Principles of General Physiology

14, except that the glass tube is left open at the top and then closed with a brass cap and litharge-glycerine cement. osmotic pressure as that of the inner solution, so that no movement of the meniscus takes place. The concentration of the sugar solution can then be ascertained by an appropriate method, say by specific gravity or rotatory power, and its osmotic pressure is obtained from the measurements of Morse and others. The method is only applicable when the membrane is not easily permeable to the solute whose osmotic pressure is to be determined, and it must obviously mil l»e acted on chemically by solvent or solute in contact with it. According to Walden (1892, p. 708) such membranes are permeable to nearly all inorganic salts. The substances tested by Fouard were lactose, glucose, mannite, asparagine, and quinine tartrate. Apparently the tannin-gelatine membrane was impermeable to these, but it is the most permeable of all the precipitation membranes tested by Walden (see page 113 above) ; the least permeable was that of copper ferrocyanide.

Vapour Pressure. — That a solution of any substance must have a higher vapour pressure than that of the pure solvent can readily be seen by the following consideration due to Arrhenius (1901, p. 33). Suppose two vessels, W and S (Fig. 49), situated in a closed space filled with air. W contains a dilute solution of a nonvolatile solute in water, and S a stronger solution of the same solute. Water will pass from W to S, since the air may be regarded as a semipermeable membrane, permeable to water as vapour, impermeable to the non-volatile solute. The pressure of water vapour over W must, therefore, be greater than over S, otherwise it would not pass from the one place to the other. Further, suppose that W and S, instead of being in separate vessels, are in one vessel but separated by a membrane, permeable to the solvent, impermeable to the solute. The water, as we know, passes to the stronger solution until the osmotic pressure of the two is the same. Now, if the pressure of water vapour were greater over S than over W, water would continually distil over to W «nd pass through the membrane to S, equilibrium would never be attained, and we should have a "perpetually automatic cyclic process, i.e., a perpetuum mobile, which would perform work at the expense of the heat of the , environment, which is contrary to

The method of calculating the exact quantitative relation between vapour pressure and osmotic pressure is beyond the scope of this book, and may be found in that of Nernst (1911, pp. 132-137). In practice, various methods of determining the vapour pressure of a solution are adopted. It may be measured directly by introduction of the solution into a Torricellian vacuum and measuring the fall of the mercury column, or by a differential method, determining the difference of pressure over the solvent and the solution. An apparatus for use in physiological work is described by Friedenthal (1903). The method has the disadvantage that the solutions are in mcuo, so that dissolved gases must be removed previously ; but, on the other hand, it can be used at the temperature of the organism from which the solutions were obtained, an advantage over the freezing point method. Another method is -that suggested by Ostwald and investigated by James Walker (1888). This depends on the fact that, when an indifferent gas is bubbled through a solution, the amount of the solvent removed by the gas is proportional to the vapour pressure of the solution. This method was employed by Berkeley and Hartley (1906, 2) to compare the vapour pressures of cane-sugar solutions

In A, the liquids are separated by air. In B, there is also a semi-permeable membrane, with which they are both in contact. with the osmotic pressures obtained by the direct method. Several improvements were introduced in order to increase its accuracy. When great sensibility is not required, Barger's method (1904) will be found very useful and easily carried out. Suppose that, in Fig. 49 (upper figure), we have a means of observing the change* in volume of the two solutions, and that we take as one of them a solution whose osmotic pressure is known, say canesugar, and that we change its concentration until no change occurs, on standing, in the volume of either of the solutions. Then the vapour pressure of the unknown solution is equal to that of the known sugar solution. Barger introduces alternate drops of the two solutions into a capillary tube, and observes the change in length of the various drops by measurement under a microscope.

It is clear that much time is saved by knowing beforehand the approximate osmotic pressure of the solution to be measured. In an application of this method to solutions of Congo-red (1911, ii. p. 233), I found no difficulty in distinguishing between concentrations of 0-020 and 0'023 molar. The boiling point of a solution also depends on its osmotic pressure, and this method is frequently in use by chemists, but is rarely applicable to physiological problems on account of changes in solutes produced by the high temperature required.

On the other hand, the method of freezing point determinations is of great value, although not so sensitive as direct measurements. A decimolar solution in water lowers the freezing point by only 0°'184, so that a very sensitive thermometer must be used. In fact, 00-001, a quantity difficult to measure with accuracy, corresponds to an osmotic pressure of 0-012 atmosphere, or about 9'1 mm. of mercury, a pressure easy of measurement, especially with a manometer containing a liquid of low density.

Solutions which have the same osmotic pressure have the same freezing point ; for the freezing point is that temperature at which the solid solvent (ice) and the solution are capable of existing together, so that they must have the same vapour pressure, otherwise isothermal distillation would occur. Solutions have a lower vapour pressure than the pure solvent, hence the ice with which they are in equilibrium at their freezing points must have a lower vapour pressure than pure ice in equilibrium with water, in other words, it must be at a lower temperature.

It is scarcely necessary to remind the reader that ice has an appreciable vapour pressure, which decreases as the temperature falls, theoretically as far as absolute zero, at which temperature water vapour, like all gases, ceases to exist as such. This fact enables desiccation of tissues to be carried out below their freezing points, as in the method of Altmann (page 17 above). In connection with the measurement of the freezing points of solutions there are two important laws to be kept in mind. The law of Blagden (1788) states that the lowering of the freezing point is proportional to the concentration of the solution, and that of Raoult (1883) states that equi molecular quantities of various substances in the same solvent lower its freezing point by the same amount.

For further theoretical treatment see Nernst's book (1911, p. 146), and for practical details of the methods used, see Findlay's monograph (1906, pp. 110-123), Nernst's book (1911, pp. 259-263), and the monographs of Raoult (1900-1901). Guye and Bogdan (1903) have modified the ordinary Beckmann apparatus in such a way as to make it available for smaller volumes of solutions, 1'5 c.c. instead of 10-20 c.c. This renders the apparatus of more use in physiological work, where it is not always possible to obtain sufficient liquid for the usual form of apparatus. A further modification, by which even less solution is required, is described by Burian and Drucker (1910). It appears, nevertheless, to give accurate results.

The value in degrees by which the freezing point of a solution is lower than that of water is denoted by the sign A- There is still another method of measurement of osmotic pressure which has been used for physiological liquids, viz., that of the effect of dissolved substances on the critical solution temperature. Many liquids are able to dissolve each other to a limited extent, as, for example, phenol and water. Above a certain temperature these two liquids are miscible in all proportions, but, as the temperature falls, phenol separates out as a distinct phase in an opalescence to begin with. This temperature is altered by dissolved substances and in proportion to their

molecular concentration. For further details, the reader is referred to the paper by Timmermans (1907), and for the application to urine, the paper by Atkins and Wallace (1913). In order to increase the osmotic pressure of a solution requires tinperformance of work just as the compression of a gas does. The amount of work depends, of course, on the volume of the solution compressed as well as on the pressure to which it is raised. It is, just as in the case of a gas, as described on page 33 above, equal to

for one gram molecule, where pl and j»2 are the lower and higher pressures respectively ; and n times this quantity for n gram-molecules. The osmotic pressure of a solution can be raised by removal of part of the solvent in any manner, and it follows, from the second law of energetics, that the work done is identical in all cases (Nernst, 1911, p. 19), provided that the process is isothermal. Suppose that a part of the solvent is removed by evaporation, it can be shown by a simple process, details of which will be found in the book by Nernst (1911, pp. 132-135), that the work done is also expressed by the formula

where m is the molecular weight of the solvent, « the specific gravity of the solution, and P the osmotic pressure of the solution. The foundation of the general theory can best be grasped by the following imaginary model, based on the considerations of van't Hoff(1887). In a vessel, W (Fig. 50), containing a solution, S, is a cylinder, C, closed below by a membrane, impermeable to the solute, permeable to the solvent. The cylinder contains a more concentrated solution of the same substance, and is fitted with a movable piston on which weights can be placed so that the osmotic pressure due to the difference in concentration of the two solutions is balanced and the system is in equilibrium. A further weight is then placed on the piston ; the result is that water is driven out through the membrane, so that the osmotic pressure is raised. In doing this, the weight falls through a certain height, thus doing a definite amount of work on the solution. If the added weight is removed again, water will enter, raising the original weight and so doing external work. We see thus that solutions, like gases, possess volume energy, which can be taken in or given out.

An important physiological application of this fact is that, when a secretion, such as urine, is formed at a higher osmotic pressure than the blood, work must be done, and that the work can be calculated. In the inversion of cane-sugar by acid, when concentrated solutions are taken, the rate is found to be not in accordance with the law of mass action, " that the rate of change is proportional to the active mass of the substance taking part in the reaction." That is, if we understand by "active mass" the actual concentration in gram-molecules per litre. But Arrhenius has shown (1899) that, if we substitute for " active mass," in the above statement, the words " osmotic pressure," the experimental results agree with the law. As Mellor (1904, p. 283) puts it : " The osmotic pressure of cane-sugar in solution, kept at a constant temperature, is proportional to the number of collisions of the sugar molecule with the ' semi-permeable ' wall of the containing vessel. Again, the amount of sugar inverted in unit time will be proportional to the number of collisions of the sugar molecule with the molecules, or rather the ions, of the acid. But

the amount of acid in the solution is constant, and consequently the number of collisions of the molecules of sugar with the molecules of the acid will be proportional to the osmotic pressure of the sugar molecules. In other words, the velocity of the reaction will be proportional to the osmotic pressure of the sugar molecules." As we have seen, in fact, the actual volume occupied by the sugar molecules must be taken into account, as was pointed out by Cohen

Substances in solution always wander from a place of higher to one of lower concentration. This is known as "diffusion" or "hydrodiffusion," and, according to the kinetic theory, is brought about by the constant movement of the molecules. The phenomena were investigated by Graham (1850), who showed that the rate varied with the nature of the substance. Later investigations showed that the rate was inversely proportional to the size of the molecule, and directly proportional to the difference of concentration between the two places between which diffusion was proceeding.

In fact, the law is completely analogous to that sometimes known as Newton's Law of Cooling or, more generally, "Law of Velocities." Any process, which is on the way to an equilibrium, becomes slower and slower as the final state gets nearer. The driving force becomes less and transfer of heat, the flow of water along a tube connecting two cylinders of water, and so on. The cylinder (C) has an accurately fitting piston, and is closed below by a membrane semi-permeable as regards the solute in S. The solution inside the cylinder becomes more concentrated than that outside when the weight is placed on the top of the piston. To do this, the piston with the weight falls, thus doing work.

In the case of diffusion, the driving force is identical with osmotic pressure in solutions, and is completely analogous to the equalisation of differences of density in gases. In the latter, however, the process takes place very rapidly, while in a liquid it is very slow, owing to the enormous friction with which the moving molecules are met in the case of liquids. It is interesting to calculate this friction from the osmotic pressure and the rate of diffusion, as can be done in a way analogous to Ohm's law. According to Nernst (1911, p. 152), it requires a force equal to the weight of 6*7x109 kg. to drive one molecule (342 g. ) of cane-sugar through water with a velocity of 1 cm. per second. We realise somewhat how slow a pure diffusion process must be. The following experiment described by Graham (1850, p. 462 of the Collected Edition) is instructive. A glass cylinder, 11 in. high, was filled to one-eighth of its capacity with a saturated solution of calcium bicarbonate, which also contained 200 gr. of sodium chloride in 8 cub. in. The jar was then filled completely with distilled water in such a way as not to disturb the lower layer, covered with a glass plate, and left to stand in a uniform temperature for six months. Samples of different strata were then removed by a syphon, and it was found that equality of concentration had not been attained, even in so long a time. The ratio of the concentrations of the sodium chloride in

the top and bottom layers was as 11 to 12, while that of calcium bicarbonate was as 1 to 4. In another set of experiments (p. 557 of Collected Papers), it was found that in foui -ti-cn <l;i\ s the concentration of sodium chloride at the top of a column of 127 mm. was only l/±> of that at the bottom, while sugar was only just to be detected at the top in that space of time, the uppermost 50 c.c. of solution contained only. (HJ05 g. of glucose. The different diffusion rates of various substances may give rise temporarily to considerable differences of osmotic pressure between two solutions in an osmometer, even when the two solutions are actually of equal osmotic pressure to Ix'u'in with, and separated by a membrane permeable to both solutes. Sodium chloride diffuses more rapidly than magnesium sulphate, so that, if we take isotonic solutions on the two sides of a membrane permeable to both solutes, the former salt will diffuse through the membrane faster than the latter, the molar concentration and osmotic pressure of the sodium chloride solution will diminish, while that of the magnesium sulphate will increase, and water will pass tu the latter. The difference in concentration is, of course, only temporary, but may give rise to considerable changes in osmotic pressure, and is of importance in the process of absorption from the alimentary canal.

When we have a solution of an electrolytically dissociated salt in contact with water, if the anion and cation move at different rates, it is clear that there will be a difference of potential between the front and back of the advancing surface of the diffusing column, the faster moving ions giving the sign of their charges to the front layer. Owing to electrostatic forces, the one set of ions cannot outdistance the other set further than their kinetic energy can carry them in opposition to the electrostatic attraction. (For the magnitude of these forces see the calculation by Arrhenius on page 179 below.) This phenomenon is a possible source of potential differences in tissues, and will be discussed later in Chapter XXII.

The osmotic pressure of a solution is found to be, by whatever method it is measured, in direct relation to the molecular concentration. If a molecule is dissociated in any way, electrolytically or hydrolytically, each fraction acts as an element, equivalent osmotically to a molecule. Similarly, if there is association of molecules, the associated group behaves as a single molecule. The measurement of osmotic pressure is thus the most valuable means of determining the actual molecular concentration of a given solution.

Have we then any reason to limit the powers of giving an osmotic pressure to associations of a small number of molecules and deny it to those where a larger number are associated, as in colloids ? Or at what particular number does osmotic pressure cease ? Some substances, moreover, as we saw in Chapter TV., owe their colloidal properties to the fact that their single molecules or ions are too large to pass through parchment paper. If colloids have no osmotic pressure, it must be denied also to some molecules, so that we may again ask, at what molecular dimensions does it cease 1

Any colloidal solution which remains in permanent suspension consists of particles in perpetual Brownian movement, precisely similar to the molecular movement postulated by the kinetic theory. Moreover, as shown by Perrin (page 85 above), each particle possesses the same mean kinetic energy as a molecule. If, then, this kinetic energy is the cause of osmotic pressure, it follows that colloidal particles must manifest it. A brief consideration will show, however, that it cannot be expected to be great, at all events as far as the association of molecules constituting a suspensoid colloid are concerned. A true solution in decimolar concentration has an osmotic pressure of 1,702 mm. of mercury at 0°, as can be seen from the following calculation. One gram-molecule of a gas, at normal temperature and pressure, occupies a volume of 22 '4 litres ; therefore, to compress it to one litre, the volume of a solute in molar solution requires, by Boyle's law, a pressure of 22 -4 atmospheres, or 17,024 mm. of mercury. But suppose that the same number of molecules as those in a decimolar solution are aggregated in masses of 500, then the solution, although containing the same amount of total solid, will have only 0'002 times the number

of active elements, or effective molar concentration, and its osmotic pressure will be only 3 '4 mm. of mercury. In the case of substances which are •colloidal on account of the large size of their single molecules, as appears to be the case with haemoglobin, it is impossible to obtain solutions of any great molar concentration. According to its content in iron, the molecular weight of haemoglobin is 12,000 to 14,000, so that a O'Ol molar solution would contain 12 per cent, of solid. Colloidal solutions of such strength cannot often be obtained, and a decimolar solution would be solid.

The above considerations appear to me to place a difficulty in the way of accepting Roaf's view (1912, 1) of a cell membrane semi -permeable only as regards colloids. Plant cells usually contain solutions with an osmotic pressure of 4 '5 atmospheres, which is that of a 0'2 molar solution ; if a protein salt, even of so low a molecular weight as 2,000, is to afford this pressure, a 40 per cent, solution would be necessary. This is higher than the total solid content of protoplasm. More difficulties seem to be attached to this view than to that of a true semi-permeable membrane, although it is suggested as a simpler one. If we are to admit semi-permeability as regards glucose,. or non-electrolyte crystalloids, it is not a great step to extend it to certain salts or even acids and alkalies.

The first clear proof that colloidal solutions have a measurable osmotic pressure was given by Starling (1896 and 1899) in the case of the colloids of blood serum. A portion of serum was filtered through gelatine by pressure; this filtrate contained all the crystalloid constituents of the serum, since gelatine holds back the colloids only. The filtrate was placed in an osmometer with a gelatine membrane, while on the other side of the membrane a portion of the unfiltered serum was situated. Any difference in osmotic pressure observed must be due to difference of molar concentration, and this again only to substances in the colloidal state. It was actually found that the colloids in blood serum gave an osmotic pressure of about 30-40 mm. of mercury. This fact will be found in later pages to have an important connection with the secretion of urine.

Moore and Parker (1902) measured the osmotic pressures of egg-white, serum, and soaps, Moore and Roaf (1907) those of serum proteins, gelatine, and gum acacia. Hiifner and Gansser (1907), and Roaf (1908), independently, made exact determinations of that of hfemoglobin. Some confusion has arisen as to the genuine nature of the osmotic pressure obtained in the case of colloidal solutions on account of the difficulty of ensuring the absence of electrolytes or other impurities of low molecular weight. It was thought that, in some way, these foreign substances, although capable of free diffusion through the membrane, might be held back by the colloid and thus afford the osmotic pressure observed. Consideration will show that this cannot be the case. If these foreign substances are in chemical combination with the colloidal one, they are obviously part and parcel of the colloidal particles, and not to be reckoned as impurities. Even if merely adsorbed, they are fixed for the time on the surface of the colloidal particles, and are inseparable from the colloidal elements to whose molar concentration the solution owes its pressure — they are, in fact, not free to exercise their own osmotic pressure ; while that due to the colloidal substance will rather, if anything, probably be slightly decreased, if the impurities are salts, owing to the increased aggregation of the colloidal particles. If, again, these foreign substances are free in solution, they will diffuse until equal in concentration on both sides of the membrane, and therefore inactive osmotically. There is, however, one special case to which reference has already been made (page 120 above), where both the colloid and the diffusible substance are electrolytes. But here the concentration of the diffusible salt becomes less in the presence of the colloid, so that it leads to a fall in the apparent osmotic pressure on the part of the colloidal solution. Foreign diffusible substances cannot, therefore, be held responsible for the actual experimental facts.

Hiifner and Gansser (1907, p. 209), moreover, find that the osmotic pressure of haemoglobin corresponds to its molecular weight, calculated on the basis of its iron content. Moore and Roaf (1907, p. 63) noticed that the addition of sodium hydroxide to a protein solution caused the osmotic pressure to rise, and interpreted the fact as due to the formation of a salt with smaller " solution aggregates " than the original protein. Now, in order to investigate the interesting and important phenomena shown by electrolytically dissociated salts, of which one or the

other ion does not pass through the membrane, it is better to take salts of which the molecular weight and chemical constitution are known, since quantitative results are easily obtained. Many of the aniline dyes with large molecular weight answer this requirement. In the work done by myself (1909, 1911), Congo-red and related dyes were found the most useful. It is necessary to devote some consideration to this question, since the conditions are rather complex, but salts of this nature are of frequent occurrence in the cell, and play an important part therein.

The exact chemical constitution of Congo-red is not material for the present purpose, except that the coloured ion is the anion and, being a substituted disulphonic acid, combines with two sodium ions. The anion is, of course, the one to which the parchment paper membrane is impermeable. Measurements of the electrical conductivity of these dyes show them to be electrolytically dissociated to a considerable degree, so that the question to be answered is whether the sodium ions are active osmotically when the membrane used is permeable to them. It might indeed be supposed that these ions would pass through the membrane to such a distance that their osmotic pressure was balanced by the electrostatic attraction of the non-diffusible ions within the membrane, and that this fact would render ineffective any pressure due to the kinetic energy of these ions on the opposite side of the membrane. It must be confessed that the conditions are difficult to grasp in thought, but it will be remembered that the osmotic pressure produced by the non-diffusible substance, consisting of the anions and the nondissociated part of the salt, shows itself in virtue of the mechanical constraint exerted by the membrane, which allows water to pass through freely, while holding back the substances named. In a similar way, the sodium ions are held back by the attraction of the opposite ions, which themselves are held back by the membrane, so that the membrane itself must actually bear the pressure of both kinds of ions. Or, to put it in another way, the pull of the anions on the cations could not be effective unless the constraint of the membrane gave the former a support to pull against.