Model IV: Summary and Abstract


The inorganic element of Model IV is an equilibrium thermodynamic model of the system H+ - NH4+ - Na+ - SO42− - NO3 - Cl - H2O.

The temperature range over which it is valid, and whether it can be used for solutions supersaturated with respect to solid salts and acid hydrates, depends upon the ions present:

The model includes the following species:

See the model description page for an explanation of how organic compounds, and an additional liquid phase, are included in the chemical system.


The development of the model is described in the following work:

E. Friese and A. Ebel (2010) Temperature dependent thermodynamic model of the system H+ - NH4+ - Na+ - SO42− - NO3 - Cl - H2O. J. Phys. Chem. A, 114, 11595-11631.

Abstract: A thermodynamic model of the system H+ - NH4+ - Na+ - SO42− - NO3 - Cl - H2O is parametrized and used to represent activity coefficients, equilibrium partial pressures of H2O, HNO3, NH3, HCl, and H2SO4, and saturation with respect to 26 solid phases (H2SO4 · H2O, H2SO4 · 2H2O, H2SO4 · 3H2O, H2SO4 · 4H2O, H2SO4 · 6.5H2O, HNO3 · H2O, HNO3 · 2H2O, HNO3 · 3H2O, HCl · 3H2O, (NH4)2SO4, NH4NO3, NH4Cl, Na2SO4 · 10H2O, Na2SO4, NaNO3 · Na2SO4 · H2O, NaNO3, NaCl, NaCl · 10H2O, (NH4)3H(SO4)2, NH4HSO4, Na3H(SO4)2, NaHSO4 · H2O, NaHSO4, Na2SO4 · (NH4)2SO4 · 4H2O, (NH4)2SO4 · 2NH4NO3, (NH4)2SO4 · 3NH4NO3, and NH4HSO4 · NH4NO3). The enthalpy of formation of the complex salts Na2SO4 · (NH4)2SO4 · 4H2O and NaNO3 · Na2SO4 · H2O is calculated. The model is valid for temperatures ≤263.15 up to 330 K and concentrations from infinite dilution to saturation with respect to the solid phases. For H2SO4 - H2O solutions the degree of dissociation of the HSO4 ion is represented near the experimental uncertainty over wide temperature and concentration ranges. The parametrization of the model for the subsystems H+ - NH4+ - SO42− - NO3 - H2O and H+ - SO42− - NO3 - Cl - H2O relies on previous studies (Clegg, S. L. et al. J. Phys. Chem. A 1998, 102, 2137-2154; Carslaw, K. S. et al. J. Phys. Chem. 1995, 99,11557-11574), which are only partly adjusted to new data. For these systems the model is applicable to temperatures below 200 K, dependent upon liquid-phase composition, and for the former system also to supersaturated solutions. Values for the model parameters are determined from literature data for the vapor pressure, osmotic coefficient, emf, degree of dissociation of HSO4, and the dissociation constant of NH3 as well as measurements of calorimetric properties of aqueous solutions like enthalpy of dilution, enthalpy of solution, enthalpy of mixing, and heat capacity. The high accuracy of the model is demonstrated by comparisons with experimentally determined mean activity coefficients of HCl in HCl - Na2SO4 - H2O solutions, solubility measurements for the quaternary systems H+ - Na+ - SO42− - Cl - H2O, NH4+ - Na+ - SO42− - Cl - H2O, and NH4+ - Na+ - SO42− - NO3 - H2O as well as vapor pressure measurements of HNO3, HCl, H2SO4, and NH3.

Revisions and Corrections

The paper of Ebel and Friese contains a number of typographical errors which have been corrected. Their calculated activity coefficient model parameters for NH4+ - SO42− interactions differ from those of E-AIM at the extremes of temperature. For consistency, parameters calculated using the equations of Ebel and Friese (which are not presented in their paper) are used here.

We have added aqueous NH3 to the model for all calculations except the "Simple" type. This allows systems that are alkaline to be treated – those in which the total ammonia present (NH4+ + NH3) is only partially neutralised by H+. However, the model is not intended to be applied to systems containing high concentrations of aqueous NH3 relative to other dissolved solutes. See the Model II description for details of how this was done.