dataset of thermodynamic data for gwb programs dataset format: jul22 activity model: h-m-w fugacity model: peng-robinson * * +++++++++++++++++++++++++++++++++++++++++++++++ * +++++++++++++++++++++++++++++++++++++++++++++++ * * Pitzer model in the Na–K–Ca–Mg–Cl–SO4 system valid from 298.15 to <200 K * up to saturated salt concentrations. The PhreeqC dataset ColdChem.dat * was converted to GWB format using TEdit in GWB Release 15. * * A low-temperature aqueous thermodynamic model for the Na-K-Ca-Mg-Cl- * SO4 system incorporating new experimental heat capacities in Na2SO4, * K2SO4, and MgSO4 solutions. * * Jonathan D. Toner* and David C. Catling * * University of Washington, Box 351310, Dept. Earth & Space Sciences, * Seattle, WA 98195, USA. * * *Corresponding author. * Address: Department of Earth and Space Sciences, * University of Washington, * Seattle, WA 98195, USA. * Tel.: +1 267 304 3488. * E-mail address: toner2@uw.edu. * * * Notes: * * The temperature dependence of log Ks and header variable Debye-Huckel A * is described with a polynomial containing up to six coefficients a-f * spread over two lines: * * log K = a + b*(Tk-Tr) + c*(Tk2-Tr2) + d*(1/Tk - 1/Tr) + e*(1/Tk2 - 1/Tr2) * + f*ln(Tk/Tr) * * where Tk is absolute temperature and Tr is 298.15 K. Hence, if c-f are * zero (or omitted), then b is the first temperature derivative. * * GWB Log K polynomial coefficients a-f were converted from coefficients * A1-A6 in PhreeqC's analytic expression as follows: * * a= log10 K(298.15 K) = A1 + A2*Tr + A3/Tr + A4*log10(Tr) + A5/Tr2 + A6*Tr2 * b= A2 * c= A6 * d= A3 * e= A5 * f= A4/ln(10) * * A temperature range of validity may optionally be set for each reaction. * If no range is set, the span of the principal temperatures is assumed. * * The GWB's H-M-W model uses the header variable Debye-Huckel A (adh) to * determine the value of A-phi as 2.303 A/3 only when its temperature * expansion is defined in polynomial form, as in this dataset. Otherwise, * when A is set as a T-table, the apps calculate A-phi internally using a * method valid above the freezing point of water. Debye-Huckel B (bdh) is * not used. * * The polynomial coefficients for Debye-Huckel A are converted from the * expression for A-phi in Toner and Catling (2017). * * Species' names have been converted to the GWB format. For example, Ca++ * replaces Ca+2. * * Suffixes (e.g. (aq) and (s)) have been added where species names were * duplicated. * * Oxide components have been added. * * To the best of our knowledge, this dataset is not subject to copyright. * * +++++++++++++++++++++++++++++++++++++++++++++++ * +++++++++++++++++++++++++++++++++++++++++++++++ * temperatures -75.0000 -60.0000 -45.0000 -30.0000 -15.0000 0.0000 12.5000 25.0000 * pressures 1.0134 1.0134 1.0134 1.0134 1.0134 1.0134 1.0134 1.0134 * debye huckel a (adh) a= 0.5100462969 b= 0.0018577945 c= -1.8648e-06 d= 744.6507863 e= -31115.48851 f= 1.8363165 * debye huckel b (bdh) a= 0 b= 0 c= 0 d= 0 e= 0 f= 0 8 elements Hydrogen (H ) mole wt.= 1.0080 g Oxygen (O ) mole wt.= 15.9990 g Calcium (Ca) mole wt.= 40.0800 g Magnesium (Mg) mole wt.= 24.3100 g Sodium (Na) mole wt.= 22.9900 g Potassium (K ) mole wt.= 39.1000 g Chlorine (Cl) mole wt.= 35.4500 g Sulfur (S ) mole wt.= 32.0640 g -end- 8 basis species H2O charge= 0 ion size= 0.0 A mole wt.= 18.0150 g 2 elements in species 2.000 H 1.000 O H+ charge= 1 ion size= 0.0 A mole wt.= 1.0080 g 1 elements in species 1.000 H Ca++ charge= 2 ion size= 0.0 A mole wt.= 40.0800 g 1 elements in species 1.000 Ca Mg++ charge= 2 ion size= 0.0 A mole wt.= 24.3100 g 1 elements in species 1.000 Mg Na+ charge= 1 ion size= 0.0 A mole wt.= 22.9900 g 1 elements in species 1.000 Na K+ charge= 1 ion size= 0.0 A mole wt.= 39.1000 g 1 elements in species 1.000 K Cl- charge= -1 ion size= 0.0 A mole wt.= 35.4500 g 1 elements in species 1.000 Cl SO4-- charge= -2 ion size= 0.0 A mole wt.= 96.0600 g 2 elements in species 4.000 O 1.000 S -end- 0 redox couples -end- 1 aqueous species OH- charge= -1 ion size= 0.0 A mole wt.= 17.0070 g 2 species in reaction -1.000 H+ 1.000 H2O * log10 K(298 K) = 14.0000 a= 14 b= 0 c= 0 d= 0 e= 0 f= 0 TminK= 298.15 TmaxK= 298.15 -end- 0 free electron -end- 33 minerals Halite type= halide formula= NaCl mole vol.= 0.0000 cc mole wt.= 58.4400 g 2 species in reaction 1.000 Na+ 1.000 Cl- * log10 K(298 K) = 1.5893 a= 1.589309643 b= -0.0713492206 c= 3.41140194e-05 d= 1412.35386 e= -72134.033 f= 19.00214347 Hydrohalite type= halide formula= NaCl:2H2O mole vol.= 0.0000 cc mole wt.= 94.4700 g 3 species in reaction 1.000 Na+ 1.000 Cl- 2.000 H2O * log10 K(298 K) = 1.5721 a= 1.57209577 b= -0.0672022066 c= 2.87396671e-05 d= 2009.72645 e= -87173.0584 f= 22.98699104 Sylvite type= halide formula= KCl mole vol.= 0.0000 cc mole wt.= 74.5500 g 2 species in reaction 1.000 K+ 1.000 Cl- * log10 K(298 K) = 0.9110 a= 0.9110407923 b= -0.0391368319 c= 4.44874215e-05 d= -9241.94776 e= 337736.436 f= -16.62325172 Bischofite type= halide formula= MgCl2:6H2O mole vol.= 0.0000 cc mole wt.= 203.3000 g 3 species in reaction 1.000 Mg++ 2.000 Cl- 6.000 H2O * log10 K(298 K) = 4.5491 a= 4.549080129 b= 0.0590910963 c= -5.56842159e-05 d= 2684.56507 e= -239877.356 f= -6.856251327 MgCl2:8H2O type= halide formula= MgCl2:8H2O mole vol.= 0.0000 cc mole wt.= 239.3300 g 3 species in reaction 1.000 Mg++ 2.000 Cl- 8.000 H2O * log10 K(298 K) = 4.1386 a= 4.138636566 b= 0.0649725432 c= -6.18927911e-05 d= 2561.0815 e= -253958.289 f= -3.186406936 MgCl2:12H2O type= halide formula= MgCl2:12H2O mole vol.= 0.0000 cc mole wt.= 311.3900 g 3 species in reaction 1.000 Mg++ 2.000 Cl- 12.000 H2O * log10 K(298 K) = 3.3623 a= 3.362306107 b= 0.0767593043 c= -7.3418584e-05 d= 3782.76461 e= -282777.364 f= 3.93533521 Antarcticite type= halide formula= CaCl2:6H2O mole vol.= 0.0000 cc mole wt.= 219.0700 g 3 species in reaction 1.000 Ca++ 2.000 Cl- 6.000 H2O * log10 K(298 K) = 3.9420 a= 3.941988124 b= 0.01632681 c= 3.89050726e-06 d= -8705.71336 e= 280039.803 f= -25.69447743 Tachyhydrite type= halide formula= CaCl2:(MgCl2)2:12H2O mole vol.= 0.0000 cc mole wt.= 517.5800 g 4 species in reaction 1.000 Ca++ 2.000 Mg++ 6.000 Cl- 12.000 H2O * log10 K(298 K) = 17.0584 a= 17.05839161 b= 0.120385179 c= -9.23150187e-05 d= -8867.46311 e= -154324.05 f= -50.90064917 Carnallite type= halide formula= KCl:MgCl2:6H2O mole vol.= 0.0000 cc mole wt.= 277.8500 g 4 species in reaction 1.000 K+ 1.000 Mg++ 3.000 Cl- 6.000 H2O * log10 K(298 K) = 4.3058 a= 4.305753242 b= 0.0203620204 c= -1.14446488e-05 d= -7006.85183 e= 98177.1561 f= -23.59861769 Thenardite type= sulfate formula= Na2SO4 mole vol.= 0.0000 cc mole wt.= 142.0400 g 2 species in reaction 2.000 Na+ 1.000 SO4-- * log10 K(298 K) = -0.2995 a= -0.2994752659 b= -0.176359486 c= 5.26794201e-05 d= 5284.79187 e= -7056.95508 f= 60.35723562 Na2SO4:7H2O type= sulfate formula= Na2SO4:7H2O mole vol.= 0.0000 cc mole wt.= 268.1450 g 3 species in reaction 1.000 SO4-- 2.000 Na+ 7.000 H2O * log10 K(298 K) = -0.6697 a= -0.6696985457 b= -0.133957871 c= 1.39735831e-05 d= 6383.20125 e= -43868.6621 f= 67.7295282 Mirabilite type= sulfate formula= Na2SO4:10H2O mole vol.= 0.0000 cc mole wt.= 322.1900 g 3 species in reaction 1.000 SO4-- 2.000 Na+ 10.000 H2O * log10 K(298 K) = -1.2216 a= -1.22157857 b= -0.115799382 c= -2.60642888e-06 d= 6954.94838 e= -59658.8151 f= 70.8932571 Arcanite type= sulfate formula= K2SO4 mole vol.= 0.0000 cc mole wt.= 174.2600 g 2 species in reaction 1.000 SO4-- 2.000 K+ * log10 K(298 K) = -1.7896 a= -1.789570643 b= -0.105584131 c= 6.96054072e-05 d= -16234.3991 e= 817047.533 f= -12.79931295 Kieserite type= sulfate formula= MgSO4:H2O mole vol.= 0.0000 cc mole wt.= 138.3850 g 3 species in reaction 1.000 Mg++ 1.000 SO4-- 1.000 H2O * log10 K(298 K) = -0.0523 a= -0.0523294866 b= 0.0176920651 c= -6.11799971e-05 d= 2640.49686 e= -63486.492 f= 4.727637182 Starkeyite type= sulfate formula= MgSO4:4H2O mole vol.= 0.0000 cc mole wt.= 192.4300 g 3 species in reaction 1.000 Mg++ 1.000 SO4-- 4.000 H2O * log10 K(298 K) = -0.7492 a= -0.7492450509 b= 0.0294897825 c= -7.25663369e-05 d= 3170.6995 e= -79887.6029 f= 9.713859943 Pentahydrite type= sulfate formula= MgSO4:5H2O mole vol.= 0.0000 cc mole wt.= 210.4450 g 3 species in reaction 1.000 Mg++ 1.000 SO4-- 5.000 H2O * log10 K(298 K) = -1.1917 a= -1.19170528 b= 0.0366908088 c= -7.66417563e-05 d= 3131.39607 e= -87453.1243 f= 9.542471011 Hexahydrite type= sulfate formula= MgSO4:6H2O mole vol.= 0.0000 cc mole wt.= 228.4600 g 3 species in reaction 1.000 Mg++ 1.000 SO4-- 6.000 H2O * log10 K(298 K) = -1.5649 a= -1.564925626 b= 0.0298849036 c= -7.5885281e-05 d= 3793.28662 e= -97759.3009 f= 14.97835602 Epsomite type= sulfate formula= MgSO4:7H2O mole vol.= 0.0000 cc mole wt.= 246.4750 g 3 species in reaction 1.000 Mg++ 1.000 SO4-- 7.000 H2O * log10 K(298 K) = -1.8533 a= -1.853282599 b= 0.0408263248 c= -8.54183412e-05 d= 3952.68946 e= -107994.396 f= 16.13839124 Meridianiite type= sulfate formula= MgSO4:11H2O mole vol.= 0.0000 cc mole wt.= 318.5350 g 3 species in reaction 1.000 Mg++ 1.000 SO4-- 11.000 H2O * log10 K(298 K) = -1.2687 a= -1.268746772 b= 0.0689739442 c= -0.000101323586 d= 3432.74278 e= -138912.702 f= 15.84036851 Anhydrite type= sulfate formula= CaSO4 mole vol.= 0.0000 cc mole wt.= 136.1400 g 2 species in reaction 1.000 Ca++ 1.000 SO4-- * log10 K(298 K) = -4.4666 a= -4.466633137 b= -0.0249527795 c= -3.78445438e-07 d= -9466.40889 e= 468580.957 f= -16.85317799 Bassanite type= sulfate formula= CaSO4:0.5H2O mole vol.= 0.0000 cc mole wt.= 145.1475 g 3 species in reaction 1.000 Ca++ 1.000 SO4-- .500 H2O * log10 K(298 K) = -3.9283 a= -3.928336816 b= -0.0242694474 c= -1.44767707e-06 d= -9097.36725 e= 464837.895 f= -15.76194717 Gypsum type= sulfate formula= CaSO4:2H2O mole vol.= 0.0000 cc mole wt.= 172.1700 g 3 species in reaction 1.000 Ca++ 1.000 SO4-- 2.000 H2O * log10 K(298 K) = -4.6046 a= -4.604648309 b= -0.0231595527 c= -4.08874814e-06 d= -8890.61112 e= 452668.487 f= -12.20081611 Glaserite type= sulfate formula= Na2SO4:3K2SO4 mole vol.= 0.0000 cc mole wt.= 664.8200 g 3 species in reaction 2.000 Na+ 6.000 K+ 4.000 SO4-- * log10 K(298 K) = -7.5308 a= -7.530837826 b= -0.493115909 c= 0.000261498202 d= -43877.1671 e= 2444082.18 f= 21.96046524 Bloedite type= sulfate formula= Na2SO4:MgSO4:4H2O mole vol.= 0.0000 cc mole wt.= 334.4700 g 4 species in reaction 1.000 Mg++ 2.000 Na+ 2.000 SO4-- 4.000 H2O * log10 K(298 K) = -2.3687 a= -2.368673131 b= -0.146894117 c= -1.98717832e-05 d= 6195.55534 e= -86966.8193 f= 70.07833478 Glauberite type= sulfate formula= Na2SO4:CaSO4 mole vol.= 0.0000 cc mole wt.= 278.1800 g 3 species in reaction 1.000 Ca++ 2.000 Na+ 2.000 SO4-- * log10 K(298 K) = -5.2690 a= -5.269023638 b= -0.201304073 c= 5.22956285e-05 d= -4601.83145 e= 461530.552 f= 43.50174172 Labile_Salt type= sulfate formula= Na4(SO4)2:CaSO4:2H2O mole vol.= 0.0000 cc mole wt.= 456.2500 g 4 species in reaction 1.000 Ca++ 4.000 Na+ 3.000 SO4-- 2.000 H2O * log10 K(298 K) = -5.6361 a= -5.636112806 b= -0.375040464 c= 0.000100769993 d= 214.771374 e= 439413.848 f= 108.2550299 Leonite type= sulfate formula= K2SO4:MgSO4:4H2O mole vol.= 0.0000 cc mole wt.= 366.6900 g 4 species in reaction 1.000 Mg++ 2.000 K+ 2.000 SO4-- 4.000 H2O * log10 K(298 K) = -3.8309 a= -3.830884462 b= -0.0760958854 c= -2.95995158e-06 d= -13524.677 e= 737158.615 f= -3.085007999 Picromerite type= sulfate formula= K2SO4:MgSO4:6H2O mole vol.= 0.0000 cc mole wt.= 402.7200 g 4 species in reaction 1.000 Mg++ 2.000 K+ 2.000 SO4-- 6.000 H2O * log10 K(298 K) = -4.3315 a= -4.331525921 b= -0.0757009316 c= -6.27878932e-06 d= -13040.2925 e= 719286.773 f= 2.179536563 Langbeinite type= sulfate formula= K2SO4:2MgSO4 mole vol.= 0.0000 cc mole wt.= 415.0000 g 3 species in reaction 2.000 Mg++ 2.000 K+ 3.000 SO4-- * log10 K(298 K) = -3.4144 a= -3.414352256 b= -0.0772219676 c= -4.61211534e-05 d= -10929.7236 e= 706598.327 f= -6.220553822 Syngenite type= sulfate formula= K2SO4:CaSO4:H2O mole vol.= 0.0000 cc mole wt.= 328.4150 g 4 species in reaction 1.000 Ca++ 2.000 K+ 2.000 SO4-- 1.000 H2O * log10 K(298 K) = -7.4656 a= -7.465575814 b= -0.129225053 c= 6.71236125e-05 d= -26013.7019 e= 1278096.3 f= -27.45426082 Kainite type= sulfate formula= KCl:MgSO4:2.75H2O mole vol.= 0.0000 cc mole wt.= 244.4612 g 5 species in reaction 1.000 Mg++ 1.000 K+ 1.000 SO4-- 1.000 Cl- 2.750 H2O * log10 K(298 K) = -0.0665 a= -0.06645275926 b= -0.0137384934 c= -2.4058416e-05 d= -6259.84683 e= 267789.365 f= -8.880601226 Polyhalite type= sulfate formula= K2SO4:MgSO4:Ca2(SO4)2:2H2O mole vol.= 0.0000 cc mole wt.= 602.9400 g 5 species in reaction 2.000 Ca++ 1.000 Mg++ 2.000 K+ 4.000 SO4-- 2.000 H2O * log10 K(298 K) = -13.1331 a= -13.13305711 b= -0.138682532 c= 6.77703603e-06 d= -32874.8928 e= 1683922.49 f= -38.82051368 Ice(s) type= formula= H2O mole vol.= 0.0000 cc mole wt.= 18.0150 g 1 species in reaction 1.000 H2O * log10 K(298 K) = 0.1033 a= 0.1032866406 b= 0.00511995404 c= -5.09587694e-06 d= 348.880086 e= -7517.72938 f= 1.586952787 -end- * Use TEdit to add solid solutions here globally, or add them locally * from the Solid Solutions... dialog in any of the GWB modeling apps. 0 solid solutions -end- 0 gases -end- 6 oxides Na2O mole wt.= 61.9790 g 3 species in reaction -2.000 H+ 2.000 Na+ 1.000 H2O CaO mole wt.= 56.0790 g 3 species in reaction -2.000 H+ 1.000 Ca++ 1.000 H2O HCl mole wt.= 36.4580 g 2 species in reaction 1.000 H+ 1.000 Cl- K2O mole wt.= 94.1990 g 3 species in reaction -2.000 H+ 2.000 K+ 1.000 H2O MgO mole wt.= 40.3090 g 3 species in reaction -2.000 H+ 1.000 Mg++ 1.000 H2O SO3 mole wt.= 80.0610 g 3 species in reaction -1.000 H2O 1.000 SO4-- 2.000 H+ -end- * Virial coefficients. * * The first value on a data line ("a= ") is the virial coefficient * value at 25 C. * * The temperature dependence of the virial coefficients beta0, beta1, * beta2, cphi, theta, lambda, and psi may be specified by appending as many * as five coefficients b-f to a data line. The new correlation equation, * used in this dataset, is * * val = a + b*(Tk-Tr) + c*(Tk2-Tr2) + d*(1/Tk - 1/Tr) + e*(1/Tk2 - 1/Tr2) * + f*ln(Tk/Tr) * * where Tk is absolute temperature and Tr is 298.15 K. Hence, if c-f are * zero (or omitted), then b is the first temperature derivative. * * The legacy correlation equation described in the Thermo Datasets chapter * of the GWB Reference Manual is also acceptable. * * A temperature range of validity may optionally be set for each species pair * or triplet, regardless of the temperature expansion chosen. If no range is * set, the span of the principal temperatures is assumed. * * Input is parsed word-by-word; therefore, there is no need to align data * by column. Cl- Na+ beta0 a= .0914649401 b= .00222963373 c= 1.52080581e-5 d= 379.801366 e= -123087.011 f= -4.90110805 beta1 a= .284765738 b= -.0165432118 c= 4.02189441e-5 d= -5296.43274 e= 249801.971 f= -14.4176456 beta2 a= -.0243653114 b= -.00745515374 c= -1.73562079e-5 d= -3895.93796 e= 344943.259 f= .470784204 cphi a= -.000144675793 b= .00298078169 c= -3.9298978e-6 d= 184.098991 e= -4715.9737 f= .310540828 alpha1 = 2.0 alpha2 = .5 Cl- K+ beta0 a= .0571195081 b= -.00164799613 c= 5.54444329e-6 d= -290.431558 e= -13082.6093 f= -1.48678192 beta1 a= .21159828 b= -.00973682396 c= 2.88345391e-5 d= -1642.14177 e= 1089.26901 f= -7.25863112 beta2 a= -.0113225945 b= -.00423447042 c= 7.65961704e-7 d= -1019.28896 e= 47790.7476 f= -1.37051659 cphi a= -.00184317106 b= -.0010487383 c= 5.99728205e-7 d= -309.193697 e= 27405.3587 f= -.244073786 alpha1 = 2.0 alpha2 = .5 Ca++ Cl- beta0 a= 3.16259193 b= -.0086540086 c= -1.31441465e-5 d= -1239.21067 e= -245290.782 f= -3.9305314 beta1 a= 1.79602312 b= -.0139156928 c= 1.11743263e-5 d= -3478.35644 e= 132399.994 f= -5.46805175 beta2 a= -3.59786737 b= .0124673606 c= 1.3037378e-5 d= 2050.38674 e= 242563.331 f= 5.20141195 cphi a= -.0625205928 b= .000554063013 c= 3.21763846e-7 d= -32.8893136 e= 10083.8661 f= -.155416953 alpha1 = 1.0 alpha2 = .1 Cl- Mg++ beta0 a= .363859308 b= .00307212441 c= -3.00517607e-7 d= 829.468216 e= -82765.8755 f= -.192141894 beta1 a= 1.66306195 b= .0367157132 c= -4.09093883e-5 d= 8794.59314 e= -419173.045 f= 17.0594977 beta2 a= -.0233325594 b= .00523142195 c= -1.58642893e-5 d= 189.902359 e= 40105.1252 f= 3.16007089 cphi a= .00454861472 b= -8.33291002e-5 c= 2.23958734e-7 d= -143.787677 e= 10874.7231 f= -.27043472 alpha1 = 2.0 alpha2 = .5 Na+ SO4-- beta0 a= -.0346325304 b= -.00104975634 c= 6.84916461e-6 d= -1239.02955 e= 39112.7017 f= -3.91132942 beta1 a= .908435489 b= .127034327 c= -9.59077709e-5 d= 292.677599 e= -243541.591 f= -24.1321273 beta2 a= .129297286 b= .021110045 c= -4.5388003e-5 d= -1611.14017 e= 167377.181 f= .974700333 cphi a= .0113534592 b= -.0248487042 c= 2.71996165e-5 d= -3218.88276 e= 197677.249 f= -3.85446069 alpha1 = 2.0 alpha2 = .5 K+ SO4-- beta0 a= -.285235185 b= -.0240952655 c= 6.03857471e-5 d= -496.002051 e= -1468.96107 f= -4.38384404 beta1 a= .380606793 b= -.301898316 c= .000335058782 d= -28780.4839 e= 1589529.51 f= -28.3183661 beta2 a= .584120931 b= -.0605359427 c= -2.94178063e-5 d= -8737.09333 e= 722133.576 f= 9.79894787 cphi a= .0703370745 b= .00913356461 c= -2.52960231e-5 d= 1085.02374 e= -17441.9961 f= 4.7451808 alpha1 = 2.0 alpha2 = .5 Ca++ SO4-- beta0 a= .0492369892 b= .979624192 c= -.00116664955 d= 72689.8202 e= -3615578.18 f= 77.648153 beta1 a= 3.61452594 b= -2.5091977 c= .00357835688 d= -200359.432 e= 8403957.76 f= -362.710742 beta2 a= -64.8536341 b= 21.5271214 c= -.0258888085 d= 1147022.15 e= -57599654.1 f= 607.285214 cphi a= -.108807759 b= -.348129067 c= .00037623219 d= -25326.6014 e= 1381333.21 f= -17.1588258 alpha1 = 1.4 alpha2 = 12.0 Mg++ SO4-- beta0 a= .221726691 b= -.00135278206 c= 1.05808689e-5 d= -3719.12474 e= 169215.288 f= -9.88159123 beta1 a= 3.31832544 b= .206266994 c= -.000396723351 d= 35930.3088 e= -1141744.4 f= 106.912025 beta2 a= -34.3527864 b= 8.71247613 c= -.014145709 d= 1310364.69 e= -58411998.2 f= 2930.8806 cphi a= .0255536866 b= .00555800908 c= 2.49279895e-7 d= -902.540124 e= 30618.0721 f= -4.17375011 alpha1 = 1.4 alpha2 = 12.0 -end- end of beta set, begin with theta set of 2nd virial coefficients K+ Na+ theta a= -.0154666879 b= .00382165106 c= -4.40548557e-6 d= 78.1083072 e= -2736.7578 f= -.148995996 Ca++ Na+ theta a= .0743104665 b= -.0155668804 c= 1.12086386e-6 d= 537.178181 e= 3953.88118 f= 6.17477295 Mg++ Na+ theta a= .0686826012 b= .00412764819 c= -4.74889815e-6 d= 62.7981446 e= 2301.80082 f= -.00936915659 Ca++ K+ theta a= .0260269977 b= -.000239668221 c= 1.14016305e-7 d= -18.8203602 e= -458.969498 f= .0923417097 K+ Mg++ theta a= .0443008071 b= 2.98865403e-5 c= -1.54009323e-7 d= -15.2685212 e= -1168.48834 f= .0868101323 Ca++ Mg++ theta a= .0259823638 b= .00118349516 c= -1.24977453e-6 d= 53.1416082 e= -3828.15635 f= .0316938224 Cl- SO4-- theta a= .0214067572 b= .00551257757 c= 2.27890059e-7 d= -230.216445 e= -857.24693 f= -2.41145539 -end- end of theta set, begin with lambda set -end- end of lambda set, begin with psi set Cl- K+ Na+ psi a= -.000875146963 b= -3.89172849e-5 c= 1.60456551e-8 d= -.131251503 e= -24.8979095 f= .0146364991 Ca++ Cl- Na+ psi a= .00710063151 b= 8.32672101e-5 c= -3.1032171e-7 d= 28.2235816 e= -1821.87238 f= .139941607 Cl- Mg++ Na+ psi a= -.00872872402 b= .00808154172 c= -7.4512357e-6 d= 243.863222 e= -14234.0505 f= -.55248236 Ca++ Cl- K+ psi a= -.00970714792 b= 9.58988655e-6 c= -5.38702035e-9 d= -4.44357423 e= 11.1108536 f= -.00310611807 Cl- K+ Mg++ psi a= -.0309323702 b= -7.69621716e-5 c= 3.67321725e-8 d= -8.72837467 e= -146.301115 f= .0295701229 Ca++ Cl- Mg++ psi a= -.0109027531 b= .0131070634 c= -8.26208145e-6 d= -410.818988 e= 7971.79489 f= -3.62754763 K+ Na+ SO4-- psi a= -.012761142 b= -6.18291854e-5 c= 1.42613139e-7 d= 2.81713911 e= -625.022041 f= -.0189525727 Ca++ Na+ SO4-- psi a= .0533425832 b= -.000967411193 c= 1.06636951e-6 d= -17.0285067 e= -123.592376 f= .0167155581 Mg++ Na+ SO4-- psi a= -.017734761 b= .000872904086 c= -8.76652003e-7 d= 38.8799968 e= -2642.88475 f= .000948702274 Ca++ K+ SO4-- psi a= -.055521073 b= .000105316015 c= -1.42380401e-7 d= 2.93518621 e= -607.472163 f= .0243344379 K+ Mg++ SO4-- psi a= -.0849399083 b= .00123884517 c= -1.64233361e-6 d= 5.98416472 e= 2265.68876 f= .0384947636 Ca++ Mg++ SO4-- psi a= .204637869 b= 3.45946e-5 c= -2.03457779e-8 d= -11.666789 e= 35.9698969 f= -.0107037103 Cl- Na+ SO4-- psi a= -.00172341289 b= -.00408042439 c= 3.99143914e-6 d= -113.56965 e= 5949.57078 f= .24109128 Cl- K+ SO4-- psi a= -.0103007766 b= .00360028981 c= -6.72334455e-6 d= 18.0071195 e= 6711.25585 f= .318747408 Ca++ Cl- SO4-- psi a= .012795758 b= -.00194285877 c= 1.28644701e-6 d= -30.547971 e= 4117.37724 f= .379027048 Cl- Mg++ SO4-- psi a= -.00346210276 b= -.0384625718 c= 3.20532585e-5 d= 174.736447 e= 12956.4286 f= 6.67767841 -end- end of psi set * * Reference. * * Toner, J.D. and D.C. Catling, 2017. A low-temperature aqueous * thermodynamic model for the Na-K-Ca-Mg-Cl-SO4 system * incorporating new experimental heat capacities in Na2SO4, K2SO4, * and MgSO4 solutions. Journal of Chemical & Engineering Data 2017 * 62 (10), 3151-3168