Equilibrium constants from 5 to 90 °C

Before this page

Validation against published data, the constants of the database at 25 °C against their sources.

Cemdata18 (Lothenbach et al., 2019) tabulates its constants at 25 °C. At another temperature they follow from the standard properties of its species: the equation of state of Helgeson et al. (1981) for the aqueous species, the heat capacities of the solids, and the water's own equation of state. The PHREEQC database (Parkhurst and Appelo, 2013) gives many of the same reactions an analytical expression fitted to measured constants over a temperature range, with its sources in comments where it gives them. The two are independent descriptions of the same equilibria, and this page compares them from 5 to 90 °C, reaction by reaction (scripts/logk_temperature_check.jl, on the copy of phreeqc.dat of PHREEQC 3.7.3, which datapath obtains).

1. The comparison

For each reaction, its constant at 25 °C in both databases, and the difference of their temperature dependences at 50 °C and at its largest between 5 and 90 °C: each constant taken from its own value at 25 °C, the two differences compared, so that what the two databases already disagree on at 25 °C is not counted twice. Where phreeqc.dat gives a reaction two expressions (gypsum), the second is used, which its comment calls the better fit.

using ChemistryLab, DynamicQuantities, Printf
include(joinpath(pkgdir(ChemistryLab), "scripts", "logk_temperature_check.jl"))

rows = lkt_compare()
println(rpad("reaction", 22), "  log K at 25 °C        difference of the temperature dependences")
println(rpad("", 22), "  PHREEQC  Cemdata18    at 50 °C   largest, 5-90 °C")
for r in rows
    @printf("%-22s %8.3f %9.3f    %+7.3f   %+6.3f at %2d °C\n", r.name, r.phreeqc25, r.cemdata25, r.at50, r.worst, r.worst_T)
end

reaction                log K at 25 °C        difference of the temperature dependences
                        PHREEQC  Cemdata18    at 50 °C   largest, 5-90 °C
water                   -13.995   -14.000     -0.008   -0.016 at 90 °C
bicarbonate              10.329    10.329     -0.006   -0.053 at 90 °C
carbon dioxide (aq)      16.681    16.681     -0.016   -0.082 at 90 °C
bisulfate                 1.988     1.988     +0.063   +0.139 at 90 °C
CO2(g)                   -1.468    -1.468     -0.001   +0.009 at  5 °C
calcite                  -8.480    -8.480     +0.045   +0.235 at 90 °C
aragonite                -8.336    -8.336     -0.013   -0.019 at 70 °C
dolomite                -17.084   -17.090     -0.042   +0.157 at 90 °C
gypsum                   -4.582    -4.581     -0.030   -0.107 at 90 °C
anhydrite                -4.278    -4.357     -0.009   -0.065 at 90 °C
quartz                   -3.980    -3.746     -0.050   -0.115 at 90 °C
amorphous silica         -2.712    -2.714     +0.020   +0.047 at 90 °C

The constants of two reactions along the range, the most and the least soluble of the calcium sulfates and carbonates:

println(" °C   calcite: PHREEQC Cemdata18    anhydrite: PHREEQC Cemdata18")
for T_C in (5, 25, 50, 75, 90)
    T = T_C + 273.15
    c = lkt_analytic("Calcite"); a = lkt_analytic("Anhydrite")
    @printf("%3d          %7.3f %9.3f               %7.3f %9.3f\n", T_C,
            lkt_phreeqc(c, T), lkt_cemdata(Dict("Ca+2" => 1, "CO3-2" => 1, "Cal" => -1), T),
            lkt_phreeqc(a, T), lkt_cemdata(Dict("Ca+2" => 1, "SO4-2" => 1, "Anh" => -1), T))
end

 °C   calcite: PHREEQC Cemdata18    anhydrite: PHREEQC Cemdata18
  5           -8.393    -8.398                -4.075    -4.185
 25           -8.480    -8.480                -4.278    -4.357
 50           -8.736    -8.691                -4.576    -4.665
 75           -9.122    -8.975                -4.908    -5.027
 90           -9.406    -9.170                -5.118    -5.263

2. What the comparison says

At 25 °C the two databases share their constants. Ten of the twelve agree within 0.01; anhydrite differs by 0.08 and quartz by 0.23, Cemdata18 making quartz the more soluble.

Up to 50 °C their temperature dependences agree within 0.07, the largest difference being that of the bisulfate ion, and by 0.05 at most for the minerals. Up to 90 °C they part by at most 0.24, for calcite, whose PHREEQC expression is a fit over 0 to 250 °C (its comment names Ellis 1959 and Plummer and Busenberg (1982)); aragonite, which PHREEQC gives another expression, agrees with Cemdata18 within 0.02 over the whole range. Gypsum and anhydrite stay within 0.11, the carbonate equilibria within 0.09, the water within 0.02. For a cement cured up to 50 °C, the equations of state of Cemdata18 carry its constants as the fits to measurements do, to a few hundredths of a log unit; at 90 °C the calcium carbonates and sulfates are known to a tenth or two, less well than at 25 °C.