Thermodynamics of Si(OH)4 in the vapor phase of water: Henry’s and vapor–liquid distribution constants, fugacity and cross virial coefficients

Abstract

The fugacity coefficients of Si(OH)4 are evaluated from solubilities of solid phases of SiO2 in the vapor phase of water. The virial equation of state, truncated at the third virial coefficient, is employed to describe the fugacity coefficients of Si(OH)4. The temperature dependencies of the second, B12, and the third, C112, cross virial coefficients for H2O–Si(OH)4 interactions are approximated by empirical relations. It is found that silica–water interactions in the vapor phase are significantly more non-ideal compared to water–water interactions. Knowledge of B12 and C112 allows calculation of solubilities of quartz (Q) and amorphous silica (AS) in steam up to the density of 200kgm−3 in satisfactory agreement with available data, and should provide reasonable solubility values at temperatures where no experimental results exist. The calculated values of the solubility of Q and AS in saturated vapor up to the critical temperature of water, Tc, are tabulated.The partial molar properties of dilute solutes close to the critical point of water are governed by the Krichevskii parameter, the value of which for Si(OH)4 is evaluated from available data (mainly vapor–liquid distribution constants for silica) to be equal to −187±10MPa. The knowledge of the thermodynamic properties of Si(OH)4 in the ideal gas state and in the state of the standard solution in liquid water allows calculating Henry’s constant, kH, for Si(OH)4 up to 623.15K at water saturation pressure P1∗. The theoretically-based equation, containing the Krichevskii parameter, allows extrapolating kH values all the way toward the critical temperature of water. This, in turn, makes possible calculation of the solubility of quartz and amorphous silica in liquid water at P1∗ at all temperatures up to Tc. The presented results should be useful for modeling solid–liquid–vapor, solid–vapor and liquid–vapor equilibria in the H2O–SiO2 system at steam densities up to 200kgm−3.