OSMOTIC PRESSURE FROM THE STANDPOINT OF THE KINETIC THEORY. Dr. T. Martin Lowry contributed a Paper entitled "Osmotic Pressure from the Standpoint of the Kinetic Theory." KINETIC THEORY OF GASES. The incessant motion of the particles, which forms the fundamental hypothesis of the kinetic theory, leads in the case of simple gases to two chief results : (I) the gas is able to expand to any extent, and (2) it exerts ,a pressure whenever this expansion is resisted by enclosing the gas. DIFFUSION IN GASES. When several gases are enclosed together the motion of the particles leads to a process of diffusion or mixing by which each gas gradually penetrates until its particles are distributed throughout the whole of the available space in much the same way as if no other gas were present.The ultimate distribution is, as a rule, uniform, but in the atmosphere where there is a very large pressure gradient the process of diffusion results in an accumulation of the less compressible gases in the higher levels, whilst the more compressible gases predominate in the lower levels (Dewar, Presi- dential Address, British Association, Belfast meeting, 1903, pp. 39-46). A similar inequality of concentration may be set up when gases of unequal compressibility are submitted to the action of centrifugal forces (V. Calzavara, " The Separatore Mazza," Padua, 1903). OSMOTIC PRESSURE IN GASES. When the process of diffusion in a composite gas is hindered the motion of the particles may manifest itself in the form of a pressure precisely analogous to that which is produced by simple gases when prevented from expanding.The simplest example of such a pressure is found in the common experiment in which a porous pot containing air is surrounded by an atmosphere of hydrogen; the hydrogen diffuses into the pot more rapidly than the air is able to escape, and a transient pressure is produced in the pot. In order to produce a permanent measured pressure it is necessary not merely to delay the mixing, but to prevent it altogether. This is usually done by means of a semi-permeable membrane, through which only one of the constituents can pass. In the case under considera- tion this might be made from platinum or palladium foil as suggested by Arrhenius (Zeit. phys. Chem., 1889, 3, 119). Ramsay has shown (Phil. Mag., 1894, 38, 206) that, when a palladium membrane heated to 6oo"is used to separate equal volumes of hydrogen and nitrogen, the nitrogen is retained on one side of the membrane, whilst the hydrogen passes through until it is equally distributed on either side, In the final condition of equilibrium there is an excess of pressure on the side of the nitrogen exactly equal to that which it exerted before the advent of the diluent hydrogen.It should I4OSMOTIC PRESSURE be noted that in this case the excess of pressure, which forms an exact analogue of osmotic pressure in liquids, is actually produced by the bom- bardment of the walls of the vessel by the nitrogen molecules and is independent of the concentration of the hydrogen, and indeed-if a suitable membrane be provided-of the nature of the diluent gas.KINETIC THEORY OF LIQUIDS. In liquids the free motion of the particles is held in check by their mutual attraction. In the interior of the liquid this attraction acts equally in all directions, and the particles are able to move with no other restriction than that imposed by their closer packing and greatly reduced range of free motion, At the surface, however, the attraction acts entirely in one direction, and produces a force which manifests itself in the surface tension and latent heat of evaporation of the liquid; this force prevents the escape of all particles except those which reach the surface with a velocity sufficiently great to break away from the attraction of their fellows. LIQUID DIFFUSION. When two liquids are mixed they may either (I) amalgarnatc completely, as in the case of gases, or (2) form two distinct layers or phases.The latter possibility is in itself sufficient to indicate that the conditions prevailing in a liquid are very different from those which exist in gases, and suggests that considerable caution is necessary in applying to liquids laws that have been deduced from experiments made with gases. In liquids of the former class the motion of the particles again leads to a process of diffusion, though this proceeds much more slowly than in gases, owing to the great reduction in the length of the mean free path of the particles. Ultimately, however, a condition of equilibrium is reached in which, almost invariably, the constituents are uniformly distributed through- out the mass? In the second case the mutual attractions of like particles are so much greater than those of the unlike particles that only a few particles of each kind are able to break away from their fellows and mingle with the particles of the other phase or layer.The conditions of equilibrium are then very similar to those which prevail between liquid and vapour, the chief difference being that there is an interchange of two kinds of particle instead of one. In this case also the motion of the particles leads to a uniform distribution of the constituents in each phase, though the relative concentrations in the two phases may differ widely. In solids the motion of the particles is mainly oscillatory, and although a tendency to diffuse may exist, the actual process of diffusion is in the majority of cases too slow to be detected.OSMOTIC PRESSURE IN LIQUIDS. The application of the equation PV = RT to the osmotic pressure of gases could be predicted on general theoretical grounds, but the conditions pre- vailing in liquids are so much more complex, that there is no h priori reason for supposing that the osmotic pressure developed by a solution would be governed by the same law, or would bear any relationship to the gas pressure produced by a gas of equal molecular concentration. The idea that the osmotic pressure of a dilute solution can be calculated from the same * If the solvent and solution are unequally compressible, varialions of pressure would produce a corresponding gradient of concentration. This, however is usually negligible.16 OSMOTIC PRESSURE FROM THE STANDPOINT formula that is used to predict the pressure exerted by a gas has been arrived at, not by intuition, but by experiment.Owing to the difficulty of discovering efficient semi-permeable membranes, accurate measurements of osmotic pressure have been confined almost exclusively to aqueous solutions of the sugars separated from the pure solvent by a membrane of copper ferro- cyanide, The experiments usually quoted are those of Pfeffer (Osmotische Untersuchurzgen, Leipzig, 1877), but the recent accurate measurements of Morse and Fraser have entirely confirmed the conclusions already arrived at from the earlier experiments, since they have shown that within the limits of M/IO to M the actual osmotic pressure produced by a cane-sugar solution agrees with that calculated from the gas-formula with an average deviation of less than 4 per cent.Indirect methods of measuring osmotic pressure by lowering of vapour pressure, elevation of boiling-point, and depression of freezing-point, have extended the observations to a very wide range of substances, and in some cases a very high degree of accuracy has been attained. In particular, Griffiths has shown that the osmotic pressure of a cane-sugar solution deduced from measurements of the freezing-point agrees with that calculated from the gas-formula with an error not exceeding 0.01 per cent. It is, however, important to notice that the formula A = -- , by which the molecular eleva- tion of the boiling-point or depression of the freezing-point can be derived from the absolute temperature T of boiling or freezing, and the latent heat q involved in the change of state is based upon the assumptions ( I ) that the change of temperature is determined by the work done against the osmotic pressure when the solution is concentrated by evaporating ,or freezing out the solvent, and (2) that this osmotic pressure can be calculated from the gas- formula ; it follows, therefore, that the validity of the gas-laws as applied to solutions is proved, not merely by a few direct measurements of the osmotic pressure of sugar solutions, iior even by isolated experiments such as those of Griffiths, but also by the countless experiments in which the Beckmann apparatus has been successfully employed in determining the molecular weights of dissolved substances.The proof of the numerical identity of osmotic pressure with gas pressure has been discussed somewhat fully because it appears to be of fundamental importance, and has been SD fully verified by experiment that it must be accepted as a fact in any consideration of the origin and mechanism of osmotic pressure. RTa Q THE MECHANISM OF OSMOTIC PRESSURE. There can at the present time be no doubt that osmotic pressure de- pends essentially on the phenomena of selective solubility. The palladium membrane acts in virtue of its ability to absorb or dissolve hydrogen, but not nitrogen ; the amount of hydrogen absorbed depends on the pressure, and equilibrium is attained when the partial pressure of the hydrogen inside the vessel is equal to its total pressure outside.A water-membrane has been used by Nernst to develop an osmotic pressure between ether and an ethereal solution of benzene, the former being soluble and the latter insoluble in water. Copper ferrocyanide, which absorbs or dissolves water and certain salts blit not sugars, forms an efficient semi-permeable membrane for aqueous sugar solutions, but not for salt solutions. The presence of the sugar diminishes the solubility of the water in the membrane, and a flow of liquid is set up because the membrane when saturated with regard to the water on one side is supersaturated with regard to the solution on the other side.OF THE KINETIC THEORY The amount of water taken up by the membrane can, however, be increased by compressing the liquid, and it is thus possible to counterbalance the decrease of solubility due to the sugar, and by equalising the solubility on the two sides of the membrane to stop the flow of solvent into the solution.The pressure required to equalise the solubilities and stop the flow is the so-called (‘ osmotic pressure,” and it may again be urged that the conditions are so far different from those prevailing in a gas, that the gas-analogy, though s u s e s - tive, would be insufficient to justify the application of the gas laws to osmotic pressure unless these could be verified experimentally or could be established on an independent theoretical basis. Pickering’s theory (Ber., 1891, 24, 3639), that the action of the semi- permeable membrane depends on the relative size of the molecules of solvent and solute, has not been confirmed ; the very similar mechanical theory of Sutherland (Phil.Mag., 1897 (v) 4, 493-498), that the membrane consists of “ meshes ” through which water but not sugar can pass, appears to be equally untenable, and need not be discussed here; Traube’s theory is referred to later. VAN’T HOFF’S GAS THEORY OF OSMOTIC PRESSURE. When the discovery was made that osmotic pressure obeyed the same laws as gas pressure it was generally assumed that the two phenomena must be essentially similar in character. Thus van’t Hoff, in his classical paper, (‘ Die Rolle des osmotischen Druckes in der Analogie zwischen Losungen und Gasen” (2eit.phys. Chem, 1887, I. 481-508), whilst recognising in general terms the attrac- tive influence of the solution for the solvent (die wasseranziekende Wirkurzg der Liisultg), attributed the osmotic pressure to the gas-like bombardment of the membrane by the molecules of the solute, the solvent being regarded as practically inert.* Three years later, at the Leeds meeting of the British Association (Report, 1890, p.356) he suggested that “the action on a semi-permeable diaphragm is due partly to the shock of the dissolved molecules, partly to the difference of forces acting upon them from the solvent on one side and from the solution on the other,” but added that ‘‘ in very dilute solutions the shock is alone the origin of pressure, as it is in gases.” In support of this view he also quoted (Zeif. jhys. Chem., 1890,5, 174-176) the case of gaseous osmotic pressure suggested by Arrhenius and subsequently verified by Ramsay as described above.van’t Hoff’s theory had at least the merit of giving a simple and quantita- tive explanation of the osmotic phenomena, and was not unreasonable when applied to the osmotic pressure of gases dissolved in liquids. The concep- tion was, however, not easy to apply to the more ordinary cases of osmotic pressure, such as those afforded by aqueous sugar solutions. In the majority of cases the solute molecules appear to have a very stiiall mobility, and in the absence of the solvent they are unable to produce any hydrostatic pressure whatever upon the walls of the containing vessel. I t is, therefore, scarcely reasonable to attribute the whole action of the solution to the relatively inert solute, whilst neglecting entirely the very active part played by the solvent (Fitzgerald, B.A. Report, 18g0, p. 327). POYNTI NG’S ‘r H EORY. Much interest was aroused by the publication in 1896 of a paper by Professor Poynting (Phil. Mag. (v) 42, 289-~oo), in which an alternative * Es handelt sich im ersten Falle um die Stosse der Gas-molekiile an die Gefasswand, im letzteren um diejenigen der Molekiile vom gelosten Korper an die halbdurchl5ssige Membran, da ja die des beiderseitig anwesenden Losungsmittels als hindurchgehend, nicht in Betracht kommen (ibid., p. 482).18 OSMOTIC PRESSURE FROM THE STANDPOINT explanation was given of the osmotic pressure of liquids. In many respects the view he advocated is very similar to that described below, but the two theories differ in one essential point, and consequently lead to widely different explanations of the origin of osmotic pressure.In particular, Poynting was led to assume that osmotic pressure was due to the formation of labile hydrates, and it became necessary, as Whetham pointed out (Nature, Oct. 15, I&$), to assume that all substances which gave a normal osmotic pressure were monohydrated, whilst the double osmotic pressure of binary salts might be ascribed to the formation of a dihydrate or of two monohydrated ions." The invariable formation of loose monohydrates was so improbable, and is so far in contradiction to recent work on the hydrates present in solution, that Poynting's theory has failed to secure general acceptance as an explanation of the osmotic phenomena. OSMOTIC PRESSURE AS A KINETIC PHENOMENON.The theory of osmotic pressure now described formed the subject of a paper read before the Chemical Society of the Central Technical College as long ago as May, 1896, but it was only recently that it was recognised as being sufficiently novel to warrant further publicity. The starting-point of the theory is a consideration of the conditions prevailing at the surface of separation of the solution and the semi-permeable membrane, which may be either a layer of copper ferrocyanide or merely the boundary between liquid and vapour or liquid and ice. The simplest of these cases is undoubtedly that which involves the equilibrium between liquid and vapour. In this case the kinetic theory postulates a continual process of evaporation, whereby rapidly moving particles are constantly escaping from the surface of the liquid into the vapour space.This is balanced by the con- densation of practicatly all the molecules of the vapour that impinge on the liquid surface. When the vapour reaches a certain concentration the rate of condensation becomes equal to the rate of evaporation, and a condition of equilibrium is attained, not because evaporation has ceased, but because it is neutralised by an equal and opposite process of condensation. In the case of a non-volatile liquid the mobility of the relatively heavy molecules or mole- cular complexes is so small that very few are able to escape, and the maximum vapour pressure of such liquids is inappreciable.If now a solution be prepared by mixing a volatile and a non-volatile liquid, or by dissolving a non-volatile solid in a volatile liquid, the surface will contain both kinds of molecules. If one of the solvent molecules be struck by a rapidly moving molecule from the interior of the liquid, it will be projected into the vapour space. If, however, one of the non-volatile molecules be struck, it will be unable to escape, and the solvent particle will rebound in much the same way as if it had struck the wall of the containing vessel. The rate of evaporation is therefore reduced by the addition to the solvent of a non-volatile solute. On the other hand, it is probable that the presertce of the raora-volatile molecules would not interfere with the rate of coltdensation of the vapour.This point is of fundamental importance, as the opposite view was advocated by Poynting, who supposed that con- densation and evaporation would be checked to an equal extent, just as if the surface had been covered by a plate of perforated zinc. It must be remem- bered, however, that a considerable upward velocity is required before a molecule can escape from the surface of a liquid, and that a molecule descending with ever. the smallest downward velocity would have little * -4 similar deduction was drawn by I. Traube ( A m . Pltys. Cltena., 1897, ii. 62, 490-506).OF THE KINETIC THEORY 19 chance of escaping when once it came within the range of attraction of the liquid. Even if, on reaching the liquid surface, a vapour molecule should strike against a non-volatile molecule of the solute the attraction of the neighbouring molecules of the solvent would be sufficient to hold it, and thus ensure its condensation.I t need scarcely be pointed out that similar conditions would prevail at the surface separating liquid and ice or at the surface of one of the more conventional semi-permeable membranes. In the former case the presence of a non-isomorphous solute might prevent the adhesion to the ice of a molecule of solvent moving towards it but separated from it by a molecule of solute. On the other hand, it would not prevent the melting off or dissolution of an ice molecule if the average kinetic energy (k, temperature) of the ice were raised by the latent heat of crystallisation of other molecules passing from thc liquid to the solid state.In the case of a membrane such as copper ferrocyanide the solute would check the escape of solvent mole- cules from the solution into the membrane, but would not oppose the return of wanderers migrating from the membrane back into the solution. This would lead to a disturbance of the equilibrium between the solvent and the liquids on either side, and would be sufficient to produce an osmotic flow and a consequent osmotic pressure. DEDUCTION OF THE GAS-FORRIULX FROM THE KINETIC THEORY OF OSMOTIC PRESSURE. Of the theories of osmotic pressure that have hitherto been put forward, that of van’t Hoff is the one that leads most directly to a simple quantitative explanation of the phenomena. Poynting, in developing his theory quantita- tively, considered that solute molecules and stable compounds of solvent and solute would merely alter the effective surface of the liquid without changing the relative rates of evaporation and condensation ; only in the case of labile compounds was it considered possible that the rate of evaporation might be checked without altering the rate of condensation ; on this basis a quantitative explanation was only possible on the impracticable assumption that all ordinary solutes are loosely monohydrated in aqueous solutions.The more recent theory that osmotic pressure depends on a disturbance in the equilibrium between simple and polymerised solvent molecules, e.g., H,O,H,,O, (Armstrong, Proc. Roy. Soc., 1906, A. 78, &4-271), has also, as yet, failed to yield a quantitative interpretation of the pressures produced.The quantitative interpretation of the kinetic theory of osmotic pressure follows at once from Nernst’s proof of the relationship between osmotic pressure and vapour pressure (TIzeoreiicaZ Clzemisfry, pp. ~ q - ~ z g ) . Thus if N be the number of gram-molecules of solvent, and n the number of gram- molecules of solute in unit volume of the solution the validity of the gas- formula for osmotic pressure is readily deducible from the equation- N A’ N + n-p’ where p is the vapour pressure of the solvent, and p’ that of the solution.* If the simple assuniption is made that the molecules of solvent are uniformly distributed in the surface layer, and that the spacing or packing is the same as in the pure solvent, it follows a t once that the rates of evaporation from unit surface of solvent and solution will be in the ratio N + n to N, and that this will also be the ratio of the vapour pressures, as required by the above * The value of N is determined by the molecular weight of the solvent as it exists in the vapour, and not by its molecular weight in the liquid state.20 OSMOTIC PRESSURE FROM THE STANDPOINT formula.The argument is, of course, identical with that used by Poynting to show that each molecule of solute must destroy the mobility of a molecule of solvent, but, whereas he was led to assume the regular formation of labile monohydrates, the theory given above merely postulates that the mobility of a solvent molecule is destroyed when its place in the surface of the liquid is occupied by a molecule of solute.SURFACE STRUCTURE OF LIQUIDS. It will at once be noticed that in its simplest form the kinetic theory of osmotic pressure would indicate .that the pressures calculated from the gas- formula might be subject to a small correction for the volume changes accompanying dissolution. Whether such corrections are necessary can only be determined by experiment, but the evidence now available points to a very close agreement between the values observed and calculated for dilute solutions. If this identity should be confirmed, it will be possible to deduce from observations of osmotic pressure some information in reference to the surface structure of liquids, since if the agreement is exact there must be an equally exact replacement of solvent by solute in the surface of the liquid.Thus in view of the different iiiasses of the molecules that may be dis- solved in the same solute and yield identical osmotic pressures, there must be a considerable spacing between the actual molecules in the surface. Again, it may be noted that this exact replacement does not take place in the interior of the liquid, where the molecular volumes of different solvents differ widely, and when calculated in the conventional way may even have a negative value. It is, however, by no means improbable that the marshalling of the molecules 011 the frontiers of the liquid may be governed by a stricter discipline than that which prevails in the interior, and that the surface molecules may even be forced to conform to the exact regulations which govern the replacement of molecules in solid solutions or isomorphous mixtures. FORhfATION OF COMPLEXES.The formation in the solution of loose complexes of solvent with solute or of solvent molecules with one another has not yet been referred to, but presents no difficulty in the development of the theory. Such complexes are usually formed without any large change of volume, and under the stricter condi- tions prevailing at the surface no alteration in the area of surface occupied need result from the linking up of the ‘‘ residual affinities ” of the molecules. Neither need it be supposed that the rate of evaporation would be affected otherwise than by a general reduction of mobility::: due to the chemical attraction of the molecules and producing equal effects in solvent and in dilute solution.Thus, as there is 110 change of energy involved in the replace- ment of one solvent molecule in a complex by another from outside, a rapidly moving particle impinging on a complex might drive a combined solvent moleculc into the vapour space and itself occupy the vacant position in the complex, the effects produced being much the same as if no complex existed. A similar statement would apply to molecules of solvent attached to the solute in the form of labile hydrates or compounds; a free solvent molecule impinging on a combined molecule in the surface of the liquid might drive it out and take its place, but if it should impinge on the nuclear solute molecule it would be repulsed and driven back into the interior, just as it would be by an uncombined molecule of solute.cohesion in a gas as represented by the quantity * Compare the reduction of mobility caused by liquid in van der Waals’ equation, 2jaOF T H E KINETIC THEORY 21 CONCENTRATED SOLUTIONS. No attempt has been made i n the above to account quantitatively for the osmotic pressure of concentrated solutions. Even in the case of gases, the equation PV = RT only applies strictly to a material gas within narrow limits of pressure, but Morse and Fraser’s experiments indicate a much wider applicability when the formula is applied to osmotic pressures, provided only that for concentrated solutions V is interpreted as the volume of solvent used to dissolve the solute and not the total volume of the solution.It need scarcely be pointed out that this modification is very similar in type to the co-volume correction in van der WBals’ equation. OSMOTIC PRESSURE AND SURFACE TENSION. In view of the close relationship that has been indicated between osmotic pressure and surface structure it would not be surprising that a relation- ship should exist between surface tension and osmotic pressure. Such a relationship has been postulated theoretically by Traube, who supposes that osmotic pressure depends on a tendency to equalise the surface tension of the two liquids, and has been confirmed experimentally by Batelli and Stephanini (Atli. R. Acad. Lincei, 1905, (v), 14, ii. pp. 3-14), who find that solutions of equal surface tension have equal osmotic pressures, even in cases in which the solutions are not nominally equimolecular. In conclusion it may be pointed out that whilst the vicws advocated above were comparatively novel ten years ago, the idea that osmotic pressure depends on the activity of the solvent rather than on that of the solute has now become widely accepted, and has been advocated, not only by Poynting, but also by Armstrong ( E m .Brit., 26. 739), Beilby, (B. A. Report, South Africa, 1905, 361), and others. At the present time, therefore, the only points for which any degree of novelty can be claimed are in reference to the mechanism by which the activity of the solvent at the surface of the liquid is reduced by the ‘‘ blocking action ” of the solute operating in one direction only, and to the possibility of deducing from the osmotic phenomena information as to the surface structure of liquids.130, HORSEFERRY ROAD, WESTMINSTER, S.W. OSMOTIC PRESSURE FROM THE STANDPOINT OF THE KINETIC THEORY. Dr. T. Martin Lowry contributed a Paper entitled "Osmotic Pressure from the Standpoint of the Kinetic Theory." KINETIC THEORY OF GASES. The incessant motion of the particles, which forms the fundamental hypothesis of the kinetic theory, leads in the case of simple gases to two chief results : (I) the gas is able to expand to any extent, and (2) it exerts ,a pressure whenever this expansion is resisted by enclosing the gas. DIFFUSION IN GASES. When several gases are enclosed together the motion of the particles leads to a process of diffusion or mixing by which each gas gradually penetrates until its particles are distributed throughout the whole of the available space in much the same way as if no other gas were present.The ultimate distribution is, as a rule, uniform, but in the atmosphere where there is a very large pressure gradient the process of diffusion results in an accumulation of the less compressible gases in the higher levels, whilst the more compressible gases predominate in the lower levels (Dewar, Presi- dential Address, British Association, Belfast meeting, 1903, pp. 39-46). A similar inequality of concentration may be set up when gases of unequal compressibility are submitted to the action of centrifugal forces (V. Calzavara, " The Separatore Mazza," Padua, 1903). OSMOTIC PRESSURE IN GASES. When the process of diffusion in a composite gas is hindered the motion of the particles may manifest itself in the form of a pressure precisely analogous to that which is produced by simple gases when prevented from expanding.The simplest example of such a pressure is found in the common experiment in which a porous pot containing air is surrounded by an atmosphere of hydrogen; the hydrogen diffuses into the pot more rapidly than the air is able to escape, and a transient pressure is produced in the pot. In order to produce a permanent measured pressure it is necessary not merely to delay the mixing, but to prevent it altogether. This is usually done by means of a semi-permeable membrane, through which only one of the constituents can pass. In the case under considera- tion this might be made from platinum or palladium foil as suggested by Arrhenius (Zeit.phys. Chem., 1889, 3, 119). Ramsay has shown (Phil. Mag., 1894, 38, 206) that, when a palladium membrane heated to 6oo"is used to separate equal volumes of hydrogen and nitrogen, the nitrogen is retained on one side of the membrane, whilst the hydrogen passes through until it is equally distributed on either side, In the final condition of equilibrium there is an excess of pressure on the side of the nitrogen exactly equal to that which it exerted before the advent of the diluent hydrogen. It should I4OSMOTIC PRESSURE be noted that in this case the excess of pressure, which forms an exact analogue of osmotic pressure in liquids, is actually produced by the bom- bardment of the walls of the vessel by the nitrogen molecules and is independent of the concentration of the hydrogen, and indeed-if a suitable membrane be provided-of the nature of the diluent gas.KINETIC THEORY OF LIQUIDS. In liquids the free motion of the particles is held in check by their mutual attraction. In the interior of the liquid this attraction acts equally in all directions, and the particles are able to move with no other restriction than that imposed by their closer packing and greatly reduced range of free motion, At the surface, however, the attraction acts entirely in one direction, and produces a force which manifests itself in the surface tension and latent heat of evaporation of the liquid; this force prevents the escape of all particles except those which reach the surface with a velocity sufficiently great to break away from the attraction of their fellows.LIQUID DIFFUSION. When two liquids are mixed they may either (I) amalgarnatc completely, as in the case of gases, or (2) form two distinct layers or phases. The latter possibility is in itself sufficient to indicate that the conditions prevailing in a liquid are very different from those which exist in gases, and suggests that considerable caution is necessary in applying to liquids laws that have been deduced from experiments made with gases. In liquids of the former class the motion of the particles again leads to a process of diffusion, though this proceeds much more slowly than in gases, owing to the great reduction in the length of the mean free path of the particles.Ultimately, however, a condition of equilibrium is reached in which, almost invariably, the constituents are uniformly distributed through- out the mass? In the second case the mutual attractions of like particles are so much greater than those of the unlike particles that only a few particles of each kind are able to break away from their fellows and mingle with the particles of the other phase or layer. The conditions of equilibrium are then very similar to those which prevail between liquid and vapour, the chief difference being that there is an interchange of two kinds of particle instead of one. In this case also the motion of the particles leads to a uniform distribution of the constituents in each phase, though the relative concentrations in the two phases may differ widely. In solids the motion of the particles is mainly oscillatory, and although a tendency to diffuse may exist, the actual process of diffusion is in the majority of cases too slow to be detected.OSMOTIC PRESSURE IN LIQUIDS. The application of the equation PV = RT to the osmotic pressure of gases could be predicted on general theoretical grounds, but the conditions pre- vailing in liquids are so much more complex, that there is no h priori reason for supposing that the osmotic pressure developed by a solution would be governed by the same law, or would bear any relationship to the gas pressure produced by a gas of equal molecular concentration. The idea that the osmotic pressure of a dilute solution can be calculated from the same * If the solvent and solution are unequally compressible, varialions of pressure would produce a corresponding gradient of concentration.This, however is usually negligible.16 OSMOTIC PRESSURE FROM THE STANDPOINT formula that is used to predict the pressure exerted by a gas has been arrived at, not by intuition, but by experiment. Owing to the difficulty of discovering efficient semi-permeable membranes, accurate measurements of osmotic pressure have been confined almost exclusively to aqueous solutions of the sugars separated from the pure solvent by a membrane of copper ferro- cyanide, The experiments usually quoted are those of Pfeffer (Osmotische Untersuchurzgen, Leipzig, 1877), but the recent accurate measurements of Morse and Fraser have entirely confirmed the conclusions already arrived at from the earlier experiments, since they have shown that within the limits of M/IO to M the actual osmotic pressure produced by a cane-sugar solution agrees with that calculated from the gas-formula with an average deviation of less than 4 per cent.Indirect methods of measuring osmotic pressure by lowering of vapour pressure, elevation of boiling-point, and depression of freezing-point, have extended the observations to a very wide range of substances, and in some cases a very high degree of accuracy has been attained. In particular, Griffiths has shown that the osmotic pressure of a cane-sugar solution deduced from measurements of the freezing-point agrees with that calculated from the gas-formula with an error not exceeding 0.01 per cent.It is, however, important to notice that the formula A = -- , by which the molecular eleva- tion of the boiling-point or depression of the freezing-point can be derived from the absolute temperature T of boiling or freezing, and the latent heat q involved in the change of state is based upon the assumptions ( I ) that the change of temperature is determined by the work done against the osmotic pressure when the solution is concentrated by evaporating ,or freezing out the solvent, and (2) that this osmotic pressure can be calculated from the gas- formula ; it follows, therefore, that the validity of the gas-laws as applied to solutions is proved, not merely by a few direct measurements of the osmotic pressure of sugar solutions, iior even by isolated experiments such as those of Griffiths, but also by the countless experiments in which the Beckmann apparatus has been successfully employed in determining the molecular weights of dissolved substances.The proof of the numerical identity of osmotic pressure with gas pressure has been discussed somewhat fully because it appears to be of fundamental importance, and has been SD fully verified by experiment that it must be accepted as a fact in any consideration of the origin and mechanism of osmotic pressure. RTa Q THE MECHANISM OF OSMOTIC PRESSURE. There can at the present time be no doubt that osmotic pressure de- pends essentially on the phenomena of selective solubility. The palladium membrane acts in virtue of its ability to absorb or dissolve hydrogen, but not nitrogen ; the amount of hydrogen absorbed depends on the pressure, and equilibrium is attained when the partial pressure of the hydrogen inside the vessel is equal to its total pressure outside.A water-membrane has been used by Nernst to develop an osmotic pressure between ether and an ethereal solution of benzene, the former being soluble and the latter insoluble in water. Copper ferrocyanide, which absorbs or dissolves water and certain salts blit not sugars, forms an efficient semi-permeable membrane for aqueous sugar solutions, but not for salt solutions. The presence of the sugar diminishes the solubility of the water in the membrane, and a flow of liquid is set up because the membrane when saturated with regard to the water on one side is supersaturated with regard to the solution on the other side.OF THE KINETIC THEORY The amount of water taken up by the membrane can, however, be increased by compressing the liquid, and it is thus possible to counterbalance the decrease of solubility due to the sugar, and by equalising the solubility on the two sides of the membrane to stop the flow of solvent into the solution.The pressure required to equalise the solubilities and stop the flow is the so-called (‘ osmotic pressure,” and it may again be urged that the conditions are so far different from those prevailing in a gas, that the gas-analogy, though s u s e s - tive, would be insufficient to justify the application of the gas laws to osmotic pressure unless these could be verified experimentally or could be established on an independent theoretical basis.Pickering’s theory (Ber., 1891, 24, 3639), that the action of the semi- permeable membrane depends on the relative size of the molecules of solvent and solute, has not been confirmed ; the very similar mechanical theory of Sutherland (Phil. Mag., 1897 (v) 4, 493-498), that the membrane consists of “ meshes ” through which water but not sugar can pass, appears to be equally untenable, and need not be discussed here; Traube’s theory is referred to later. VAN’T HOFF’S GAS THEORY OF OSMOTIC PRESSURE. When the discovery was made that osmotic pressure obeyed the same laws as gas pressure it was generally assumed that the two phenomena must be essentially similar in character. Thus van’t Hoff, in his classical paper, (‘ Die Rolle des osmotischen Druckes in der Analogie zwischen Losungen und Gasen” (2eit.phys. Chem, 1887, I.481-508), whilst recognising in general terms the attrac- tive influence of the solution for the solvent (die wasseranziekende Wirkurzg der Liisultg), attributed the osmotic pressure to the gas-like bombardment of the membrane by the molecules of the solute, the solvent being regarded as practically inert.* Three years later, at the Leeds meeting of the British Association (Report, 1890, p. 356) he suggested that “the action on a semi-permeable diaphragm is due partly to the shock of the dissolved molecules, partly to the difference of forces acting upon them from the solvent on one side and from the solution on the other,” but added that ‘‘ in very dilute solutions the shock is alone the origin of pressure, as it is in gases.” In support of this view he also quoted (Zeif.jhys. Chem., 1890,5, 174-176) the case of gaseous osmotic pressure suggested by Arrhenius and subsequently verified by Ramsay as described above. van’t Hoff’s theory had at least the merit of giving a simple and quantita- tive explanation of the osmotic phenomena, and was not unreasonable when applied to the osmotic pressure of gases dissolved in liquids. The concep- tion was, however, not easy to apply to the more ordinary cases of osmotic pressure, such as those afforded by aqueous sugar solutions. In the majority of cases the solute molecules appear to have a very stiiall mobility, and in the absence of the solvent they are unable to produce any hydrostatic pressure whatever upon the walls of the containing vessel.I t is, therefore, scarcely reasonable to attribute the whole action of the solution to the relatively inert solute, whilst neglecting entirely the very active part played by the solvent (Fitzgerald, B. A. Report, 18g0, p. 327). POYNTI NG’S ‘r H EORY. Much interest was aroused by the publication in 1896 of a paper by Professor Poynting (Phil. Mag. (v) 42, 289-~oo), in which an alternative * Es handelt sich im ersten Falle um die Stosse der Gas-molekiile an die Gefasswand, im letzteren um diejenigen der Molekiile vom gelosten Korper an die halbdurchl5ssige Membran, da ja die des beiderseitig anwesenden Losungsmittels als hindurchgehend, nicht in Betracht kommen (ibid., p. 482).18 OSMOTIC PRESSURE FROM THE STANDPOINT explanation was given of the osmotic pressure of liquids.In many respects the view he advocated is very similar to that described below, but the two theories differ in one essential point, and consequently lead to widely different explanations of the origin of osmotic pressure. In particular, Poynting was led to assume that osmotic pressure was due to the formation of labile hydrates, and it became necessary, as Whetham pointed out (Nature, Oct. 15, I&$), to assume that all substances which gave a normal osmotic pressure were monohydrated, whilst the double osmotic pressure of binary salts might be ascribed to the formation of a dihydrate or of two monohydrated ions." The invariable formation of loose monohydrates was so improbable, and is so far in contradiction to recent work on the hydrates present in solution, that Poynting's theory has failed to secure general acceptance as an explanation of the osmotic phenomena. OSMOTIC PRESSURE AS A KINETIC PHENOMENON.The theory of osmotic pressure now described formed the subject of a paper read before the Chemical Society of the Central Technical College as long ago as May, 1896, but it was only recently that it was recognised as being sufficiently novel to warrant further publicity. The starting-point of the theory is a consideration of the conditions prevailing at the surface of separation of the solution and the semi-permeable membrane, which may be either a layer of copper ferrocyanide or merely the boundary between liquid and vapour or liquid and ice.The simplest of these cases is undoubtedly that which involves the equilibrium between liquid and vapour. In this case the kinetic theory postulates a continual process of evaporation, whereby rapidly moving particles are constantly escaping from the surface of the liquid into the vapour space. This is balanced by the con- densation of practicatly all the molecules of the vapour that impinge on the liquid surface. When the vapour reaches a certain concentration the rate of condensation becomes equal to the rate of evaporation, and a condition of equilibrium is attained, not because evaporation has ceased, but because it is neutralised by an equal and opposite process of condensation. In the case of a non-volatile liquid the mobility of the relatively heavy molecules or mole- cular complexes is so small that very few are able to escape, and the maximum vapour pressure of such liquids is inappreciable.If now a solution be prepared by mixing a volatile and a non-volatile liquid, or by dissolving a non-volatile solid in a volatile liquid, the surface will contain both kinds of molecules. If one of the solvent molecules be struck by a rapidly moving molecule from the interior of the liquid, it will be projected into the vapour space. If, however, one of the non-volatile molecules be struck, it will be unable to escape, and the solvent particle will rebound in much the same way as if it had struck the wall of the containing vessel. The rate of evaporation is therefore reduced by the addition to the solvent of a non-volatile solute.On the other hand, it is probable that the presertce of the raora-volatile molecules would not interfere with the rate of coltdensation of the vapour. This point is of fundamental importance, as the opposite view was advocated by Poynting, who supposed that con- densation and evaporation would be checked to an equal extent, just as if the surface had been covered by a plate of perforated zinc. It must be remem- bered, however, that a considerable upward velocity is required before a molecule can escape from the surface of a liquid, and that a molecule descending with ever. the smallest downward velocity would have little * -4 similar deduction was drawn by I. Traube ( A m . Pltys. Cltena., 1897, ii. 62, 490-506).OF THE KINETIC THEORY 19 chance of escaping when once it came within the range of attraction of the liquid.Even if, on reaching the liquid surface, a vapour molecule should strike against a non-volatile molecule of the solute the attraction of the neighbouring molecules of the solvent would be sufficient to hold it, and thus ensure its condensation. I t need scarcely be pointed out that similar conditions would prevail at the surface separating liquid and ice or at the surface of one of the more conventional semi-permeable membranes. In the former case the presence of a non-isomorphous solute might prevent the adhesion to the ice of a molecule of solvent moving towards it but separated from it by a molecule of solute. On the other hand, it would not prevent the melting off or dissolution of an ice molecule if the average kinetic energy (k, temperature) of the ice were raised by the latent heat of crystallisation of other molecules passing from thc liquid to the solid state.In the case of a membrane such as copper ferrocyanide the solute would check the escape of solvent mole- cules from the solution into the membrane, but would not oppose the return of wanderers migrating from the membrane back into the solution. This would lead to a disturbance of the equilibrium between the solvent and the liquids on either side, and would be sufficient to produce an osmotic flow and a consequent osmotic pressure. DEDUCTION OF THE GAS-FORRIULX FROM THE KINETIC THEORY OF OSMOTIC PRESSURE. Of the theories of osmotic pressure that have hitherto been put forward, that of van’t Hoff is the one that leads most directly to a simple quantitative explanation of the phenomena.Poynting, in developing his theory quantita- tively, considered that solute molecules and stable compounds of solvent and solute would merely alter the effective surface of the liquid without changing the relative rates of evaporation and condensation ; only in the case of labile compounds was it considered possible that the rate of evaporation might be checked without altering the rate of condensation ; on this basis a quantitative explanation was only possible on the impracticable assumption that all ordinary solutes are loosely monohydrated in aqueous solutions. The more recent theory that osmotic pressure depends on a disturbance in the equilibrium between simple and polymerised solvent molecules, e.g., H,O,H,,O, (Armstrong, Proc. Roy.Soc., 1906, A. 78, &4-271), has also, as yet, failed to yield a quantitative interpretation of the pressures produced. The quantitative interpretation of the kinetic theory of osmotic pressure follows at once from Nernst’s proof of the relationship between osmotic pressure and vapour pressure (TIzeoreiicaZ Clzemisfry, pp. ~ q - ~ z g ) . Thus if N be the number of gram-molecules of solvent, and n the number of gram- molecules of solute in unit volume of the solution the validity of the gas- formula for osmotic pressure is readily deducible from the equation- N A’ N + n-p’ where p is the vapour pressure of the solvent, and p’ that of the solution.* If the simple assuniption is made that the molecules of solvent are uniformly distributed in the surface layer, and that the spacing or packing is the same as in the pure solvent, it follows a t once that the rates of evaporation from unit surface of solvent and solution will be in the ratio N + n to N, and that this will also be the ratio of the vapour pressures, as required by the above * The value of N is determined by the molecular weight of the solvent as it exists in the vapour, and not by its molecular weight in the liquid state.20 OSMOTIC PRESSURE FROM THE STANDPOINT formula.The argument is, of course, identical with that used by Poynting to show that each molecule of solute must destroy the mobility of a molecule of solvent, but, whereas he was led to assume the regular formation of labile monohydrates, the theory given above merely postulates that the mobility of a solvent molecule is destroyed when its place in the surface of the liquid is occupied by a molecule of solute.SURFACE STRUCTURE OF LIQUIDS. It will at once be noticed that in its simplest form the kinetic theory of osmotic pressure would indicate .that the pressures calculated from the gas- formula might be subject to a small correction for the volume changes accompanying dissolution. Whether such corrections are necessary can only be determined by experiment, but the evidence now available points to a very close agreement between the values observed and calculated for dilute solutions. If this identity should be confirmed, it will be possible to deduce from observations of osmotic pressure some information in reference to the surface structure of liquids, since if the agreement is exact there must be an equally exact replacement of solvent by solute in the surface of the liquid.Thus in view of the different iiiasses of the molecules that may be dis- solved in the same solute and yield identical osmotic pressures, there must be a considerable spacing between the actual molecules in the surface. Again, it may be noted that this exact replacement does not take place in the interior of the liquid, where the molecular volumes of different solvents differ widely, and when calculated in the conventional way may even have a negative value. It is, however, by no means improbable that the marshalling of the molecules 011 the frontiers of the liquid may be governed by a stricter discipline than that which prevails in the interior, and that the surface molecules may even be forced to conform to the exact regulations which govern the replacement of molecules in solid solutions or isomorphous mixtures. FORhfATION OF COMPLEXES.The formation in the solution of loose complexes of solvent with solute or of solvent molecules with one another has not yet been referred to, but presents no difficulty in the development of the theory. Such complexes are usually formed without any large change of volume, and under the stricter condi- tions prevailing at the surface no alteration in the area of surface occupied need result from the linking up of the ‘‘ residual affinities ” of the molecules.Neither need it be supposed that the rate of evaporation would be affected otherwise than by a general reduction of mobility::: due to the chemical attraction of the molecules and producing equal effects in solvent and in dilute solution. Thus, as there is 110 change of energy involved in the replace- ment of one solvent molecule in a complex by another from outside, a rapidly moving particle impinging on a complex might drive a combined solvent moleculc into the vapour space and itself occupy the vacant position in the complex, the effects produced being much the same as if no complex existed. A similar statement would apply to molecules of solvent attached to the solute in the form of labile hydrates or compounds; a free solvent molecule impinging on a combined molecule in the surface of the liquid might drive it out and take its place, but if it should impinge on the nuclear solute molecule it would be repulsed and driven back into the interior, just as it would be by an uncombined molecule of solute. cohesion in a gas as represented by the quantity * Compare the reduction of mobility caused by liquid in van der Waals’ equation, 2jaOF T H E KINETIC THEORY 21 CONCENTRATED SOLUTIONS. No attempt has been made i n the above to account quantitatively for the osmotic pressure of concentrated solutions. Even in the case of gases, the equation PV = RT only applies strictly to a material gas within narrow limits of pressure, but Morse and Fraser’s experiments indicate a much wider applicability when the formula is applied to osmotic pressures, provided only that for concentrated solutions V is interpreted as the volume of solvent used to dissolve the solute and not the total volume of the solution. It need scarcely be pointed out that this modification is very similar in type to the co-volume correction in van der WBals’ equation. OSMOTIC PRESSURE AND SURFACE TENSION. In view of the close relationship that has been indicated between osmotic pressure and surface structure it would not be surprising that a relation- ship should exist between surface tension and osmotic pressure. Such a relationship has been postulated theoretically by Traube, who supposes that osmotic pressure depends on a tendency to equalise the surface tension of the two liquids, and has been confirmed experimentally by Batelli and Stephanini (Atli. R. Acad. Lincei, 1905, (v), 14, ii. pp. 3-14), who find that solutions of equal surface tension have equal osmotic pressures, even in cases in which the solutions are not nominally equimolecular. In conclusion it may be pointed out that whilst the vicws advocated above were comparatively novel ten years ago, the idea that osmotic pressure depends on the activity of the solvent rather than on that of the solute has now become widely accepted, and has been advocated, not only by Poynting, but also by Armstrong ( E m . Brit., 26. 739), Beilby, (B. A. Report, South Africa, 1905, 361), and others. At the present time, therefore, the only points for which any degree of novelty can be claimed are in reference to the mechanism by which the activity of the solvent at the surface of the liquid is reduced by the ‘‘ blocking action ” of the solute operating in one direction only, and to the possibility of deducing from the osmotic phenomena information as to the surface structure of liquids. 130, HORSEFERRY ROAD, WESTMINSTER, S.W.