A solution which is far from being satu rated, by reason of the solvent being present in great excess, is said to be °dilute.° The phys ical phenomena manifested by dilute solutions are much more simple than those of solutions that are nearly saturated, in precisely the same way that the phenomena exhibited by an attenu ated gas are simpler than those exhibited by the same gas in a strongly compressed state.
A solution which is not homogeneous throughout with respect to concentration, but which is dilute in some places and approxi mates to saturation in others, tends to become of uniform concentration throughout, by a process known as °diffusion.° This consists in the gradual passage of the dissolved solid away from those regions in which the concentration is greatest and toward those in which it is least. This tendency was first discovered by Parrot, in 1815. It was experimentally investi gated by Graham (1850), so far as concerns its manifestation in solutions whose internal mo tions are not restricted in any way; and Fick, in 1855, gave the fundamental mathematical theory of the process. In Fick's theory it was as sumed that the quantity of dissolved salt which diffuses across a given sectional area of the solution in a given time is proportional to the rate of variation of the concentration of the solution per unit of length of the straight line that is perpendicular to the sectional area under consideration. This is entirely analogous to the assumption made by Fourier with regard to the conduction of heat through a solid; and, there fore, Fick was able to apply the results of Fourier's powerful analysis directly to the prob lem of diffusion in liquids. The subject being essentially mathematical in nature, reference must be made, for further particulars, to the works cited at the end of this article.
It was known in the 18th century that if a glass vessel is filled with alcohol and the open ing is tightly covered with a bladder, and the whole is then immersed in water, the contents of the vessel increase so that the bladder is dis tended and sometimes bursts. This is evidently due to the fact that water enters the closed vessel by passing through the more or less porous bladder. In other words, it is a dif fusion phenomenon, which takes place between two parts of a non-homogeneous fluid system, which are separated from each other by means of a partially permeable partition. The sys tematic study of diffusion phenomena of this kind has led to many interesting and important results. Pfeffer (1877), by improving upon a suggestion due to Traube (1867), prepared dia phragms that were far superior to the bladders used by earlier experimenters; his method con sisting in forming a precipitate of ferrocyanide of copper within the pores of a cell of porous earthenware. The earthenware, as thus pre
pared, was rendered °semi-permeable," inas much as it would allow of the passage of water through itself, while it would not permit of the passage of any dissolved substance that the water might contain. The porous cell, as thus prepared, was filled with a solution of some sub stance such as sugar or nitre, and was then carefully sealed up, save for one small opening to which a delicate mercury manometer was attached. The prepared cell being then im mersed in a vessel of pure water, it was found that water will enter the cell, until the mercury manometer registers a very considerable pres sure ;— a pressure of three atmospheres being observed in the case of a per cent solution of nitre. The passage of a liquid in this man ner through a membrane or other porous septum is called osmosis (q.v.), and the maxi mum or limiting pressure that is attained when the system arrives at its ultimate condition of equilibrium is called the °osmotic pressure" of the solution. The osmotic pressure produced by any given solution is found to be propor tional to the concentration of the solution, this relation being surprisingly accurate so long as the solution does not approach too closely to saturation. The osmotic pressure is further found to vary with the temperature of the solu tion; and the remarkable fact has been brought to light, partly by experiment and partly by theory, that for any given solution of constant concentration, the osmotic pressure is approxi mately proportional to the absolute tempera ture. De Vries has also shown that for non electrolytes (such as solutions of sugar or glycerine in pure water), solutions of different substances possess the same osmotic pressures, provided their temperatures are the same, and they contain the same number of gram molecules of dissolved substance per unit mass of the solvent. (A ugram-molecule° of any substance is a quantity such that its weight, in grams, is numerically equal to the molecular weight of the substance). It is evident, there fore, that the osmotic pressure of a dilute solu tion follows laws that are closely analogous to those that hold true for attenuated gases. Much of the modern theory of solutions has been built up on this fact; and while some of the reason ing by which students of physical chemistry draw upon the known facts of gaseous ther modynamics for information concerning solu tions appears to be more or less imperfect, it must be admitted that the known analogies be tween attenuated gases and dilute, non-elec trolytic solutions are highly interesting and suggestive.