ATOMIC WEIGHT AND VAPOUR DENSITY

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These elements unite together in the following proportions:

The combining weights of the gaseous elements are either directly proportional to their densities or to a simple multiple of their densities. The simplest hypothesis is that the atomic weights are proportional to the densities, i.e. to the weight of equal volumes of the gases. That is to say, that under similar conditions of temperature and pressure equal volumes of the different gaseous elements contain the same number of atoms. Berzelius made this assumption in opposition to Dalton's views. When this law was applied to elements which only assume the gaseous state at high temperatures the following results were obtained :—

In these cases the densities compared with hydrogen cannot be regarded as the atomic weights; for the many analogies between oxygen and sulphur show that the atomic weight of the latter is almost exactly double that of the former, i.e. 31.98, not 95.94. The close analogy between the compounds of nitrogen and those of phosphorus and arsenic indicate that if N=14, then P=31 and As=75; that is, the atomic weights are, in the case of phosphorus and arsenic, only half the densities; for only in the latter case will the corresponding hydrides have the analogous formulæ, NH, PH, and AsH ̧; if the atomic weights are doubled the two latter must be represented by the formulæ PH and AsH. There are also good grounds for doubting that the atom of mercury is only 100 times heavier than the atom of hydrogen; consequently

Berzelius was obliged to regard it as 200 times the weight of a hydrogen atom. The same is true of other atomic weights deduced from the density in the gaseous state; but some atomic weights arrived at by this method, e.g. those of iodine and bromine, agree with the results obtained for chlorine and others in the first group of elements.

§ 18. Want of Agreement between the different Equivalents. The different methods used in determining the equivalent weights of the elements led to different results. The atomic weights deduced by the chemical, electrolytic, crystallographic or thermic methods occasionally agreed and occasionally disagreed. It is not surprising, therefore, that there was a great want of unanimity in the views which chemists held concerning these fundamental values.

In spite of great difficulties, Berzelius understood how to make use of first one and then another of these physical auxiliaries and with such success that, with a few exceptions, the atomic weights he proposed are in use at the present day, although they were for a time replaced by the values proposed by Leopold Gmelin, which were based on Dalton's results. It is true the victory of the atomic weights of Berzelius was not won by himself, but to a certain extent by his most active opponents, whose views he strongly disputed.

The result of this long and complex discussion was to clear and strengthen our views. In the present day a difference of opinion may exist for a time regarding an element which has not been thoroughly investigated, but no dispute can arise on the fundamental principles involved in the determination of atomic weights. These principles were first clearly explained by S. Cannizzaro in 1858, when the apparent contradictions between certain results were satisfactorily cleared away.

§ 19. Avogadro's Hypothesis.-Cannizzaro was the first to point out that an entirely false construction had been placed on the relation which exists between the density of a gas or vapour and the combining weight, in spite of the fact that in 1811 Amadeus Avogadro had given perfectly correct instructions as to the manner in which this relationship was to be employed. Starting from Gay Lussac's recently discovered law of combining volumes, Avogadro enunciated the hypothesis that under similar

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AVOGADRO'S HYPOTHESIS

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conditions of temperature and pressure, equal volumes of gases. contain the same number of particles, which need not of necessity be atoms. He called these particles molecules,' from molecula, a small mass (moles).

Although Avogadro's hypothesis was not the only one possible, it was by far the most probable. Nevertheless for a long time it failed to meet with approval, and the views held by chemists were in many ways directly opposed to it. For example, for half a century no one opposed the views held by Dalton and Gmelin, that water contains one atom of oxygen and one atom of hydrogen, although as a necessary consequence it follows that a volume of oxygen must contain twice as many atoms as a volume of hydrogen.

If each particle of water contains the same number of atoms of each constituent, then one volume of oxygen must contain the same number of atoms as are contained in two volumes of hydrogen. For two volumes of hydrogen unite with one volume of oxygen to form water.

The chief reason why Avogadro's hypothesis failed to meet with recognition was that at this time there was no real necessity for applying it (as Avogadro had done) not only to the elements but to their compounds. At this period only a few gaseous compounds were known, and little importance was attached to the manner in which their chemical formulæ were written. About the middle of the present century the necessity of a systematic classification of the numerous newly discovered carbon compounds, the so-called organic compounds, made itself felt. Avogadro's hypothesis, which had so long lain dormant, was admirably adapted for this purpose. At first its application was partial and limited, until C. Gerhardt made a logical use of it, although mainly with the object of classifying chemical compounds.

§ 20. Physical Basis of Avogadro's Hypothesis. The Kinetic Theory of Gases.-Avogadro had pointed out the extraordinary similarity in the physical properties of different gases, more particularly the uniformity exhibited by the influence of temperature and pressure on their volume and density, as stated in Boyle's or Mariotte's law and in Gay Lussac's law. He was of opinion that the only possible explanation lay in the hypothesis

that all gases contain the same number of particles in equal volumes, measured under similar conditions of temperature and pressure. For if one gas contained double or treble the number of particles contained in another, it would be almost impossible to understand how the relations between density, temperature, and pressure could agree under these conditions; but it is obvious that if the same number of particles of different gases are contained in equal volumes, then the same change in pressure will be effected if the volume is increased or diminished to a certain extent or the temperature altered by a certain number of degrees.

This idea of Avogadro has received decisive confirmation as a result of the new development of the mechanical theory of heat. This theory starts from an old hypothesis which was developed by Daniel Bernouilli in 1738. According to this theory, the individual particles of matter in the solid state occupy definite positions with regard to each other. In the liquid state, although the particles have the power of moving about freely they are attracted to each other; but in the gaseous state the particles are entirely detached from each other: each particle moves about with great rapidity and rushes forward in a straight line until it comes in contact with another particle or some other impediment, from which it rebounds like an elastic ball and continues its movement in a new direction. The pressure of a gas results from the sum of the impacts which the particles exert on the body they come in contact with the sides of a vessel, for example. Consequently the pressure increases, as the number of particles in a given space and as the velocity of the particles increases.

This old hypothesis was rediscovered in 1850 by Krönig, Joule, and Clausius, and received a more systematic development at the hands of Clausius. It forms the basis of the theory known as the theory of molecular impacts or the molecular theory of gases. According to this theory the pressure exerted by a given volume of gas is proportional to the sum of the kinetic energy of the rectilinear motion of all the particles contained in the unit of volume. By kinetic energy we understand half the product of the mass into the square of the velocity. The pressure of the gas is proportional to the sum of the products obtained by

multiplying the mass of each individual particle by half the square of its velocity. And as, according to Gay Lussac's law, the pressure varies in proportion to the temperature, it follows that the sum of these products is also proportional to the temperature, and consequently for constant mass the temperature is proportional to the square of the velocity.

If we have equal volumes of two different gases at the same temperature and under the same pressure, then the total kinetic energy is the same in each volume. But according to Avogadro's hypothesis the number of particles in both gases is identical; consequently the average kinetic energy of each individual particle will be the same. If the two gases are brought into communication with each other, they mix together without any change of temperature or pressure taking place, providing of course that the gases do not exert any chemical action on each other. In this mixture, again, every particle will have the same kinetic energy.

Without the aid of Avogadro's hypothesis, we are at once. surrounded by difficulties. Let us assume that one gas contains twice as many particles in a certain volume as another gas, then each particle of the first gas has only half the kinetic energy of the particles of the second, for the total kinetic energy is shared by double the number of particles. By the laws of mechanics, it is impossible that this condition should continue when the gases are mixed together; and as the particles are frequently coming into collision with each other, those doubly endowed with kinetic energy must give up a portion of their energy to the other particles. But if this transference of energy takes place, then the two gases will cease to be under the same temperature and pressure, because temperature and pressure are proportional to the kinetic energy of the gases. Avogadro's hypothesis is the only means of arriving at results conforming to the laws of mechanics.

This is one of the most powerful arguments in support of Avogadro's hypothesis. Its truth is now no longer disputed.

§ 21. Molecular Weights of Gases.—The relative values for the molecular weights of all gases can be easily determined by means of Avogadro's hypothesis. The absolute weight of the molecules cannot be ascertained. The method depends on the

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