The System  H+ - NH4+ - Na+ - K+ - Ca2+ - Mg2+ - SO42− - NO3 - Cl - CO32− - OH - H2O  at  298.15 K

Here we present a model of activities, acid/base equilibrium, equilibrium vapour pressures, and saturation with respect to solids for the above system. The model is limited to concentrations up to saturation with respect to the solids that can form (equivalent to water activities above about 0.7 - 0.8 for systems containing soluble salts), and is described below. (Click here to go directly to the input page for the model.)


Sea salt consists mainly of Na+ and Cl- (about 80 mol%), plus smaller amounts of K+, Mg2+, Ca2+, SO42−, and CO32− (CO32−, HCO3 and dissolved CO2 buffer the pH of sea water). Harvie and Weare (1) and later Harvie, Moller, and Weare (2) developed a Pitzer activity coefficient model of this system, for concentrations up to saturation with respect to the solids that can form, and reproducing measured solubilities. Their model, using the activity coefficient parameters and other thermodynamic quantities given in refs. (1) and (2), is made available on this site for interactive calculations.

We have added the species NH4+, NO3, and NH3 to the system treated by Harvie et al. (2). The extra interaction parameters for the Pitzer activity coefficient model, and the acid dissociation constant of NH4+, are taken from the work of Clegg and Whitfield (3,4), Clegg and Brimblecombe (5) and Clegg et al. (6). The Henry's law constants of H2SO4, HCl, HNO3 and NH3 are the same as those used in Models I - III on this site. Follow this link to see the complete list of activity coefficient parameters used in the model.

The model calculates the following aqueous equilibria: ammonia/ammonium, carbonate/bicarbonate/dissolved CO2, sulphate/bisulphate, and the dissociation of water. Harvie et al. (2) also found it necessary to include the formation of MgCO3° and CaCO3° ion pairs and the ion MgOH+ in order to fit the available measurements for systems containing the two alkaline earth ions. These species are included in the model here, and their equilibrium concentrations are calculated.

The activity coefficient model developed by Harvie et al. (1,2) is limited to maximum solute concentrations up to and including saturation with respect to solid salts. Many of the Pitzer interaction parameters were determined from measured salt solubilities, which are reproduced quite accurately by the model. In practical terms, the model is limited to individual salt molalities of up to about 6 mol kg−1 for the most soluble salts. (Others, such as CaSO4 and CaCO3, are much less soluble of course).


The model is able to calculate the degree of saturation of aqueous solutions with respect to the following solid phases:

NaCl Na2SO4 Na2SO4 · 10H2O
Na2CO3 · H2O Na2CO3 · 7H2O Na2CO3 · 10H2O
NaHCO3 Na3H(SO4)2 Na3H(CO3)2 · 2H2O
NaK3(SO4)2 Na2Mg(SO4)2 · 4H2O Na2Ca(SO4)2
Na4Ca(SO4)3 · 2H2O Na2Ca(CO3)2 · 2H2O Na6CO3(SO4)2
KCl K2SO4 (K2CO3)2 · 3H2O
K8H6(SO4)7 K8H4(CO3)6 · 3H2O KNaCO3 · 6H2O
K2NaH(CO3)2 · 2H2O KMgCl3 · 6H2O KMgClSO4 · 3H2O
K2Mg(SO4)2 · 4H2O K2Mg(SO4)2 · 6H2O K2MgCa2(SO4)4 · 2H2O
K2Ca(SO4)2 · H2O MgCl2 · 6H2O MgSO4 · 6H2O
MgSO4 · 7H2O MgSO4 · H2O MgCO3
MgCO3 · 3H2O Mg(OH)2 Mg2CaCl6 · 12H2O
Mg2Cl(OH)3 · 4H2O CaCl2 · 4H2O CaCl6 · H2O
CaSO4 CaSO4 · 2H2O CaCO3(Aragonite)
CaCO3(Calcite) Ca(OH)2 CaNa2(CO3)2 · 5H2O
CaMg(CO3)2 Ca4Cl2(OH)6 · 13H2O Ca2Cl2(OH)2 · H2O
(NH4)2SO4 [•] (NH4)3H(SO4)2 [•] Na2SO4 · (NH4)2SO4 · 4H2O [•]
NH4Cl [•]

Solids marked with "[•]" in the table contain the ions added to the system by us, and are not in the model of Harvie et al. (1,2). A number of very highly soluble salts have been omitted, as have mixed salts containing NH4+ and K+, for example.


Equilbrium partial pressures of the gases H2SO4, HCl, HNO3, NH3 and CO2 over the aqueous phase are calculated by the model from the activities of the solutes and their Henry's law constants. The inclusion of ion - NH3 interactions in the activity coefficient code means that calculated equilibrium pNH3 are likely to be more accurate than the values given by Models II and III on this site.


The equilibrium state of the aqueous solution is solved by Gibbs energy minimisation, as described by Wexler and Clegg (7) (see their equation 23), but expressing activities on a molality rather than a mole fraction basis. The standard chemical potentials of solids and solution components used in the model are given in Table 4 of Harvie et al. (2), with the following additions determined by us:

Species μ°/RT
NH4+(aq) -31.9935
NO3-(aq) -44.8781
NH3(aq) -10.707048
HNO3(g) -30.096117
HCl(g) -38.426448
NH3(g) -6.600771
H2SO4(g) -260.861289
(NH4)2SO4(s) -364.283598
(NH4)3H(SO4)2(s) -698.660511
Na2SO4 · (NH4)2SO4 · 4H2O(s) -1262.389401
NH4Cl(s) -82.093609


(1)  C. E. Harvie and J. H. Weare (1980) The prediction of mineral solubilities in natural waters: the Na-K-Mg-Ca-Cl-SO4-H2O systems from zero to high concentration at 25 C. Geochim. et Cosmochim. Acta 44, 981-997.

(2)  C. E. Harvie, N. Moller, and J. H. Weare (1984) The prediction of mineral solubilities in natural waters: the Na-K-Mg-Ca-H-Cl-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25 C. Geochim. et Cosmochim. Acta 48, 723-751.

(3)  S. L. Clegg and M. Whitfield (1991) Activity coefficients in natural waters. In 'Activity Coefficients in Electrolyte Solutions', 2nd Ed., ed. K. S. Pitzer, CRC Press, Boca Raton, p279-434.

(4)  S. L. Clegg and M. Whitfield (1995) A chemical model of seawater including dissolved ammonia, and the stoichiometric dissociation constant of ammonia in estuarine water and seawater from -2° to 40 °C. Geochim. et Cosmochim. Acta 59, 2403-2421.

(5)  S. L. Clegg and P. Brimblecombe (1989) The solubility of ammonia in pure aqueous and multicomponent solutions. J. Phys. Chem. 93, 7237-7248.

(6)  S. L. Clegg, S. Milioto and D. A. Palmer (1996) Osmotic and activity coefficients of aqueous (NH4)2SO4 as a function of temperature, and (NH4)2SO4 - H2SO4 mixtures at 298.15 K and 323.15 K. J. Chem. Eng. Data 41, 455-467.

(7)  A. S. Wexler and S. L. Clegg (2002) Atmospheric aerosol models for systems including the ions H+, NH4+, Na+, SO42−, NO3-, Cl-, Br-, and H2O. J. Geophys. Res.-Atmos. 107, D14, Art. No. 4207.