STATISTICAL-MECHANICAL THEORY OF OSMOTIC-PRESSURE OF ONE-DIMENSIONAL MULTICOMPONENT SYSTEMS .2. EXPANSION IN TERMS OF THE RELATIVE MOLARITIES OF THE SOLUTES

The osmotic pressure is discussed for the one-dimensional solution of molecules having hard cores and attractions of infinite range and of infinitesimal strength. The volumes of the solution and of the pure solvent kept in contact with the solution through a semipermeable membrane (permitting the passage of the solvent only), the total number of solvent molecules, the number of molecules of each solute and the temperature in equilibrium are assumed to be known. The expansion of the osmotic pressure, in terms of the relative molarities of the solutes, is obtained to the fourth order. The present theory is regarded as an approximate theory of osmotic pressure of a three-dimensional solution, and can also give the number of solvent molecules spontaneously flowing into the solution through the semipermeable membrane till the equilibrium is attained.