This page lists the Pitzer activity coefficient interaction parameters used in the model. Shown first are the β(0), β(1), β(2), C0φ and C1φ parameters for the interactions of single cations with single anions. Columns "a1" and "a2" list values of constants α1 and α2 that apply to each cation - anion pair. The column "Limit" gives the upper limit of molality (where known) for each set of parameters in pure aqueous solutions of the electrolyte. A "*" in the column "Fit" indicates that the parameters were not taken from the paper of Harvie et al. but are from other (usually later) studies which present equations for the parameters as functions of temperature.
Next, parameters that apply to mixed solutions are listed (only those that are non-zero). These are θ(cc') and θ(aa'), followed by ψ(cc'a) and ψ(aa'c) where a and a' are two distinguishable (different) anions, and c anc c' are two different cations.
Last, the parameters for interactions involving neutral species are listed: λ(nn'), λ(nc), λ(na), μ(nn'c), μ(nn'a) and ζ(nca), where n and n' are two distinguishable neutral solute species. Again, only non-zero values are listed. Note that we have adjusted the values given by Harvie et al. for CO2 - ion interactions from a basis of λ(CO2,H) = 0.0 to λ(CO2,Cl) = 0.0 in order to be consistent with values for ammonia interactions.
A number of parameters are not known and are therefore set to zero. These are mainly ternary ( θ(ii') and ψ(ii'j) ) parameters for interactions between ions in the model of Harvie et al. and those added by us (NH4+ and NO3-).
See Pitzer (1991) for a full description of the model, and equations for activity and osmotic coefficients. The extended equations used here (which include the additional parameter C1φ) are given by Clegg et al. (1994).
K. S. Pitzer (1991) Ion interaction approach: theory and data correlation. In 'Activity Coefficients in Electrolyte Solutions', 2nd Ed., ed. K. S. Pitzer, CRC Press, Boca Raton, p279-434.
S. L. Clegg, J. A. Rard and K. S. Pitzer (1994) thermodynamic properties of 0 - 6 mol kg−1 aqueous sulphuric acid from 273.15 to 328.15 K. J. Chem. Soc. Faraday Trans. 90, 1875-1894.
************************* PITZER MODEL PARAMETER LIST ************************ CaTIONS: 7 ANIONS: 7 NEUTRALS: 4 SYMBOL CHARGE SYMBOL CHARGE SYMBOL H 1.0 HSO4 1.0 NH3 NH4 1.0 SO4 2.0 CO2 Na 1.0 NO3 1.0 CaCO3 K 1.0 Cl 1.0 MgCO3 Ca 2.0 HCO3 1.0 Mg 2.0 CO3 2.0 MgOH 1.0 OH 1.0 CONDITIONS: ------------------------------------------------------------------ TEMPERATURE: 25.00 C PRESSURE: 1.00 BAR ION INTERACTION PARAMETERS: ---- calculations at constant temperature -------- B, C (+-) TERMS AT 25.00 C: b0 b1 b2 C0(phi) C1(phi) a1 a2 -Ions- Limit Fit 0.2959 0.4005 0.00 -0.011316 -0.8187 2.00 H HSO4 6.0 * -0.0084 0.3147 0.00 0.028828 -0.9155 2.00 H SO4 6.0 * 0.1168 0.3546 0.00 -0.005390 0.0000 2.00 H NO3 6.0 0.1769 0.2972 0.00 0.000724 0.0000 2.00 H Cl 6.0 * 0.0000 0.0000 0.00 0.000000 0.0000 2.00 H HCO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 H CO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 H OH 0.0328 0.4684 0.00 0.002307 -0.6974 2.00 NH4 HSO4 6.0 0.0374 0.5345 0.00 -0.000616 0.4646 2.00 NH4 SO4 6.0 * -0.0020 0.0879 0.00 -0.000086 -0.0230 2.00 NH4 NO3 40.0 0.0548 0.2132 0.00 -0.003304 -0.0694 2.00 NH4 Cl 6.0 0.0000 0.0000 0.00 0.000000 0.0000 2.00 NH4 HCO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 NH4 CO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 NH4 OH 0.0454 0.3980 0.00 0.000000 0.0000 2.00 Na HSO4 -0.0173 0.7534 0.00 0.011745 0.0000 1.40 Na SO4 4.0 * 0.0068 0.1783 0.00 -0.000720 0.0000 2.00 Na NO3 6.0 0.0806 0.2631 0.00 0.000525 -0.0201 2.00 Na Cl 6.0 * 0.0277 0.0411 0.00 0.000000 0.0000 2.00 Na HCO3 0.0399 1.3890 0.00 0.004400 0.0000 2.00 Na CO3 0.0864 0.2528 0.00 0.004255 0.0000 2.00 Na OH 6.0 * -0.0003 0.1735 0.00 0.000000 0.0000 2.00 K HSO4 0.0000 0.6179 0.00 0.009155 0.0000 1.40 K SO4 0.7 * -0.0816 0.0494 0.00 0.006600 0.0000 2.00 K NO3 3.8 0.0481 0.2188 0.00 -0.000788 0.0000 2.00 K Cl 4.8 * 0.0296 -0.0130 0.00 -0.008000 0.0000 2.00 K HCO3 0.1488 1.4300 0.00 -0.001500 0.0000 2.00 K CO3 0.1298 0.3200 0.00 0.004100 0.0000 2.00 K OH 5.5 0.2145 2.5300 0.00 0.000000 0.0000 2.00 Ca HSO4 0.2000 3.1973 -54.24 0.000000 0.0000 1.40 12.0 Ca SO4 0.2108 1.4090 0.00 -0.020140 0.0000 2.00 Ca NO3 2.0 0.3053 1.7081 0.00 0.002142 0.0000 2.00 Ca Cl 4.0 * 0.4000 2.9770 0.00 0.000000 0.0000 2.00 Ca HCO3 0.0000 0.0000 0.00 0.000000 0.0000 1.40 12.0 Ca CO3 -0.1747 -0.2303 -5.72 0.000000 0.0000 2.00 Ca OH 0.4746 1.7290 0.00 0.000000 0.0000 2.00 Mg HSO4 0.2151 3.3663 -32.77 0.027919 0.0000 1.40 12.0 Mg SO4 3.0 * 0.3671 1.5847 0.00 -0.020620 0.0000 2.00 Mg NO3 2.0 0.3511 1.6512 0.00 0.006507 0.0000 2.00 Mg Cl 4.5 * 0.3290 0.6072 0.00 0.000000 0.0000 2.00 Mg HCO3 0.0000 0.0000 0.00 0.000000 0.0000 1.40 12.0 Mg CO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 Mg OH 0.0000 0.0000 0.00 0.000000 0.0000 2.00 MgOH HSO4 0.0000 0.0000 0.00 0.000000 0.0000 2.00 MgOH SO4 0.0000 0.0000 0.00 0.000000 0.0000 2.00 MgOH NO3 -0.1000 1.6580 0.00 0.000000 0.0000 2.00 MgOH Cl 0.0000 0.0000 0.00 0.000000 0.0000 2.00 MgOH HCO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 MgOH CO3 0.0000 0.0000 0.00 0.000000 0.0000 2.00 MgOH OH MIXTURE PARAMETERS ---------------------------------------------- THETA(++) TERMS: THETA(--) TERMS: -0.0190 H NH4 -0.0060 HSO4 Cl 0.0360 H Na 0.0926 SO4 NO3 0.0050 H K 0.0200 SO4 Cl 0.0920 H Ca 0.0100 SO4 HCO3 0.1000 H Mg 0.0200 SO4 CO3 0.0044 NH4 Na -0.0130 SO4 OH 0.0124 NH4 Mg 0.0160 NO3 Cl -0.0120 Na K 0.0300 Cl HCO3 0.0700 Na Ca -0.0200 Cl CO3 0.0700 Na Mg -0.0500 Cl OH 0.0320 K Ca -0.0400 HCO3 CO3 0.0070 Ca Mg 0.1000 CO3 OH PSI(++-) TERMS: -0.00865 H NH4 HSO4 -0.02245 H NH4 SO4 -0.01000 H NH4 NO3 -0.00910 H NH4 Cl -0.01290 H Na HSO4 -0.00300 H Na NO3 -0.00400 H Na Cl -0.02650 H K HSO4 0.19700 H K SO4 -0.01000 H K NO3 -0.01100 H K Cl -0.01500 H Ca Cl -0.01780 H Mg HSO4 -0.01100 H Mg Cl -0.00326 NH4 Na SO4 -0.00310 NH4 Na Cl -0.04390 NH4 Mg SO4 -0.02490 NH4 Mg Cl -0.01000 Na K SO4 -0.00120 Na K NO3 -0.00180 Na K Cl -0.00300 Na K HCO3 0.00300 Na K CO3 -0.05500 Na Ca SO4 -0.00700 Na Ca Cl -0.01500 Na Mg SO4 -0.01200 Na Mg Cl -0.02500 K Ca Cl -0.04800 K Mg SO4 -0.02200 K Mg Cl 0.02400 Ca Mg SO4 -0.01200 Ca Mg Cl 0.02800 Mg MgOH Cl PSI(--+) TERMS: -0.00842 HSO4 SO4 NH4 -0.00940 HSO4 SO4 Na -0.06770 HSO4 SO4 K -0.04250 HSO4 SO4 Mg 0.01300 HSO4 Cl H -0.00600 HSO4 Cl Na 0.00660 SO4 NO3 Na -0.00460 SO4 NO3 K 0.00140 SO4 Cl Na -0.01800 SO4 Cl Ca -0.00400 SO4 Cl Mg -0.00500 SO4 HCO3 Na -0.16100 SO4 HCO3 Mg -0.00500 SO4 CO3 Na -0.00900 SO4 CO3 K -0.00900 SO4 OH Na -0.05000 SO4 OH K -0.00600 NO3 Cl Na -0.00600 NO3 Cl K -0.01700 NO3 Cl Ca -0.01500 Cl HCO3 Na -0.09600 Cl HCO3 Mg 0.00850 Cl CO3 Na 0.00400 Cl CO3 K -0.00600 Cl OH Na -0.00600 Cl OH K -0.02500 Cl OH Ca 0.00200 HCO3 CO3 Na 0.01200 HCO3 CO3 K -0.01700 CO3 OH Na -0.01000 CO3 OH K NEUTRAL SPECIES PARAMETERS ------------------------------------------------ LAMBDA(N,N) SPECIES MU(N,N,C) SPECIES 0.01478 NH3 NH3 -0.000750 NH3 NH3 NH4 -0.000311 NH3 NH3 Na -0.000321 NH3 NH3 K LAMBDA(N,C) SPECIES 0.01750 NH3 Na 0.04540 NH3 K -0.08100 NH3 Ca MU(N,N,A) SPECIES -0.21000 NH3 Mg 0.000000 NH3 NH3 SO4 -0.00500 CO2 H -0.000437 NH3 NH3 NO3 0.09500 CO2 Na 0.000625 NH3 NH3 CO3 0.04600 CO2 K 0.17300 CO2 Ca 0.17300 CO2 Mg -0.00500 CO2 MgOH ZETA(N,C,A) SPECIES -0.009180 NH3 NH4 SO4 0.023100 NH3 K OH LAMBDA(N,A) SPECIES -0.008040 NH3 Ca Cl 0.14000 NH3 SO4 -0.01000 NH3 NO3 0.18000 NH3 CO3 0.10300 NH3 OH 0.00200 CO2 HSO4 0.10700 CO2 SO4 0.00500 CO2 HCO3 0.01000 CO2 CO3 0.00500 CO2 OH ****************************************************************************