Equations implemented in PHREEQC (under construction)

Reactions' thermodynamic constant (K) dependency to pressure

General equation

From Appelo et al. (2014) and Wikipedia, we have the following formula : $$ log~K_{T,P} = log~K_{T,P=1} - \frac{\Delta\overline{V}_r \cdot (P-1)}{2.303 \cdot R \cdot T} $$ , where \(K_{T,P}\) is the \(K\) value at \(T\) (°K) and \(P\) (atm), \(K_{T,P=1}\) the \(K\) value at \(T\) and \(P=1~atm\) (when 0 < \(T\) < 100 °C) or \(P=P_{SAT}\) (saturation vapor pressure of water, when 100 < \(T\) < 374 °C), and \(R\) the ideal gas constant. \(Log~K_{T,P=1}\) is calculated by either the van't Hoff equation (-log_k and -delta_h) or the polynomial (-analytic). \(\Delta\overline{V}_r\) is the reaction's volume change, which is handled differently according to the type of reaction (see below).

Volume change of in-water and solid-water reactions

For in-water reactions (occuring in aqueous solution, between aqueous species) as well as for solid dissolution reactions that can be written as : $$ \ce{ \alpha~A + \beta~B <=> \gamma~C + \delta~D } $$ , the volume change of reaction is calculated as follows : $$ \Delta\overline{V}_r = (\gamma~\overline{V}_C + \delta~\overline{V}_D) - (\alpha~\overline{V}_A + \beta~\overline{V}_B) $$ , where \(\overline{V}_i\)'s for aqueous species \(i\) are the T, P and I-dependent 'specific volumes' given in the output file :

--------------------Distribution and properties of species---------------------
  
Species         Molality     Activity    Gamma    mole V   f_VISC¹   t_SC²
                mol/kgw        -          -       cm³/mol    %         %   
  

Calcite
CaCO3 = CO3-2 + Ca+2
  -log_k -8.45; -delta_h -3.15 kcal
  -analytic -67.87 -5.1813e-2 0 30.25746 # 0 - 300°C, Ellis, 1959, Plummer and Busenberg, 1982
  -Vm 36.9 cm3/mol # MW (100.09 g/mol) / rho (2.71 g/cm3)

Volume change of gas-water reactions

For gas-water (gas dissolution) reactions : $$ \ce{ i_{(g)} <=> i_{(aq)} } $$ , as explained in the paragraph including the Equation 16 of Appelo et al. (2014), \(\Delta\overline{V}_r\) is equal to the dissolved (aqueous) species T, P and I-dependent 'specific volume' \(\overline{V}_{i_{(aq)}}\) : $$ \Delta\overline{V}_r = \overline{V}_{i_{(aq)}} $$ As an aqueous species, \(\overline{V}_{i_{(aq)}}\) is given in the output file :

--------------------Distribution and properties of species---------------------
  
Species         Molality     Activity    Gamma    mole V   f_VISC¹   t_SC²
                mol/kgw        -          -       cm³/mol    %         %