Chapter XIV

., note 50, solubility of CaCl_{2}.)

Curves of solubility give the means of estimating the _amount of salt separated_ by the cooling to a known extent of a solution saturated at a given temperature. For instance, if 200 parts of a solution of potassium chloride in water saturated at a temperature of 60° be taken, and it be asked how much of the salt will be separated by cooling the solution to 0°, if its solubility at 60° = 45·7 and at 0° = 29·2? The answer is obtained in the following manner: At 60° a saturated solution contains 45·7 parts of potassium chloride per 100 parts by weight of water, consequently 145·7 parts by weight of the solution contain 45·7 parts, or, by proportion, 200 parts by weight of the solution contain 62·7 parts of the salt. The amount of salt remaining in solution at 0° is calculated as follows; In 200 grams taken there will be 137·3 grams of water; consequently, this amount of water is capable of holding only 40·1 grams of the salt, and therefore in lowering the temperature from 60° to 0° there should separate from the solution 62·7-40·1 = 22·6 grams of the dissolved salt.

The difference in the solubility of salts, &c., with a rise or fall of temperature is often taken advantage of, especially in technical work, for the separation of salts, in intermixture from each other. Thus a mixture of potassium and sodium chlorides (this mixture is met with in nature at Stassfurt) is separated from a saturated solution by subjecting it alternately to boiling (evaporation) and cooling. The sodium chloride separates out in proportion to the amount of water expelled from the solution by boiling, and is removed, whilst the potassium chloride separates out on cooling, as the solubility of this salt rapidly decreases with a lowering in temperature. Nitre, sugar, and many other soluble substances are purified (refined) in a similar manner.

Although in the majority of cases the solubility of solids increases with the temperature, yet there are some solid substances whose solubilities decrease on heating. Glauber's salt, or sodium sulphate, forms a particularly instructive example of the case in question. If this salt be taken in an ignited state (deprived of its water of crystallisation), then its solubility in 100 parts of water varies with the temperature in the following manner: at 0°, 5 parts of the salt form a saturated solution; at 20°, 20 parts of the salt, at 33° more than 50 parts. The solubility, as will be seen, increases with the temperature, as is the case with nearly all salts; but starting from 33° it suddenly diminishes, and at a temperature of 40°, less than 50 parts of the salt dissolve, at 60° only 45 parts of the salt, and at 100° about 43 parts of the salt in 100 parts of water. This phenomenon may be traced to the following facts: Firstly, that this salt forms various compounds with water, as will be afterwards explained; secondly, that at 33° the compound Na_{2}SO_{4} + 10H_{2}O formed from the solution at lower temperatures, melts; and thirdly, that on evaporation at a temperature above 33° an anhydrous salt, Na_{2}SO_{4} separates out. It will be seen from this example how complicated such an apparently simple phenomenon as solution really is; and all data concerning solutions lead to the same conclusion. This complexity becomes evident in investigating the _heat of solution_. If solution consisted of a physical change only, then in the solution of gases there would be evolved--and in the solution of solids, there would be absorbed--just that amount of heat corresponding to the change of state; but in reality a large amount of heat is always evolved in solution, depending on the fact that in the process of solution chemical combination takes place accompanied by an evolution of heat. Seventeen grams of ammonia (this weight corresponds with its formula NH_{3}), in passing from a gaseous into a liquid state, evolve 4,400 units of heat (latent heat); that is, the quantity of heat necessary to raise the temperature of 4,400 grams of water 1°. The same quantity of ammonia, in dissolving in an excess of water, evolves twice as much heat--namely 8,800 units--showing that the combination with water is accompanied by the evolution of 4,400 units of heat. Further, the chief part of this heat is separated in dissolving in small quantities of water, so that 17 grams of ammonia, in dissolving in 18 grams of water (this weight corresponds with its composition H_{2}O), evolve 7,535 units of heat, and therefore the formation of the solution NH_{3} + H_{2}O evolves 3,135 units of heat beyond that due to the change of state. As in the solution of gases, the heat of liquefaction (of physical change of state) and of chemical combination with water are both positive (+), therefore in the _solution of gases_ in water a _heat effect_ is always observed. This phenomenon is different in the solution of solid substances, because their passage from a solid to a liquid state is accompanied by an absorption of heat (negative,-heat), whilst their chemical combination with water is accompanied by an evolution of heat (+ heat); consequently, their sum may either be a cooling effect, when the positive (chemical) portion of heat is less than the negative (physical), or it may be, on the contrary, a heating effect. This is actually the case. 124 grams of sodium thiosulphate (employed in photography) Na_{2}S_{2}O_{3},5H_{2}O in melting (at 48°) absorbs 9,700 units of heat, but in dissolving in a large quantity of water at the ordinary temperature it absorbs 5,700 units of heat, which shows the evolution of heat (about + 4,000 units), notwithstanding the cooling effect observed in the process of solution, in the act of the chemical combination of the salt with water.[25] But in most cases solid substances in dissolving in water evolve heat, notwithstanding the passage into a liquid state, which indicates so considerable an evolution of (+) heat in the act of combination with water that it exceeds the absorption of (-) heat dependent on the passage into a liquid state, Thus, for instance, calcium chloride, CaCl_{2}, magnesium sulphate, MgSO_{4}, and many other salts evolve heat in dissolving; for example, 60 grams of magnesium sulphate evolve about 10,000 units of heat. Therefore, _in the solution of solid bodies_ either a cooling[26] or a heating[27] effect is produced, according to the difference of the reacting affinities. When they are considerable--that is, when water is with difficulty separated from the resultant solution, and only with a rise of temperature (such substances absorb water vapour)--then much heat is evolved in the process of solution, just as in many reactions of direct combination, and therefore a considerable heating of the solution is observed. Of such a kind, for instance, is the solution of sulphuric acid (oil of vitriol H_{2}SO_{4}), and of caustic soda (NaHO), &c., in water.[28]

[25] The latent heat of fusion is determined at the temperature of fusion, whilst solution takes place at the ordinary temperature, and one must think that at this temperature the latent heat would be different, just as the latent heat of evaporation varies with the temperature (see Note 11). Besides which, in dissolving, disintegration of the particles of both the solvent and the substance dissolved takes place, a process which in its mechanical aspect resembles evaporation, and therefore must consume much heat. The heat emitted in the solution of a solid must therefore be considered (Personne) as composed of three factors--(1) positive, the effect of combination; (2) negative, the effect of transference into a liquid state; and (3) negative, the effect of disintegration. In the solution of a liquid by a liquid the second factor is removed; and therefore, if the heat evolved in combination is greater than that absorbed in disintegration a heating effect is observed, and in the reverse case a cooling effect; and, indeed, sulphuric acid, alcohol, and many liquids evolve heat in dissolving in each other. But the solution of chloroform in carbon bisulphide (Bussy and Binget), or of phenol (or aniline) in water (Alexéeff), produces cold. In the solution of a small quantity of water in acetic acid (Abasheff), or hydrocyanic acid (Bussy and Binget), or amyl alcohol (Alexéeff), cold is produced, whilst in the solution of these substances in an excess of water heat is evolved.

The relation existing between the solubility of solid bodies and the heat and temperature of fusion and solution has been studied by many investigators, and more recently (1893) by Schröder, who states that in the solution of a solid body in a solvent which does not act chemically upon it, a very simple process takes place, which differs but little from the intermixture of two gases which do not react chemically upon each other. The following relation between the heat of solution _Q_ and the heat of fusion _p_ may then be taken: _P_/_T__{0} = _Q_/_T_ = constant, where _T__{0} and _T_ are the absolute (from -273°) temperatures of fusion and saturation. Thus, for instance, in the case of naphthalene the calculated and observed magnitudes of the heat of solution differ but slightly from each other.

The fullest information concerning the solution of liquids in liquids has been gathered by W. T. Alexéeff (1883-1885); these data are, however, far from being sufficient to solve the mass of problems respecting this subject. He showed that two liquids which dissolve in each other, intermix together in all proportions at a certain temperature. Thus the solubility of phenol, C_{6}H_{6}O, in water, and the converse, is limited up to 70°, whilst above this temperature they intermix in all proportions. This is seen from the following figures, where p is the percentage amount of phenol and _t_ the temperature at which the solution becomes turbid--that is, that at which it is saturated:--

_p_ = 7·12 10·20 15·31 26·15 28·55 36·70 48·86 61·15 71·97 _t_ = 1° 45° 60° 67° 67° 67° 65° 53° 20°

It is exactly the same with the solution of benzene, aniline, and other substances in molten sulphur. Alexéeff discovered a similar complete intermixture for solutions of secondary butyl alcohol in water at about 107°; at lower temperatures the solubility is not only limited, but between 50° and 70° it is at its minimum, both for solutions of the alcohol in water and for water in the alcohol; and at a temperature of 5° both solutions exhibit a fresh change in their scale of solubility, so that a solution of the alcohol in water which is saturated between 5° and 40° will become turbid when heated to 60°. In the solution of liquids in liquids, Alexéeff observed a lowering in temperature (an absorption of heat) and an absence of change in specific heat (calculated for the mixture) much more frequently than had been done by previous observers. As regards his hypothesis (in the sense of a mechanical and not a chemical representation of solutions) that substances in solution preserve their physical states (as gases, liquids, or solids), it is very doubtful, for it would necessitate admitting the presence of ice in water or its vapour.

From what has been said above, it will be clear that even in so very simple a case as solution, it is impossible to calculate the heat emitted by chemical action alone, and that the chemical process cannot be separated from the physical and mechanical.

[26] The cooling effect produced in the solution of solids (and also in the expansion of gases and in evaporation) is applied to the _production of low temperatures_. Ammonium nitrate is very often used for this purpose; in dissolving in water it absorbs 77 units of heat per each part by weight. On evaporating the solution thus formed, the solid salt is re-obtained. The application of the various _freezing mixtures_ is based on the same principle. Snow or broken ice frequently enters into the composition of these _mixtures_, advantage being taken of its latent heat of fusion in order to obtain the lowest possible temperature (without altering the pressure or employing heat, as in other methods of obtaining a low temperature). For laboratory work recourse is most often had to a mixture of three parts of snow and one part of common salt, which causes the temperature to fall from 0° to -21° C. Potassium thiocyanate, KCNS, mixed with water (3/4 by weight of the salt) gives a still lower temperature. By mixing ten parts of crystallised calcium chloride, CaCl_{2},6H_{2}O, with seven parts of snow, the temperature may even fall from 0° to -55°.

[27] The heat which is evolved in solution, or even in the dilution of solutions, is also sometimes made use of in practice. Thus caustic soda (NaHO), in dissolving or on the addition of water to a strong solution of it, evolves so much heat that it can replace fuel. In a steam boiler, which has been previously heated to the boiling point, another boiler is placed containing caustic soda, and the exhaust steam is made to pass through the latter; the formation of steam then goes on for a somewhat long period of time without any other heating. Norton makes use of this for smokeless street locomotives.

[28] [Illustration: FIG. 17.--Curves expressing the contraction, quantity of heat, and rises of temperature produced by mixing sulphuric acid with water. Percentage of H_{2}SO_{4} is given along the axis of abscissae.]

The temperatures obtained by mixing monohydrated sulphuric acid, H_{2}SO_{4}, with different quantities of water, are shown on the lowest curve in fig. 17, the relative proportions of both substances being expressed in percentages by weight along the horizontal axis. The greatest rise of temperature is 149°. It corresponds with the greatest evolution of heat (given on the middle curve) corresponding with a definite volume (100 c.c.) of the solution produced. The top curve expresses the degree of contraction, which also corresponds with 100 volumes of the solution produced. The greatest contraction, as also the greatest rise of temperature, corresponds with the formation of a trihydrate, H_{2}SO_{4},2H_{2}O (= 73·1 p.c. H_{2}SO_{4}), which very likely repeats itself in a similar form in other solutions, although all the phenomena (of contraction, evolution of heat, and rise of temperature) are very complex and are dependent on many circumstances. One would think, however, judging from the above examples, that all other influences are feebler in their action than chemical attraction, especially when it is so considerable as between sulphuric acid and water.

Solution is a reversible reaction; for, if the water be expelled from a solution, the substance originally taken is obtained again. But it must be borne in mind that the expulsion of the water taken for solution is not always accomplished with equal facility, because water has different degrees of chemical affinity for the substance dissolved. Thus, if a solution of sulphuric acid, which mixes with water in all proportions, be heated, it will be found that very different degrees of heat are required to expel the water. When it is in a large excess, water is given off at a temperature slightly above 100°, but if it be in but a small proportion there is such an affinity between it and the sulphuric acid that at 120°, 150°, 200°, and even at 300°, water is still retained by the sulphuric acid. The bond between the remaining quantity of water and the sulphuric acid is evidently stronger than the bond between the sulphuric acid and the excess of water. The force acting in solutions is consequently of different intensity, starting from so feeble an attraction that the properties of water--as, for instance, its power of evaporation--are but very little changed, and ending with cases of strong attraction between the water and the substance dissolved in or chemically combined with it. In consideration of the very important significance of the phenomena, and of the cases of the breaking up of solutions with separation of water or of the substance dissolved from them, we shall further discuss them separately, after having acquainted ourselves with certain peculiarities of the solution of gases and of solid bodies.

The solubility of gases, which is usually measured by the volume of gas[29] (at 0° and 760 mm. pressure) per 100 volumes of water, varies not only with the nature of the gas (and also of the solvent), and with the temperature, but also with the pressure, because gases themselves change their volume considerably with the pressure. As might be expected, (1) gases which are easily liquefied (by pressure and cold) are more soluble than those which are liquefied with difficulty. Thus, in 100 volumes of water only two volumes of hydrogen dissolve at 0° and 760 mm., three volumes of carbonic oxide, four volumes of oxygen, &c., for these are gases which are liquefied with difficulty; whilst there dissolve 180 volumes of carbonic anhydride, 130 of nitrous oxide, and 437 of sulphurous anhydride, for these are gases which are rather easily liquefied. (2) The solubility of a gas is diminished by heating, which is easily intelligible from what has been said previously--the elasticity of a gas becomes greater, it is removed further from a liquid state. Thus 100 volumes of water at 0° dissolve 2·5 volumes of air, and at 20° only 1·7 volume. For this reason cold water, when brought into a warm room, parts with a portion of the gas dissolved in it.[30] (3) The quantity of the gas dissolved varies directly with the pressure. This rule is called the _law of Henry and Dalton_, and is applicable to those gases which are little soluble in water. Therefore a gas is separated from its solution in water in a vacuum, and water saturated with a gas under great pressure parts with it if the pressure be diminished. Thus many mineral springs are saturated underground with carbonic anhydride under the great pressure of the column of water above them. On coming to the surface, the water of these springs boils and foams on giving up the excess of dissolved gas. Sparkling wines and aërated waters are saturated under pressure with the same gas. They hold the gas so long as they are in a well-corked vessel. When the cork is removed and the liquid comes in contact with air at a lower pressure, part of the gas, unable to remain in solution at a lower pressure, is separated as froth with the hissing sound familiar to all. It must be remarked that the law of Henry and Dalton belongs to the class of _approximate laws_, like the laws of gases (Gay-Lussac's and Mariotte's) and many others--that is, it expresses only a portion of a complex phenomenon, the limit towards which the phenomenon aims. The matter is rendered complicated from the influence of the degree of solubility and of affinity of the dissolved gas for water. Gases which are little soluble--for instance, hydrogen, oxygen, and nitrogen--follow the law of Henry and Dalton the most closely. Carbonic anhydride exhibits a decided deviation from the law, as is seen from the determinations of Wroblewski (1882). He showed that at 0° a cubic centimetre of water absorbs 1·8 cubic centimetre of the gas under a pressure of one atmosphere; under 10 atmospheres, 16 cubic centimetres (and not 18, as it should be according to the law); under 20 atmospheres, 26·6 cubic centimetres (instead of 36), and under 30 atmospheres, 33·7 cubic centimetres.[31] However, as the researches of Sechenoff show, the absorption of carbonic anhydride within certain limits of change of pressure, and at the ordinary temperature, by water--and even by solutions of salts which are not chemically changed by it, or do not form compounds with it--very closely follows the law of Henry and Dalton, so that the chemical bond between this gas and water is so feeble that the breaking up of the solution with separation of the gas is accomplished by a decrease of pressure alone.[32] The case is different if a considerable affinity exists between the dissolved gas and water. Then it might even be expected that the gas would not be entirely separated from water in a vacuum, as should be the case with gases according to the law of Henry and Dalton. Such gases--and, in general, all those which are very soluble--exhibit a distinct deviation from the law of Henry and Dalton. As examples, ammonia and hydrochloric acid gas may be taken. The former is separated by boiling and decrease of pressure, while the latter is not, but they both deviate distinctly from the law.

+---------------+-----------------+--------------------+ |Pressure in mm.|Ammonia dissolved| Hydrochloric acid | | of mercury | in 100 grams of |gas dissolved in 100| | | water at 0° |grams of water at 0°| +---------------+-----------------+--------------------+ | | Grams | Grams | | 100 | 28·0 | 65·7 | | 500 | 69·2 | 78·2 | | 1,000 | 112·6 | 85·6 | | 1,500 | 165·6 | -- | +---------------+-----------------+--------------------+

[29] If a volume of gas _v_ be measured under a pressure of _h_ mm. of mercury (at 0°) and at a temperature _t_° Centigrade, then, according to the combined laws of Boyle, Mariotte, and of Gay-Lussac, its volume at 0° and 760 mm. will equal the product of _v_ into 760 divided by the product of _h_ into 1 + _a__t_°, where _a_ is the co-efficient of expansion of gases, which is equal to 0·00367. The weight of the gas will be equal to its volume at 0° and 760 mm. multiplied by its density referred to air and by the weight of one volume of air at 0° and 760 mm. The weight of one litre of air under these conditions being = 1·293 gram. If the density of the gas be given in relation to hydrogen this must be divided by 14·4 to bring it in relation to air. If the gas be measured when saturated with aqueous vapour, then it must be reduced to the volume and weight of the gas when dry, according to the rules given in Note 1. If the pressure be determined by a column of mercury having a temperature _t_, then by dividing the height of the column by 1 + 0·00018_t_ the corresponding height at 0° is obtained. If the gas be enclosed in a tube in which a liquid stands above the level of the mercury, the height of the column of the liquid being = H and its density = D, then the gas will be under a pressure which is equal to the barometric pressure less HD/13·59, where 13·59 is the density of mercury. By these methods the _quantity of a gas_ is determined, and its observed volume reduced to normal conditions or to parts by weight. The physical data concerning vapours and gases must be continually kept in sight in dealing with and measuring gases. The student must become perfectly familiar with the calculations relating to gases.

[30] According to Bunsen, Winkler, Timofeeff, and others, 100 vols. of water under a pressure of one atmosphere absorb the following volumes of gas (measured at 0° and 760 mm.):--

1 2 3 4 5 6 7 8 9 10 11 0° 4·82 2·35 2·15 179·7 3·54 130·5 437·1 688·6 5·4 104960 7·38 20° 3·10 1·54 1·83 90·1 2·32 67·0 290·5 362·2 3·5 65400 4·71

1, oxygen; 2, nitrogen; 3, hydrogen; 4, carbonic anhydride; 5, carbonic oxide; 6, nitrous oxide; 7, hydrogen sulphide; 8, sulphurous anhydride; 9, marsh gas; 10, ammonia; 11, nitric oxide. The decrease of solubility with a rise of temperature varies for different gases; it is greater, the greater the molecular weight of the gas. It is shown by calculation that this decrease varies (Winkler) as the cube root of the molecular weight of the gas. This is seen from the following table:

+--------------+-------------+---------------+ | Decrease of | Cube root of| Ratio between | | solubility | molecular | decrease and | | per 20° in | weight. | cube root of | | per cent. | | mol. wt. | +--------------+-------------+---------------+ | H_{2} 15·32 | 1·259 | 12·17 | | N_{2} 34·33 | 3·037 | 11·30 | | CO 34·44 | 3·037 | 11·34 | | NO 36·24 | 3·107 | 11·66 | | O_{2} 36·55 | 3·175 | 11·51 | +--------------+-------------+---------------+

The decrease in the coefficient of absorption with the temperature must be connected with a change in the physical properties of the water. Winkler (1891) remarked a certain relation between the internal friction and the coefficient of absorption at various temperatures.

[31] These figures show that the co-efficient of solubility decreases with an increase of pressure, notwithstanding that the carbonic anhydride approaches a liquid state. As a matter of fact, liquefied carbonic anhydride does not intermix with water, and does not exhibit a rapid increase in solubility at its temperature of liquefaction. This indicates, in the first place, that solution does not consist in liquefaction, and in the second place that the solubility of a substance is determined by a peculiar attraction of water for the substance dissolving. Wroblewski even considered it possible to admit that a dissolved gas retains its properties as a gas. This he deduced from experiments, which showed that the rate of diffusion of gases in a solvent is, for gases of different densities, inversely proportional to the square roots of their densities, just as the velocities of gaseous molecules (see Note 34). Wroblewski showed the affinity of water, H_{2}O, for carbonic anhydride, CO_{2}, from the fact that on expanding moist compressed carbonic anhydride (compressed at 0° under a pressure of 10 atmospheres) he obtained (a fall in temperature takes place from the expansion) a very unstable definite crystalline compound, CO_{2} + 8H_{2}O.

[32] As, according to the researches of Roscoe and his collaborators, ammonia exhibits a considerable deviation at low temperatures from the law of Henry and Dalton, whilst at 100° the deviation is small, it would appear that the dissociating influence of temperature affects all gaseous solutions; that is, at high temperatures, the solutions of all gases will follow the law, and at lower temperatures there will in all cases be a deviation from it.

It will be remarked, for instance, from this table that whilst the pressure increased 10 times, the solubility of ammonia only increased 4-1/2 times.

A number of examples of such cases of the absorption of gases by liquids might be cited which do not in any way, even approximately, agree with the laws of solubility. Thus, for instance, carbonic anhydride is absorbed by a solution of caustic potash in water, and if sufficient caustic potash be present it is not separated from the solution by a decrease of pressure. This is a case of more intimate chemical combination. A correlation less completely studied, but similar and clearly chemical, appears in certain cases of the solution of gases in water, and we shall afterwards find an example of this in the solution of hydrogen iodide; but we will first stop to consider a remarkable application of the law of Henry and Dalton[33] in the case of the solution of a mixture of two gases, and this we must do all the more because the phenomena which there take place cannot be foreseen without a clear theoretical representation of the nature of gases.[34]

[33] The ratio between the pressure and the amount of gas dissolved was discovered by Henry in 1805, and Dalton in 1807 pointed out the adaptability of this law to cases of gaseous mixtures, introducing the conception of partial pressures which is absolutely necessary for a right comprehension of Dalton's law. The conception of partial pressures essentially enters into that of the diffusion of vapours in gases (footnote 1); for the pressure of damp air is equal to the sum of the pressures of dry air and of the aqueous vapour in it, and it is admitted as a corollary to Dalton's law that evaporation in dry air takes place as in a vacuum. It is, however, necessary to remark that the volume of a mixture of two gases (or vapours) is only approximately equal to the sum of the volumes of its constituents (the same, naturally, also refers to their pressures)--that is to say, in mixing gases a change of volume occurs, which, although small, is quite apparent when carefully measured. For instance, in 1888 Brown showed that on mixing various volumes of sulphurous anhydride (SO_{2}) with carbonic anhydride (at equal pressures of 760 mm. and equal temperatures) a decrease of pressure of 3·9 millimetres of mercury was observed. The possibility of a chemical action in similar mixtures is evident from the fact that equal volumes of sulphurous and carbonic anhydrides at -19° form, according to Pictet's researches in 1888, a liquid which may be regarded as an unstable chemical compound, or a solution similar to that given when sulphurous anhydride and water combine to an unstable chemical whole.

[34] The origin of the kinetic theory of gases now generally accepted, according to which they are animated by a rapid progressive motion, is very ancient (Bernouilli and others in the last century had already developed a similar representation), but it was only generally accepted after the mechanical theory of heat had been established, and after the work of Krönig (1855), and especially after its mathematical side had been worked out by Clausius and Maxwell. The pressure, elasticity, diffusion, and internal friction of gases, the laws of Boyle, Mariotte, and of Gay-Lussac and Avogadro-Gerhardt are not only explained (deduced) by the kinetic theory of gases, but also expressed with perfect exactitude; thus, for example, the magnitude of the internal friction of different gases was foretold with exactitude by Maxwell, by applying the theory of probabilities to the impact of gaseous particles. The kinetic theory of gases must therefore be considered as one of the most brilliant acquisitions of the latter half of the present century. The velocity of the progressive motion of the particles of a gas, one cubic centimetre of which weighs _d_ grams, is found, according to the theory, to be equal to the square root of the product of 3_pDq_ divided by _d_, where _p_ is the pressure under which _d_ is determined expressed in centimetres of the mercury column, _D_ the weight of a cubic centimetre of mercury in grams (_D_ = 13·59, _p_ = 76, consequently the normal pressure = 1,033 grams on a sq. cm.), and _g_ the acceleration of gravity in centimetres (_g_ = 980·5, at the sea level and long. 45° = 981·92 at St. Petersburg; in general it varies with the longitude and altitude of the locality). Therefore, at 0° the velocity of hydrogen is 1,843, and of oxygen 461, metres per second. This is the average velocity, and (according to Maxwell and others) it is probable that the velocities of individual particles are different; that is, they occur in, as it were, different conditions of temperature, which it is very important to take into consideration in investigating many phenomena proper to matter. It is evident from the above determination of the velocity of gases, that different gases at the same temperature and pressure have average velocities, which are inversely proportional to the square roots of their densities; this is also shown by direct experiment on the flow of gases through a fine orifice, or through a porous wall. This _dissimilar velocity of flow_ for different gases is frequently taken advantage of in chemical researches (see Chap. II. and also Chap. VII.) in order to separate two gases having different densities and velocities. The difference of the velocity of flow of gases also determines the phenomenon cited in the following footnote for demonstrating the existence of an internal motion in gases.

If for a certain mass of a gas which fully and exactly follows the laws of Mariotte and Gay-Lussac the temperature _t_ and the pressure _p_ be changed simultaneously, then the entire change would be expressed by the equation _pv_ = _C_(1 + _at_), or, what is the same, _pv_ = _RT_, where _T_ = _t_ + 273 and _C_ and _R_ are constants which vary not only with the units taken but with the nature of the gas and its mass. But as there are discrepancies from both the fundamental laws of gases (which will be discussed in the following chapter), and as, on the one hand, a certain attraction between the gaseous molecules must be admitted, while on the other hand the molecules of gases themselves must occupy a portion of a space, hence for ordinary gases, within any considerable variation of pressure and temperature, recourse should be had to Van der Waal's formula--

(_p_ + _a_/_v_^2)(_v_-_p_) = R(1 + _at_)

where _a_ is the true co-efficient of expansion of gases.

The formula of Van der Waals has an especially important significance in the case of the passage of a gas into a liquid state, because the fundamental properties of both gases and liquids are equally well expressed by it, although only in their general features.

The further development of the questions referring to the subjects here touched on, which are of especial interest for the theory of solutions, must be looked for in special memoirs and works on theoretical and physical chemistry. A small part of this subject will be partially considered in the footnotes of the following chapter.

_The law of partial pressures_ is as follows:--The solubility of gases in intermixture with each other does not depend on the influence of the total pressure acting on the mixture, but on the influence of that portion of the total pressure which is due to the volume of each given gas in the mixture. Thus, for instance, if oxygen and carbonic anhydride were mixed in equal volumes and exerted a pressure of 760 millimetres, then water would dissolve so much of each of these gases as would be dissolved if each separately exerted a pressure of half an atmosphere, and in this case, at 0° one cubic centimetre of water would dissolve 0·02 cubic centimetre of oxygen and 0·90 cubic centimetre of carbonic anhydride. If the pressure of a gaseous mixture equals _h_, and in _n_ volumes of the mixture there be _a_ volumes of a given gas, then its solution will proceed as though this gas were dissolved under a pressure (_h_ × _a_)/_n_. That portion of the pressure under influence of which the solution proceeds is termed the 'partial' pressure.

In order to clearly understand the cause of the law of partial pressures, an explanation must be given of the fundamental properties of gases. Gases are elastic and disperse in all directions. We are led from what we know of gases to the assumption that these fundamental properties of gases are due to a rapid progressive motion, in all directions, which is proper to their smallest particles (molecules).[35] These molecules in impinging against an obstacle produce a pressure. The greater the number of molecules impinging against an obstacle in a given time, the greater the pressure. The pressure of a separate gas or of a gaseous mixture depends on the sum of the pressures of all the molecules, on the number of blows in a unit of time on a unit of surface, and on the mass and velocity (or the _vis viva_) of the impinging molecules. The nature of the different molecules is of no account; the obstacle is acted on by a pressure due to the sum of their _vis viva_. But, in a chemical action such as the solution of gases, the nature of the impinging molecules plays, on the contrary, the most important part. In impinging against a liquid, a portion of the gas enters into the liquid itself, and is held by it so long as other gaseous molecules impinge against the liquid--exert a pressure on it. As regards the solubility of a given gas, for the number of blows it makes on the surface of a liquid, it is immaterial whether other molecules of gases impinge side by side with it or not. Hence, the solubility of a given gas will be proportional, not to the total pressure of a gaseous mixture, but to that portion of it which is due to the given gas separately. Moreover, the saturation of a liquid by a gas depends on the fact that the molecules of gases that have entered into a liquid do not remain at rest in it, although they enter in a harmonious kind of motion with the molecules of the liquid, and therefore they throw themselves off from the surface of the liquid (just like its vapour if the liquid be volatile). If in a unit of time an equal number of molecules penetrate into (leap into) a liquid and leave (or leap out of) a liquid, it is saturated. It is a case of mobile equilibrium, and not of rest. Therefore, if the pressure be diminished, the number of molecules departing from the liquid will exceed the number of molecules entering into the liquid, and a fresh state of mobile equilibrium only takes place under a fresh equality of the number of molecules departing from and entering into the liquid. In this manner the main features of the solution are explained, and furthermore of that special (chemical) attraction (penetration and harmonious motion) of a gas for a liquid, which determines both the measure of solubility and the degree of stability of the solution produced.

[35] Although the actual motion of gaseous molecules, which is accepted by the kinetic theory of gases, cannot be seen, yet its existence may be rendered evident by taking advantage of the difference in the velocities undoubtedly belonging to different gases which are of different densities under equal pressures. The molecules of a light gas must move more rapidly than the molecules of a heavier gas in order to produce the same pressure. Let us take, therefore, two gases--hydrogen and air; the former is 14·4 times lighter than the latter, and hence the molecules of hydrogen must move almost four times more quickly than air (more exactly 3·8, according to the formula given in the preceding footnote). Consequently, if a porous cylinder containing air is introduced into an atmosphere of hydrogen, then in a given time the volume of hydrogen which succeeds in entering the cylinder will be greater than the volume of air leaving the cylinder, and therefore the pressure inside the cylinder will rise until the gaseous mixture (of air and hydrogen) attains an equal density both inside and outside the cylinder. If now the experiment be reversed and air surround the cylinder, and hydrogen be inside the cylinder, then more gas will leave the cylinder than enters it, and hence the pressure inside the cylinder will be diminished. In these considerations we have replaced the idea of the number of molecules by the idea of volumes. We shall learn subsequently that equal volumes of different gases contain an equal number of molecules (the law of Avogadro-Gerhardt), and therefore instead of speaking of the number of molecules we can speak of the number of volumes. If the cylinder be partially immersed in water the rise and fall of the pressure can be observed directly, and the experiment consequently rendered self-evident.

The consequences of the law of partial pressures are exceedingly numerous and important. All liquids in nature are in contact with the atmosphere, which, as we shall afterwards see more fully, consists of an intermixture of gases, chiefly four in number--oxygen, nitrogen, carbonic anhydride, and aqueous vapour. 100 volumes of air contain, approximately, 78 volumes of nitrogen, and about 21 volumes of oxygen; the quantity of carbonic anhydride, by volume, does not exceed 0·05. Under ordinary circumstances, the quantity of aqueous vapour is much greater than this, but it varies of course with climatic conditions. We conclude from these numbers that the solution of nitrogen in a liquid in contact with the atmosphere will proceed under a partial pressure of (78/100) × 760 mm. if the atmospheric pressure equal 760 mm.; similarly, under a pressure of 600 mm. of mercury, the solution of oxygen will proceed under a partial pressure of about 160 mm., and the solution of carbonic anhydride only under the very small pressure of 0·4 mm. As, however, the solubility of oxygen in water is twice that of nitrogen, the ratio of O to N dissolved in water will be greater than the ratio in air. It is easy to calculate what quantity of each of the gases will be contained in water, and taking the simplest case we will calculate what quantity of oxygen, nitrogen, and carbonic anhydride will be dissolved from air having the above composition at 0° and 760 mm. pressure. Under a pressure of 760 mm. 1 cubic centimetre of water dissolves 0·0203 cubic centimetre of nitrogen or under the partial pressure of 600 mm. it will dissolve 0·0203 × 600/760, or 0·0160 cubic centimetre; of oxygen 0·0411 × 160/760, or 0·0086 cubic centimetre; of carbonic anhydride 1·8 × 0·4/760 or 0·00095 cubic centimetre: hence, 100 cubic centimetres of water will contain at 0° altogether 2·55 cubic centimetres of atmospheric gases, and 100 volumes of air dissolved in water will contain about 62 p.c. of nitrogen, 34 p.c. of oxygen, and 4 p.c. of carbonic anhydride. The water of rivers, wells, &c. usually contains more carbonic anhydride. This proceeds from the oxidation of organic substances falling into the water. The amount of oxygen, however, dissolved in water appears to be actually about 1/3 the dissolved gases, whilst air contains only 1/5 of it by volume.

According to the law of partial pressures, whatever gas be dissolved in water will be expelled from the solution in an atmosphere of another gas. This depends on the fact that gases dissolved in water escape from it in a vacuum, because the pressure is nil. An atmosphere of another gas acts like a vacuum on a gas dissolved in water. Separation then proceeds, because the molecules of the dissolved gas no longer impinge upon the liquid, are not dissolved in it, and those previously held in solution leave the liquid in virtue of their elasticity.[36] For the same reason a gas may be entirely expelled from a gaseous solution by boiling--at least, in many cases when it does not form particularly stable compounds with water. In fact the surface of the boiling liquid will be occupied by aqueous vapour, and therefore all the pressure acting on the gas will be due to the aqueous vapour. On this account, the partial pressure of the dissolved gas will be very inconsiderable, and this is the sole reason why _a gas separates from a solution on boiling the liquid containing it_. At the boiling point of water the solubility of gases in water is still sufficiently great for a considerable quantity of a gas to remain in solution. The gas dissolved in the liquid is carried away, together with the aqueous vapour; if boiling be continued for a long time, all the gas will finally be separated.[37]

[36] Here two cases occur; either the atmosphere surrounding the solution may be limited, or it may be proportionally so vast as to be unlimited, like the earth's atmosphere. If a gaseous solution be brought into an atmosphere of another gas which is limited--for instance, as in a closed vessel--then a portion of the gas held in solution will be expelled, and thus pass over into the atmosphere surrounding the solution, and will produce its partial pressure. Let us imagine that water saturated with carbonic anhydride at 0° and under the ordinary pressure is brought into an atmosphere of a gas which is not absorbed by water; for instance, that 10 c.c. of an aqueous solution of carbonic anhydride is introduced into a vessel holding 10 c.c. of such a gas. The solution will contain 18 c.c. of carbonic anhydride. The expulsion of this gas proceeds until a state of equilibrium is arrived at. The liquid will then contain a certain amount of carbonic anhydride, which is retained under the partial pressure of that gas which has been expelled. Now, how much gas will remain in the liquid and how much will pass over into the surrounding atmosphere? In order to solve this problem, let us suppose that _x_ cubic centimetres of carbonic anhydride are retained in the solution. It is evident that the amount of carbonic anhydride which passed over into the surrounding atmosphere will be 18-_x_, and the total volume of gas will be 10 + 18-_x_ or 28-_x_ cubic centimetres. The partial pressure under which the carbonic anhydride is then dissolved will be (supposing that the common pressure remains constant the whole time) equal to (18-_x_)/(28-_x_), hence there is not in solution 18 c.c. of carbonic anhydride (as would be the case were the partial pressure equal to the atmospheric pressure), but only 18(18-_x_)/(28-_x_), which is equal to _x_, and we therefore obtain the equation 18(18-_x_)/(28-_x_) = _x_, hence _x_ = 8·69. Again, where the atmosphere into which the gaseous solution is introduced is not only that of another gas but also unlimited, then the gas dissolved will, on passing over from the solution, diffuse into this atmosphere, and produce an infinitely small pressure in the unlimited atmosphere. Consequently, no gas can be retained in solution under this infinitely small pressure, and it will be entirely expelled from the solution. For this reason water saturated with a gas which is not contained in air, will be entirely deprived of the dissolved gas if left exposed to the air. Water also passes off from a solution into the atmosphere, and it is evident that there might be such a case as a constant proportion between the quantity of water vaporised and the quantity of a gas expelled from a solution, so that not the gas alone, but the entire gaseous solution, would pass off. A similar case is exhibited in solutions which are not decomposed by heat (such as those of hydrogen chloride and iodide), as will afterwards be considered.

[37] However, in those cases when the variation of the co-efficient of solubility with the temperature is not sufficiently great, and when a known quantity of aqueous vapour and of the gas passes off from a solution at the boiling point, an atmosphere may be obtained having the same composition as the liquid itself. In this case the amount of gas passing over into such an atmosphere will not be greater than that held by the liquid, and therefore such a gaseous solution will distil over unchanged. The solution will then represent, like a solution of hydriodic acid in water, a liquid which is not altered by distillation, while the pressure under which this distillation takes place remains constant. Thus in all its aspects solution presents gradations from the most feeble affinities to examples of intimate chemical combination. The _amount of heat_ evolved in the solution of equal volumes of different gases is in distinct relation with these variations of stability and solubility of different gases. 22·3 litres of the following gases (at 760 mm. pressure) evolve the following number of (gram) units of heat in dissolving in a large mass of water; carbonic anhydride 5,600, sulphurous anhydride 7,700, ammonia 8,800, hydrochloric acid 17,400, and hydriodic acid 19,400. The two last-named gases, which are not expelled from their solution by boiling, evolve approximately twice as much heat as gases like ammonia, which are separated from their solutions by boiling, whilst gases which are only slightly soluble evolve very much less heat.

It is evident that the conception of the partial pressures of gases should be applied not only to the formations of solutions, but also to all cases of chemical action of gases. Especially numerous are its applications to the physiology of respiration, for in these cases it is only the oxygen of the atmosphere that acts.[38]

[38] Among the numerous researches concerning this subject, certain results obtained by Paul Bert are cited in