The microscale, physicomechanical cause of osmosis and osmotic pressure in systems involving permeable and semipermeable membranes is not well understood, and no fully satisfactory mechanism has been offered to explain these phenomena. A general theory, albeit limited to dilute systems of inert, noninteracting solute particles, is presented which demonstrates that short-range forces exerted by the membrane on the dispersed solute particles constitute the origin of osmotic phenomena. At equilibrium, the greater total force exerted by the membrane on those solute particles present in the reservior containing the more concentrated of the two solutions bathing the membrane is balanced by a macroscopically observable pressure difference between the two reservoirs. The latter constitutes the so-called osmotic pressure difference. Under nonequilibrium conditions, the membrane-solute force is transmitted to the solvent, thus driving the convective flow of solvent observed macroscopically as osmosis. While elements of these ideas have been proposed previously in various forms, the general demonstration offered here of the physicomechanical source of osmotic phenomena is novel. Beyond the purely academic interest that exists in establishing a mechanical understanding of osmotic pressure, our analysis lays the foundation underlying a quantitative theory of osmosis in dilute, nonequilibrium systems outlined in a companion paper.