parameters are available. COSMO-RS is a theoretical method which is less dependent on model parameters as required information is obtained from quantum mechanics calculations specific to each molecule (sigma profiles) combined with a statistical thermodynamics treatment of surface segments. For uncharged species, the activity coefficient γ0 mostly follows a salting-out model: This simple model predicts activities of many species (dissolved undissociated gases such as CO2, H2S, NH3, undissociated acids and bases) to high ionic strengths (up to 5 mol/kg). The value of the constant b for CO2 is 0.11 at 10 °C and 0.20 at 330 °C. For water as solvent, the activity aw can be calculated using: where ν is the number of ions produced from the dissociation of one molecule of the dissolved salt, b is the molality of the salt dissolved in water, φ is the osmotic coefficient of water, and the constant 55.51 represents the molality of water. In the above equation, the activity of a solvent (here water) is represented as inversely proportional to the number of particles of salt versus that of the solvent. Link to ionic diameter The ionic activity coefficient is connected to the ionic diameter by the formula obtained from Debye–Hückel theory of electrolytes: where A and B are constants, zi is the valence number of the ion, and I is ionic strength. Dependence on state parameters The derivative of an activity coefficient with respect to temperature is related to excess molar enthalpy by Similarly, the derivative of an activity coefficient with respect to pressure can be related to excess molar volume. Application to chemical equilibrium At equilibrium, the sum of the chemical potentials of the reactants is equal to the sum of the chemical potentials of the products. The Gibbs free energy change for the reactions, ΔrG, is equal to the difference between these sums and therefore, at equilibrium, is equal to zero. Thus, for an equilibrium such as Substitute in the expressions for the chemical potential of each reactant: Upon rearrangement this expression becomes The sum is the standard free energy change for the reaction, . Therefore, where is the equilibrium constant. Note that activities and equilibrium constants are dimensionless numbers. This derivation serves two purposes. It shows the relationship between standard free energy change and equilibrium constant. It also shows that an equilibrium constant is defined as a quotient of activities. In practical terms this is inconvenient. When