Calculation of activity coefficients and degrees of formation of neutral ion pairs in supercritical electrolyte solutions
Although hydrothermal solutions at high temperatures and low pressures where the solution density is low are widely regarded as highly associated alkali chloride solutions in which neutral ion pairs are the predominant solute species, reconsideration in the present study of experimental conductance data reported by QUIST and MARSHALL ( 1968a,b,c), DUNN and MARSHALL (1969) and FRANTZ and MARSHALL (1984) for 1:1 electrolytes suggests that this may not be the case. Quist, Marshall, and their coworkers interpreted their high temperature/pressure conductance data in part by considering the activity coefficients of the neutral species to be negligibly different from unity in dilute solutions. However, these data can also be interpreted by regarding the logarithm of the activity coefficients of neutral complexes ( ̄ggn ) to be a linear function of the effective ionic strength ( Ī), which is consistent with both the SETCHÉNOW (1892) and HÜCKEL (1925) equations ( HELGESON et al., 1981). Accordingly, supercritical conductance data for five electrolytes were regressed in the present study using the HÜCKEL (1925), SETCHÉNOW (1892), and SHEDLOVSKY (1938) equations, together with the law of mass action and values of the limiting equivalent conductances of the electrolytes taken from OELKERS and HELGESON (1989) for the temperatures and pressures of the experiments to generate simultaneously the logarithms of dissociation constants ( log K 1) and Setchénow coefficients ( b γ,n) for neutral 1:1 complexes. The resulting values of log K 1 are in close agreement with corresponding values originally reported by Marshall and coworkers. However, the regression calculations indicate that b γ,n and thus the activity coefficients of neutral species in concentrated electrolyte solutions increase dramatically with increasing temperature and decreasing pressure, which opposes the effect on ion pair formation of the accompanying decrease in log K 1. Distribution of species calculations using these values of log K 1 and b γ,n with and without provision for the formation of triple ions ( OELKERS and HELGESON, 1990) indicate that the degrees of formation of neutral 1:1 ion pairs maximize at stoichiometric ionic strengths of 0.2 molal and become negligible at stoichiometric ionic strengths greater than 0.8 molal in the temperature range 400 to 800°C at pressures to 4 kb. Consequently, it appears that these neutral species may account for only a minor part of the solute in concentrated hydrothermal solutions at supercritical temperatures and pressures.This observation is supported also by electrostatic considerations, which indicate that higher order complexes may predominate in concentrated electrolyte solutions at supercritical temperatures and pressures ( PITZER and SCHREIBER, 1987; OELKERS and HELGESON, 1990).