The Debye-Hückel theory (and the extended Debye-Hückel limiting law) is used to calculate the mean activity coefficients (\(\gamma_\pm\)) of ions in dilute electrolyte solutions. It accounts for electrostatic interactions between ions. The answer 'None of these' is correct because the given options — solubility, ionic strength, or Gibbs free energy directly — are not what Debye-Hückel primarily calculates; it calculates activity coefficients.