Pt = P0 (T / 273) or Pt / T = P0 / 273 = a constant.16

That is, the pressure of a gas varies directly as its absolute temperature, if the volume is kept constant.

Pfeffer's results, on the osmotic pressure of sugar solutions at different temperatures, were not sufficiently accurate to enable van 't Hoff to use them to confirm positively the rigorous thermodynamic proof (footnote 3, p. 12), that the osmotic pressure must increase proportionally to the absolute temperature, as required by Gay-Lussac's law. But the data did show, uniformly, a marked increase of the osmotic pressure with the temperature and, frequently, excellent agreement between theory and experiment. More striking were the results obtained by van 't Hoff in testing the correctness of this extension of Gay-Lussac's law by means of Soret's results on the diffusion of a solute from a warmer to a colder place. It was found that the concentrations, obtained by Soret when equilibrium was reached, agreed closely with the demand that the osmotic pressures in the colder and the warmer parts of the solution should be equal, and that the osmotic pressure of a given weight of solute in a given volume should increase proportionally to the absolute temperature. An elevation of temperature, in a portion of a uniform solution, will increase the osmotic pressure of this part. Diffusion will follow, until the loss in concentration of the solute, and therefore the loss of osmotic pressure (Boyle's law), of the warmer part, and the increased concentration and increased pressure of the colder portion result in all parts of the solution having the same osmotic pressure. [p015] As an example, a concentration of 17.33% copper sulphate at 20° was found to be in equilibrium with a concentration of 14.03% at 80°. Now, if the 17.33% solution had an osmotic pressure of P mm. at 20°, a 14.03% solution at the same temperature would have a pressure of (14.03 / 17.33) × P mm. (Boyle's law), and this would increase to (14.03 / 17.33) × P × (353 / 293) mm. at 80° C., or 0.975 P mm.—a result showing that the osmotic pressure in the hot part was practically the same as that, (P), in the cold part of the solution.17

It is a source of great satisfaction, that the recent very exact and painstaking work of Morse and Frazer,18 in measuring osmotic pressures directly, completely confirms this fundamentally important conclusion, that the osmotic pressure of a solution does increase proportionally to its absolute temperature.

The Avogadro-van 't Hoff Hypothesis.

—For chemists, the most important part of van 't Hoff's work lies in the extension of the Avogadro Hypothesis to solutions. As van 't Hoff expresses it, "equal volumes of the most different solutions, having the same osmotic pressure and the same temperature, contain the same number of dissolved molecules,—that number, namely, which would be found in the same volume of a gas at the same gas pressure and temperature."19 [p016]

Pfeffer's measurements, with solutions of 1 g. of sugar in 100 c.c. of water (the volume of the solution is 100.6 c.c.), were shown to prove, that the observed osmotic pressures agreed excellently with the gas pressures, calculated for the equimolar weight of hydrogen, in the same volume and at the same temperature:

Temperature. Osmotic Pressure
Found.
Atmosphere.		 Calculated.20
Atmosphere.
6.8 0.664 0.665
13.7 0.691 0.681
14.2 0.671 0.682
15.5 0.684 0.686
22   0.721 0.701
32   0.716 0.725
36   0.746 0.735

Morse's more recent and more exact results show, that the osmotic pressure of solutions of cane sugar and of glucose (corrected for the volume occupied by the sugar, see footnote, p. 15) agrees within 6% with the values demanded by van 't Hoff's theory, being about 6% larger for concentrations ranging from 0.1 to 1.0 molar. The difference of 6% is noteworthy and is probably due to secondary causes, but suggests extended investigation of its source.

Indirect Determinations of Osmotic Pressure.

—The experimental results given have been obtained by direct measurements of osmotic pressures with the aid of semipermeable membranes. [p017] Perfect membranes are very difficult to prepare, and membranes of this kind can be used only with a few solutes. Nature offers us, however, forms of semipermeable "walls" between solutions and pure solvents, which in many instances are perfect. The atmosphere, above a volatile pure solvent and a solution of a nonvolatile substance in that solvent, when both liquids are placed side by side in a closed space, would serve as a semipermeable wall: the solvent vaporizes and may pass freely from solvent to solution and vice versa, but the solute, in the case under consideration, is nonvolatile and therefore cannot pass through the atmosphere. The vapor pressure of a pure solvent being always found to be higher than that of a solution in this solvent, at the same temperature, the solvent would pass in such a closed space as vapor from the pure solvent and would condense in the solution; it thereby dilutes the solution and the solute, and the solvent in the solution, expand, exactly as in the absorption of a solvent by a solution through a semipermeable membrane. Again, the vapor pressure of a solution being lower than that of the pure solvent, the solution (of a nonvolatile solute) must be heated higher than the pure solvent, to bring both to the boiling-point; that is, there is an elevation of the boiling-point, when a nonvolatile solute is dissolved in a solvent. The solute being nonvolatile, only the solvent passes off in the process of boiling, the solute becomes more concentrated, and, according to van 't Hoff's extension of Boyle's law, the osmotic pressure of the solution increases. Similarly, when a solution is cooled until freezing occurs, provided the solute does not crystallize out with the solvent, the concentration of the solute is again increased, and therefore the osmotic pressure of the solution is also increased. Van 't Hoff recognized the relations existing between the freezing, boiling and vaporization of solutions, on the one hand, and the changes of their osmotic pressures on the other. By developing rigorously the relations between the lowering of the vapor tension, the raising of the boiling-point, the lowering of the freezing-point of a solvent by a solute and the osmotic pressure of the solution, he made it possible21 to use [p018] extensive experimental material,22 on the elevation of boiling-points and the lowering of freezing-points and of vapor tensions, to determine the osmotic pressures of solutions. The theory of the relation of osmotic pressure to gas pressure is fully confirmed by these measurements, for those cases to which it may properly be applied, namely, to sufficiently dilute solutions and such as have only negligible heats of dilution, i.e. in which dilution does not involve chemical changes.

Apparent Exceptions.

—Instead of discussing the vast amount of material of this kind, which agrees with van 't Hoff's theory, we may consider, more profitably, typical cases of apparent exceptions. The most important instance of this kind, the case of solutions of compounds which undergo electrolytic dissociation or ionization, will be separately discussed in the next chapter, and we shall find that van 't Hoff's great generalization is a vital element in the evidence of this important form of dissociation. Of other apparent exceptions, we may note the fact that some solutes seem to give "abnormally" low osmotic pressures23 in certain solutions. For instance, benzoic acid, in benzene solutions, gives only a little more than half as great an osmotic pressure as it does in aqueous solutions of the same concentration and temperature, and as would be calculated on the basis of the Avogadro-van 't Hoff Hypothesis for a compound of the formula C6H5COOH and the molecular weight 122. But a rigorous study24 of the distribution of benzoic acid between water and benzene, when solutions of the acid in the two solvents are shaken together until equilibrium is established (Chapter VIII), has proved that the distribution is strictly in accord with the assumption that benzoic acid, in aqueous solution, has the molecular weight 122 and the composition C6H5COOH, and that, in benzene solution, it has the molecular weight 244 and the composition (C6H5COOH)2; only a small part of the acid (C6H5COOH)2 is decomposed in benzene solution into the simpler molecules, of the composition C6H5COOH. In other words, the simpler molecules C6H5COOH are polymerized or associated to form larger molecules in benzene solution, much as the gas nitrogen dioxide NO2 goes over more or less into the gas N2O4, especially at low temperatures, and as hydrogen fluoride at low temperatures has the composition H2F2, while at higher temperatures it is HF. The divergence of the benzene solutions of benzoic acid from the Avogadro-van 't Hoff principle is therefore only an apparent one, not a real one, inasmuch as the osmotic pressure of the solutions agrees perfectly with that calculated for solutions of a substance (C6H5COOH)2, of molecular weight 244. Such associated molecules (of organic acids, alcohols, phenols, etc.) occur [p019] particularly readily in liquids of small dissociating power, like benzene, and such solutions show marked absorption of heat on dilution,25 the dilution being accompanied by a chemical change. The associated molecules are dissociated more and more completely [(C6H5COOH)2 ⇄ 2 C6H5COOH], even in these solvents, as the solutions are diluted. Since dilution results in a chemical increase in the number of molecules, the osmotic pressure cannot decrease proportionally with the increase of volume in such a case as this. Nor does gas pressure, it must be remembered, decrease proportionally to the volume in the case of gases which show chemical changes with change of volume, e.g. in the case of nitrogen tetroxide, for which we have N2O4 ⇄ 2 NO2.

In still other instances, apparently too high osmotic pressures, or too low molecular weights, have been found by the application of the Avogadro-van 't Hoff Hypothesis to solutions: for instance, the molecular weight of sodium, when dissolved in mercury, was found by Ramsay to vary from 21.6, in dilute, to 15.1 in concentrated solutions. But Cady found that the heat of dilution of sodium in mercury solution is considerable, and by taking this properly into account, Bancroft was able to show that the molecular weight, correctly calculated in a given experiment, is 22.7 (agreeing well with the theoretical weight 23), in place of 16.5, as calculated without making the required allowance for the heat of dilution.26 These determinations are most instructive in showing that the sources of some of the most important deviations from the van 't Hoff-Avogadro principle, deviations which have been brought forward as arguments against its assumptions, are due, not to any untrustworthiness of the general principle, but to the error of neglecting to observe the limiting conditions of the formulation, or of neglecting to make corresponding corrections for the non-observance thereof.

Summary.

—Van 't Hoff's theory of solution—that the osmotic pressure of substances in solution obeys the laws of gases, and that equal volumes of the most varied dilute solutions, having the same temperature and osmotic pressure, contain the same number of dissolved molecules, that number, namely, which would be found in the same volume of a gas at the same temperature and gas pressure,—accords thus, not only with the demands of thermodynamics,27 but is also, within the limits demanded by the theory itself, in agreement with the best experimental measurements of osmotic pressures that have been made in recent years. The apparent exceptions, as in the cases just described and, as we shall find, in the case of electrolytic dissociation, are found to be no exceptions, when the conclusions, reached on the assumption that [p020] the theory is correct, are tested rigorously by independent methods of investigation.28

The fundamental laws of gases and the Avogadro Hypothesis may be condensed into the following general equation, expressing all of the laws, viz.: P V = n R T. This equation applies equally to the osmotic pressures of dilute solutions, the osmotic pressure being substituted for the gas pressure. In the equation, T is the absolute temperature of the gas or solution, P the gaseous or osmotic pressure, V the free space of the gas volume, i.e. the volume of the gas less the volume occupied by the gas molecules, or the volume of the pure solvent in the solution used, i.e. the volume of the solution less the volume of the solute. R is the so-called gas-constant, and represents the work done against the external pressure when one gram molecule, or mole, of the gas is heated one degree and allowed to expand, say at constant pressure P, against an external pressure P; n represents the number of gram molecules or moles of gas or solute used (the total weight of solute or gas, divided by the average weight of a mole in the gas or solute). If a given weight of a gas or solute is taken, and no dissociation or association occurs (such as would involve appreciable heats of dilution), then n is a given number; and, therefore, at a given temperature T, all the factors on the right side of the general equation being given numbers, P V is a constant (Boyle's law). For a given quantity of gas or solute (n is a given number), kept at constant volume V, the pressure must vary as the absolute temperature (Gay-Lussac's law); P / T = n R / V = a constant. When the pressure, volume and temperature of two gases, or two dilute solutions, are equal, n, the number of gas or solute molecules present, must be the same (Avogadro-van 't Hoff Hypothesis); n = P V / (R T), and all the factors of the right side are the same for the gases and solutions which we are comparing. Finally, if the pressure is expressed in atmospheres, the volume in litres, and the temperature in absolute degrees, the gas-constant R = P V / T = 1 × 22.4 / 273 = 0.082.

Chapter II Footnotes

[3] Even after a solution of uniform concentration of the solute is formed, the tendency toward diffusion, and the diffusion itself, and the resulting pressure must still persist. But a state of dynamic (or flowing) equilibrium must be considered now to exist, the loss caused by the moving away of the solute, from a given part of the solution, being balanced by the diffusion (into that part) of the solute from the neighboring parts. Whether one ascribes the diffusion to inherent molecular velocities of the solute, or to an attraction between solvent and solute, the discrete particles of the solute in a solution of uniform concentration will continue to have such inherent velocities (Chap. III), and will also continue to be surrounded by pure solvent, exactly as in solutions of unequal concentrations, where the diffusion may be observed, because the net result, in such a case, is a one-sided action.

[4] This again holds equally for the solvent.

[5] See below.

[6] At the same time, the change is also in the direction of an expansion of the solvent in the solution. The two changes are not opposed to each other, but supplementary.

[7] Am. Chem. J., 28, 1 (1902); 40, 266, 325 (1908) (Stud.).

[8] Am. Chem. J., 34, 1 (1905); 36, 39 (1906); 37, 324, 425, 558 (1907); 38, 175 (1907).

[9] The exact concentration of the solution at the point of equilibrium is determined by subsequent analysis.

[10] Cf. Smith's Inorganic Chemistry, p. 287.

[11] Berkeley and Hartley, Phil. Trans. Roy. Soc. A, 206, 481 (1906).

[12] When appreciable heat of dilution is shown by a solution, some chemical change, resulting from dilution, is indicated (such as, dissociation of the solute, hydration, hydrolysis, etc.). In such a case, the Avogadro-van 't Hoff principle holds for each concentration for its actual composition, and the principle may often be used to determine the extent of the chemical change produced by dilution. But then the osmotic pressure will not obey Boyle's and Gay-Lussac's laws. The same exception applies also to gases which undergo chemical changes, as the result of dilution or change of temperature. In the case, for instance, of nitrogen tetroxide, which dissociates according to N2O4 ⇄ 2 NO2, the extent of the dissociation varies with changes of concentration (pressure) and of temperature, and the gas does not obey the laws of Gay-Lussac and of Boyle. In regard to the rôle of heat of dilution in connection with osmotic pressure, see Bancroft, J. Phys. Chem., 10, 319 (1906).

[13] See p. 15 for a more rigorous statement concerning the volume. Cf. Morse and Frazer, Am. Chem. J., 34, 1 (1905).

[14] As a result of numerous vain endeavors, as well as of much direct evidence of a positive character, the scientific world has, for many years, held the opinion that any sort of "perpetual motion machine" is impossible. Every one now admits that a machine which would be able to work continuously, without consuming energy, is an impossibility—that is, that a "perpetuum mobile of the first class," as it is called, is impossible (law of the conservation of energy or first law of thermodynamics). From this law it does not of necessity follow, however, that it would be impossible to make a machine or device that would convert continuously into available energy or work, say, the enormous amounts of heat energy of the earth or of large bodies of water ("dissipated energy") which would thereby be cooled below the temperatures of their surroundings. Such a hypothetical process has been termed a "perpetuum mobile of the second class"; it has never been realized and is universally conceded to be an impossibility; the so-called "second law of thermodynamics" gives expression to this fact.

Now van 't Hoff [Z. phys. Chem., 1, 481 (1887)] showed, first, that a gas like oxygen, nitrogen, hydrogen, etc., which is soluble in proportion to its gas pressure (Henry's law), must exert, in solution, an osmotic pressure equal to the gas pressure, which it would have, if present in the same quantity as a gas in the same volume at the same temperature; for, if such were not the case, the solution and gas could be used to produce a perpetuum mobile of the second class, which, according to the above law, is an impossibility. Similar proofs were given by Rayleigh [Nature, 55, 253 (1897)] and by Larmor [Phil. Trans., 190, 266 (1897), Nature, 55, 545 (1897)] that the principle applies to solutions of other solutes.

Provided, then, that we have (1) perfect semipermeable membranes, (2) sufficiently dilute solutions, and (3) none but negligible heats of dilution (p. 12), van 't Hoff's generalization, concerning the relation of osmotic pressure and the laws of gases, must hold, if the perpetuum mobile of the second class is impossible, as is demanded by the second law of thermodynamics.

[15] See p. 15 in regard to the relation for concentrated solutions.

[16] The pressure P0 of a given quantity (weight) of a gas at 0° C., in a given constant volume, is also a given number and consequently P0/273 is a constant under these conditions.

[17] The slight differences in the ionization of copper sulphate solutions of 14% and 17% and at 20° and 80° are not included in the calculation, ionization being unknown, when van 't Hoff made his calculations.

[18] Am. Chem. J., 41, 258 (1909).

[19] In the light of recent work, especially by Morse and Frazer, the law would state, more exactly, that a substance in solution produces the osmotic pressure, at a given temperature, which it would exert, if it were contained as a gas, at the same temperature, in the volume occupied by the pure solvent of the solution. For sufficiently dilute solutions, the volume of the solution and the volume of the solvent may be considered identical; for more concentrated solutions, there is a decided difference, and the correct volume to use in calculation is the volume of the solvent alone, i.e. the volume of the solution reduced by the volume of the pure solute. This corresponds to the correction of the volume in the more accurate expression for the behavior of gases, developed by van der Waals; in place of v, the total gas volume, (v − b), the total volume of the gas less the volume of the spheres of action of the gas particles, is used, especially for strongly compressed or concentrated gases. It may be added that van 't Hoff's thermodynamic proof involves the same correct definition of the volume that Morse and Frazer subsequently developed experimentally. Cf. Bancroft, J. Phys. Chem., 10, 319 (1906).

[20] One gram of cane sugar, C12H22O11 (the mol. wt. is 342) corresponds to 1 / 342 gram molecule or mole and, therefore, to 2.02 / 342 gram of hydrogen. The volume containing this quantity of hydrogen is 100.6 c.c.; a liter would contain 2.02 / 342 × 1000 / 100.6 gram of hydrogen. The pressure of a mole or 2.02 grams of hydrogen, contained in a liter at 0°, is 22.4 atmospheres, and the pressure of the quantity of hydrogen given above, in a liter, would be (2.02 × 1000) / (342 × 100.6) × (22.4 / 2.02) at 0°. At 36° C., for instance, the pressure would be 309 / 273 times as great, or Pcalculated = (2.02 × 1000 × 22.4 × 309) / (342 × 100.6 × 2.02 × 273) = 0.735 atmosphere.

[21] The exact relations are discussed in van 't Hoff's Lectures on Physical Chemistry, Part II, pp. 42–59, Nernst's Theoretical Chemistry (1904), pp. 142 and 148, and H. C. Jones's The Elements of Physical Chemistry (1909), pp. 252, 271.

[22] Vide Raoult, Scientific Memoir Series, 4, 71, 127.

[23] I.e. abnormally small depressions of freezing-points or elevations of boiling-points.

[24] Nernst, Theoretical Chemistry, p. 486; Hendrixson, Z. anorg. Chem., 13, 73 (1897).

[25] Cf. Bancroft, J. Phys. Chem., 10, 319 (1906).

[26] For the discussion of other instances, vide Bancroft, loc. cit.

[27] Footnote 3, p. 12.

[28] For example, determinations of distribution coefficients (p. 18), heats of dilution (p. 19), conductivities and chemical activity (Chapters IV–VI).

CHAPTER III OSMOTIC PRESSURE AND THE THEORY OF SOLUTION II

[p021] TOC

Accepting van 't Hoff's theory of solutions, then, as based on experimental evidence as well as on sound thermodynamic reasoning, we find a number of interesting questions still confronting us. Most insistent is the question as to the source of the remarkable agreement between the osmotic pressure of a solute and the gas pressure, which it would exert in the same volume, as a gas, at the same temperature, and as to the identity of the laws governing the two forms of pressure. Then, we may also ask, what is the mechanism of the process by which osmotic pressure reveals itself, especially in the case of cells with semipermeable membranes. And, finally, we may ask what is the cause of the semipermeability of the membranes.

Semipermeability.

—Taking up the last question first, as the simplest one, we find that it was long ago recognized that permeability depends on the power of membranes to dissolve certain substances, or to form unstable combinations with them. A membrane is semipermeable if it will dissolve one component only of a solution, the solute or the solvent, and not the other.29

We find the simplest evidence of the cause of semipermeability in the case of gases. Palladium, especially when heated, dissolves hydrogen readily, but not nitrogen or oxygen, and a wall of palladium may be used as a semipermeable membrane to separate a mixture of hydrogen and nitrogen from pure hydrogen, just as copper ferrocyanide membranes are used with aqueous sugar solutions and water. The results with the gases duplicate in every particular the observations made on the solutions (see below, p. 24). Certain gases, such as ammonia and hydrogen chloride, are easily soluble in water, while others, like oxygen, nitrogen and hydrogen, are very difficultly soluble, and a film of [p022] water may be used as a semipermeable membrane for such gases.30

Exp. If the moist membrane of a cell (Fig. 4), containing air, is covered with an atmosphere of hydrogen, there is no increase of pressure produced in the cell, as indicated by the column of colored oil in the manometer in which the cell ends: hydrogen, being very little soluble in water, cannot pass through the film of water in the few minutes it is allowed to act. If now an atmosphere of ammonia is substituted for the hydrogen, the gas passes through the film into the cell. It turns the color of a piece of litmus paper placed in the cell and produces an increased pressure in the cell, the air remaining in the latter, because oxygen and nitrogen are very little soluble in water.

Fig. 4.

Membranes will be, similarly, semipermeable to solvent or solute, when only one of these is soluble in the membrane, or is capable of forming an unstable compound with it. For instance, salts, holding water of crystallization which is readily lost and recovered, may easily be conceived of as assuming the rôle of semipermeable membranes, allowing the passage of water say from a wet atmosphere to a dry one, or from pure water to a solution; and Tammann31 has realized such membranes by the use of zeolites—silicates, which hold water of crystallization but are insoluble in water. Kahlenberg32 has recently used rubber membranes, that are permeable for solvents like benzene, pyridine, etc., which are soluble in rubber, but not permeable for water, which is insoluble in rubber.

Fig. 5.

Osmosis.

—The recognition of this rôle of the semipermeable membrane leads to the second question raised, namely as to the mechanism of the process by means of which osmotic pressures are measured directly with the aid of such membranes (p. 11). [p023] The answer hinges on the question of the mechanism of the diffusion of the solvent into the cell, a diffusion which is called its osmosis.33 If we consider the pure solvent, say water, on one side of a semipermeable membrane, and a solution (e.g. of sugar in water) on the other side, it is obvious that the solvent itself has a higher concentration on the side where it is pure, than on the side of the solution, where it is diluted—distended by the solute in it. The solvent is soluble in the membrane, and its solubility will be proportional34 to its own (the solvent's) concentration; it will, consequently, be more soluble in the membrane on the side of the pure solvent than on the side of the solution. If we bring such a membrane first into contact with the pure solvent (Fig. 5), the membrane will take up the solvent (from the side A) until it is saturated with it. Let the solubility, which represents the concentration of the solvent in the membrane at this stage, be called c. The membrane may then be considered to be taking up in unit time just as many molecules from the solvent as it gives up to it (dynamic equilibrium), exactly as, when water is in equilibrium with water vapor, we consider the water to be vaporizing just as fast as vapor is condensing to form water. Now, if a solution of sugar is placed on the other side of the membrane, the solvent will pass out of the membrane into the solution just as fast as it passes back into the pure solvent. At first the concentration of the solvent on the surface B of the membrane is just as great (c) as on the surface A; but the membrane will here receive the solvent more slowly from the solution, which is less concentrated as to the solvent; and consequently the membrane will lose water to the solution. The solubility (c′) of the solvent at this surface B of the membrane, corresponding to the smaller concentration of the solvent in the solution, will be less than the solubility (c) at A, where the membrane is in contact with the pure solvent, and water will pass into the solution at B, until the concentration of the water in the membrane at B has fallen [p024] from (c) to (c′). In such a membrane, as in every solution or gas, there must be a tendency towards the establishing of uniform concentration by diffusion from points of higher concentration to those of lower, and the solvent will, therefore, diffuse from points along the surface A of the membrane to points along the surface B; the surface A will become unsaturated and will take up solvent from the pure liquid bathing it, and the surface B will be kept continuously supersaturated and will lose solvent continually to the solution. Consequently, the solvent will pass continuously through the membrane from the pure solvent to the solution. Equilibrium will be reached, and the flow will cease, only when the solution has become infinitely dilute, equal hydrostatic pressure obtaining on solution and solvent, or when the disturbing influence of the solute, which dilutes the solvent in the solution, is exactly counterbalanced by an external hydrostatic pressure, exerted on the solution. When such a pressure on the surface of the solution balances the force exerted against the solvent by the solute we shall have equilibrium. It is clear, then, that the osmosis, or passage of the solvent through the membrane, is brought about by the unequal concentrations (or, more exactly, the resulting unequal partial pressures) of the solvent itself. But this inequality is produced by the presence of the solute, and it is a characteristic and significant fact, that the effect of the latter, in dilute solutions, may be overcome by a hydrostatic pressure, corresponding to the gas pressure which the same number of molecules of a gas in the same volume at the same temperature would exert against this hydrostatic pressure.
Fig. 6.

Osmosis and Gas Pressure.

—The legitimacy of the interpretation given is most strikingly shown by experiments with a membrane, semipermeable for gases, which enables us to measure gas pressures, that may be unknown, by exactly the same process as is used to measure the unknown osmotic pressure of a solute in solution. Van 't Hoff35 and Arrhenius36 predicted such a result, and Ramsay37 proved by experiment the correctness of their assumptions. A mixture of nitrogen and hydrogen may be enclosed in a palladium vessel connected with a manometer (see Fig. 6).38 The partial pressure PN of the nitrogen may be [p025] determined by surrounding the palladium vessel with pure hydrogen, at a pressure which is known and is greater than the partial pressure of the hydrogen in the vessel, and by observing the final total gas pressure which is obtained in the vessel. The hydrogen diffuses from the point of higher concentration, outside of the vessel, through the palladium, into the interior where the concentration of the hydrogen is lower. The experiment may be carried out at 280°, a temperature at which palladium readily dissolves hydrogen and is permeable to it. The metal does not dissolve nitrogen and is not permeable to it. The volume of the enclosed gas is kept constant by raising the mercury level in the outside arm of the manometer, and the total pressure of the enclosed gas is measured when equilibrium is reached. If this total pressure is Pfinal and the known pressure of the hydrogen outside of the vessel is PH, then, if equilibrium is reached when the hydrogen on both sides of the semipermeable palladium membrane has the same concentration (pressure), PH + PN = Pfinal and PN = Pfinal − PH. In other words, the excess of the final combined pressure inside, over the outside pressure of the hydrogen, is equal to the pressure of the nitrogen in the vessel. Ramsay's results showed that the amount of hydrogen actually entering the vessel was 90–97% of the amount predicted by the theory on the basis of the assumption that equilibrium will be reached, when the hydrogen has the same concentration (pressure) on both sides of the palladium membrane.

The experiment is particularly instructive, in the first place, because it illustrates with a gas, subject to the laws of gases, why and how osmosis takes place through a semipermeable membrane—namely as a result of the solubility of the diffusing substance in the membrane, and through the flow of the diffusing substance [p026] from higher to lower concentrations. In the second place, while the increase in total pressure in the inner chamber undoubtedly is brought about by the osmosis of hydrogen into the chamber, the excess pressure when equilibrium has been reached, necessarily measures accurately the partial pressure of the nitrogen. In other words, the semipermeable membrane is merely a means or device for measuring the partial pressure of the nitrogen—the membrane is not the cause of the pressure; the latter is a definite one, whether we know what it is or not, and the osmosis of the hydrogen through the palladium merely gives us a means of ascertaining it. Similarly, it would be wrong to consider that the osmotic pressure of a solution is caused, or brought about, by the flow of the solvent through a semipermeable membrane (osmosis); the latter simply is a device which enables us to recognize and measure the pressure that exists in the solution, both in the presence and the absence of such a membrane.

We may consider, then, that the osmosis, or migration of the solvent through a semipermeable membrane into a solution, is the result of the reduced concentration (or partial pressure) of the solvent in the solution, resulting from the presence of the solute.

Inasmuch as the effect of the solute on the solvent can be overcome by a pressure on the surface of the solution, one is led to the conclusion that the solute acts by exerting, in turn, a force or pressure against the surfaces of the solvent, in the directions opposite to the hydrostatic pressure required to overcome it. The significant identity of the value of this pressure, as thus measured, with the gas pressure that would be exerted by a gas of the same number of molecules, in the same volume and at the same temperature, leads us to the last of the three questions which have been raised, namely, the question concerning the theory of the intimate relations between gas and osmotic pressures (p. 21).