Note 34 — Chapter I · ON WATER AND ITS COMPOUNDS
George Kamensky translation
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.
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 / v2 )(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.