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Raoult's law, published in 1887, is taught in chemistry and chemical engineering fields as a first approximation to the vapor pressure and activity of solutes and solvents in mixtures. In ideal solutions, it is exact but many solutions are known to have substantial deviations from Raoult's law as conventionally interpreted. In 1908, Callendar showed that water hydrated to the solute can explain some of the departures from Raoult's law in aqueous solution. Here, we show that by simply assuming equilibria between the free water in solution and its hydrated forms, Raoult's law and Callendar's extension are valid over the full range of concentrations, while also showing how water and solutes interact in solution. This model of solutions has importance in highly concentrated solutions common in atmosphere aerosols relevant to climate change and air quality, and in numerous industrial processes.