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 = mΔ/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.