Erratum to: Prediction of the thermodynamic properties of metal–arsenate and metal–arsenite aqueous complexes to high temperatures and pressures and some geological consequences

Erratum to: Environ Geol (2007) 52:1343–1363 DOI 10.1007/s00254-006-0578-5

Marini and Accornero (2007) evaluated the standard thermodynamic properties ($\Updelta G_{\text{f}}^{\text{o}}$, $\Updelta H_{\text{f}}^{\text{o}}$, S ^o, $C_{\text{P}}^{\text{o}}$, V ^o, ω) of several aqueous complexes formed by dissolved metals and dihydrogenarsenate, monohydrogenarsenate, arsenate and dihydrogenarsenite ions at reference pressure, Pr = 1 bar, and reference temperature, Tr = 298.15 K, as well as the pressure- and temperature-independent coefficients of the revised Helgeson–Kirkham–Flowers (HKF) equations of state a _1,ML, a _2,ML, a _3,ML, a _4,ML, c _1,ML, and c _2,ML, where the subscript ML identifies a generic aqueous complex formed by metal M and ligand L.

Unfortunately, we recently realized that there is a wrong sign in the Eq. 37 of Sverjensky et al. (1997), corresponding to Eq. 48 of Marini and Accornero (2007), which was used to calculate the EOS coefficient c _1,ML. In the correct equation:

$$ c_{{1,{\text{ML}}}} = 0.6087 \cdot C_{{P,{\text{ML,Pr,Tr}}}}^{\text{o}} - \omega_{\text{ML,Pr,Tr}} \cdot 298.15 \cdot X_{\text{Pr,Tr}} + 5.85 $$

(1)

the term containing the solvent Born function X must have a negative sign. This is easy inferable by solving the HKF equation of state (see Marini and Accornero 2007 for the explanation of symbols):

$$ C_{{P,{\text{ML,Pr,T}}}}^{\text{o}} = \omega_{\text{ML}} \cdot T \cdot X + 2 \cdot T \cdot Y\left( {{\frac{{\partial \omega_{\text{ML}} }}{\partial T}}} \right)_{P} - T\left( {{\frac{1}{\varepsilon }} - 1} \right) \cdot \left( {{\frac{{\partial^{2} \omega_{\text{ML}} }}{{\partial T^{2} }}}} \right)_{P} + c_{{1,{\text{ML}}}} + {\frac{{c_{{2,{\text{ML}}}} }}{{(T - \Uptheta )^{2} }}} , $$

(2)

for T = Tr and rearranging it as follows:

$$ c_{{1,{\text{ML}}}} = C_{{P,{\text{ML,Pr,}}T}}^{\text{o}} - \omega_{\rm ML} \cdot 298.15 \cdot X_{\text{Pr,Tr}} - {\frac{{c_{{2,{\text{ML}}}} }}{{(298.15 - \Uptheta )^{2} }}} . $$

(3)

The wrong values obtained by Marini and Accornero (2007) for the EOS coefficient c _1,ML determine increasingly large errors in the thermodynamic properties of the aqueous complexes of interest at temperatures increasingly different from Tr and, consequently, in the log K of their destruction reactions.

To compute the correct values of the EOS coefficient c _1,ML, Eq. 3 was used, in which the value of c _2,ML is given by (Sverjensky et al. 1997):

$$ c_{{2,{\text{ML}}}} = 2037 \cdot C_{{P,{\text{ML,Pr,Tr}}}}^{\text{o}} - 30460 . $$

(4)

The calculated values of the EOS coefficient c _1,ML are reported in Table 1, together with all other estimated standard partial molal thermodynamic properties, at Pr, Tr, for the metal–arsenate and metal–arsenite complexes of interest as well as the equation-of-state parameters for calculating the corresponding properties at high temperatures and pressures. In addition to the new values of the EOS coefficient c _1,ML, little modifications in the $\Updelta H_{\text{f}}^{\text{o}}$ and S ^o of the complexes MgAsO₄ ⁻, CaAsO₄ ⁻, MnAsO₄ ⁻, AlAsO ^o₄ , and FeAsO ^o₄ were introduced.

Table 1 Estimated standard partial molal thermodynamic properties of metal–arsenate and metal–arsenite complexes at 25°C, 1 bar and estimated equation-of-state parameters for calculation of the corresponding properties at high temperatures and pressures

The SUPCRT-generated logarithms of the thermodynamic constants of the reactions of destruction (consistent with the requirements of the software package EQ3/6) for all the considered aqueous complexes, at 1.013 bar and 0.01, 25, 60, 100°C and at saturation pressure and 150, 200, 250 and 300°C, are listed in Table 2.

Table 2 Logarithms of thermodynamic constants of the reactions of destruction (as required by the software package EQ3/6) of the aqueous complexes containing arsenate and arsenite ions at 1.013 bar and 0.01, 25, 60, 100°C and at saturation pressure and 150, 200, 250 and 300°C

All the data reported in Tables 1 and 2 are also given in the electronic supplementary material 1 (which is a patch for supcrt) and electronic supplementary material 2 (which is a patch for eq3/6).