[17] The researches of Graham, Fick, Nernst, and others showed that the quantity of a dissolved substance which is transmitted (rises) from one stratum of liquid to another in a vertical cylindrical vessel is not only proportional to the time and to the sectional area of the cylinder, but also to the amount and nature of the substance dissolved in a stratum of liquid, so that each substance has its corresponding co-efficient of diffusion. The cause of the diffusion of solutions must be considered as essentially the same as the cause of the diffusion of gases—that is, as dependent on motions which are proper to their molecules; but here most probably those purely chemical, although feebly-developed, forces, which incline the substances dissolved to the formation of definite compounds, also play their part.
Fig. 15.—Dialyser. Apparatus for the separation of substances which pass through a membrane from those which do not. Description in text.
The rate of diffusion—like the rate of transmission—through membranes, or dialysis (which plays an important part in the vital processes of organisms and also in technical processes), presents, according to Graham's researches, a sharply defined change in passing from such crystallisable substances as the majority of salts and acids to substances which are capable of giving jellies (gum, gelatin, &c.) The former diffuse into solutions and pass through membranes much more rapidly than the latter, and Graham therefore distinguishes between crystalloids, which diffuse rapidly, and colloids, which diffuse slowly. On breaking solid colloids into pieces, a total absence of cleavage is remarked. The fracture of such substances is like that of glue or glass. It is termed a ‘conchoidal’ fracture. Almost all the substances of which animal and vegetable bodies consist are colloids, and this is, at all events, partly the reason why animals and plants have such varied forms, which have no resemblance to the crystalline forms of the majority of mineral substances. The colloid solid substances in organisms—that is, in animals and plants—almost always contain water, and take most peculiar forms, of networks, of granules, of hairs, of mucous, shapeless masses, &c., which are quite different from the forms taken by crystalline substances. When colloids separate out from solutions, or from a molten state, they present a form which is similar to that of the liquid from which they were formed. Glass may he taken as the best example of this. Colloids are distinguishable from crystalloids, not only by the absence of crystalline form, but by many other properties which admit of clearly distinguishing both these classes of solids, as Graham showed. Nearly all colloids are capable of passing, under certain circumstances, from a soluble into an insoluble state. The best example is shown by white of eggs (albumin) in the raw and soluble form, and in the hard-boiled and insoluble form. The majority of colloids, on passing into an insoluble form in the presence of water, give substances having a gelatinous appearance, which is familiar to every one in starch, solidified glue, jelly, &c. Thus gelatin, or common carpenter's glue, when soaked in water, swells up into an insoluble jelly. If this jelly be heated, it melts, and is then soluble in water, but on cooling it again forms a jelly which is insoluble in water. One of the properties which distinguish colloids from crystalloids is that the former pass very slowly through a membrane, whilst the latter penetrate very rapidly. This may be shown by taking a cylinder, open at both ends, and by covering its lower end with a bladder or with vegetable parchment (unsized paper immersed for two or three minutes in a mixture of sulphuric acid and half its volume of water, and then washed), or any other membranous substance (all such substances are themselves colloids in an insoluble form). The membrane must be firmly tied to the cylinder, so as not to leave any opening. Such an apparatus is called a dialyser (fig. [15]), and the process of separation of crystalloids from colloids by means of such a membrane is termed dialysis. An aqueous solution of a crystalloid or colloid, or a mixture of both, is poured into the dialyser, which is then placed in a vessel containing water, so that the bottom of the membrane is covered with water. Then, after a certain period of time, the crystalloid passes through the membrane, whilst the colloid, if it does pass through at all, does so at an incomparably slower rate. The crystalloid naturally passes through into the water until the solution attains the same strength on both sides of the membrane. By replacing the outside water with fresh water, a fresh quantity of the crystalloid may be separated from the dialyser. While a crystalloid is passing through the membrane, a colloid remains almost entirely in the dialyser, and therefore a mixed solution of these two kinds of substances may be separated from each other by a dialyser. The study of the properties of colloids, and of the phenomena of their passage through membranes, should elucidate much respecting the phenomena which are accomplished in organisms.
[19] The formation of solutions may be considered in two aspects, from a physical and from a chemical point of view, and it is more evident in solutions than in any other department of chemistry how closely these provinces of natural science are allied together. On the one hand solutions form a particular case of a physico-mechanical interpenetration of homogeneous substances, and a juxtaposition of the molecules of the substance dissolved and of the solvent, similar to the juxtaposition which is exhibited in homogeneous substances. From this point of view this diffusion of solutions is exactly similar to the diffusion of gases, with only this difference, that the nature and store of energy are different in gases from what they are in liquids, and that in liquids there is considerable friction, whilst in gases there is comparatively little. The penetration of a dissolved substance into water is likened to evaporation, and solution to the formation of vapour. This resemblance was clearly expressed even by Graham. In recent years the Dutch chemist, Van't Hoff, has developed this view of solutions in great detail, having shown (in a memoir in the Transactions of the Swedish Academy of Science, Part 21, No. 17, ‘Lois de l'équilibre chimique dans l'état dilué, gazeux ou dissous,’ 1886), that for dilute solutions the osmotic pressure follows the same laws of Boyle, Mariotte, Gay-Lussac, and Avogadro-Gerhardt as for gases. The osmotic pressure of a substance dissolved in water is determined by means of membranes which allow the passage of water, but not of a substance dissolved in it, through them. This property is found in animal protoplasmic membranes and in porous substances covered with an amorphous precipitate, such as is obtained by the action of copper sulphate on potassium ferrocyanide (Pfeffer, Traube). If, for instance, a one p.c. solution of sugar he placed in such a vessel, which is then closed and placed in water, the water passes through the walls of the vessel and increases the pressure by 50 mm. of the barometric column. If the pressure be artificially increased inside the vessel, then the water will be expelled through the walls. De Vries found a convenient means of determining isotonic solutions (those presenting a similar osmotic pressure) in the cells of plants. For this purpose a portion of the soft part of the leaves of the Tradescantis discolor, for instance, is cut away and moistened with the solution of a given salt and of a given strength. If the osmotic pressure of the solution taken be less than that of the sap contained in the cells they will change their form or shrink; if, on the other hand, the osmotic pressure be greater than that of the sap, then the cells will expand, as can easily be seen under the microscope. By altering the amount of the different salts in solution it is possible to find for each salt the strength of solution at which the cells begin to swell, and at which they will consequently have an equal osmotic pressure. As it increases in proportion to the amount of a substance dissolved per 100 parts of water, it is possible, knowing the osmotic pressure of a given substance—for instance, sugar at various degrees of concentration of solution—and knowing the composition of isotonic solutions compared with sugar, to determine the osmotic pressure of all the salts investigated. The osmotic pressure of dilute solutions determined in this manner directly or indirectly (from observations made by Pfeffer and De Vries) was shown to follow the same laws as those of the pressure of gases; for instance, by doubling or increasing the quantity of a salt (in a given volume) n times, the pressure is doubled or increases n times. So, for example, in a solution containing one part of sugar per 100 parts of water the osmotic pressure (according to Pfeffer) = 58·5 cm. of mercury, if 2 parts of sugar = 101·6, if 4 parts = 208·2 and so on, which proves that the ratio is true within the limits of experimental error. (2) Different substances for equal strengths of solutions, show very different osmotic pressures, just as gases for equal parts by weight in equal volumes show different tensions. (3) If, for a given dilute solution at 0°, the osmotic pressure equal p°, then at t° it will be greater and equal to p°(1 + 0·00367t), i.e. it increases with the temperature in exactly the same manner as the tension of gases increases. (4) If in dilute solutions of such substances as do not conduct an electric current (for instance, sugar, acetone, and many other organic bodies) the substances be taken in the ratio of their molecular weights (expressed by their formulæ, see Chapter [VII].), then not only will the osmotic pressure be equal, but its magnitude will be determined by that tension which would be proper to the vapours of the given substances when they would be contained in the space occupied by the solution, just as the tension of the vapours of molecular quantities of the given substances will be equal, and determined by the laws of Gay-Lussac, Mariotte, and Avogadro-Gerhardt. Those formulæ (Chapter VII., Notes [23] and [24]) by which the gaseous state of matter is determined, may also be applied in the present case. So, for example, the osmotic pressure p, in centimetres of mercury, of a one per cent. solution of sugar, may be calculated according to the formula for gases:
Mp = 6200s(273 + t),
where M is the molecular weight, s the weight in grams of a cubic centimetre of vapour, and t its temperature. For sugar M = 342 (because its molecular composition is C12H22O11). The specific gravity of the solution of sugar is 1·003, hence the weight of sugar s contained in a 1 per cent. solution = 0·01003 gram. The observation was made at t = 14°. Hence, according to the formula, we find p = 52·2 centimetres. And experiments carried on at 14° gave 53·5 centimetres, which is very near to the above. (5) For the solutions of salts, acids, and similar substances, which conduct an electric current, the calculated pressure is usually (but not always in a definite or multiple number of times) less than the observed by i times, and this i for dilute solutions of MgSO4 is nearly 1, for CO2 = 1, for KCl, NaCl, KI, KNO3 greater than 1, and approximates to 2, for BaCl2, MgCl2, K2CO3, and others between 2 and 3, for HCl, H2SO4, NaNO3, CaN2O6, and others nearly 2 and so on. It should be remarked that the above deductions are only applicable (and with a certain degree of accuracy) to dilute solutions, and in this respect resemble the generalisations of Michel and Kraft (see Note [44]). Nevertheless, the arithmetical relation found by Van't Hoff between the formation of vapours and the transition into dilute solutions forms an important scientific discovery, which should facilitate the explanation of the nature of solutions, while the osmotic pressure of solutions already forms a very important aspect of the study of solutions. In this respect it is necessary to mention that Prof. Konovaloff (1891, and subsequently others also) discovered the dependence (and it may be a sufficient explanation) of the osmotic pressure upon the differences of the tensions of aqueous vapours and aqueous solutions; this, however, already enters into a special province of physical chemistry (certain data are given in Note [49] and following), and to this physical side of the question also belongs one of the extreme consequences of the resemblance of osmotic pressure to gaseous pressure, which is that the concentration of a uniform solution varies in parts which are heated or cooled. Soret (1881) indeed observed that a solution of copper sulphate containing 17 parts of the salt at 20° only contained 14 parts after heating the upper portion of the tube to 80° for a long period of time. This aspect of solution, which is now being very carefully and fully worked out, may be called the physical side. Its other aspect is purely chemical, for solution does not take place between any two substances, but requires a special and particular attraction or affinity between them. A vapour or gas permeates any other vapour or gas, but a salt which dissolves in water may not be in the least soluble in alcohol, and is quite insoluble in mercury. In considering solutions as a manifestation of chemical force (and of chemical energy), it must be acknowledged that they are here developed to so feeble an extent that the definite compounds (that is, those formed according to the law of multiple proportions) formed between water and a soluble substance dissociate even at the ordinary temperature, forming a homogeneous system—that is, one in which both the compound and the products into which it decomposes (water and the aqueous compound) occur in a liquid state. The chief difficulty in the comprehension of solutions depends on the fact that the mechanical theory of the structure of liquids has not yet been so fully developed as the theory of gases, and solutions are liquids. The conception of solutions as liquid dissociated definite chemical compounds is based on the following considerations: (1) that there exist certain undoubtedly definite chemical crystallised compounds (such as H2SO4,H2O; or NaCl,2H2O; or CaCl2,6H2O; &c.) which melt on a certain rise of temperature, and then form true solutions; (2) that metallic alloys in a molten condition are real solutions, but on cooling they often give entirely distinct and definite crystallised compounds, which are recognised by the properties of alloys; (3) that between the solvent and the substance dissolved there are formed, in a number of cases, many undoubtedly definite compounds, such as compounds with water of crystallisation; (4) that the physical properties of solutions, and especially their specific gravities (a property which can be very accurately determined), vary with a change in composition, and in such a manner as would be required by the formation of one or more definite but dissociating compounds. Thus, for example, on adding water to fuming sulphuric acid its density is observed to decrease until it attains the definite composition H2SO4, or SO3 + H2O, when the specific gravity increases, although on further diluting with water it again falls. Moreover (Mendeléeff, The Investigation of Aqueous Solutions from their Specific Gravities, 1887), the increase in specific gravity (ds), varies in all well-known solutions with the proportion of the substance dissolved (dp), and this dependence can be expressed by a formula ( ds / dp = A + Bp) between the limits of definite compounds whose existence in solutions must be admitted, and this is in complete accordance with the dissociation hypothesis. Thus, for instance, from H2SO4 to H2SO4 + H2O (both these substances exist as definite compounds in a free state), the fraction ds / dp = 0·0729 - 0·000749p (where p is the percentage amount of H2SO4). For alcohol C2H6O, whose aqueous solutions have been more accurately investigated than all others, the definite compound C2H6O + 3H2O, and others must be acknowledged in its solutions.
The two aspects of solution above mentioned, and the hypotheses which have as yet been applied to the examination of solutions, although they have somewhat different starting points, will doubtless in time lead to a general theory of solutions, because the same common laws govern both physical and chemical phenomena, inasmuch as the properties and motions of molecules, which determine physical properties, depend on the motions and properties of atoms, which determine chemical reactions. For details of the questions dealing with theories of solution, recourse must now be had to special memoirs and to works on theoretical (physical) chemistry; for this subject forms one of special interest at the present epoch of the development of our science. In working out chiefly the chemical side of solutions, I consider it to be necessary to reconcile the two aspects of the question; this seems to me to be all the more possible, as the physical side is limited to dilute solutions only, whilst the chemical side deals mainly with strong solutions.