That a gas may be looked upon as an association of particles—hard elastic spheres—moving backwards and forwards in right lines with great velocity, and possessing in the aggregate a very small proportion of the space through which they travel, was first conceived by Daniel Bernoulli in 1738. By means of this hypothesis he explained the direct proportionality between the density and pressure of a gas. If the gas consists of moving particles, and the pressure which it exerts on the sides of the containing vessel is due to the impacts of these particles, it is obvious that by halving the original volume of the containing space we halve the space through which the particles travel, and therefore double the number of their impacts in a given time; in other words, by compressing the gas to half its initial volume we double the pressure it exerts, which is nothing else than the law of Boyle. This conception of the nature of a gas is known as the kinetic theory of gases; it was further developed by Waterston in 1845, still more fully by Clausius in 1857, and was subsequently placed in its present position by Maxwell and Boltzmann.
That gases actually do move, and at rates depending on their specific nature, was rendered probable—apart from this explanation of Boyle’s law—by many phenomena observed by chemists and physicists in the eighteenth and early part of the nineteenth century. It was known from the observations of Leslie in 1804 that specifically light gases moved or diffused faster than heavy gases. Attempts to determine these rates were made by Schmidt in 1820, and by Graham in 1846, both of whom found that the rate of movement of a gas was independent of its chemical nature, and was determined solely by its mass: gases move at rates inversely proportional to the square roots of their densities. The following table given by Graham shows the experimentally ascertained relative rates for a number of gases compared with the rates demanded by the “law of gaseous diffusion.” Column one gives the name of the gas; column two, the observed rate of diffusion; and column three, the square root of the density of the gas (air = 1):
| Gas. | Time of diffusion. | √density. |
|---|---|---|
| Air | 1 | 1 |
| Hydrogen | 0.276 | 0.263 |
| Marsh gas | 0.753 | 0.745 |
| Ethylene | 0.987 | 0.985 |
| Nitrogen | 0.986 | 0.986 |
| Oxygen | 1.053 | 1.051 |
| Carbon dioxide | 1.203 | 1.237 |
Nitrogen and ethylene are, chemically, totally dissimilar gases, but they have the same density and hence the same rate of movement. As Graham showed, it is possible to separate more or less completely a mixture of gases, if the constituents are of different densities, by taking advantage of their different rates of movement. Such an atmolytic method was employed by Rayleigh and Ramsay to prove that atmospheric nitrogen contained argon.
The fact that all gaseous substances, however different their chemical nature, conform in the main to certain simple “laws” indicates the probability that their mechanical structure is similar and comparatively simple. The so-called gaseous “laws”—the laws of Boyle, Dalton, Gay Lussac, Avogadro, and Graham—are to-day explained on the assumption that a gas consists of an aggregation of molecules, moving incessantly in straight lines and with great rapidity. The rate of movement of the particles is variable by reason of their mutual encounters; at the same instant some are moving rapidly, others more slowly. As already explained, to this ceaseless movement of the molecules is to be ascribed the pressure they exert; the pressure which a gas exerts on any containing surface is the aggregate effect of the impact of its molecules. The law of Boyle states that the product of the volume V and pressure P of a given mass of gas is invariable so long as the temperature is unchanged: PV = constant. It was found by Regnault, Magnus, Natterer, and Amagat that all gases, with the exception of hydrogen, show a departure from Boyle’s law in the sense that PV is less than theory demands. In the case of hydrogen PV is greater than theory. This exception, however, is only apparent. Every gas, if maintained above a certain temperature, shows, after a certain pressure has been reached, a deviation in the same sense as that exhibited by hydrogen.
The deviations from Boyle’s law are probably due to two causes: (1) to the effect of cohesion among the molecules, whereby the volume, and hence PV, is less than theory requires; (2) the molecules are not mathematical points—they have a certain volume; hence, with increasing pressure, PV is greater than theory demands. The effect of the molecule having a certain magnitude will be clear from the following figure: Let M be a molecule moving backwards and forwards within a certain space, a b:
Assume, now, we halve the containing space:
It will be seen that M, since its volume is unchanged, will have less than half the original distance to travel or, in other words, it will strike the boundaries of the containing space more than twice as frequently in the same interval of time as before; hence P, and therefore PV, becomes greater than Boyle’s law demands.