It is shown how the leading terms of a semi grand canonical partition function (GCPF) can be used to develop analytic expressions relating activity to concentrations in two-component systems. The simple analytic expressions for activity coefficients can be fitted to activity coefficient versus concentration data for a wide range of aqueous solute systems. Only one or two parameters are required to accurately describe the activity coefficients of nonelectrolyte and electrolyte aqueous solute systems over their entire range of solubility. These forms derive from low-order number expressions of the GCPF that take into account the effective solvent interactions with the solute and between solute molecules for a variable amount of solvent. The GCPF leading terms and fitting parameters define apparent solute-solute oligomerization and solute packing phenomena that increase with solute concentration. Advantages using this grand canonical approach versus previous approaches are discussed.