1993) J. Aerosol Sci. 24, 1-17.

(2)  M. Semmler, B. P. Luo, and T. Koop (2006) Atmos. Environ. 40, 467-483.

(3)  I. N. Tang (1997) J. Geophys. Res. 102, 1883-1893.

(4)  D. G. Miller (1995) J. Solut. Chem. 24, 967-987.