CHAPTER IV

ATOMS AND MOLECULES: ATOMIC WEIGHTS AND EQUIVALENTS

It has already been pointed out that the discovery by Gay Lussac, and independently by Dalton, that gases combine in simple proportions by volume, and that the volume of the gaseous product, measured under comparable conditions of temperature and pressure, stand in simple relation to the volumes of the constituents, seemed to most of Dalton’s contemporaries, but not to Dalton himself, to afford strong evidence of the validity of his explanation of the essential nature of chemical combination. It appeared obvious from the facts that there must exist some simple relation between the densities, or specific gravities, of the elementary gases and their atomic weights. When, however, the principle underlying Gay Lussac’s law was extended so as to include gases in general—both simple and compound—difficulties were met with which were only satisfactorily cleared away during the latter half of the nineteenth century. The first rational attempt to explain the facts observed by Dalton and Gay Lussac, concerning the volumetric relations of gases, was made in 1813 by Amedeo Avogadro by the assumption that a given volume of all gases—simple or compound—contains the same number of integral molecules; hence the relative weights of these volumes represent the relative weights of the molecules. According to Avogadro, in the case of the simple gases the integral molecules are composed of a certain number of elementary molecules of _the same kind_, whereas the integral molecules of compound gases and vapours are made up of elementary molecules _of different kinds_. The _elementary molecule_ of Avogadro is now termed the _atom_; his _integral molecule_ we call simply a _molecule_. Similar conceptions were published independently by Ampère in 1814. It follows from the doctrine of Avogadro and Ampère that, as the number of integral molecules is the same in equal volumes of all gases, these molecules must be equidistant from each other, their mutual distances depending upon pressure and temperature. This at once serves to explain the laws of Boyle and Dalton that gases, no matter what their chemical nature, behave identically, as regards change of volume, when compressed by pressure or expanded by heat.

The true significance of the hypotheses of Avogadro and Ampère was long obscured, first on account of their imperfect appreciation by the great leaders of chemical thought during the first half of the nineteenth century—Berzelius, Gay Lussac, Wollaston, and Gmelin—and, secondly, on account of the almost universal practice of deducing atomic weights from purely chemical considerations of equivalence. At the same time, it must be admitted that the recognition of the value of these hypotheses was still further retarded by the seeming anomalies which resulted from a more extended knowledge of the vapour densities of elements and compounds. Thus the vapour densities of mercury, sulphur, phosphorus, and arsenic, as ascertained by Dumas and Mitscherlich, were plainly inconsistent with chemical analogies and the law of Dulong and Petit. So, too, what appeared to be the vapour densities of sal-ammoniac, phosphorus pentachloride, sulphuric acid, calomel, and of other substances that might be mentioned, were not in accordance with the values demanded by other well-ascertained facts.

By the middle of the nineteenth century the hypothesis of Avogadro was practically forgotten and the law of volumes ignored. The atomic weights of the elements, and the system of notation universally employed in England and Germany, were based wholly upon equivalents. The anomalies thus created were clearly pointed out by Gerhardt, and subsequently by Laurent who showed how a consistent and harmonious explanation of the facts could be reached by regarding as true equivalents equal volumes—for example, of steam, ammonia, hydrogen chloride, carbon dioxide, marsh gas, etc.; by assuming, in other words, that equal numbers of the molecules of these various substances are contained in equal volumes of the gases, as contended by Avogadro and Ampère. The simplicity and consistency of the new notation gradually won for it the adhesion of chemists. This adhesion was facilitated by the memorable researches of Williamson on etherification, of Gerhardt on the anhydrides, and by the work of Frankland on the radicals; and it reached its logical conclusion when │Cannizzaro│—on the basis of Avogadro’s hypothesis—discussed, in 1858, the true atomic weights of the metallic elements as distinguished from their equivalent values. In certain of its aspects the new table of atomic weights drawn up by Cannizzaro resembled that originally proposed by Berzelius; but the numbers adopted by the Swedish chemist were founded on no uniform or rational basis, and were frequently inconsistent.

Our present tables of atomic weight bring, therefore, the values for the several elements into harmony with the doctrine of Avogadro and Ampère, with the law of Dulong and Petit, and with the facts of isomorphism. The values are, in fact, in unison with all the criteria which serve to indicate the atomic weights of the elements. As a result, our present system of notation, which is, of course, based upon these atomic weights, assigns formulæ to compounds which indicate their true relative molecular weights and simplify the accurate expression of their relationships and chemical transformations. One by one the instances of anomalous vapour density, which were so many stumbling blocks to the universal acceptance of a system based upon the law of gaseous volumes, have been shown to be not only not inconsistent with it, but actually so many corroborative proofs. Thus, in the case of ammonium chloride, the observed vapour density of which was found to be practically half its calculated value, it has been proved that the vapour of this salt, when heated to the temperature at which the observations were made, is mainly resolved into molecules of ammonia and hydrogen chloride, which together occupy double the space of the ammonium chloride molecule. Phosphorus pentachloride vapour, on being sufficiently heated, is similarly more or less resolved into phosphorus trichloride and chlorine.

Moreover, it has been found, by a more accurate study of the action of heat upon the vapour of ammonium chloride and of phosphorus pentachloride, that within certain narrow limits of temperature these substances can actually exist as such in the gaseous state, and that the density of their vapours does actually conform to that demanded by theory. Moreover, phosphorus pentafluoride, the analogue of the pentachloride, is gaseous at ordinary temperatures, and has a normal density. It may be heated to a high temperature without showing any sign of decomposition.

Limitations of space will not allow of a fuller explanation of the apparent anomalies already alluded to. They have each in turn been experimentally attacked and satisfactorily explained. No valid exception is now known to the universal applicability of the principle.

To-day the chemical history of a substance, whether elementary or compound, if vaporisable, is not complete until its vapour density is known, since a knowledge of this constant affords the most certain means of establishing the relative weight of its molecule. Accordingly many chemists have endeavoured to simplify and render more convenient the modes of determining vapour densities. Thanks to the efforts of Hofmann and Victor Meyer, the processes associated with the names of Dumas, Gay Lussac, Deville, and Troost, which have furnished us with valuable information in the past, have now given way to comparatively simple and rapid methods, which, although not necessarily more accurate, furnish the required information with less expenditure of time and trouble; that is to say, they serve to indicate which of two, or more, presumed molecular weights is correct, and so enable us to establish the molecular formula of the substance. The chemical formula of a substance is a condensed expression of a number of facts connected with its history. Thus the expression H2O—the chemical formula for water—indicates that the substance is composed of hydrogen and oxygen, in the proportion, using round numbers, of 2 parts by weight of hydrogen and 16 parts by weight of oxygen; or, in other words, of 2 atoms of hydrogen, each weighing 1, and 1 atom of oxygen weighing 16. The formula, moreover, connotes the fact that when the gases combine 2 volumes of hydrogen unite with 1 volume of oxygen to form 2 volumes of water-vapour (steam). So, too, the formula HCl—which represents hydrogen chloride—means that the substance is a compound of 1 atom of hydrogen weighing 1 united with 1 atom of chlorine weighing 35.5; it also denotes the fact that in the act of union 1 volume of hydrogen combines with 1 volume of chlorine to form 2 volumes of hydrogen chloride. Lastly, the formula NH3 signifies that the molecule of ammonia is composed of 1 atom of nitrogen weighing 14, and 3 atoms of hydrogen, each weighing 1; it further indicates that when ammonia gas is resolved into its constituents, as it can be when sufficiently heated, 2 volumes of ammonia gas are increased to 4 volumes of a mixture made up of 1 volume of nitrogen and 3 volumes of hydrogen.

In short, all the formulæ are what are called _two-volume formulæ_; that is, the relative molecular weights of the substances occupy the same volume as two relative parts by weight of hydrogen. Hence their vapour densities—referred to hydrogen as unity—are the halves respectively of their molecular weights. Steam is 9 times, hydrogen chloride 18.25 times, and ammonia 8.5 times heavier than hydrogen, when measured under identical conditions of temperature and pressure. The quantities expressed by the formulæ H2, H2O, HCl, NH3, occupy the same volume. This is equally true of the quantities expressed by O2, N2, Cl2, etc. These expressions signify that the molecules of the elements of hydrogen, oxygen, nitrogen, and chlorine consist each of 2 atoms of the respective substances: the molecule of water consists of 3 atoms—2 of hydrogen and 1 of oxygen; the molecule of hydrogen chloride of 2 atoms—1 of hydrogen and 1 of chlorine; whereas the molecule of ammonia contains 4 atoms—1 atom of nitrogen and 3 atoms of hydrogen.

Certain of the elementary bodies are, as already stated, capable of existing in different allotropic states. Thus there is a modification of oxygen known as _ozone_. This substance has long been recognised as being formed from air under the influence of the electric discharge. It was the subject of study by Schönbein as far back as 1839; but that it was a condensed form of oxygen and not a peroxide of hydrogen—as was at one time surmised—was first established by Andrews and Tait. The degree of its condensation was definitely ascertained by Soret by observing its rate of diffusion, from which, on the basis of Graham’s law, its density could be inferred. It was found to be 1½ times that of ordinary oxygen. Hence, if the molecule of oxygen consists of 2 atoms, that of ozone consists of 3 atoms. The chemical symbol of ozone is, therefore, O3.

It has been found also that the molecule of sulphur, in the state of solution, contains eight atoms. This complex molecule in the gaseous state gradually breaks down as the temperature is increased, and at temperatures above 850° contains, like its analogue oxygen, only two atoms. The molecules of phosphorus and arsenic, in the gaseous state, are each found to consist of four atoms. On the other hand, the molecules of mercury, zinc, and cadmium each consist of only one atom. As will be shown later, Kundt and Warburg established, in 1875, the fact that mercury vapour is a monatomic gas, by determining the rate at which sound is propagated through it. In the same way it was shown that helium, argon, and its congeners are also, as already stated, monatomic gases.

The applicability of the law of Dulong and Petit to the determination of atomic weights has been frequently exemplified during the last sixty years; and a number of these constants have been rectified by its means—_e.g._, of thallium, uranium, glucinum, indium, etc. The anomalies presented by the cases of elements of low atomic weight—_e.g._, carbon, boron, silicon—have been further inquired into; and it has been shown by Weber, and independently by Dewar, that in the case of these substances the specific heat rapidly increases with the temperature, and approximates at high temperatures to a value required by the law of Dulong and Petit.

Within recent years other methods of ascertaining molecular weights have been put at the disposal of chemists. These methods are especially valuable in the case of bodies which cannot be volatilised. They depend upon the influence of the substance (1) upon the freezing-point and (2) upon the boiling-point of a solvent. It has long been known that a substance in solution affects the freezing-point of the solvent, and in the great majority of cases depresses it. Sir Charles Blagden, as far back as 1788, showed that in aqueous solutions of inorganic salts the depression was proportional to the amount dissolved. It was subsequently found by Coppet that, in a number of solutions of similar salts where these were present in the ratio of their molecular weights, the solutions froze at practically the same temperature: the molecular depressions of the freezing-points differ from group to group but are nearly equal in groups of similar compounds. Raoult further observed that, when certain quantities of the same substance are successively dissolved in a solvent on which it exerts no chemical action, there is a progressive lowering of the point of solidification of the solution, and this depression is proportional to the weight of the substance dissolved in a constant weight of the solvent. In the case of a large number of solvents the depressions of the freezing-point, calculated for amounts proportional to the molecular weights of the dissolved substance, were nearly constant. Raoult pointed out that these relations between the molecular weights and the lowering in the freezing-point may be employed to determine the molecular weight of a soluble substance. The molecular weight _m_ is found from the expression _m_ = K/A, where A is the quotient obtained by dividing the observed depression in the freezing-point of the solvent by the percentage content of the solution, and K (the molecular depression) is a constant dependent on the solvent. Thus in the case of phosphorous oxide it was found that 0.6760 gram added to 20.698 grams of benzene—in which the oxide is soluble without change—lowered the freezing-point of the 3.16 per cent. benzene solution by 0°.68. Since the value of K for benzene is 49, we have (3.16 × 49)/0.68 = 227, which serves to indicate that P4O6 is the true molecular formula for phosphorous oxide. This result is confirmed by vapour-density observations.

The effect of adding a substance to a solvent is to diminish the vapour pressure of the liquid. Hence, since the boiling-point of a liquid is that temperature at which the vapour pressure is equal to the atmospheric pressure, the effect of adding the soluble substance is to raise the boiling-point, since a higher temperature is required in order that the pressure of the vapour shall equal that of the atmosphere. It has been proved that equal volumes of solutions in the same solvent which have the same boiling-point contain an equal number of molecules of the dissolved substance.

The equation for the molecular increment of the boiling-point for a solvent is _d_ = 0.02T²/_w_, in which _d_ is the increment of the boiling-point caused by the solution of one gram-molecule of a substance in 100 grams of the solvent, T the _absolute_ boiling-point of the solvent, and _w_ the heat of vaporisation of the solvent for one gram. The molecular rise of the boiling-point is therefore independent of the nature of the dissolved substance.

The molecular weight of the substance _m_ is obtained from the formula _m_ = _pd_/Δ, in which _p_ = the percentage weight of the dissolved substance, _d_ = the molecular increment in boiling-point (0.02T²/_w_), Δ = the observed rise in boiling-point. If the latent heat of vaporisation of the liquid is unknown, the value of _d_ may be obtained by preliminary experiments with a substance of known molecular weight; in this case _d_ = _m_Δ/_p_.

The calculation of the molecular weight _m_ may also be made by the formula _m_ = K(_s_/ΔL) × 100, in which Δ is the rise in boiling-point, _s_ the weight of dissolved substance, L the weight of solvent, and K the molecular boiling-point increment. Convenient forms of apparatus for using these methods have been devised by Beckmann, and are now in general use.

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From the time of Berzelius, each successive generation of chemists has striven to better the example of that master of determinative chemistry in the effort to obtain accurate values for the atomic weights of the elements.

Among the immediate successors of Berzelius in this work should be mentioned Turner, Penny, Dumas, and Marignac. Dumas in 1859 published the results of an extensive revision of the atomic weights of the elements. On this he based the far-reaching generalisation that, in the language of Prout, “the combining or atomic weights of bodies bear certain simple relations to one another, frequently by multiple, and consequently that many of them must necessarily be multiples of some one unit.” Dumas further agreed with Prout that “there seems to be no reason why bodies still lower in the scale than hydrogen (similarly, however, related to one another, as well as to those above hydrogen) may not exist, of which other bodies may be multiples, without being actually multiples of the intermediate hydrogen.”

The Belgian chemist, Stas, who had been associated with Dumas in a classical determination of the atomic weight of carbon, set himself to determine, with the highest degree of precision then possible, the atomic weights of about a dozen of the elements, with a view of ascertaining (1) whether an atomic weight is a definite and constant quantity, or whether, as suggested by Marignac, and subsequently by Crookes, an atomic weight represents “a mean value around which the actual weights of the atoms vary within certain narrow limits”; (2) whether, if the atomic weights of the elements are respectively definite and invariable, the numbers are commensurable as alleged by Prout and Dumas; and (3) if it should turn out that the numbers are severally fixed and commensurable, whether this necessarily indicates that the elements are built up of a primordial matter, the πρώτη ιλη of the ancients, referred to by Prout in 1816.

Stas devoted many years to the solution of these questions, working on a scale and with an accuracy and manipulative skill previously unapproached. The main results of his labour appeared in 1865. He concluded (1) that the atomic weights of the elements are absolutely constant values, and are not affected by the nature of the compounds in which they occur, or the physical conditions of their existence; (2) that the numbers so obtained are not commensurable: to quote his own words: “_On doit considérer la loi de Prout comme une pure illusion._” Hence the elements must, on the basis of Stas’s experimental evidence, be regarded as “_individualités à part_,” as he expressed it—each a primordial and unalterable substance.

The appearance of this monumental work, which will ever remain one of the classics of chemistry, created a great impression. Its effect persists to this day. It constituted a model and furnished a standard which each successive worker has striven to emulate, with the result that atomic weights to-day are among the best ascertained of physical constants.

Space will not permit of any detailed account of the work done in connection with atomic weights during the forty-five years which have elapsed since the publication of Stas’s memoirs; and the reader who desires fuller information must be referred to the special treatises on the subject, such as the _Constants of Nature_ of F. W. Clarke, or the monographs of Meyer and Seubert, Becker, Sebelien, and Van der Plaats.

Reference, however, must be made to the determinations by Lord Rayleigh, Leduc, Morley, Noyes, Guye, Dixon, and Edgar of values which, like those of oxygen, hydrogen, nitrogen, silver, and the halogens, are largely made use of as fiduciary values in atomic-weight work.

Lastly, it should be mentioned, the re-determination of the atomic weights of the elements with the highest attainable precision and by the most refined and most modern methods has for some years past been a special feature of the work of the Harvard Laboratory, under the direction of Theodore Richards; and some of the most trustworthy and best established values we possess have been ascertained by him and his pupils. Atomic weights are of such fundamental importance that the various nations interested in the pursuit of chemistry have consented to the establishment of an International Committee, which will take cognisance of the work done from time to time in this department of operative chemistry, examine and assess its value, and draw up an annual report on the subject.

Despite the accumulated testimony of this work in relation to the validity of the law of the conservation of mass, the sufficiency of the evidence has now and again been impugned. This aspect of the matter has within recent years been directly investigated by Landolt; and as the result of a painstaking series of experiments, in which every recognised source of error was removed or allowed for, it would appear that there is absolutely no ground for the belief that there is any dissipation of mass in the course of, or as the result of, a chemical change.