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nitrogen are as 16 to 14; the rate of diffusion, therefore, of nitrogen is slightly greater than that of oxygen.

Effusion is the term applied by Graham to the passage of gases through a fine opening in a very thin wall, and he found that it followed the same law as diffusion. Bunsen utilised this principle for determining the density, and therefore the molecular weights, of certain gases. The method, in essence, is as follows :-A straight glass eudiometer is so constructed, that a gas contained in it can be put into conmmunication with the outer air through a minute pin-hole in a thin platinum plate. The gas is confined in the tube, which is placed in a cylindrical mercury trough, by means of a stop-cock at the top. When the tube is depressed in the mercury, and the cock opened, the gas escapes through the minute perforation in the platinum plate, and its rate of effusion is determined by the time occupied by a glass float placed in the tube in rising a graduated distance within the eudiometer.

The flow of gases through capillary tubes is called transpiration of gases. In this case the friction between the gas and the tubes becomes a factor in the movement, so that this phenomenon is not governed by the same law as gaseous diffusion.

The Kinetic Theory of Gases.—The term kinetic signifies motion, and as applied to this theory it expresses the modern views of physicists concerning matter in the gaseous state, and serves to harmonise and explain the physical laws relating to the properties of gases. Matter in the state of gas or vapour is regarded as an aggregation of molecules in which the attractive forces which tend to hold them together are reduced to a minimum, and in which the spaces that separate them are at a maximum. These molecules are in a state of rapid motion, each one moving in a straight line until it strikes some other molecule, or rebounds from the walls of the containing vessel, when it continues its movement in another direction until it is once more diverted by another encounter. As they constantly encounter and rebound from each other, it will be evident that at any given instant some will be moving with a greater speed than others; the majority, however, will have an average velocity. In these encounters no loss of energy results so long as the temperature remains constant, but any change of temperature results in a change in the velocity of movement of the molecules, the speed being increased with increased heat. The actual volume of the molecules is very small as compared with the space occupied by the mass ; the space

between the molecules, therefore, in which they pass to and fro, is relatively very great. . As the molecules are constantly colliding and rebounding, the distances between them, as well as their speed, will be sometimes greater and sometimes less ; but there will be an average distance, which is known as the mean free path of the molecule.

The pressure exerted by a gas, or its elastic force, is the combined effect of the bombardment of its molecules against the containing vessel ; in other words, the pressure of a gas is proportional to the sum of the products obtained by multiplying the mass of each molecule by half the square of its velocity. It will be obvious that if the space within which a given mass of gas is confined be reduced, the number of impacts of the molecules against the walls of the containing vessel, in a given time, will be increased, and therefore the pressure it exerts, or its elastic force, will also be increased. If the space be reduced to one-half the original, the number of these impacts will be doubled, or in other words, the number of impacts in a given time is inversely as the volume. This statement is simply the law of Boyle stated in the language of the kinetic theory.

When a given mass of gas contained in a confined space is heated, the pressure it exerts, or its elastic force, is increased. But as the number of molecules present has not been increased by raising the temperature of the gas (provided no chemical decomposition of the gas is brought about by the change of temperature the increased pressure can only have resulted from the greater frequency, and greater energy, of the impacts of the molecules against the walls of the vessel, owing to their greater velocity.

Two equal volumes of different gases under the same conditions of temperature and pressure, exert the same elastic force upon the containing vessels, that is to say, the kinetic energy in each volume is the same. According to Avogadro's hypothesis, equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules, however much the weight of these molecules may vary ; therefore the average kinetic energy of each individual molecule will be the same. It follows from this that the mean velocities of different molecules must vary, and the calculated numbers representing the actual velocities of movement of the molecules of different gases show that these rates are proportional to the inverse square roots of their respective densities. But according to the law of gaseous diffusion (Graham's law), the relative rapidity of diffusion of gases is inversely proportional to the square roots of their densities, hence by purely mathematical processes, based upon the kinetic theory of gases, the law of gaseous diffusion is proved to be true. Similarly, the kinetic theory is applicable to the consideration of the phenomena of evaporation and condensation (see page 126), and to the processes of solution (page 148).

The deviations from the laws of Boyle and Charles, already referred to, * are also explained by the dynamical theory of gases, from considerations of the following order :

1. That the molecules themselves are not mathematical points, but occupy a space ; in other words, the space occupied by the actual particles of matter is not infinitely small as compared with the entire volume of the gas, i.e. the bulk of the particle plus the intermolecular spaces.

While the pressure upon a gas is only slight, and therefore the total volume occupied by a given mass of the gas is great, the bulk of the actual particles themselves becomes a vanishing quantity in comparison with the total volume (i.e. the space occupied by particles, plus the intermolecular spaces), and the gas under these circumstances tends to approach more nearly to the conditions of an ideal gas. But when the pressure is increased, and the total volume thereby greatly reduced, then the bulk of the particles themselves begins to bear an appreciable proportion to the total volume occupied by the gas.

2. That the impact of the molecules against each other and against the containing envelope occupies time ; or, in other words, the time occupied by the impacts is not infinitely small compared with the time elapsing between the impacts.

3. That the molecules themselves are not entirely without attraction for each other ; that is to say, although the attractive force between the molecules which holds them together in the liquid and solid states of matter is at a minimum in the case of gases, it is not entirely absent.

* See page 71.




DISSOCIATION is the term employed to denote a special class of chemical decompositions. When potassium chlorate is heated it breaks up into potassium chloride and oxygen, thus

2KCIO3 = 2KCl + 309, and when calcium carbonate (chalk) is heated it breaks up into calcium oxide (ime) and carbon dioxide

CaCO3 = CaO + CO, In the first case the oxygen is incapable of reuniting with the potassium chloride, but in the second, the carbon dioxide can recombine with the lime and reproduce calcium carbonate : therefore both the following expressions are possible

CaCO, = CaO + CO2, and

CaO + CO, = CaCO. Reactions of this order are known as reversible or balanced actions, and the breaking up of calcium carbonate by the action of heat is termed dissociation, while that of the potassium chloride under similar circumstances is simple decomposition.

When ammonia is passed through a tube heated to a dull red heat, the gas is decomposed into nitrogen and hydrogen

2NH, = N2 + 3H, and the two gases pass out of the heated tube as separated gases, and do not recombine again.*

But when steam is strongly heated it is dissociated into oxygen * Nitrogen and hydrogen can be caused to unite under suitable conditions (see Ammonia).

and hydrogen, and as these separated gases pass away from the heated region they reunite, forming molecules of water vapour. Such a reversible reaction may be thus expressed

21,0 2H, + 0.2. Again, when the gases ammonia and hydrochloric acid are brought together at the ordinary temperature, they unite to form solid ammonium chloride, and when ammonium chloride is heated it dissociates into its two generators,* hence we have the expression

NH3 + HCI Í NH,CI. The corresponding compound containing phosphorus in the place of nitrogen dissociates at a temperature as low as - 20°, hence when phosphoretted hydrogen and hydrochloric acid are mixed at ordinary temperatures no combination takes place, the separate molecules are in the same relation to one another as those of ammonia and hydrochloric acid at a high temperature. When, however, the mixture of gases is cooled below – 20°, union takes place and crystals of phosphonium chloride are formed, which at once begin to dissociate into the original gases as the temperature again rises. The change, as before, may be represented as a reversible one

PH3 + HCl + PH,Cl.

In such cases of dissociation as that of calcium carbonate, where one of the products is gaseous and the other solid, no difficulty exists in separating the simpler compounds that result from the decomposition ; but where the products are entirely gaseous, special methods have to be adopted to withdraw the one from the other, while they still exist as separate molecules, and before they reunite again. One such method, which is well adapted for the qualitative illustration of dissociation, is based on the law of gaseous diffusion. If when ammonium chloride is heated it is dissociated into ammonia, NH,, and hydrochloric acid, HCI, these two gases, having the relative densities of 8.5 and 18.25, will diffuse through a porous medium at very different rates. According to the law of diffusion, these rates will be inversely as the square roots of the densities of the gases ; if, therefore, the conditions are so arranged

* Baker has shown (May 1894) that when absolutely dry, these gases do not combine; and also, that when aqueous vapour is entirely absent, ammonium chloride does not undergo this dissociation.

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