The paper by Harold C. Helgeson discusses the thermodynamic properties of hydrothermal systems at elevated temperatures and pressures, focusing on the chemical relations involving minerals, aqueous species, gases, and concentrated sodium chloride solutions. The author presents methods for calculating equilibrium constants for a wide range of hydrothermal reactions using available thermodynamic data. When data are incomplete, he employs entropy estimates, average heat capacities, and assumptions about temperature dependence and electrostatic interactions. High-temperature stoichiometric activity coefficients for ions are calculated using deviation functions derived from osmotic coefficients of concentrated sodium chloride solutions. The results are presented in tables and diagrams, allowing for the calculation of solubilities of various minerals and the evaluation of mass transfer in hydrothermal systems. The paper also covers predictive methods for equilibrium constants, including the use of average heat capacities and a combination of average and actual heat capacities. Additionally, it discusses the estimation of entropy and heat capacity for reactions where data are limited, and the calculation of standard enthalpies of formation for minerals. The thermodynamic properties of sodium chloride solutions are analyzed, and the effects of complexing are considered. The paper provides a comprehensive overview of the thermodynamic framework for understanding hydrothermal processes at high temperatures and pressures.The paper by Harold C. Helgeson discusses the thermodynamic properties of hydrothermal systems at elevated temperatures and pressures, focusing on the chemical relations involving minerals, aqueous species, gases, and concentrated sodium chloride solutions. The author presents methods for calculating equilibrium constants for a wide range of hydrothermal reactions using available thermodynamic data. When data are incomplete, he employs entropy estimates, average heat capacities, and assumptions about temperature dependence and electrostatic interactions. High-temperature stoichiometric activity coefficients for ions are calculated using deviation functions derived from osmotic coefficients of concentrated sodium chloride solutions. The results are presented in tables and diagrams, allowing for the calculation of solubilities of various minerals and the evaluation of mass transfer in hydrothermal systems. The paper also covers predictive methods for equilibrium constants, including the use of average heat capacities and a combination of average and actual heat capacities. Additionally, it discusses the estimation of entropy and heat capacity for reactions where data are limited, and the calculation of standard enthalpies of formation for minerals. The thermodynamic properties of sodium chloride solutions are analyzed, and the effects of complexing are considered. The paper provides a comprehensive overview of the thermodynamic framework for understanding hydrothermal processes at high temperatures and pressures.