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man running rapidly would be retarded so soon as he came into a throng.. The crowding together of the gaseous particles cannot, however, be so great, for a comparison of the density of gases and liquids shows that the particles of a gas fill only a thousandth of the space taken up by the mass; consequently in the spaces between them there must exist for their movements to and fro a thousand times as much space as that filled by the mass. But at the same time the average distance between the particles can only be very small when their number is great and the mass of each correspondingly small. Starting with these assumptions from the known rate of diffusion, the conductivity for heat, the internal friction of gases, &c., the average distance which a particle must travel before it collides with a second has been calculated-this distance Clausius has styled the mean free path.

The length of path is shown to be extremely small-less, in fact, than any length microscopically visible in the case of gases at normal pressure. With the majority of gases at the average temperature and a pressure of an atmosphere the distance is less than the ten-thousandth part of a millimetre. With a velocity of several hundred metres per second the number of times which a given particle must collide with others is quite inconceivable, and, according to calculation, it must be from four to ten thousand million times per second.

These calculations show the subdivision of matter in the gaseous state to be excessively great, since at the average temperature and under the pressure of one atmosphere a cubic centimetre of any given gas, and therefore in accordance with Avogadro's law, of all gases, will contain approximately some twenty trillion particles. As the weight of this mass can be determined, and, in fact, is known, the weight of a single molecule may be approximately ascertained. The weight of a molecule of hydrogen has thus been found to be

0·000,000,000,000,000,000,004 milligramme;

or a quadrillion of particles of hydrogen would weigh about four grammes. Although these numbers cannot lay claim to any special accuracy, still they serve to give some idea of the magnitude (or, rather, the minuteness) of molecules and of atoms also.

Not only may the weight but also the dimensions of the particles be similarly estimated. The hindrances to its free movement experienced by a particle produced by collision with others is determined, not only by its velocity, but also by its dimensions; for the larger the particles the more they will interfere with one another. The path, therefore, will be shorter the larger the particles. The knowledge of the frequency of their collisions may further serve to enable us to form an estimate of and to measure approximately their dimensions. According to the calculations of O. E. Meyer, a cubic centimetre of hydrogen measured at 20° C. and under pressure of 760mm. contains so many molecules that if they were laid side by side they would cover 9500 square centimetres, or very nearly a square metre. Accordingly for each twenty trillion particles but a very small surface would be required, for in the length of a millimetre some four to five million particles could be arranged in a series.

The relative size of the molecules of two different gases or vapours may be calculated with greater exactness than can their absolute dimensions. By similar calculation it has been shown by the author that in the case of most substances the actual spaces filled by the gaseous particles stand to one another approximately in the same proportion as that which obtains in the liquid state.

§ 89. Boyle's Law.-The behaviour of gases under all conditions is determined by the dimensions, the mass, and the velocity of the particles. The deviations from the fundamental laws of gases exhibited in individual cases can be explained in a satisfactory manner as arising from these several influences. According to Boyle's law, the volume of a given mass of gas is inversely proportional to the pressure upon it, and therefore the product of the pressure into the volume or the quotient of the pressure and density remains constant. This law is not, however, absolutely true of any gas; for every gas, with the single exception of hydrogen, exhibits a greater diminution in volume with increase in pressure than should be the case if the law were absolutely true, i.e. the value of the product PV diminishes. So soon, however, as the pressure increases to a considerable number of atmospheres then the value of the product PV becomes greater, arising from the fact that the volume decreases less rapidly than the pressure increases. Hydrogen

as far as it has been investigated always shows this increase in the value of the product P V, and not the diminution. The first of these deviations from the theoretical laws is explained by the assumption that the particles of the gas at temperatures much above that at which liquefaction takes place exert an action upon each other, showing itself as an attraction, becoming stronger the more frequently the particles strike one another. The deviation in the opposite direction finds its explanation in the reduction by increased pressure of the space between the particles, and not of that occupied by the particles themselves. The proportion which the latter bears to the total space occupied by the increases with the pressure. gas,

Van der Waals has shown that both these deviations from Boyle's law afford an explanation of the lack of exact proportion to the absolute temperature and the changes in pressure and volume with alterations in temperature.

The kinetic theory of gases, although it still requires further extension and further experimental investigation, is capable of giving a very satisfactory explanation of the behaviour and properties of gases; consequently this theory, in opposition to which at first many facts were cited, has now received general acceptance and recognition.

§ 90. Mixture of Gases. Diffusion. Effusion. Transpiration. When two or more gases come in contact with one another, each will flow into the space filled by the others, even when they are both under the same pressure. The origin of this mixing or diffusion is the exceedingly great velocity of the particles, which, as already mentioned in § 88, despite its magnitude, can only effect a slow and gradual admixture on account of the frequent collisions of the particles with one another. The diffusion takes place most quickly with gases of small molecular weight, the particles of which have consequently greater velocities. In this respect hydrogen far exceeds all other gases; the rate of diffusion depends also upon the dimensions of the particles of the several gases themselves; since they form the barrier opposed to the free movement of the gaseous particles. It follows, therefore, that for any particular gas the nature of the gas into which it diffuses is important, and its rate of diffusion, therefore, is determined by the nature of the other gas.

When the surface separating the two gases is relatively large then the pressure, being the same on both sides, remains unchanged during and after the mixing of the gases. If the gases are separated by a porous partition or by a partition with a small opening, then the pressure will rise on the side towards which the gas with smaller molecular weight diffuses, because the other gas cannot pass through at a rate sufficiently great to compensate for the inequality of pressure. In course of time, however, this difference in pressure disappears.

In the flow of gases through narrow tubes or channels, which Graham styled 'transpiration,' the internal friction comes into play, and this being dependent upon the free path of the particles may be utilised for the purpose of determining the

same.

The flow through a narrow opening in a very thin wall, described as 'effusion' by Graham, takes place with velocities which are inversely as the square root of the densities, and are consequently proportional to the velocities of the rectilinear motion of the particles. This property may therefore, as was proposed by Bunsen, be utilised to measure these velocities and also to determine the molecular weights.

§ 91. Mixing of Gases and Liquids. Absorption of Gases.When a gas comes in contact with a liquid, then, as a rule, the gas passes into the liquid as it would into a vacuum or a space already filled by another gas, whilst at the same time the liquid evaporates to some extent into the gas. The taking up of the gas by the liquid is, when there is no chemical action between the two, spoken of as absorption. It is, however, frequently difficult, if not impossible, to draw a sharp line of distinction between absorption and chemical combination. The solution of a gas in a liquid is spoken of as absorption when it takes place in accordance with Henry's law, i.e. when it is proportional to the pressure of the gas, and is described as chemical combination when it is independent of the pressure. There are many instances which stand midway between these two extremes, in which whilst the amount of gas absorbed varies with the pressure it is not proportional to it. Such cases will be considered later in the discussion of chemical change (§ 92 et seq.).

True absorption, which is proportional to the pressure, takes

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place very slowly when the gas is in simple contact with the surface of the liquid. When the two are brought into more intimate contact by shaking, then the absorption takes place rapidly. The absorption of the gas by the liquid proceeds until a certain relation between the density of the gas absorbed and that of the unabsorbed gas is reached, at which point equilibrium between the particles of gas absorbed and passing out of the liquid is maintained. This relation is called the coefficient of absorption it is dependent upon the nature of the gas and of the liquid, and also upon the temperature. Many liquids, as for example mercury, and possibly other molten metals (perhaps with the exception of silver, which absorbs oxygen), are practically impervious to gases; others absorb but little; whilst others, again, are capable of absorbing considerable proportions of gases. The following table contains the coefficients of absorption by water of several gases at 0° C., 10° C., and 20° C., as found by Bunsen:

These numbers show that the quantity of gas taken up by a unit volume of water is in some cases greater, in others considerably less, than is contained in an equal volume of the free gas itself. In the case of hydrogen the amount of gas absorbed by the unit volume of water is about 2 per cent. of the quartity of hydrogen contained in the unit volume; in fact, this proportion is maintained for parts by weight or for volume, assuming that in the latter case the volumes are measured under the same conditions of pressure and of temperature as those at which the absorption takes place.1

A litre of water at 10° absorbs only 20 c.c. of hydrogen

1 For practical reasons Bunsen measures all the gas absorbed at 0°; consequently his coefficients at 10° and 20° would differ somewhat from those given in the above table.

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