[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 + at°, 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 + 0·00018t 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 solubility per 20° in per cent. | Cube root of molecular weight. | Ratio between decrease and cube root of mol. wt. | |
| H2 | 15·32 | 1·259 | 12·17 |
| N2 | 34·33 | 3·037 | 11·30 |
| CO | 34·44 | 3·037 | 11·34 |
| NO | 36·24 | 3·107 | 11·66 |
| O2 | 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, H2O, for carbonic anhydride, CO2, 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, CO2 + 8H2O.
[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.
[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 (SO2) 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 3pDq 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.