Accurate models of water and solute activities in aqueous atmospheric aerosols are central to predicting aerosol size, optical properties and cloud formation. A powerful method has been recently developed (Dutcher et al. JPC 2011, 2012, 2013) for representing the thermodynamic properties of multicomponent aerosols at low and intermediate levels of RH (< 90%RH) by applying the principles of multilayer sorption to ion hydration in solutions. In that work, statistical mechanics was used to model sorption of a solvent (water), onto each solute or ion in solution as n energetically distinct layers. This corresponds to n hydration layers surrounding each solute molecule. Here, we extend the model to the 100% RH limit and reduce the number of adjustable model parameters, allowing for a unified thermodynamic treatment for a wider range of atmospheric systems. The long-range interactions due to electrostatic screening of ions in solution are included as a mole fraction based Pitzer-Debye-Hückel (PDH) term. Equations for the Gibbs free energy, solvent and solute activity, and solute concentration are derived, yielding remarkable agreement between measured and fitted solute concentration and osmotic coefficients for solutions over the entire 0 to 100% RH range. By relating the values of the energy of sorption in each hydration layer to known short-range Coulombic electrostatic relationships governed by the size and dipole moment of the solute and solvent molecules, it may be possible to reduce the number of parameters for each solute. Modified equations for mixtures that take into account the long range PDH term will also be presented; these equations include no additional parameters.