A brief review of the visualization of aqueous osmosis and past methods for its calculations.
The phenomenology of the term “osmosis”, the flow of solvent across a semipermeable membrane from a region of lower to higher solute concentration as discussed by Kramer and Meyers (2012), is the same for liquids, gases and supercritical liquids. However, “aqueous osmosis” may be visualized as the flow of pure water through a semi-permeable membrane that blocks the passage of any solutes that may be dissolved within it. -The semi-permeable membrane function has been discussed by several authors including Einstein many years ago (Fermi, 1956). As noted by Lachish (2007), the flow direction and rate of the solvent in an enclosed system separating pure liquid from a liquid plus solute solution are controlled by pressure put on the liquid solution. -The pressure of a system that stops the flow of solvent where the dissolved solute is on one side of the membrane, is termed the “osmotic pressure”. The “osmotic potential” is simply the negative value of the osmotic pressure.
In 1887 van’t Hoff (1888) developed a formula for the estimation of osmotic pressure based on the gas laws and on the premise that osmosis was solely a function of the number of solute particles in solution; viz: “ P = cRT, where P is the osmotic pressure, c is the molar solute concentration, R is the gas constant and T the absolute temperature. Van’t Hoff”s formula was derived using an analogy with the pressure of an ideal gas of the same concentration and temperature, and is a direct outcome of the second law of thermodynamics. This analogy has been the basis of osmotic pressure “equations” for many years. Van’t Hoff’s empirical relationship for the estimation of osmotic pressure gave reasonable estimates of osmotic pressure, but only for very low solute levels. Incidentally, van’t Hoff received the first Nobel prize in chemistry for his osmotic work in 1902.
Other early workers on the formulation of aqueous osmosis introduced the concept of “hydration numbers” and developed varying coefficients to extend the predictability of van’t Hoff’s equation for more concentrated solutions; they assigned varying values for different solute concentrations and temperatures. Like van’t Hoff, Porter (1917), considered that osmosis was due to the “kinetic” movement of solute particles. It only became apparent many years later with the work of several authors especially Edelfsen (1941), that the energy for osmosis was inherent in the solvent molecules. Robinson and Stokes (1959) recognized this, and recorded a series of “osmotic coefficients” rather than hydration numbers for the calculation of the osmotic pressure of concentrated solutions to conform to thermodynamic principals; their coefficients vary with solute concentrations and temperatures. They record coefficients for molal NaCl solutions between 0 and 250C, which vary somewhat with those recorded by Lang 1967). -Very little information has been recorded in the literature for estimating the osmotic pressure of other solutions beyond 250C.
Many equations still currently used for calculating aqueous osmotic pressure or potential are still based on the thermodynamic theory of osmosis and invariably require tables of osmotic coefficients, (or water activities), which vary with the change in concentration of individual solutes. Such tables, for example those recorded by Robinson and Stokes (1959), and later authors including Marine and Fritz (1981), are generally recognized as being accurate only for electrolytes at low solute concentrations.