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:

M_p_ = 6200_s_(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 C_{12}H_{22}O_{11}). 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 MgSO_{4} is nearly 1, for CO_{2} = 1, for KCl, NaCl, KI, KNO_{3} greater than 1, and approximates to 2, for BaCl_{2}, MgCl_{2}, K_{2}CO_{3}, and others between 2 and 3, for HCl, H_{2}SO_{4}, NaNO_{3}, CaN_{2}O_{6}, 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 H_{2}SO_{4},H_{2}O; or NaCl,2H_{2}O; or CaCl_{2},6H_{2}O; &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 H_{2}SO_{4}, or SO_{3} + H_{2}O, 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 + B_p_) 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 H_{2}SO_{4} to H_{2}SO_{4} + H_{2}O (both these substances exist as definite compounds in a free state), the fraction _ds_/_dp_ = 0·0729-0·000749_p_ (where _p_ is the percentage amount of H_{2}SO_{4}). For alcohol C_{2}H_{6}O, whose aqueous solutions have been more accurately investigated than all others, the definite compound C_{2}H_{6}O + 3H_{2}O, 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.

In the consideration of the process of solution, besides the conception of diffusion, another fundamental conception is necessary--namely, that of the _saturation of solutions_.

Just as moist air may be diluted with any desired quantity of dry air, so also an indefinitely large quantity of a liquid solvent may be taken, and yet a uniform solution will be obtained. But more than a definite quantity of aqueous vapour cannot be introduced into a certain volume of air at a certain temperature. The excess above the point of saturation will remain in the liquid state.[20] The relation between water and substances dissolved in it is similar. More than a definite quantity of a substance cannot, at a certain temperature, dissolve in a given quantity of water; the excess does not unite with the water. Just as air or a gas becomes saturated with vapour, so water becomes saturated with a substance dissolved in it. If an excess of a substance be added to water which is already saturated with it, it will remain in its original state, and will not diffuse through the water. The quantity of a substance (either by volume with gases, or by weight with solids and liquids) which is capable of saturating 100 parts of water is called the _co-efficient of solubility_ or the _solubility_. In 100 grams of water at 15°, there can be dissolved not more than 35·86 grams of common salt. Consequently, its solubility at 15° is equal to 35·86.[21] It is most important to turn attention to the _existence of the solid insoluble substances of nature_, because on them depends the shape of the substances of the earth's surface, and of plants and animals. There is so much water on the earth's surface, that were the surface of substances formed of soluble matters it would constantly change, and however substantial their forms might be, mountains, river banks and sea shores, plants and animals, or the habitations and coverings of men, could not exist for any length of time.[22]

[20] A system of (chemically or physically) re-acting substances in different states of aggregation--for instance, some solid, others liquid or gaseous--is termed a heterogeneous system. Up to now it is only systems of this kind which can be subjected to detailed examination in the sense of the mechanical theory of matter. Solutions (_i.e._ unsaturated ones) form fluid homogeneous systems, which at the present time can only be investigated with difficulty.

In the case of limited solution of liquids in liquids, _the difference between the solvent and the substance dissolved_ is clearly seen. The former (that is, the solvent) may be added in an unlimited quantity, and yet the solution obtained will always be uniform, whilst only a definite saturating proportion of the substance dissolved can be taken, We will take water and common (sulphuric) ether. On shaking the ether with the water, it will be remarked that a portion of it dissolves in the water. If the ether be taken in such a quantity that it saturates the water and a portion of it remains undissolved, then this remaining portion will act as a solvent, and water will diffuse through it and also form a saturated solution of water in the ether taken. Thus two saturated solutions will be obtained. One solution will contain ether dissolved in water, and the other solution will contain water dissolved in ether. These two solutions will arrange themselves in two layers, according to their density; the ethereal solution of water will be on the top. If the upper ethereal solution be poured off from the aqueous solution, any quantity of ether may be added to it; this shows that the dissolving substance is ether. If water be added to it, it is no longer dissolved in it; this shows that water saturates the ether--here water is the substance dissolved. If we act in the same manner with the lower layer, we shall find that water is the solvent and ether the substance dissolved. By taking different amounts of ether and water, the degree of solubility of ether in water, and of water in ether, may be easily determined. Water approximately dissolves 1/10 of its volume of ether, and ether dissolves a very small quantity of water. Let us now imagine that the liquid poured in dissolves a considerable amount of water, and that water dissolves a considerable amount of the liquid. Two layers could not be formed, because the saturated solutions would resemble each other, and therefore they would intermix in all proportions. This is, consequently, a case of a phenomenon where two liquids present considerable co-efficients of solubility in each other, but where it is impossible to say what these co-efficients are, because it is impossible to obtain a saturated solution.

[21] The solubility, or co-efficient of solubility, of a substance is determined by various methods. Either a solution is expressly prepared with a clear excess of the soluble substance and saturated at a given temperature, and the quantity of water and of the substance dissolved in it determined by evaporation, desiccation, or other means; or else, as is done with gases, definite quantities of water and of the soluble substance are taken and the amount remaining undissolved is determined.

[Illustration: FIG. 16.--Bunsen's absorptiometer. Apparatus for determining the solubility of gases in liquids.]

The solubility of a gas in water is determined by means of an apparatus called an _absorptiometer_ (fig. 16). It consists of an iron stand _f_, on which an india-rubber ring rests. A wide glass tube is placed on this ring, and is pressed down on it by the ring _h_ and the screws _i i_. The tube is thus firmly fixed on the stand. A cock _r_, communicating with a funnel _r_, passes into the lower part of the stand. Mercury can be poured into the wide tube through this funnel, which is therefore made of steel, as copper would be affected by the mercury. The upper ring _h_ is furnished with a cover _p_, which can be firmly pressed down on to the wide tube, and hermetically closes it by means of an india-rubber ring. The tube _r r_ can be raised at will, and so by pouring mercury into the funnel the height of the column of mercury, which produces pressure inside the apparatus, can be increased. The pressure can also be diminished at will, by letting mercury out through the cock _r_. A graduated tube _e_, containing the gas and liquid to be experimented on, is placed inside the wide tube. This tube is graduated in millimetres for determining the pressure, and it is calibrated for volume, so that the number of volumes occupied by the gas and liquid dissolving it can be easily calculated. This tube can also be easily removed from the apparatus. The lower portion of this tube when removed from the apparatus is shown to the right of the figure. It will be observed that its lower end is furnished with a male screw _b_, fitting in a nut _a_. The lower surface of the nut _a_ is covered with india-rubber, so that on screwing up the tube its lower end presses upon the india-rubber, and thus hermetically closes the whole tube, for its upper end is fused up. The nut _a_ is furnished with arms _c c_, and in the stand _f_ there are corresponding spaces, so that when the screwed-up internal tube is fixed into stand _f_, the arms _c c_ fix into these spaces cut in _f_. This enables the internal tube to be fixed on to the stand _f_. When the internal tube is fixed in the stand, the wide tube is put into its right position, and mercury and water are poured into the space between the two tubes, and communication is opened between the inside of the tube _e_ and the mercury between the interior and exterior tubes. This is done by either revolving the interior tube _e_, or by a key turning the nut about the bottom part of _f_. The tube _e_ is filled with gas and water as follows: the tube is removed from the apparatus, filled with mercury, and the gas to be experimented on is passed into it. The volume of the gas is measured, the temperature and pressure determined, and the volume it would occupy at 0° and 760 mm. calculated. A known volume of water is then introduced into the tube. The water must be previously boiled, so as to be quite freed from air in solution. The tube is then closed by screwing it down on to the india-rubber on the nut. It is then fixed on to the stand _f_, mercury and water are poured into the intervening space between it and the exterior tube, which is then screwed up and closed by the cover _p_, and the whole apparatus is left at rest for some time, so that the tube _e_, and the gas in it, may attain the same temperature as that of the surrounding water, which is marked by a thermometer _k_ tied to the tube _e_. The interior tube is then again closed by turning it in the nut, the cover _p_ again shut, and the whole apparatus is shaken in order that the gas in the tube _e_ may entirely saturate the water. After several shakings, the tube _e_ is again opened by turning it in the nut, and the apparatus is left at rest for a certain time; it is then closed and again shaken, and so on until the volume of gas does not diminish after a fresh shaking--that is, until saturation ensues. Observations are then made of the temperature, the height of the mercury in the interior tube, and the level of the water in it, and also of the level of the mercury and water in the exterior tube. All these data are necessary in order to calculate the pressure under which the solution of the gas takes place, and what volume of gas remains undissolved, and also the quantity of water which serves as the solvent. By varying the temperature of the surrounding water, the amount of gas dissolved at various temperatures may be determined. Bunsen, Carius, and many others determined the solution of various gases in water, alcohol, and certain other liquids, by means of this apparatus. If in a determination of this kind it is found that _n_ cubic centimetres of water at a pressure _h_ dissolve _m_ cubic centimetres of a given gas, measured at 0° and 760 mm., when the temperature under which solution took place was _t_°, then it follows that at the temperature _t the co-efficient of solubility of the gas_ in 1 volume of the liquid will be equal to _m_/_n_ × 760/_h_.

This formula is very clearly understood from the fact that the co-efficient of solubility of gases is that quantity measured at 0° and 760 mm., which is absorbed at a pressure of 760 mm. by one volume of a liquid. If _n_ cubic centimetres of water absorb _m_ cubic centimetres of a gas, then one cubic centimetre absorbs _m_/_n_. If _m_/_n_ c.c. of a gas are absorbed under a pressure of _h_ mm., then, according to the law of the variation of solubility of a gas with the pressure, there would he dissolved, under a pressure of 760 mm., a quantity varying in the same ratio to _m_/_n_ as 760 : _h_. In determining the residual volume of gas its moisture (note 1) must be taken into consideration.

Below are given the number of grams of several substances saturating 100 grams of water--that is, their co-efficients of solubility by weight at three different temperatures:--

+----------------------------------------------+--------+---------+ | | | | | At 0° | At 20° | At 100° | +----------------------------------------------+--------+---------+ | {Oxygen, O_{2} 6/1000 | 4/1000 | -- | |Gases {Carbonic anhydride, CO_{2} 35/100 | 18/100 | -- | | {Ammonia, NH_{3} 90·0 | 51·8 | 7·3 | | {Phenol, C_{6}H_{6}O 4·9 | 5·2 | [oo] | |Liquids {Amyl alcohol, C_{5}H_{12}O 4·4 | 2·9 | -- | | {Sulphuric acid, H_{2}SO_{4} [oo] | [oo] | [oo] | | {Gypsum, CaSO_{4},2H_{2}O 1/5 | 1/4 | 1/5 | | {Alum, AlKS_{2}O_{8},12H_{2}O 3·3 | 15·4 | 357·5 | |Solids {Anhydrous sodium sulphate, 4·5 | 20 | 43 | | { Na_{2}SO_{4} | | | | {Common Salt, NaCl 35·7 | 36·0 | 39·7 | | {Nitre, KNO_{3} 13·3 | 31·7 | 246·0 | +----------------------------------------------+--------+---------+

Sometimes a substance is so slightly soluble that it may be considered as insoluble. Many such substances are met with both in solids and liquids, and such a gas as oxygen, although it does dissolve, does so in so small a proportion by weight that it might be considered as zero did not the solubility of even so little oxygen play an important part in nature (as in the respiration of fishes) and were not an infinitesimal quantity of a gas by weight so easily measured by volume. The sign [oo], which stands on a line with sulphuric acid in the above table, indicates that it intermixes with water in all proportions. There are many such cases among liquids, and everybody knows, for instance, that spirit (absolute alcohol) can be mixed in any proportion with water.

[22] Just as the existence must he admitted of substances which are completely undecomposable (chemically) at the ordinary temperature--and of substances which are entirely non-volatile at such a temperature (as wood and gold), although capable of decomposing (wood) or volatilising (gold) at a higher temperature--so also the existence must be admitted of substances which are totally insoluble in water without some degree of change in their state. Although mercury is partially volatile at the ordinary temperature, there is no reason to think that it and other metals are soluble in water, alcohol, or other similar liquids. However, mercury forms solutions, as it dissolves other metals. On the other hand, there are many substances found in nature which are so very slightly soluble in water, that in ordinary practice they may be considered as insoluble (for example, barium sulphate). For the comprehension of that general plan according to which a change of state of substances (combined or dissolved, solid, liquid, or gaseous) takes place, it is very important to make a distinction at this boundary line (on approaching zero of decomposition, volatility, or solubility) between an insignificant amount and zero, but the present methods of research and the data at our disposal at the present time only just touch such questions (by studying the electrical conductivity of dilute solutions and the development of micro-organisms in them). It must be remarked, besides, that water in a number of cases does not dissolve a substance as such, but acts on it chemically and forms a soluble substance. Thus glass and many rocks, especially if taken as powder, are chemically changed by water, but are not directly soluble in it.

Substances which are easily soluble in water bear a certain resemblance to it. Thus sugar and salt in many of their superficial features remind one of ice. Metals, which are not soluble in water, have no points in common with it, whilst on the other hand they dissolve each other in a molten state, forming alloys, just as oily substances dissolve each other; for example, tallow is soluble in petroleum and in olive oil, although they are all insoluble in water. From this it is evident that the _analogy of substances forming a solution_ plays an important part, and as aqueous and all other solutions are liquids, there is good reason to believe that in the process of solution solid and gaseous substances change in a physical sense, passing into a liquid state. These considerations elucidate many points of solution--as, for instance, the variation of the co-efficient of solubility with the temperature and the evolution or absorption of heat in the formation of solutions.

The solubility--that is, the quantity of a substance necessary for saturation--_varies with the temperature_, and, further, with an increase in temperature the solubility of solid substances generally increases, and that of gases decreases; this might be expected, as solid substances by heating, and gases by cooling, approach to a liquid or dissolved state.[23] A graphic method is often employed to express the variation of solubility with temperature. On the axis of abscissæ or on a horizontal line, temperatures are marked out and perpendiculars are raised corresponding with each temperature, whose length is determined by the solubility of the salt at that temperature--expressing, for instance, one part by weight of a salt in 100 parts of water by one unit of length, such as a millimetre. By joining the summits of the perpendiculars, a curve is obtained which expresses the degree of solubility at different temperatures. For solids, the curve is generally an ascending one--_i.e._ recedes from the horizontal line with the rise in temperature. These curves clearly show by their inclination the degree of rapidity of increase in solubility with the temperature. Having determined several points of a curve--that is, having made a determination of the solubility for several temperatures--the solubility at intermediary temperatures may be determined from the form of the curve so obtained; in this way the empirical law of solubility may be examined.[24] The results of research have shown that the solubility of certain salts--as, for example, common table salt--varies comparatively little with the temperature; whilst for other substances the solubility increases by equal amounts for equal increments of temperature. Thus, for example, for the saturation of 100 parts of water by potassium chloride there is required at 0°, 29·2 parts, at 20°, 34·7, at 40°, 40·2, at 60°, 45·7; and so on, for every 10° the solubility increases by 2·75 parts by weight of the salt. Therefore the solubility of the potassium chloride in water may be expressed by a direct equation: _a_ = 29·2 + 0·275_t_, where _a_ represents the solubility at _t_°. For other salts, more complicated equations are required. For example, for nitre: _a_ = 13·3 + 0·574_t_ + 0·01717_t_^2 + 0·0000036_t_^3, which shows that when _t_ = 0° _a_ = 13·3, when _t_ = 10° _a_ = 20·8, and when _t_ = 100° _a_ = 246·0.

[23] Beilby (1883) experimented on paraffin, and found that one litre of solid paraffin at 21° weighed 874 grams, and when liquid, at its melting-point 38°, 783 grams, at 49°, 775 grams, and at 60°, 767 grams, from which the weight of a litre of liquefied paraffin would be 795·4 grams at 21° if it could remain liquid at that temperature. By dissolving solid paraffin in lubricating oil at 21° Beilby found that 795·6 grams occupy one cubic decimetre, from which he concluded that the solution contained liquefied paraffin.

[24] Gay-Lussac was the first to have recourse to such a graphic method of expressing solubility, and he considered, in accordance with the general opinion, that by joining up the summits of the ordinates in one harmonious curve it is possible to express the entire change of solubility with the temperature. Now, there are many reasons for doubting the accuracy of such an admission, for there are undoubtedly critical points in curves of solubility (for example, of sodium sulphate, as shown further on), and it may be that definite compounds of dissolved substances with water, in decomposing within known limits of temperature, give critical points more often than would be imagined; it may even be, indeed, that instead of a continuous curve, solubility should be expressed--if not always, then not unfrequently--by straight or broken lines. According to Ditte, the solubility of sodium nitrate, NaNO_{3}, is expressed by the following figures per 100 parts of water:--

0° 4° 10° 15° 21° 29° 36° 51° 68° 66·7 71·0 76·3 80·6 85·7 92·9 99·4 113·6 125·1

In my opinion (1881) these data should be expressed with exactitude by a straight line, 67·5 + 0·87_t_, which entirely agrees with the results of experiment. According to this the figure expressing the solubility of salt at 0° exactly coincides with the composition of a definite chemical compound--NaNO_{3},7H_{2}O. The experiments made by Ditte showed that all saturated solutions between 0° and -15·7° have such a composition, and that at the latter temperature the solution completely solidifies into one homogeneous whole. Between 0° and -15·7° the solution NaNO_{3},7H_{2}O does not deposit either salt or ice. Thus the solubility of sodium nitrate is expressed by a broken straight line. In recent times (1888) Étard discovered a similar phenomenon in many of the sulphates. Brandes, in 1830, shows a diminution in solubility below 100° for manganese sulphate. The percentage by weight (_i.e._ per 100 parts of the solution, and not of water) of saturation for ferrous sulphate, FeSO_{4}, from -2° to +65° = 13·5 + 0·3784_t_--that is, the solubility of the salt increases. The solubility remains constant from 65° to 98° (according to Brandes the solubility then increases; this divergence of opinion requires proof), and from 98° to 150° it falls as = 104·35 - 0·6685_t_. Hence, at about +156° the solubility should = 0, and this has been confirmed by experiment. I observe, on my part, that Étard's formula gives 38·1 p.c. of salt at 65° and 38·8 p.c. at 92°, and this maximum amount of salt in the solution very nearly corresponds with the composition FeSO_{4},14H_{2}O, which requires 37·6 p.c. From what has been said, it is evident that the data concerning solubility require a new method of investigation, which should have in view the entire scale of solubility--from the formation of completely solidified solutions (cryohydrates, which we shall speak of presently) to the separation of salts from their solutions, if this is accomplished at a higher temperature (for manganese and cadmium sulphates there is an entire separation, according to Étard), or to the formation of a constant solubility (for potassium sulphate the solubility, according to Étard, remains constant from 163° to 220° and equals 24·9 p.c.) (See