Footnotes:[1]If the weight be indicated by P, the density by D, and the volume by V, thenP/D=KVwhereKis a coefficient depending on the system of the expressions P, D, and V. If D be the weight of a cubic measure of a substance referred to the weight of the same measure of water—if, as in the metrical system (Chapter I., Note9), the cubic measure of one part by weight of water be taken as a unit of volume—thenK= 1. But, whatever it be, it is cancelled in dealing with the comparison of volumes, because comparative and not absolute measures of volumes are taken. In this chapter, as throughout the book, the weight P is given in grams in dealing with absolute weights; and if comparative, as in the expression of chemical composition, then the weight of an atom is taken as unity. The density of gases, D, is also taken in reference to the density of hydrogen, and the volume V in metrical units (cubic centimetres), if it be a matter of absolute magnitudes of volumes, and if it be a matter of chemical transformations—that is, of relative volumes—then the volume of an atom of hydrogen, or of one part by weight of hydrogen, is taken as unity, and all volumes are expressed according to these units.[2]As the volumetric relations of vapours and gases, next to the relations of substances by weight, form the most important province of chemistry, and a most important means for the attainment of chemical conclusions, and inasmuch as these volumetric relations are determined by the densities of gases and vapours, necessarily the methods of determining the densities of vapours (and also of gases) are important factors in chemical research. These methods are described in detail in works on physics and physical and analytical chemistry, and therefore we here only touch on the general principles of the subject.see captionFig.52.—Apparatus for determining the vapour density by Dumas' method. A small quantity of the liquid whose vapour density is to be determined is placed in the glass globe, and heated in a water or oil bath to a temperature above the boiling point of the liquid. When all the liquid has been converted into vapour and has displaced all the air from the globe, the latter is sealed up and weighed. The capacity of the globe is then measured, and in this manner the volume occupied by a known weight of vapour at a known temperature is determined.see captionFig.53.—Deville and Troost's apparatus for determining the vapour densities, according to Dumas' method, of substances which boil at high temperatures. A porcelain globe containing the substance whose vapour density is to be determined is heated in the vapour of mercury (350°), sulphur (410°), cadmium (850°), or zinc (1,040°). The globe is sealed up in an oxyhydrogen flame.see captionFig.54.—Hofmann's apparatus for determining vapour densities. The internal tube, about one metre long, which is calibrated and graduated, is filled with mercury and inverted in a mercury bath. A small bottle (depicted in its natural size on the left) containing a weighed quantity of the liquid whose vapour density is to be determined, is introduced into the Torricellian vacuum. Steam, or the vapour of amyl alcohol, &c., is passed through the outer tube, and heats the internal tube to the temperaturet, at which the volume of vapour is measured.see captionFig.55.—Victor Meyer's apparatus for determining vapour densities. The tubebis heated in the vapour of a liquid of constant boiling point. A glass tube, containing the liquid to be experimented upon, is caused to fall fromd. The air displaced is collected in the cylindere, in the troughf.If we know the weightpand volumev, occupied by the vapour of a given substance at a temperaturetand pressureh, then its density may be directly obtained by dividingpby the weight of a volumevof hydrogen (if the density be expressed according to hydrogen,seeChapter II., Note23) attandh. Hence, the methods of determining the density of vapours and gases are based on the determination ofp,v,t, andh. The two last data (the temperaturetand pressureh) are given by the thermometer and barometer and the heights of mercury or other liquid confining the gas, and therefore do not require further explanation. It need only be remarked that: (1) In the case of easily volatile liquids there is no difficulty in procuring a bath with a constant temperature, but that it is nevertheless best (especially considering the inaccuracy of thermometers) to have a medium of absolutely constant temperature, and therefore to take either a bath in which some substance is melting—such as melting ice at 0° or crystals of sodium acetate, melting at +56°—or, as is more generally practised, to place the vessel containing the substance to be experimented with in the vapour of a liquid boiling at a definite temperature, and knowing the pressure under which it is boiling, to determine the temperature of the vapour. For this purpose the boiling points of water at different pressures are given in Chapter I., Note11, and the boiling points of certain easily procurable liquids at various pressures are given in Chapter II., Note27. (2) With respect to temperatures above 300° (below which mercurial thermometers may be conveniently employed), they are most simply obtained constant (to give time for the weight and volume of a substance being observed in a given space, and to allow that space to attain the calculated temperaturet) by means of substances boiling at a high temperature. Thus, for instance, at the ordinary atmospheric pressure the temperaturetof the vapour of sulphur is about 445°, of phosphorus pentasulphide 518°, of tin chloride 606°, of cadmium 770°, of zinc 930° (according to Violle and others), or 1040° (according to Deville), &c. (3) The indications of the hydrogen thermometer must be considered as the most exact (but as hydrogen diffuses through incandescent platinum, nitrogen is usually employed). (4) The temperature of the vapours used as the bath should in every case be several degrees higher than the boiling point of the liquid whose density is to be determined, in order that no portion should remain in a liquid state. But even in this case, as is seen from the example of nitric peroxide (ChapterVI.), the vapour density does not always remain constant with a change oft, as it should were the law of the expansion of gases and vapours absolutely exact (Chapter II., Note26). If variations of a chemical and physical nature similar to that which we saw in nitric peroxide take place in the vapours, the main interest is centred inconstantdensities, which do not vary witht, and therefore the possible effect ofton the density must always be kept in mind in having recourse to this means of investigation. (5) Usually, for the sake of convenience of observation, the vapour density is determined at the atmospheric pressure which is read on the barometer; but in the case of substances which are volatilised with difficulty, and also of substances which decompose, or, in general, vary at temperatures near their boiling points, it is best or even indispensable to conduct the determination at low pressures, whilst for substances which decompose at low pressures the observations have to be conducted under a more or less considerably increased pressure. (6) In many cases it is convenient to determine the vapour density of a substance in admixture with other gases, and consequently under the partial pressure, which may be calculated from the volume of the mixture and that of the intermixed gas (seeChapter I., Note 1). This method is especially important for substances which are easily decomposable, because, as shown by the phenomena of dissociation, a substance is able to remain unchanged in the atmosphere of one of its products of decomposition. Thus, Wurtz determined the density of phosphoric chloride, PCl5, in admixture with the vapour of phosphorous chloride, PCl3. (7) It is evident, from the example of nitric peroxide, that a change of pressure may alter the density and aid decomposition, and therefore identical results are sometimes obtained (if the density be variable) by raisingtand loweringh; but if the density does not vary under these variable conditions (at least, to an extent appreciably exceeding the limits of experimental error), then thisconstantdensity indicates thegaseousandinvariablestate of a substance. The laws hereafter laid down refer only to such vapour densities. But the majority of volatile substances show such a constant density at a certain degree above their boiling points up to the starting point of decomposition. Thus, the density of aqueous vapour does not vary fortbetween the ordinary temperature and 1000° (there are no trustworthy determinations beyond this) and for pressures varying from fractions of an atmosphere up to several atmospheres. If, however, the density does vary considerably with a variation ofhandt, the fact may serve as a guide for the investigation of the chemical changes which are undergone by the substance in a state of vapour, or at least as an indication of a deviation from the laws of Boyle, Mariotte, and Gay-Lussac (for the expansion of gases witht). In certain cases the separation of one form of deviation from the other may be explained by special hypotheses.With respect to the means of determiningpandv, with a view to finding the vapour density, we may distinguish three chief methods: (a) by weight, by ascertaining the weight of a definite volume of vapour; (b) by volume, by measuring the volume occupied by the vapour of a definite weight of a substance; and (c) by displacement. The last-mentioned is essentially volumetric, because a known weight of a substance is taken, and the volume of the air displaced by the vapour at a giventandhis determined.The method by weight (a) is the most trustworthy and historically important.Dumas' methodis typical. An ordinary spherical glass or porcelain vessel, like those shown respectively in figs.52and54, is taken, and an excess of the substance to be experimented upon is introduced into it. The vessel is heated to a temperaturethigher than the boiling point of the liquid: this gives a vapour which displaces the air, and fills the spherical space. When the air and vapour cease escaping from the sphere, it is fused up or closed by some means; and when cool, the weight of the vapour remaining in the sphere is determined (either by direct weighing of the vessel with the vapour and introducing the necessary corrections for the weight of the air and of the vapour itself, or the weight of the volatilised substance is determined by chemical methods), and the volume of the vapour attand the barometric pressurehare then calculated.The volumetric method(b) originally employed by Gay-Lussac and then modified by Hofmann and others is based on the principle that a weighed quantity of the liquid to be experimented with (placed in a small closed vessel, which is sometimes fused up before weighing, and, if quite full of the liquid, breaks when heated in a vacuum) is introduced into a graduated cylinder heated tot, or simply into a Torricellian vacuum, as shown in fig.54, and the number of volumes occupied by the vapour noted when the space holding it is heated to the desired temperaturet.The method of displacement(c) proposed by Victor Meyer is based on the fact that a spacebis heated to a constant temperaturet(by the surrounding vapours of a liquid of constant boiling point), and the air (or other gas enclosed in this space) is allowed to attain this temperature, and when it has done so a glass bulb containing a weighed quantity of the substance to be experimented with is dropped into the space. The substance is immediately converted into vapour, and displaces the air into the graduated cylindere. The amount of this air is calculated from its volume, and hence the volume att, and therefore also the volume occupied by the vapour, is found. The general arrangement of the apparatus is given in fig.55.[3]Vapours and gases, as already explained in thesecond chapter, are subject to the same laws, which are, however, only approximate. It is evident that for the deduction of the laws which will presently be enunciated it is only possible to take into consideration a perfect gaseous state (far removed from the liquid state) and chemical invariability in which thevapour density is constant—that is, the volume of a given gas or vapour varies like a volume of hydrogen, air, or other gas, with the pressure and temperature.It is necessary to make this statement in order that it may be clearly seen that the laws of gaseous volumes, which we shall describe presently, are in the most intimate connection with the laws of the variations of volumes with pressure and temperature. And as these latter laws (ChapterII.) are not infallible, but only approximately exact, the same, therefore, applies to the laws about to be described. And as it is possible to find more exact laws (a second approximation) for the variation ofvwithpandt(for example, van der Waals' formula, Chapter II., Note33), so also a more exact expression of the relation between the composition and the density of vapours and gases is also possible. But to prevent any doubt arising at the very beginning as to the breadth and general application of the laws of volumes, it will be sufficient to mention that the density of such gases as oxygen, nitrogen, and carbonic anhydride is already known toremain constant(within the limits of experimental error) between the ordinary temperature and a white heat; whilst, judging from what is said in my work on the ‘Tension of Gases’ (vol. i. p. 9), it may be said that, as regards pressure, the relative density remains very constant, even when the deviations from Mariotte's law are very considerable. However, in this respect the number of data is as yet too small to arrive at an exact conclusion.[4]We must recollect that this law is only approximate, like Boyle and Mariotte's law, and that, therefore, like the latter, a more exact expression may be found for the exceptions.[5]This second law of volumes may be considered as a consequence of the first law. The first law requires simple ratios between the volumes of the combining substancesAandB. A substanceABis produced by their combination. It may, according to the law of multiple proportion, combine, not only with substancesC,D, &c., but also withAand withB. In this new combination the volume ofAB, combining with the volume ofA, should be in simple multiple proportion with the volume ofA; hence the volume of the compoundABis in simple proportion to the volume of its component parts. Therefore only one law of volumes need be accepted. We shall afterwards see that there is a third law of volumes embracing also the two first laws.[6]It must not be forgotten that Newton's law of gravity was first a hypothesis, but it became a trustworthy, perfect theory, and acquired the qualities of a fundamental law owing to the concord between its deductions and actual facts. All laws, all theories, of natural phenomena, are at first hypotheses. Some are rapidly established by their consequences exactly agreeing with facts; others only take root by slow degrees; and there are many which are destined to be refuted owing to their consequences being found to be at variance with facts.[7]This is not only seen from the above calculations, but may be proved by experiment. A glass tube, divided in the middle by a stopcock, is taken and one portion filled withdryhydrogen chloride (the dryness of the gases is very necessary, because ammonia and hydrogen chloride are both very soluble in water, so that a small trace of water may contain a large amount of these gases in solution) and the other with dry ammonia, under the atmospheric pressure. One orifice (for instance, of that portion which contains the ammonia) is firmly closed, and the other is immersed under mercury, and the cock is then opened. Solid sal-ammoniac is formed, but if the volume of one gas be greater than that of the other, some of the first gas will remain. By immersing the tube in the mercury in order that the internal pressure shall equal the atmospheric pressure, it may easily be shown that the volume of the remaining gas is equal to the difference between the volumes of the two portions of the tube, and that this remaining gas is part of that whose volume was the greater.[8]Let us demonstrate this by figures. From 122 grams of benzoic acid there are obtained (a) 78 grams of benzene, whose density referred to hydrogen = 39, hence the relative volume = 2; and (b) 44 grams of carbonic anhydride, whose density = 22, and hence the volume = 2. It is the same in other cases.[9]A large number of such generalised reactions, showing reaction by equal volumes, occur in the case of the hydrocarbon derivatives, because many of these compounds are volatile. The reactions of alkalis on acids, or anhydrides on water, &c., which are so frequent between mineral substances, present but few such examples, because many of these substances are not volatile and their vapour densities are unknown. But essentially the same is seen in these cases also; for instance, sulphuric acid, H2SO4, breaks up into the anhydride, SO3, and water, H2O, which exhibit an equality of volumes. Let us take another example where three substances combine in equal volumes: carbonic anhydride, CO2, ammonia, NH3, and water, H2O (the volumes of all are equal to 2), form acid ammonium carbonate, (NH4)HCO3.[10]This opinion which I have always held (since the first editions of this work), as to the primary origin of hydrogen peroxide and of the formation of water by means of its decomposition, has in latter days become more generally accepted, thanks more especially to the work of Traube. Probably it explains most simply the necessity for the presence of traces of water in many reactions, as, for instance, in the explosion of carbonic oxide with oxygen, and perhaps the theory of the explosion of detonating gas itself and of the combustion of hydrogen will gain in clearness and truth if we take into consideration the preliminary formation of hydrogen peroxide and its decomposition. We may here point out the fact that Ettingen (at Dorpat, 1888) observed the existence of currents and waves in the explosion of detonating gas by taking photographs, which showed the periods of combustion and the waves of explosion, which should be taken into consideration in the theory of this subject. As the formation of H2O2from O2and H2corresponds with a less amount of heat than the formation of water from H2and O, it may be that the temperature of the flame of detonating gas depends on the pre-formation of hydrogen peroxide.[11]The possibility of reactions between unequal volumes, notwithstanding the general application of the law of Avogadro-Gerhardt, may, in addition to what has been said above, depend on the fact that the participating substances, at the moment of reaction, undergo a preliminary modification, decomposition, isomeric (polymeric) transformation, &c. Thus, if NO2, seems to proceed from N2O4, if O2is formed from O3, and the converse, then it cannot be denied that the production of molecules containing only one atom is also possible—for instance, of oxygen—as also of higher polymeric forms—as the molecule N from N2, or H3from H2. In this manner it is obviously possible, by means of a series of hypotheses, to explain the cases of the formation of ammonia, NH3, from 3 vols. of hydrogen and 1 vol. of nitrogen. But it must be observed that perhaps our information in similar instances is, as yet, far from being complete. If hydrazine or diamide N2H4(Chapter VI. Note20 bis) is formed and the imide N2H2in which 2 vols. of hydrogen are combined with 2 vols. of nitrogen, then the reaction here perhaps first takes place between equal volumes. If it be shown that diamide gives nitrogen and ammonia (3N2H4= N2+ 4NH3) under the action of sparks, heat, or the silent discharge, &c., then it will be possible to admit that it is formed before ammonia. And perhaps the still less stable imide N2H2, which may also decompose with the formation of ammonia, is produced before the amide N2H4.I mention this to show that the fact of apparent exceptions existing to the law of reactions between equal volumes does not prove the impossibility of their being included under the law on further study of the subject. Having put forward a certain law or hypothesis, consequences must be deduced from it, and if by their means clearness and consistency are attained—and especially, if by their means that which could not otherwise be known can be predicted—then the consequences verify the hypothesis. This was the case with the law now under discussion. The mere simplicity of the deduction of the weights proper to the atoms of the elements, or the mere fact that having admitted the law it follows (as will afterwards be shown) that thevis vivaof the molecules of all gases is a constant quantity, is quite sufficient reason for retaining the hypothesis, if not for believing in it as a fact beyond doubt. And such is the whole doctrine of atoms. And since by the acceptance of the law it became possible to foretell even the properties and atomic weights of elements which had not yet been discovered, and these predictions afterwards proved to be in agreement with the actual facts, it is evident that the law of Avogadro-Gerhardt penetrates deeply into the nature of the chemical relation of substances. This being granted, it is possible at the present time to exhibit and deduce the truth under consideration in many ways, and in every case, like all that is highest in science (for example, the laws of the indestructibility of matter, of the conservation of energy, of gravity, &c.), it proves to be not an empirical conclusion from direct observation and experiment, not a direct result of analysis, but a creation, or instinctive penetration, of the inquiring mind, guided and directed by experiment and observation—a synthesis of which the exact sciences are capable equally with the highest forms of art. Without such a synthetical process of reasoning, science would only be a mass of disconnected results of arduous labour, and would not be distinguished by that vitality with which it is really endowed when once it succeeds in attaining a synthesis, or concordance of outward form with the inner nature of things, without losing sight of the diversities of individual parts; in short, when it discovers by means of outward phenomena, which are apparent to the sense of touch, to observation, and to the common mind, the internal signification of things—discovering simplicity in complexity and uniformity in diversity. And this is the highest problem of science.[12]As the density of aqueous vapour remains constant within the limits of experimental accuracy, even at 1,000°, when dissociation has certainly commenced, it would appear that only a very small amount of water is decomposed at these temperatures. If even 10 p.c. of water were decomposed, the density would be 8·57 and the quotient M/D = 2·1, but at the high temperatures here concerned the error of experiment is not greater than the difference between this quantity and 2. And probably at 1,000° the dissociation is far from being equal to 10 p.c.Hence the variation in the vapour density of water does not give us the means of ascertaining the amount of its dissociation.[13]This explanation of the vapour density of sal-ammoniac, sulphuric acid, and similar substances which decompose in being distilled was the most natural to resort to as soon as the application of the law of Avogadro-Gerhardt to chemical relations was begun; it was, for instance, given in my work onSpecific Volumes, 1856, p. 99. The formula, M/D = 2, which was applied later by many other investigators, had already been made use of in that work.[14]The beginner must remember that an experiment and the mode in which it is carried out must be determined by the principle or fact which it is intended to illustrate, and notvice versa, as some suppose. The idea which determines the necessity of an experiment is the chief consideration.[15]It is important that the tubes, asbestos, and sal-ammoniac should be dry, as otherwise the moisture retains the ammonia and hydrogen chloride.[15 bis]Baker (1894) showed that the decomposition of NH4Cl in the act of volatilising only takes place in the presence of water, traces of which are amply sufficient, but that in the total absence of moisture (attained by carefully drying with P2O5) there is no decomposition, and the vapour density of the sal-ammoniac is found to be normal,i.e., nearly 27. It is not yet quite clear what part the trace of moisture plays here, and it must be presumed that the phenomenon belongs to the category of electrical and contact phenomena, which have not yet been fully explained (seeChapter IX., Note29).[16]Just as we saw (Chapter VI. Note46) an increase of the dissociation of N2O4and the formation of a large proportion of NO2, with a decrease of pressure. The decomposition of I2into I + I is a similar dissociation.[17]Although at first there appeared to be a similar phenomenon in the case of chlorine, it was afterwards proved that if there is a decrease of density it is only a small one. In the case of bromine it is not much greater, and is far from being equal to that for iodine.As in general we very often involuntarily confuse chemical processes with physical, it may be that a physical process of change in the coefficient of expansion with a change of temperature participates with a change in molecular weight, and partially, if not wholly, accounts for the decrease of the density of chlorine, bromine, and iodine. Thus, I have remarked (Comptes Rendus, 1876) that the coefficient of expansion of gases increases with their molecular weight, and (Chapter II., Note26) the results of direct experiment show the coefficient of expansion of hydrobromic acid (M = 81) to be 0·00386 instead of 0·00367, which is that of hydrogen (M = 2). Hence, in the case of the vapour of iodine (M = 254) a very large coefficient of expansion is to be expected, and from this cause alone the relative density would fall. As the molecule of chlorine Cl2is lighter (= 71) than that of bromine (= 160), which is lighter than that of iodine (= 254), we see that the order in which the decomposability of the vapours of these haloids is observed corresponds with the expected rise in the coefficient of expansion. Taking the coefficient of expansion of iodine vapour as 0·004, then at 1,000° its density would be 116. Therefore the dissociation of iodine may be only an apparent phenomenon. However, on the other hand, the heavy vapour of mercury (M = 200, D = 100) scarcely decreases in density at a temperature of 1,500° (D = 98, according to Victor Meyer); but it must not be forgotten that the molecule of mercury contains only one atom, whilst that of iodine contains two, and this is very important. Questions of this kind which are difficult to decide by experimental methods must long remain without a certain explanation, owing to the difficulty, and sometimes impossibility, of distinguishing between physical and chemical changes.[18]And so it was in the fifties. Some took O = 8, others O = 16. Water in the first case would be HO and hydrogen peroxide HO2, and in the second case, as is now generally accepted, water H2O and hydrogen peroxide H2O2or HO. Disagreement and confusion reigned. In 1860 the chemists of the whole world met at Carlsruhe for the purpose of arriving at some agreement and uniformity of opinion. I was present at this Congress, and well remember how great was the difference of opinion, and how a compromise was advocated with great acumen by many scientific men, and with what warmth the followers of Gerhardt, at whose head stood the Italian professor, Canizzaro, followed up the consequences of the law of Avogadro. In the spirit of scientific freedom, without which science would make no progress, and would remain petrified as in the middle ages, and with the simultaneous necessity of scientific conservatism, without which the roots of past study could give no fruit, a compromise was not arrived at, nor ought it to have been, but instead of it truth, in the form of the law of Avogadro-Gerhardt, received by means of the Congress a wider development, and soon afterwards conquered all minds. Then the new so-called Gerhardt atomic weights established themselves, and in the seventies they were already in general use.[19]A bubble of gas, a drop of liquid, or the smallest crystal, presents an agglomeration of a number of molecules, in a state of continual motion (like the stars of the Milky Way), distributing themselves evenly or forming new systems. If the aggregation of all kinds of heterogeneous molecules be possible in a gaseous state, where the molecules are considerably removed from each other, then in a liquid state, where they are already close together, such an aggregation becomes possible only in the sense of the mutual reaction between them which results from their chemical attraction, and especially in the aptitude of heterogeneous molecules for combining together. Solutions and other so-called indefinite chemical compounds should be regarded in this light. According to the principles developed in this work we should regard them as containing both the compounds of the heterogeneous molecules themselves and the products of their decomposition, as in peroxide of nitrogen, N2O4and NO2. And we must consider that those molecules A, which at a given moment are combined with B in AB, will in the following moment become free in order to again enter into a combined form. The laws of chemical equilibrium proper to dissociated systems cannot be regarded in any other light.[20]This strengthens the fundamental idea of the unity and harmony of type of all creation and is one of those ideas which impress themselves on man in all ages, and give rise to a hope of arriving in time, by means of a laborious series of discoveries, observations, experiments, laws, hypotheses, and theories, at a comprehension of the internal and invisible structure of concrete substances with that same degree of clearness and exactitude which has been attained in the visible structure of the heavenly bodies. It is not many years ago since the law of Avogadro-Gerhardt took root in science. It is within the memory of many living scientific men, and of mine amongst others. It is not surprising, therefore, that as yet little progress has been made in the province of molecular mechanics; but the theory of gases alone, which is intimately connected with the conception of molecules, shows by its success that the time is approaching when our knowledge of the internal structure of matter will be defined and established.[21]If Be = 9, and beryllium chloride be BeCl2, then for every 9 parts of beryllium there are 71 parts of chlorine, and the molecular weight of BeCl2= 80; hence the vapour density should be 40 orn40. If Be = 13·5, and beryllium chloride be BeCl3, then to 13·5 of beryllium there are 106·5 of chlorine; hence the molecular weight would be 120, and the vapour density 60 orn60. The composition is evidently the same in both cases, because 9 : 71 ∷ 13·5 : 106·5. Thus, if the symbol of an element designate different atomic weights, apparently very different formulæ may equally well express both the percentage composition of compounds, and those properties which are required by the laws of multiple proportions and equivalents. The chemists of former days accurately expressed the composition of substances, and accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6, Si = 14, &c. The Gerhardt equivalents are also satisfied by them, because O = 16, C = 12, Si = 28, &c., are multiples of them. The choice of one or the other multiple quantity for the atomic weight is impossible without a firm and concrete conception of the molecule and atom, and this is only obtained as a consequence of the law of Avogadro-Gerhardt, and hence the modern atomic weights are the results of this law (seeNote28).[22]The percentage amounts of the elements contained in a given compound may be calculated from its formula by a simple proportion. Thus, for example, to find the percentage amount of hydrogen in hydrochloric acid we reason as follows:—HCl shows that hydrochloric acid contains 35·5 of chlorine and 1 part of hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1 part by weight of hydrogen, consequently 100 parts by weight of hydrochloric acid will contain as many more units of hydrogen as 100 is greater than 36·5; therefore, the proportion is as follows—x: 1 ∷ 100 : 36·5 orx=100/36·5= 2·739. Therefore 100 parts of hydrochloric acid contain 2·739 parts of hydrogen. In general, when it is required to transfer a formula into its percentage composition, we must replace the symbols by their corresponding atomic weights and find their sum, and knowing the amount by weight of a given element in it, it is easy by proportion to find the amount of this element in 100 or any other quantity of parts by weight. If, on the contrary, it be required to find the formula from a given percentage composition, we must proceed as follows: Divide the percentage amount of each element entering into the composition of a substance by its atomic weight, and compare the figures thus obtained—they should be in simple multiple proportion to each other. Thus, for instance, from the percentage composition of hydrogen peroxide, 5·88 of hydrogen and 94·12 of oxygen, it is easy to find its formula; it is only necessary to divide the amount of hydrogen by unity and the amount of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained, which are in the ratio 1 : 1, which means that in hydrogen peroxide there is one atom of hydrogen to one atom of oxygen.The following is a proof of the practical rule given abovethat to find the ratio of the number of atoms from the percentage composition, it is necessary to divide the percentage amounts by the atomic weights of the corresponding substances, and to find the ratio which these numbers bear to each other. Let us suppose that two radicles (simple or compound), whose symbols and combining weights are A and B, combine together, forming a compound composed ofxatoms of A andyatoms of B. The formula of the substance will be AxBy. From this formula we know that our compound containsxA parts by weight of the first element, andyB of the second. In 100 parts of our compound there will be (by proportion)100.xA/xA +yBof the first element, and100.yB/xA +yBof the second. Let us divide these quantities, expressing the percentage amounts by the corresponding combining weights; we then obtain100x/xA +yBfor the first element and100y/xA +yBfor the second element. And these numbers are in the ratiox:y—that is, in the ratio of the number of atoms of the two substances.It may be further observed that even the very language or nomenclature of chemistry acquires a particular clearness and conciseness by means of the conception of molecules, because then the names of substances may directly indicate their composition. Thus the term ‘carbon dioxide’ tells more about and expresses CO2better than carbonic acid gas, or even carbonic anhydride. Such nomenclature is already employed by many. But expressing the composition without an indication or even hint as to the properties, would be neglecting the advantageous side of the present nomenclature. Sulphur dioxide, SO2, expresses the same as barium dioxide, BaO2, but sulphurous anhydride indicates the acid properties of SO2. Probably in time one harmonious chemical language will succeed in embracing both advantages.[23]This formula (which is given in my work on ‘The Tension of Gases,’ and in a somewhat modified form in the ‘Comptes Rendus,’ Feb. 1876) is deduced in the following manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is the molecular weight and D the density referred to hydrogen. But it is equal to the weights0of a cubic centimetre of a gas in grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the weightsof a cubic centimetre of a gas at a temperaturetand under a pressurep(in centimetres) is equal tos0p/76(1 +at). Therefore,s0=s.76(1 +at)/p; hence D = 76.s(1 +at)/0·0000898p, whence M = 152s(1 +at)/0·0000898p, which gives the above expression, because 1/a= 273, and 152 multiplied by 273 and divided by 0·0000898 is nearly 6200. In place ofs,m/vmay be taken, wheremis the weight andvthe volume of a vapour.[24]The above formula may be directly applied in order to ascertain the molecular weight from the data; weight of vapourmgrms., its volumevc.c., pressurepcm., and temperaturet°; fors= the weight of vapourm, divided by the volumev, and consequently M = 6,200m(273 +t)/pv. Therefore, instead of the formula (seeChapter II., Note 34),pv= R(273 +t), where R varies with the mass and nature of a gas, we may apply the formulapv= 6,200(m/M)(273 +t). These formulæ simplify the calculations in many cases. For example, required the volumevoccupied by 5 grms. of aqueous vapour at a temperaturet= 127° and under a pressurep= 76 cm. According to the formula M = 6,200m(273 +t)/pv, we find thatv= 9,064 c.c., as in the case of water M = 18,min this instance = 5 grms. (These formulæ, however, like the laws of gases, are only approximate.)[25]Chapter I., Note34.[26]The velocity of the transmission of sound through gases and vapoursclosely bears on this. It = √(Kpg)/D(1 +at), whereKis the ratio between the two specific heats (it is approximately 1·4 for gases containing two atoms in a molecule),pthe pressure of the gas expressed by weight (that is, the pressure expressed by the height of a column of mercury multiplied by the density ofa= 0·00367, andtthe temperature. Hence, ifKbe known, and as D can he found from the composition of a gas, we can calculate the velocity of the transmission of sound in that gas. Or if this velocity be known, we can findK. The relative velocities of sound in two gases can he easily determined (Kundt).If a horizontal glass tube (about 1 metre long and closed at both ends) be full of a gas, and be firmly fixed at its middle point, then it is easy to bring the tube and gas into a state of vibration, by rubbing it from centre to end with a damp cloth. The vibration of the gas is easily rendered visible, if the interior of the tube be dusted with lycopodium (the yellow powder-dust or spores of the lycopodium plant is often employed in medicine), before the gas is introduced and the tube fused up. The fine lycopodium powder arranges itself in patches, whose number depends on the velocity of sound in the gas. If there be 10 patches, then the velocity of sound in the gas is ten times slower than in glass. It is evident that this is an easy method of comparing the velocity of sound in gases. It has been demonstrated by experiment that the velocity of sound in oxygen is four times less than in hydrogen, and the square roots of the densities and molecular weights of hydrogen and oxygen stand in this ratio.[27]If the conception of the molecular weights of substances does not give an exact law when applied to the latent heat of evaporation, at all events it brings to light a certain uniformity in figures, which otherwise only represent the simple result of observation. Molecular quantities of liquids appear to expend almost equal amounts of heat in their evaporation. It may be said that the latent heat of evaporation of molecular quantities is approximately constant, because thevis vivaof the motion of the molecules is, as we saw above, a constant quantity. According to thermodynamics the latent heat of evaporation is equal tot+ 273/xA +yB(n′ -n)dp/dT× 13·59, wheretis the boiling point,n′ the specific volume (i.e.the volume of a unit of weight) of the vapour, andnthe specific volume of the liquid,dp/dT the variation of the tension with a rise of temperature per 1°, and 13·89 the density of the mercury according to which the pressure is measured. Thus the latent heat of evaporation increases not only with a decrease in the vapour density (i.e.the molecular weight), but also with an increase in the boiling point, and therefore depends on different factors.[27 bis]The osmotic pressure, vapour tension of the solvent, and several other means applied like the cryoscopic method to dilute solutions for determining the molecular weight of a substance in solution, are more difficult to carry out in practice, and only the method ofdetermining the rise of the boiling pointof dilute solutions can from its facility be placed parallel with the cryoscopic method, to which it bears a strong resemblance, as in both the solvent changes its state and is partially separated. In the boiling point method it passes off in the form of a vapour, while in cryoscopic determinations it separates out in the form of a solid body.Van't Hoff, starting from the second law of thermodynamics, showed that the dependence of the rise of pressure (dp) upon a rise of temperature (dT) is determined by the equationdp= (kmp/2T2)dT, wherekis the latent heat of evaporation of the solvent,mits molecular weight,pthe tension of the saturated vapour of the solvent at T, and T the absolute temperature (T = 273 +t), while Raoult found that the quantity (p-p′)/p(Chapter I., Note50) or the measure of the relative fall of tension (pthe tension of the solvent or water, andp′of the solution) is found by the ratio of the number of molecules,nof the substance dissolved, and N of the solvent, so that (p-p′)/p= Cn/(N +n) where C is a constant. With very dilute solutionsp- p′may be taken as equal todp, and the fractionn/(N +n) as equal ton/N (because in that case the value of N is very much greater thann), and then, judging from experiment, C is nearly unity—hence:dp/p=n/N ordp=np/N, and on substituting this in the above equation we have (kmp/2T2)dT =np/N. Taking a weight of the solventm/N = 100, and of the substance dissolved (per 100 of the solvent)q, whereqevidently =nM, if M be the molecular weight of the substance dissolved, we find thatn/N =qm/100M, and hence, according to the preceding equation, we have M =0·02T2/k·q/dT, that is, by taking a solution ofqgrms. of a substance in 100 grms. of a solvent, and determining by experiment the rise of the boiling pointdT, we find the molecular weight M of the substance dissolved, because the fraction 0·02T2/kis (for a given pressure and solvent) a constant; for water at 100° (T = 373°) whenk= 534 (Chapter I., Note11), it is nearly 5·2, for ether nearly 21, for bisulphide of carbon nearly 24, for alcohol nearly 11·5, &c. As an example, we will cite from the determinations made by Professor Sakurai, of Japan (1893), that when water was the solvent and the substance dissolved, corrosive sublimate, HgCl2, was taken in the quantityq= 8·978 and 4·253 grms., the rise in the boiling pointdT was = O°·179 and 0°·084, whence M = 261 and 263, and when alcohol was the solvent,q= 10·873 and 8·765 anddT = 0°·471 and 0°·380, whence M = 266 and 265, whilst the actual molecular weight of corrosive sublimate = 271, which is very near to that given by this method. In the same manner for aqueous solutions of sugar (M = 342), whenqvaried from 14 to 2·4, and the rise of the boiling point from 0°·21 to 0°·035, M was found to vary between 339 and 364. For solutions of iodine I2in ether, the molecular weight was found by this method to be between 255 and 262, and I2= 254. Sakurai obtained similar results (between 247 and 262) for solutions of iodine in bisulphide of carbon.We will here remark that in determining M (the molecular weight of the substance dissolved) at small but increasing concentrations (per 100 grms. of water), the results obtained by Julio Baroni (1893) show that the value of M found by the formula may either increase or decrease. An increase, for instance, takes place in aqueous solutions of HgCl2(from 255 to 334 instead of 271), KNO3(57–66 instead of 101), AgNO3(104–107 instead of 170), K2SO4(55–89 instead of 174), sugar (328–348 instead of 342), &c. On the contrary the calculated value of M decreases as the concentration increases, for solutions of KCl (40–39 instead of 74·5), NaCl (33–28 instead of 58·5), NaBr (60–49 instead of 103), &c. In this case (as also for LiCl, NaI, C2H3NaO2, &c.) the value ofi(Chapter I., Note49), or the ratio between the actual molecular weight and that found by the rise of the boiling point, was found to increase with the concentration,i.e.to be greater than 1, and to differ more and more from unity as the strength of the solution becomes greater. For example, according to Schlamp (1894), for LiCl, with a variation of from 1·1 to 6·7 grm. LiCl per 100 of water,ivaries from 1·63 to 1·89. But for substances of the first series (HgCl2, &c.), although in very dilute solutionsiis greater than 1, it approximates to 1 as the concentration increases, and this is the normal phenomenon for solutions which do not conduct an electric current, as, for instance, of sugar. And with certain electrolytes, such as HgCl2, MgSO4, &c.,iexhibits a similar variation; thus, for HgCl2the value of M is found to vary between 255 and 334; that is,i(as the molecular weight = 271) varies between 1·06 and 0·81. Hence I do not believe that the difference betweeniand unity (for instance, for CaCl2,iis about 3, for KI about 2, and decreases with the concentration) can at present be placed at the basis of any general chemical conclusions, and it requires further experimental research. Among other methods by which the value ofiis now determined for dilute solutions is the study of their electroconductivity, admitting thati= 1 +a(k- 1), wherea= the ratio of the molecular conductivity to the limiting conductivity corresponding to an infinitely large dilution (seePhysical Chemistry), andkis the number of ions into which the substance dissolved can split up. Without entering upon a criticism of this method of determiningi, I will only remark that it frequently gives values ofivery close to those found by the depression of the freezing point and rise of the boiling point; but that this accordance of results is sometimes very doubtful. Thus for a solution containing 5·67 grms. CaCl2per 100 grms. of water,i, according to the vapour tension = 2·52, according to the boiling point = 2·71, according to the electroconductivity = 2·28, while for solutions in propyl alcohol (Schlamp 1894)iis near to 1·33. In a word, although these methods of determining the molecular weight of substances in solution show an undoubted progress in the general chemical principles of the molecular theory, there are still many points which require explanation.We will add certain general relations which apply to these problems. Isotonic (Chapter I., Note19) solutions exhibit not only similar osmotic pressures, but also the same vapour tension, boiling point and freezing temperature. The osmotic pressure bears the same relation to the fall of the vapour tension as the specific gravity of a solution does to the specific gravity of the vapour of the solvent. The general formulæ underlying the whole doctrine of the influence of the molecular weight upon the properties of solutions considered above, are: 1. Raoult in 1886–1890 showed thatp-p′/p·100/a·M/m= a constant Cwherepandp′ are the vapour tensions of the solvent and substance dissolved,athe amount in grms. of the substance dissolved per 100 grms. of solvent, M andmthe molecular weights of the substance dissolved and solvent. 2. Raoult and Recoura in 1890 showed that the constant above C = the ratio of the actual vapour densityd′ of the solvent to the theoretical densitydcalculated according to the molecular weight. This deduction may now be considered proved, because both the fall of tension and the ratio of the vapour densitiesd′/dgive, for water 1·03, for alcohol 1·02, for ether 1·04, for bisulphide of carbon 1·00, for benzene 1·02, for acetic acid 1·63. 3. By applying the principles of thermodynamics and calling L1the latent heat of fusion and T1the absolute (=t+ 273) temperature of fusion of the solvent, and L2and T2the corresponding values for the boiling point, Van't Hoff in 1886–1890 deduced:—Depression of freezing point/Rise of boiling point=L2/L1·T12/T22Depression of freezing point =AT12a/L1M1Rise of boiling point =AT22a/L2M1where A = 0·01988 (or nearly 0·02 as we took it above),ais the weight in grms. of the substance dissolved per 100 grms. of the solvent, M1the molecular weight of the dissolved substance (in the solution), and M the molecular weight of this substance according to its composition and vapour density, theni= M/M1. The experimental data and theoretical considerations upon which these formulæ are based will be found in text-books of physical and theoretical chemistry.[28]A similar conclusion respecting the molecular weight of liquid water (i.e.that its molecule in a liquid state is more complex than in a gaseous state, or polymerized into H8O4, H6O3or in general intonH2O) is frequently met in chemico-physical literature, but as yet there is no basis for its being fully admitted, although it is possible that a polymerization or aggregation of several molecules into one takes place in the passage of water into a liquid or solid state, and that there is a converse depolymerization in the act of evaporation. Recently, particular attention has been drawn to this subject owing to the researches of Eötvös (1886) and Ramsay and Shields (1893) on the variation of the surface tension N with the temperature (N = the capillary constanta2multiplied by the specific gravity and divided by 2, for example, for water at 0° and 100° the value ofa2= 15·41 and 12·58 sq. mm., and the surface tension 7·92 and 6·04). Starting from the absolute boiling point (Chapter II., Note29) and adding 6°, as was necessary from all the data obtained, and calling this temperature T, it is found that AS =kT, where S is the surface of a gram-molecule of the liquid (if M is its weight in grams,sits sp. gr., then its sp. volume = M/s, and the surface S = ∛(M/s)2), A the surface tension (determined by experiment at T), andka constant which is independent of the composition of the molecule. The equation AS =kT is in complete agreement with the well-known equation for gasesvp= RT (p.140) which serves for deducing the molecular weight from the vapour density. Ramsay's researches led him to the conclusion that the liquid molecules of CS2, ether, benzene, and of many other substances, have the same value as in a state of vapour, whilst with other liquids this is not the case, and that to obtain an accordance, that is, thatkshall be a constant, it is necessary to assume the molecular weight in the liquid state to bentimes as great. For the fatty alcohols and acidsnvaries from 1½ to 3½, for water from 2¼ to 4, according to the temperature (at which the depolymerization takes place). Hence, although this subject offers a great theoretical interest, it cannot be regarded as firmly established, the more so since the fundamental observations are difficult to make and not sufficiently numerous; should, however, further experiments confirm the conclusions arrived at by Professor Ramsay, this will give another method of determining molecular weights.[28 bis]Their variance is expressed in the same manner as was done by Van't Hoff (Chapter I., Notes19and49) by the quantityi, taking it as = 1 whenk= 1·05, in that case for KI,iis nearly 2, for borax about 4, &c.[29]We will cite one more example, showing the direct dependence of the properties of a substance on the molecular weight. If one molecular part by weight of the various chlorides—for instance, of sodium, calcium, barium, &c.—be dissolved in 200 molecular parts by weight of water (for instance, in 3,600 grams) then it is found that the greater the molecular weight of the salt dissolved, the greater is the specific gravity of the resultant solution.MolecularweightSp. gr. at 15°MolecularweightSp. gr. at 15°HCl36·51·0041CaCl21111·0236NaCl58·51·0106NiCl21301·0328KCl74·51·0121ZnCl21361·0331BeCl2801·0138BaCl22081·0489MgCl2951·0203[29 bis]With respect to the optical refractive power of substances, it must first be observed that the coefficient of refraction is determined by two methods: (a) either all the data are referred to one definite ray—for instance, to the Fraunhofer (sodium) line D of the solar spectrum—that is, to a ray of definite wave length, and often to that red ray (of the hydrogen spectrum) whose wave length is 656 millionths of a millimetre; (b) or Cauchy's formula is used, showing the relation between the coefficient of refraction and dispersion to the wave lengthn= A +B/λ, where A and B are two constants varying for every substance but constant for all rays of the spectrum, and λ is the wave length of that ray whose coefficient of refraction isn. In the latter method the investigation usually concerns the magnitudes of A, which are independent of dispersion. We shall afterwards cite the data, investigated by the first method, by which Gladstone, Landolt, and others established the conception of the refraction equivalent.It has long been known that thecoefficient of refraction nfor a given substance decreases with the density of a substance D, so that the magnitude (n- 1) ÷ D = C is almost constant for a given ray (having a definite wave length) and for a given substance. This constant is called therefractive energy, and its product with the atomic or molecular weight of a substance therefraction equivalent. The coefficient of refraction of oxygen is 1·00021, of hydrogen 1·00014, their densities (referred to water) are 0·00143 and 0·00009, and their atomic weights, O = 16, H = 1; hence their refraction equivalents are 3 and 1·5. Water contains H2O, consequently the sum of the equivalents of refraction is (2 × 1·5) + 3 = 6. But as the coefficient of refraction of water = 1·331, its refraction equivalent = 5·958, or nearly 6. Comparison shows that, approximately, the sum of the refraction equivalents of the atoms forming compounds (or mixtures) is equal to the refraction equivalent of the compound. According to the researches of Gladstone, Landolt, Hagen, Brühl and others, the refraction equivalents of the elements are—H = 1·3, Li = 3·8, B = 4·0, C = 5·0, N = 4·1 (in its highest state of oxidation, 5·3), O = 2·9, F = 1·4, Na = 4·8, Mg = 7·0, Al = 8·4, Si = 6·8, P = 18·3, S = 16·0, Cl = 9·9, K = 8·1, Ca = 10·4, Mn = 12·2, Fe = 12·0 (in the salts of its higher oxides, 20·1), Co = 10·8, Cu = 11·6, Zn = 10·2, As = 15·4, Bi = 15·3, Ag = 15·7, Cd = 13·6, I = 24·5, Pt = 26·0, Hg = 20·2, Pb = 24·8, &c. The refraction equivalents of many elements could only be calculated from the solutions of their compounds. The composition of a solution being known it is possible to calculate the refraction equivalent of one of its component parts, those for all its other components being known. The results are founded on the acceptance of a law which cannot be strictly applied. Nevertheless the representation of the refraction equivalents gives an easy means for directly, although only approximately, obtaining the coefficient of refraction from the chemical composition of a substance. For instance, the composition of carbon bisulphide is CS2= 76, and from its density, 1·27, we find its coefficient of refraction to be 1·618 (because the refraction equivalent = 5 + 2 × 16 = 37), which is very near the actual figure. It is evident that in the above representation compounds are looked on as simple mixtures of atoms, and the physical properties of a compound as the sum of the properties present in the elementary atoms forming it. If this representation of the presence of simple atoms in compounds had not existed, the idea of combining by a few figures a whole mass of data relating to the coefficient of refraction of different substances could hardly have arisen. For further details on this subject, see works onPhysical Chemistry.
Footnotes:
[1]If the weight be indicated by P, the density by D, and the volume by V, thenP/D=KVwhereKis a coefficient depending on the system of the expressions P, D, and V. If D be the weight of a cubic measure of a substance referred to the weight of the same measure of water—if, as in the metrical system (Chapter I., Note9), the cubic measure of one part by weight of water be taken as a unit of volume—thenK= 1. But, whatever it be, it is cancelled in dealing with the comparison of volumes, because comparative and not absolute measures of volumes are taken. In this chapter, as throughout the book, the weight P is given in grams in dealing with absolute weights; and if comparative, as in the expression of chemical composition, then the weight of an atom is taken as unity. The density of gases, D, is also taken in reference to the density of hydrogen, and the volume V in metrical units (cubic centimetres), if it be a matter of absolute magnitudes of volumes, and if it be a matter of chemical transformations—that is, of relative volumes—then the volume of an atom of hydrogen, or of one part by weight of hydrogen, is taken as unity, and all volumes are expressed according to these units.
[1]If the weight be indicated by P, the density by D, and the volume by V, then
P/D=KV
whereKis a coefficient depending on the system of the expressions P, D, and V. If D be the weight of a cubic measure of a substance referred to the weight of the same measure of water—if, as in the metrical system (Chapter I., Note9), the cubic measure of one part by weight of water be taken as a unit of volume—thenK= 1. But, whatever it be, it is cancelled in dealing with the comparison of volumes, because comparative and not absolute measures of volumes are taken. In this chapter, as throughout the book, the weight P is given in grams in dealing with absolute weights; and if comparative, as in the expression of chemical composition, then the weight of an atom is taken as unity. The density of gases, D, is also taken in reference to the density of hydrogen, and the volume V in metrical units (cubic centimetres), if it be a matter of absolute magnitudes of volumes, and if it be a matter of chemical transformations—that is, of relative volumes—then the volume of an atom of hydrogen, or of one part by weight of hydrogen, is taken as unity, and all volumes are expressed according to these units.
[2]As the volumetric relations of vapours and gases, next to the relations of substances by weight, form the most important province of chemistry, and a most important means for the attainment of chemical conclusions, and inasmuch as these volumetric relations are determined by the densities of gases and vapours, necessarily the methods of determining the densities of vapours (and also of gases) are important factors in chemical research. These methods are described in detail in works on physics and physical and analytical chemistry, and therefore we here only touch on the general principles of the subject.see captionFig.52.—Apparatus for determining the vapour density by Dumas' method. A small quantity of the liquid whose vapour density is to be determined is placed in the glass globe, and heated in a water or oil bath to a temperature above the boiling point of the liquid. When all the liquid has been converted into vapour and has displaced all the air from the globe, the latter is sealed up and weighed. The capacity of the globe is then measured, and in this manner the volume occupied by a known weight of vapour at a known temperature is determined.see captionFig.53.—Deville and Troost's apparatus for determining the vapour densities, according to Dumas' method, of substances which boil at high temperatures. A porcelain globe containing the substance whose vapour density is to be determined is heated in the vapour of mercury (350°), sulphur (410°), cadmium (850°), or zinc (1,040°). The globe is sealed up in an oxyhydrogen flame.see captionFig.54.—Hofmann's apparatus for determining vapour densities. The internal tube, about one metre long, which is calibrated and graduated, is filled with mercury and inverted in a mercury bath. A small bottle (depicted in its natural size on the left) containing a weighed quantity of the liquid whose vapour density is to be determined, is introduced into the Torricellian vacuum. Steam, or the vapour of amyl alcohol, &c., is passed through the outer tube, and heats the internal tube to the temperaturet, at which the volume of vapour is measured.see captionFig.55.—Victor Meyer's apparatus for determining vapour densities. The tubebis heated in the vapour of a liquid of constant boiling point. A glass tube, containing the liquid to be experimented upon, is caused to fall fromd. The air displaced is collected in the cylindere, in the troughf.If we know the weightpand volumev, occupied by the vapour of a given substance at a temperaturetand pressureh, then its density may be directly obtained by dividingpby the weight of a volumevof hydrogen (if the density be expressed according to hydrogen,seeChapter II., Note23) attandh. Hence, the methods of determining the density of vapours and gases are based on the determination ofp,v,t, andh. The two last data (the temperaturetand pressureh) are given by the thermometer and barometer and the heights of mercury or other liquid confining the gas, and therefore do not require further explanation. It need only be remarked that: (1) In the case of easily volatile liquids there is no difficulty in procuring a bath with a constant temperature, but that it is nevertheless best (especially considering the inaccuracy of thermometers) to have a medium of absolutely constant temperature, and therefore to take either a bath in which some substance is melting—such as melting ice at 0° or crystals of sodium acetate, melting at +56°—or, as is more generally practised, to place the vessel containing the substance to be experimented with in the vapour of a liquid boiling at a definite temperature, and knowing the pressure under which it is boiling, to determine the temperature of the vapour. For this purpose the boiling points of water at different pressures are given in Chapter I., Note11, and the boiling points of certain easily procurable liquids at various pressures are given in Chapter II., Note27. (2) With respect to temperatures above 300° (below which mercurial thermometers may be conveniently employed), they are most simply obtained constant (to give time for the weight and volume of a substance being observed in a given space, and to allow that space to attain the calculated temperaturet) by means of substances boiling at a high temperature. Thus, for instance, at the ordinary atmospheric pressure the temperaturetof the vapour of sulphur is about 445°, of phosphorus pentasulphide 518°, of tin chloride 606°, of cadmium 770°, of zinc 930° (according to Violle and others), or 1040° (according to Deville), &c. (3) The indications of the hydrogen thermometer must be considered as the most exact (but as hydrogen diffuses through incandescent platinum, nitrogen is usually employed). (4) The temperature of the vapours used as the bath should in every case be several degrees higher than the boiling point of the liquid whose density is to be determined, in order that no portion should remain in a liquid state. But even in this case, as is seen from the example of nitric peroxide (ChapterVI.), the vapour density does not always remain constant with a change oft, as it should were the law of the expansion of gases and vapours absolutely exact (Chapter II., Note26). If variations of a chemical and physical nature similar to that which we saw in nitric peroxide take place in the vapours, the main interest is centred inconstantdensities, which do not vary witht, and therefore the possible effect ofton the density must always be kept in mind in having recourse to this means of investigation. (5) Usually, for the sake of convenience of observation, the vapour density is determined at the atmospheric pressure which is read on the barometer; but in the case of substances which are volatilised with difficulty, and also of substances which decompose, or, in general, vary at temperatures near their boiling points, it is best or even indispensable to conduct the determination at low pressures, whilst for substances which decompose at low pressures the observations have to be conducted under a more or less considerably increased pressure. (6) In many cases it is convenient to determine the vapour density of a substance in admixture with other gases, and consequently under the partial pressure, which may be calculated from the volume of the mixture and that of the intermixed gas (seeChapter I., Note 1). This method is especially important for substances which are easily decomposable, because, as shown by the phenomena of dissociation, a substance is able to remain unchanged in the atmosphere of one of its products of decomposition. Thus, Wurtz determined the density of phosphoric chloride, PCl5, in admixture with the vapour of phosphorous chloride, PCl3. (7) It is evident, from the example of nitric peroxide, that a change of pressure may alter the density and aid decomposition, and therefore identical results are sometimes obtained (if the density be variable) by raisingtand loweringh; but if the density does not vary under these variable conditions (at least, to an extent appreciably exceeding the limits of experimental error), then thisconstantdensity indicates thegaseousandinvariablestate of a substance. The laws hereafter laid down refer only to such vapour densities. But the majority of volatile substances show such a constant density at a certain degree above their boiling points up to the starting point of decomposition. Thus, the density of aqueous vapour does not vary fortbetween the ordinary temperature and 1000° (there are no trustworthy determinations beyond this) and for pressures varying from fractions of an atmosphere up to several atmospheres. If, however, the density does vary considerably with a variation ofhandt, the fact may serve as a guide for the investigation of the chemical changes which are undergone by the substance in a state of vapour, or at least as an indication of a deviation from the laws of Boyle, Mariotte, and Gay-Lussac (for the expansion of gases witht). In certain cases the separation of one form of deviation from the other may be explained by special hypotheses.With respect to the means of determiningpandv, with a view to finding the vapour density, we may distinguish three chief methods: (a) by weight, by ascertaining the weight of a definite volume of vapour; (b) by volume, by measuring the volume occupied by the vapour of a definite weight of a substance; and (c) by displacement. The last-mentioned is essentially volumetric, because a known weight of a substance is taken, and the volume of the air displaced by the vapour at a giventandhis determined.The method by weight (a) is the most trustworthy and historically important.Dumas' methodis typical. An ordinary spherical glass or porcelain vessel, like those shown respectively in figs.52and54, is taken, and an excess of the substance to be experimented upon is introduced into it. The vessel is heated to a temperaturethigher than the boiling point of the liquid: this gives a vapour which displaces the air, and fills the spherical space. When the air and vapour cease escaping from the sphere, it is fused up or closed by some means; and when cool, the weight of the vapour remaining in the sphere is determined (either by direct weighing of the vessel with the vapour and introducing the necessary corrections for the weight of the air and of the vapour itself, or the weight of the volatilised substance is determined by chemical methods), and the volume of the vapour attand the barometric pressurehare then calculated.The volumetric method(b) originally employed by Gay-Lussac and then modified by Hofmann and others is based on the principle that a weighed quantity of the liquid to be experimented with (placed in a small closed vessel, which is sometimes fused up before weighing, and, if quite full of the liquid, breaks when heated in a vacuum) is introduced into a graduated cylinder heated tot, or simply into a Torricellian vacuum, as shown in fig.54, and the number of volumes occupied by the vapour noted when the space holding it is heated to the desired temperaturet.The method of displacement(c) proposed by Victor Meyer is based on the fact that a spacebis heated to a constant temperaturet(by the surrounding vapours of a liquid of constant boiling point), and the air (or other gas enclosed in this space) is allowed to attain this temperature, and when it has done so a glass bulb containing a weighed quantity of the substance to be experimented with is dropped into the space. The substance is immediately converted into vapour, and displaces the air into the graduated cylindere. The amount of this air is calculated from its volume, and hence the volume att, and therefore also the volume occupied by the vapour, is found. The general arrangement of the apparatus is given in fig.55.
[2]As the volumetric relations of vapours and gases, next to the relations of substances by weight, form the most important province of chemistry, and a most important means for the attainment of chemical conclusions, and inasmuch as these volumetric relations are determined by the densities of gases and vapours, necessarily the methods of determining the densities of vapours (and also of gases) are important factors in chemical research. These methods are described in detail in works on physics and physical and analytical chemistry, and therefore we here only touch on the general principles of the subject.
see captionFig.52.—Apparatus for determining the vapour density by Dumas' method. A small quantity of the liquid whose vapour density is to be determined is placed in the glass globe, and heated in a water or oil bath to a temperature above the boiling point of the liquid. When all the liquid has been converted into vapour and has displaced all the air from the globe, the latter is sealed up and weighed. The capacity of the globe is then measured, and in this manner the volume occupied by a known weight of vapour at a known temperature is determined.
Fig.52.—Apparatus for determining the vapour density by Dumas' method. A small quantity of the liquid whose vapour density is to be determined is placed in the glass globe, and heated in a water or oil bath to a temperature above the boiling point of the liquid. When all the liquid has been converted into vapour and has displaced all the air from the globe, the latter is sealed up and weighed. The capacity of the globe is then measured, and in this manner the volume occupied by a known weight of vapour at a known temperature is determined.
see captionFig.53.—Deville and Troost's apparatus for determining the vapour densities, according to Dumas' method, of substances which boil at high temperatures. A porcelain globe containing the substance whose vapour density is to be determined is heated in the vapour of mercury (350°), sulphur (410°), cadmium (850°), or zinc (1,040°). The globe is sealed up in an oxyhydrogen flame.
Fig.53.—Deville and Troost's apparatus for determining the vapour densities, according to Dumas' method, of substances which boil at high temperatures. A porcelain globe containing the substance whose vapour density is to be determined is heated in the vapour of mercury (350°), sulphur (410°), cadmium (850°), or zinc (1,040°). The globe is sealed up in an oxyhydrogen flame.
see captionFig.54.—Hofmann's apparatus for determining vapour densities. The internal tube, about one metre long, which is calibrated and graduated, is filled with mercury and inverted in a mercury bath. A small bottle (depicted in its natural size on the left) containing a weighed quantity of the liquid whose vapour density is to be determined, is introduced into the Torricellian vacuum. Steam, or the vapour of amyl alcohol, &c., is passed through the outer tube, and heats the internal tube to the temperaturet, at which the volume of vapour is measured.
Fig.54.—Hofmann's apparatus for determining vapour densities. The internal tube, about one metre long, which is calibrated and graduated, is filled with mercury and inverted in a mercury bath. A small bottle (depicted in its natural size on the left) containing a weighed quantity of the liquid whose vapour density is to be determined, is introduced into the Torricellian vacuum. Steam, or the vapour of amyl alcohol, &c., is passed through the outer tube, and heats the internal tube to the temperaturet, at which the volume of vapour is measured.
see captionFig.55.—Victor Meyer's apparatus for determining vapour densities. The tubebis heated in the vapour of a liquid of constant boiling point. A glass tube, containing the liquid to be experimented upon, is caused to fall fromd. The air displaced is collected in the cylindere, in the troughf.
Fig.55.—Victor Meyer's apparatus for determining vapour densities. The tubebis heated in the vapour of a liquid of constant boiling point. A glass tube, containing the liquid to be experimented upon, is caused to fall fromd. The air displaced is collected in the cylindere, in the troughf.
If we know the weightpand volumev, occupied by the vapour of a given substance at a temperaturetand pressureh, then its density may be directly obtained by dividingpby the weight of a volumevof hydrogen (if the density be expressed according to hydrogen,seeChapter II., Note23) attandh. Hence, the methods of determining the density of vapours and gases are based on the determination ofp,v,t, andh. The two last data (the temperaturetand pressureh) are given by the thermometer and barometer and the heights of mercury or other liquid confining the gas, and therefore do not require further explanation. It need only be remarked that: (1) In the case of easily volatile liquids there is no difficulty in procuring a bath with a constant temperature, but that it is nevertheless best (especially considering the inaccuracy of thermometers) to have a medium of absolutely constant temperature, and therefore to take either a bath in which some substance is melting—such as melting ice at 0° or crystals of sodium acetate, melting at +56°—or, as is more generally practised, to place the vessel containing the substance to be experimented with in the vapour of a liquid boiling at a definite temperature, and knowing the pressure under which it is boiling, to determine the temperature of the vapour. For this purpose the boiling points of water at different pressures are given in Chapter I., Note11, and the boiling points of certain easily procurable liquids at various pressures are given in Chapter II., Note27. (2) With respect to temperatures above 300° (below which mercurial thermometers may be conveniently employed), they are most simply obtained constant (to give time for the weight and volume of a substance being observed in a given space, and to allow that space to attain the calculated temperaturet) by means of substances boiling at a high temperature. Thus, for instance, at the ordinary atmospheric pressure the temperaturetof the vapour of sulphur is about 445°, of phosphorus pentasulphide 518°, of tin chloride 606°, of cadmium 770°, of zinc 930° (according to Violle and others), or 1040° (according to Deville), &c. (3) The indications of the hydrogen thermometer must be considered as the most exact (but as hydrogen diffuses through incandescent platinum, nitrogen is usually employed). (4) The temperature of the vapours used as the bath should in every case be several degrees higher than the boiling point of the liquid whose density is to be determined, in order that no portion should remain in a liquid state. But even in this case, as is seen from the example of nitric peroxide (ChapterVI.), the vapour density does not always remain constant with a change oft, as it should were the law of the expansion of gases and vapours absolutely exact (Chapter II., Note26). If variations of a chemical and physical nature similar to that which we saw in nitric peroxide take place in the vapours, the main interest is centred inconstantdensities, which do not vary witht, and therefore the possible effect ofton the density must always be kept in mind in having recourse to this means of investigation. (5) Usually, for the sake of convenience of observation, the vapour density is determined at the atmospheric pressure which is read on the barometer; but in the case of substances which are volatilised with difficulty, and also of substances which decompose, or, in general, vary at temperatures near their boiling points, it is best or even indispensable to conduct the determination at low pressures, whilst for substances which decompose at low pressures the observations have to be conducted under a more or less considerably increased pressure. (6) In many cases it is convenient to determine the vapour density of a substance in admixture with other gases, and consequently under the partial pressure, which may be calculated from the volume of the mixture and that of the intermixed gas (seeChapter I., Note 1). This method is especially important for substances which are easily decomposable, because, as shown by the phenomena of dissociation, a substance is able to remain unchanged in the atmosphere of one of its products of decomposition. Thus, Wurtz determined the density of phosphoric chloride, PCl5, in admixture with the vapour of phosphorous chloride, PCl3. (7) It is evident, from the example of nitric peroxide, that a change of pressure may alter the density and aid decomposition, and therefore identical results are sometimes obtained (if the density be variable) by raisingtand loweringh; but if the density does not vary under these variable conditions (at least, to an extent appreciably exceeding the limits of experimental error), then thisconstantdensity indicates thegaseousandinvariablestate of a substance. The laws hereafter laid down refer only to such vapour densities. But the majority of volatile substances show such a constant density at a certain degree above their boiling points up to the starting point of decomposition. Thus, the density of aqueous vapour does not vary fortbetween the ordinary temperature and 1000° (there are no trustworthy determinations beyond this) and for pressures varying from fractions of an atmosphere up to several atmospheres. If, however, the density does vary considerably with a variation ofhandt, the fact may serve as a guide for the investigation of the chemical changes which are undergone by the substance in a state of vapour, or at least as an indication of a deviation from the laws of Boyle, Mariotte, and Gay-Lussac (for the expansion of gases witht). In certain cases the separation of one form of deviation from the other may be explained by special hypotheses.
With respect to the means of determiningpandv, with a view to finding the vapour density, we may distinguish three chief methods: (a) by weight, by ascertaining the weight of a definite volume of vapour; (b) by volume, by measuring the volume occupied by the vapour of a definite weight of a substance; and (c) by displacement. The last-mentioned is essentially volumetric, because a known weight of a substance is taken, and the volume of the air displaced by the vapour at a giventandhis determined.
The method by weight (a) is the most trustworthy and historically important.Dumas' methodis typical. An ordinary spherical glass or porcelain vessel, like those shown respectively in figs.52and54, is taken, and an excess of the substance to be experimented upon is introduced into it. The vessel is heated to a temperaturethigher than the boiling point of the liquid: this gives a vapour which displaces the air, and fills the spherical space. When the air and vapour cease escaping from the sphere, it is fused up or closed by some means; and when cool, the weight of the vapour remaining in the sphere is determined (either by direct weighing of the vessel with the vapour and introducing the necessary corrections for the weight of the air and of the vapour itself, or the weight of the volatilised substance is determined by chemical methods), and the volume of the vapour attand the barometric pressurehare then calculated.
The volumetric method(b) originally employed by Gay-Lussac and then modified by Hofmann and others is based on the principle that a weighed quantity of the liquid to be experimented with (placed in a small closed vessel, which is sometimes fused up before weighing, and, if quite full of the liquid, breaks when heated in a vacuum) is introduced into a graduated cylinder heated tot, or simply into a Torricellian vacuum, as shown in fig.54, and the number of volumes occupied by the vapour noted when the space holding it is heated to the desired temperaturet.
The method of displacement(c) proposed by Victor Meyer is based on the fact that a spacebis heated to a constant temperaturet(by the surrounding vapours of a liquid of constant boiling point), and the air (or other gas enclosed in this space) is allowed to attain this temperature, and when it has done so a glass bulb containing a weighed quantity of the substance to be experimented with is dropped into the space. The substance is immediately converted into vapour, and displaces the air into the graduated cylindere. The amount of this air is calculated from its volume, and hence the volume att, and therefore also the volume occupied by the vapour, is found. The general arrangement of the apparatus is given in fig.55.
[3]Vapours and gases, as already explained in thesecond chapter, are subject to the same laws, which are, however, only approximate. It is evident that for the deduction of the laws which will presently be enunciated it is only possible to take into consideration a perfect gaseous state (far removed from the liquid state) and chemical invariability in which thevapour density is constant—that is, the volume of a given gas or vapour varies like a volume of hydrogen, air, or other gas, with the pressure and temperature.It is necessary to make this statement in order that it may be clearly seen that the laws of gaseous volumes, which we shall describe presently, are in the most intimate connection with the laws of the variations of volumes with pressure and temperature. And as these latter laws (ChapterII.) are not infallible, but only approximately exact, the same, therefore, applies to the laws about to be described. And as it is possible to find more exact laws (a second approximation) for the variation ofvwithpandt(for example, van der Waals' formula, Chapter II., Note33), so also a more exact expression of the relation between the composition and the density of vapours and gases is also possible. But to prevent any doubt arising at the very beginning as to the breadth and general application of the laws of volumes, it will be sufficient to mention that the density of such gases as oxygen, nitrogen, and carbonic anhydride is already known toremain constant(within the limits of experimental error) between the ordinary temperature and a white heat; whilst, judging from what is said in my work on the ‘Tension of Gases’ (vol. i. p. 9), it may be said that, as regards pressure, the relative density remains very constant, even when the deviations from Mariotte's law are very considerable. However, in this respect the number of data is as yet too small to arrive at an exact conclusion.
[3]Vapours and gases, as already explained in thesecond chapter, are subject to the same laws, which are, however, only approximate. It is evident that for the deduction of the laws which will presently be enunciated it is only possible to take into consideration a perfect gaseous state (far removed from the liquid state) and chemical invariability in which thevapour density is constant—that is, the volume of a given gas or vapour varies like a volume of hydrogen, air, or other gas, with the pressure and temperature.
It is necessary to make this statement in order that it may be clearly seen that the laws of gaseous volumes, which we shall describe presently, are in the most intimate connection with the laws of the variations of volumes with pressure and temperature. And as these latter laws (ChapterII.) are not infallible, but only approximately exact, the same, therefore, applies to the laws about to be described. And as it is possible to find more exact laws (a second approximation) for the variation ofvwithpandt(for example, van der Waals' formula, Chapter II., Note33), so also a more exact expression of the relation between the composition and the density of vapours and gases is also possible. But to prevent any doubt arising at the very beginning as to the breadth and general application of the laws of volumes, it will be sufficient to mention that the density of such gases as oxygen, nitrogen, and carbonic anhydride is already known toremain constant(within the limits of experimental error) between the ordinary temperature and a white heat; whilst, judging from what is said in my work on the ‘Tension of Gases’ (vol. i. p. 9), it may be said that, as regards pressure, the relative density remains very constant, even when the deviations from Mariotte's law are very considerable. However, in this respect the number of data is as yet too small to arrive at an exact conclusion.
[4]We must recollect that this law is only approximate, like Boyle and Mariotte's law, and that, therefore, like the latter, a more exact expression may be found for the exceptions.
[4]We must recollect that this law is only approximate, like Boyle and Mariotte's law, and that, therefore, like the latter, a more exact expression may be found for the exceptions.
[5]This second law of volumes may be considered as a consequence of the first law. The first law requires simple ratios between the volumes of the combining substancesAandB. A substanceABis produced by their combination. It may, according to the law of multiple proportion, combine, not only with substancesC,D, &c., but also withAand withB. In this new combination the volume ofAB, combining with the volume ofA, should be in simple multiple proportion with the volume ofA; hence the volume of the compoundABis in simple proportion to the volume of its component parts. Therefore only one law of volumes need be accepted. We shall afterwards see that there is a third law of volumes embracing also the two first laws.
[5]This second law of volumes may be considered as a consequence of the first law. The first law requires simple ratios between the volumes of the combining substancesAandB. A substanceABis produced by their combination. It may, according to the law of multiple proportion, combine, not only with substancesC,D, &c., but also withAand withB. In this new combination the volume ofAB, combining with the volume ofA, should be in simple multiple proportion with the volume ofA; hence the volume of the compoundABis in simple proportion to the volume of its component parts. Therefore only one law of volumes need be accepted. We shall afterwards see that there is a third law of volumes embracing also the two first laws.
[6]It must not be forgotten that Newton's law of gravity was first a hypothesis, but it became a trustworthy, perfect theory, and acquired the qualities of a fundamental law owing to the concord between its deductions and actual facts. All laws, all theories, of natural phenomena, are at first hypotheses. Some are rapidly established by their consequences exactly agreeing with facts; others only take root by slow degrees; and there are many which are destined to be refuted owing to their consequences being found to be at variance with facts.
[6]It must not be forgotten that Newton's law of gravity was first a hypothesis, but it became a trustworthy, perfect theory, and acquired the qualities of a fundamental law owing to the concord between its deductions and actual facts. All laws, all theories, of natural phenomena, are at first hypotheses. Some are rapidly established by their consequences exactly agreeing with facts; others only take root by slow degrees; and there are many which are destined to be refuted owing to their consequences being found to be at variance with facts.
[7]This is not only seen from the above calculations, but may be proved by experiment. A glass tube, divided in the middle by a stopcock, is taken and one portion filled withdryhydrogen chloride (the dryness of the gases is very necessary, because ammonia and hydrogen chloride are both very soluble in water, so that a small trace of water may contain a large amount of these gases in solution) and the other with dry ammonia, under the atmospheric pressure. One orifice (for instance, of that portion which contains the ammonia) is firmly closed, and the other is immersed under mercury, and the cock is then opened. Solid sal-ammoniac is formed, but if the volume of one gas be greater than that of the other, some of the first gas will remain. By immersing the tube in the mercury in order that the internal pressure shall equal the atmospheric pressure, it may easily be shown that the volume of the remaining gas is equal to the difference between the volumes of the two portions of the tube, and that this remaining gas is part of that whose volume was the greater.
[7]This is not only seen from the above calculations, but may be proved by experiment. A glass tube, divided in the middle by a stopcock, is taken and one portion filled withdryhydrogen chloride (the dryness of the gases is very necessary, because ammonia and hydrogen chloride are both very soluble in water, so that a small trace of water may contain a large amount of these gases in solution) and the other with dry ammonia, under the atmospheric pressure. One orifice (for instance, of that portion which contains the ammonia) is firmly closed, and the other is immersed under mercury, and the cock is then opened. Solid sal-ammoniac is formed, but if the volume of one gas be greater than that of the other, some of the first gas will remain. By immersing the tube in the mercury in order that the internal pressure shall equal the atmospheric pressure, it may easily be shown that the volume of the remaining gas is equal to the difference between the volumes of the two portions of the tube, and that this remaining gas is part of that whose volume was the greater.
[8]Let us demonstrate this by figures. From 122 grams of benzoic acid there are obtained (a) 78 grams of benzene, whose density referred to hydrogen = 39, hence the relative volume = 2; and (b) 44 grams of carbonic anhydride, whose density = 22, and hence the volume = 2. It is the same in other cases.
[8]Let us demonstrate this by figures. From 122 grams of benzoic acid there are obtained (a) 78 grams of benzene, whose density referred to hydrogen = 39, hence the relative volume = 2; and (b) 44 grams of carbonic anhydride, whose density = 22, and hence the volume = 2. It is the same in other cases.
[9]A large number of such generalised reactions, showing reaction by equal volumes, occur in the case of the hydrocarbon derivatives, because many of these compounds are volatile. The reactions of alkalis on acids, or anhydrides on water, &c., which are so frequent between mineral substances, present but few such examples, because many of these substances are not volatile and their vapour densities are unknown. But essentially the same is seen in these cases also; for instance, sulphuric acid, H2SO4, breaks up into the anhydride, SO3, and water, H2O, which exhibit an equality of volumes. Let us take another example where three substances combine in equal volumes: carbonic anhydride, CO2, ammonia, NH3, and water, H2O (the volumes of all are equal to 2), form acid ammonium carbonate, (NH4)HCO3.
[9]A large number of such generalised reactions, showing reaction by equal volumes, occur in the case of the hydrocarbon derivatives, because many of these compounds are volatile. The reactions of alkalis on acids, or anhydrides on water, &c., which are so frequent between mineral substances, present but few such examples, because many of these substances are not volatile and their vapour densities are unknown. But essentially the same is seen in these cases also; for instance, sulphuric acid, H2SO4, breaks up into the anhydride, SO3, and water, H2O, which exhibit an equality of volumes. Let us take another example where three substances combine in equal volumes: carbonic anhydride, CO2, ammonia, NH3, and water, H2O (the volumes of all are equal to 2), form acid ammonium carbonate, (NH4)HCO3.
[10]This opinion which I have always held (since the first editions of this work), as to the primary origin of hydrogen peroxide and of the formation of water by means of its decomposition, has in latter days become more generally accepted, thanks more especially to the work of Traube. Probably it explains most simply the necessity for the presence of traces of water in many reactions, as, for instance, in the explosion of carbonic oxide with oxygen, and perhaps the theory of the explosion of detonating gas itself and of the combustion of hydrogen will gain in clearness and truth if we take into consideration the preliminary formation of hydrogen peroxide and its decomposition. We may here point out the fact that Ettingen (at Dorpat, 1888) observed the existence of currents and waves in the explosion of detonating gas by taking photographs, which showed the periods of combustion and the waves of explosion, which should be taken into consideration in the theory of this subject. As the formation of H2O2from O2and H2corresponds with a less amount of heat than the formation of water from H2and O, it may be that the temperature of the flame of detonating gas depends on the pre-formation of hydrogen peroxide.
[10]This opinion which I have always held (since the first editions of this work), as to the primary origin of hydrogen peroxide and of the formation of water by means of its decomposition, has in latter days become more generally accepted, thanks more especially to the work of Traube. Probably it explains most simply the necessity for the presence of traces of water in many reactions, as, for instance, in the explosion of carbonic oxide with oxygen, and perhaps the theory of the explosion of detonating gas itself and of the combustion of hydrogen will gain in clearness and truth if we take into consideration the preliminary formation of hydrogen peroxide and its decomposition. We may here point out the fact that Ettingen (at Dorpat, 1888) observed the existence of currents and waves in the explosion of detonating gas by taking photographs, which showed the periods of combustion and the waves of explosion, which should be taken into consideration in the theory of this subject. As the formation of H2O2from O2and H2corresponds with a less amount of heat than the formation of water from H2and O, it may be that the temperature of the flame of detonating gas depends on the pre-formation of hydrogen peroxide.
[11]The possibility of reactions between unequal volumes, notwithstanding the general application of the law of Avogadro-Gerhardt, may, in addition to what has been said above, depend on the fact that the participating substances, at the moment of reaction, undergo a preliminary modification, decomposition, isomeric (polymeric) transformation, &c. Thus, if NO2, seems to proceed from N2O4, if O2is formed from O3, and the converse, then it cannot be denied that the production of molecules containing only one atom is also possible—for instance, of oxygen—as also of higher polymeric forms—as the molecule N from N2, or H3from H2. In this manner it is obviously possible, by means of a series of hypotheses, to explain the cases of the formation of ammonia, NH3, from 3 vols. of hydrogen and 1 vol. of nitrogen. But it must be observed that perhaps our information in similar instances is, as yet, far from being complete. If hydrazine or diamide N2H4(Chapter VI. Note20 bis) is formed and the imide N2H2in which 2 vols. of hydrogen are combined with 2 vols. of nitrogen, then the reaction here perhaps first takes place between equal volumes. If it be shown that diamide gives nitrogen and ammonia (3N2H4= N2+ 4NH3) under the action of sparks, heat, or the silent discharge, &c., then it will be possible to admit that it is formed before ammonia. And perhaps the still less stable imide N2H2, which may also decompose with the formation of ammonia, is produced before the amide N2H4.I mention this to show that the fact of apparent exceptions existing to the law of reactions between equal volumes does not prove the impossibility of their being included under the law on further study of the subject. Having put forward a certain law or hypothesis, consequences must be deduced from it, and if by their means clearness and consistency are attained—and especially, if by their means that which could not otherwise be known can be predicted—then the consequences verify the hypothesis. This was the case with the law now under discussion. The mere simplicity of the deduction of the weights proper to the atoms of the elements, or the mere fact that having admitted the law it follows (as will afterwards be shown) that thevis vivaof the molecules of all gases is a constant quantity, is quite sufficient reason for retaining the hypothesis, if not for believing in it as a fact beyond doubt. And such is the whole doctrine of atoms. And since by the acceptance of the law it became possible to foretell even the properties and atomic weights of elements which had not yet been discovered, and these predictions afterwards proved to be in agreement with the actual facts, it is evident that the law of Avogadro-Gerhardt penetrates deeply into the nature of the chemical relation of substances. This being granted, it is possible at the present time to exhibit and deduce the truth under consideration in many ways, and in every case, like all that is highest in science (for example, the laws of the indestructibility of matter, of the conservation of energy, of gravity, &c.), it proves to be not an empirical conclusion from direct observation and experiment, not a direct result of analysis, but a creation, or instinctive penetration, of the inquiring mind, guided and directed by experiment and observation—a synthesis of which the exact sciences are capable equally with the highest forms of art. Without such a synthetical process of reasoning, science would only be a mass of disconnected results of arduous labour, and would not be distinguished by that vitality with which it is really endowed when once it succeeds in attaining a synthesis, or concordance of outward form with the inner nature of things, without losing sight of the diversities of individual parts; in short, when it discovers by means of outward phenomena, which are apparent to the sense of touch, to observation, and to the common mind, the internal signification of things—discovering simplicity in complexity and uniformity in diversity. And this is the highest problem of science.
[11]The possibility of reactions between unequal volumes, notwithstanding the general application of the law of Avogadro-Gerhardt, may, in addition to what has been said above, depend on the fact that the participating substances, at the moment of reaction, undergo a preliminary modification, decomposition, isomeric (polymeric) transformation, &c. Thus, if NO2, seems to proceed from N2O4, if O2is formed from O3, and the converse, then it cannot be denied that the production of molecules containing only one atom is also possible—for instance, of oxygen—as also of higher polymeric forms—as the molecule N from N2, or H3from H2. In this manner it is obviously possible, by means of a series of hypotheses, to explain the cases of the formation of ammonia, NH3, from 3 vols. of hydrogen and 1 vol. of nitrogen. But it must be observed that perhaps our information in similar instances is, as yet, far from being complete. If hydrazine or diamide N2H4(Chapter VI. Note20 bis) is formed and the imide N2H2in which 2 vols. of hydrogen are combined with 2 vols. of nitrogen, then the reaction here perhaps first takes place between equal volumes. If it be shown that diamide gives nitrogen and ammonia (3N2H4= N2+ 4NH3) under the action of sparks, heat, or the silent discharge, &c., then it will be possible to admit that it is formed before ammonia. And perhaps the still less stable imide N2H2, which may also decompose with the formation of ammonia, is produced before the amide N2H4.
I mention this to show that the fact of apparent exceptions existing to the law of reactions between equal volumes does not prove the impossibility of their being included under the law on further study of the subject. Having put forward a certain law or hypothesis, consequences must be deduced from it, and if by their means clearness and consistency are attained—and especially, if by their means that which could not otherwise be known can be predicted—then the consequences verify the hypothesis. This was the case with the law now under discussion. The mere simplicity of the deduction of the weights proper to the atoms of the elements, or the mere fact that having admitted the law it follows (as will afterwards be shown) that thevis vivaof the molecules of all gases is a constant quantity, is quite sufficient reason for retaining the hypothesis, if not for believing in it as a fact beyond doubt. And such is the whole doctrine of atoms. And since by the acceptance of the law it became possible to foretell even the properties and atomic weights of elements which had not yet been discovered, and these predictions afterwards proved to be in agreement with the actual facts, it is evident that the law of Avogadro-Gerhardt penetrates deeply into the nature of the chemical relation of substances. This being granted, it is possible at the present time to exhibit and deduce the truth under consideration in many ways, and in every case, like all that is highest in science (for example, the laws of the indestructibility of matter, of the conservation of energy, of gravity, &c.), it proves to be not an empirical conclusion from direct observation and experiment, not a direct result of analysis, but a creation, or instinctive penetration, of the inquiring mind, guided and directed by experiment and observation—a synthesis of which the exact sciences are capable equally with the highest forms of art. Without such a synthetical process of reasoning, science would only be a mass of disconnected results of arduous labour, and would not be distinguished by that vitality with which it is really endowed when once it succeeds in attaining a synthesis, or concordance of outward form with the inner nature of things, without losing sight of the diversities of individual parts; in short, when it discovers by means of outward phenomena, which are apparent to the sense of touch, to observation, and to the common mind, the internal signification of things—discovering simplicity in complexity and uniformity in diversity. And this is the highest problem of science.
[12]As the density of aqueous vapour remains constant within the limits of experimental accuracy, even at 1,000°, when dissociation has certainly commenced, it would appear that only a very small amount of water is decomposed at these temperatures. If even 10 p.c. of water were decomposed, the density would be 8·57 and the quotient M/D = 2·1, but at the high temperatures here concerned the error of experiment is not greater than the difference between this quantity and 2. And probably at 1,000° the dissociation is far from being equal to 10 p.c.Hence the variation in the vapour density of water does not give us the means of ascertaining the amount of its dissociation.
[12]As the density of aqueous vapour remains constant within the limits of experimental accuracy, even at 1,000°, when dissociation has certainly commenced, it would appear that only a very small amount of water is decomposed at these temperatures. If even 10 p.c. of water were decomposed, the density would be 8·57 and the quotient M/D = 2·1, but at the high temperatures here concerned the error of experiment is not greater than the difference between this quantity and 2. And probably at 1,000° the dissociation is far from being equal to 10 p.c.Hence the variation in the vapour density of water does not give us the means of ascertaining the amount of its dissociation.
[13]This explanation of the vapour density of sal-ammoniac, sulphuric acid, and similar substances which decompose in being distilled was the most natural to resort to as soon as the application of the law of Avogadro-Gerhardt to chemical relations was begun; it was, for instance, given in my work onSpecific Volumes, 1856, p. 99. The formula, M/D = 2, which was applied later by many other investigators, had already been made use of in that work.
[13]This explanation of the vapour density of sal-ammoniac, sulphuric acid, and similar substances which decompose in being distilled was the most natural to resort to as soon as the application of the law of Avogadro-Gerhardt to chemical relations was begun; it was, for instance, given in my work onSpecific Volumes, 1856, p. 99. The formula, M/D = 2, which was applied later by many other investigators, had already been made use of in that work.
[14]The beginner must remember that an experiment and the mode in which it is carried out must be determined by the principle or fact which it is intended to illustrate, and notvice versa, as some suppose. The idea which determines the necessity of an experiment is the chief consideration.
[14]The beginner must remember that an experiment and the mode in which it is carried out must be determined by the principle or fact which it is intended to illustrate, and notvice versa, as some suppose. The idea which determines the necessity of an experiment is the chief consideration.
[15]It is important that the tubes, asbestos, and sal-ammoniac should be dry, as otherwise the moisture retains the ammonia and hydrogen chloride.
[15]It is important that the tubes, asbestos, and sal-ammoniac should be dry, as otherwise the moisture retains the ammonia and hydrogen chloride.
[15 bis]Baker (1894) showed that the decomposition of NH4Cl in the act of volatilising only takes place in the presence of water, traces of which are amply sufficient, but that in the total absence of moisture (attained by carefully drying with P2O5) there is no decomposition, and the vapour density of the sal-ammoniac is found to be normal,i.e., nearly 27. It is not yet quite clear what part the trace of moisture plays here, and it must be presumed that the phenomenon belongs to the category of electrical and contact phenomena, which have not yet been fully explained (seeChapter IX., Note29).
[15 bis]Baker (1894) showed that the decomposition of NH4Cl in the act of volatilising only takes place in the presence of water, traces of which are amply sufficient, but that in the total absence of moisture (attained by carefully drying with P2O5) there is no decomposition, and the vapour density of the sal-ammoniac is found to be normal,i.e., nearly 27. It is not yet quite clear what part the trace of moisture plays here, and it must be presumed that the phenomenon belongs to the category of electrical and contact phenomena, which have not yet been fully explained (seeChapter IX., Note29).
[16]Just as we saw (Chapter VI. Note46) an increase of the dissociation of N2O4and the formation of a large proportion of NO2, with a decrease of pressure. The decomposition of I2into I + I is a similar dissociation.
[16]Just as we saw (Chapter VI. Note46) an increase of the dissociation of N2O4and the formation of a large proportion of NO2, with a decrease of pressure. The decomposition of I2into I + I is a similar dissociation.
[17]Although at first there appeared to be a similar phenomenon in the case of chlorine, it was afterwards proved that if there is a decrease of density it is only a small one. In the case of bromine it is not much greater, and is far from being equal to that for iodine.As in general we very often involuntarily confuse chemical processes with physical, it may be that a physical process of change in the coefficient of expansion with a change of temperature participates with a change in molecular weight, and partially, if not wholly, accounts for the decrease of the density of chlorine, bromine, and iodine. Thus, I have remarked (Comptes Rendus, 1876) that the coefficient of expansion of gases increases with their molecular weight, and (Chapter II., Note26) the results of direct experiment show the coefficient of expansion of hydrobromic acid (M = 81) to be 0·00386 instead of 0·00367, which is that of hydrogen (M = 2). Hence, in the case of the vapour of iodine (M = 254) a very large coefficient of expansion is to be expected, and from this cause alone the relative density would fall. As the molecule of chlorine Cl2is lighter (= 71) than that of bromine (= 160), which is lighter than that of iodine (= 254), we see that the order in which the decomposability of the vapours of these haloids is observed corresponds with the expected rise in the coefficient of expansion. Taking the coefficient of expansion of iodine vapour as 0·004, then at 1,000° its density would be 116. Therefore the dissociation of iodine may be only an apparent phenomenon. However, on the other hand, the heavy vapour of mercury (M = 200, D = 100) scarcely decreases in density at a temperature of 1,500° (D = 98, according to Victor Meyer); but it must not be forgotten that the molecule of mercury contains only one atom, whilst that of iodine contains two, and this is very important. Questions of this kind which are difficult to decide by experimental methods must long remain without a certain explanation, owing to the difficulty, and sometimes impossibility, of distinguishing between physical and chemical changes.
[17]Although at first there appeared to be a similar phenomenon in the case of chlorine, it was afterwards proved that if there is a decrease of density it is only a small one. In the case of bromine it is not much greater, and is far from being equal to that for iodine.
As in general we very often involuntarily confuse chemical processes with physical, it may be that a physical process of change in the coefficient of expansion with a change of temperature participates with a change in molecular weight, and partially, if not wholly, accounts for the decrease of the density of chlorine, bromine, and iodine. Thus, I have remarked (Comptes Rendus, 1876) that the coefficient of expansion of gases increases with their molecular weight, and (Chapter II., Note26) the results of direct experiment show the coefficient of expansion of hydrobromic acid (M = 81) to be 0·00386 instead of 0·00367, which is that of hydrogen (M = 2). Hence, in the case of the vapour of iodine (M = 254) a very large coefficient of expansion is to be expected, and from this cause alone the relative density would fall. As the molecule of chlorine Cl2is lighter (= 71) than that of bromine (= 160), which is lighter than that of iodine (= 254), we see that the order in which the decomposability of the vapours of these haloids is observed corresponds with the expected rise in the coefficient of expansion. Taking the coefficient of expansion of iodine vapour as 0·004, then at 1,000° its density would be 116. Therefore the dissociation of iodine may be only an apparent phenomenon. However, on the other hand, the heavy vapour of mercury (M = 200, D = 100) scarcely decreases in density at a temperature of 1,500° (D = 98, according to Victor Meyer); but it must not be forgotten that the molecule of mercury contains only one atom, whilst that of iodine contains two, and this is very important. Questions of this kind which are difficult to decide by experimental methods must long remain without a certain explanation, owing to the difficulty, and sometimes impossibility, of distinguishing between physical and chemical changes.
[18]And so it was in the fifties. Some took O = 8, others O = 16. Water in the first case would be HO and hydrogen peroxide HO2, and in the second case, as is now generally accepted, water H2O and hydrogen peroxide H2O2or HO. Disagreement and confusion reigned. In 1860 the chemists of the whole world met at Carlsruhe for the purpose of arriving at some agreement and uniformity of opinion. I was present at this Congress, and well remember how great was the difference of opinion, and how a compromise was advocated with great acumen by many scientific men, and with what warmth the followers of Gerhardt, at whose head stood the Italian professor, Canizzaro, followed up the consequences of the law of Avogadro. In the spirit of scientific freedom, without which science would make no progress, and would remain petrified as in the middle ages, and with the simultaneous necessity of scientific conservatism, without which the roots of past study could give no fruit, a compromise was not arrived at, nor ought it to have been, but instead of it truth, in the form of the law of Avogadro-Gerhardt, received by means of the Congress a wider development, and soon afterwards conquered all minds. Then the new so-called Gerhardt atomic weights established themselves, and in the seventies they were already in general use.
[18]And so it was in the fifties. Some took O = 8, others O = 16. Water in the first case would be HO and hydrogen peroxide HO2, and in the second case, as is now generally accepted, water H2O and hydrogen peroxide H2O2or HO. Disagreement and confusion reigned. In 1860 the chemists of the whole world met at Carlsruhe for the purpose of arriving at some agreement and uniformity of opinion. I was present at this Congress, and well remember how great was the difference of opinion, and how a compromise was advocated with great acumen by many scientific men, and with what warmth the followers of Gerhardt, at whose head stood the Italian professor, Canizzaro, followed up the consequences of the law of Avogadro. In the spirit of scientific freedom, without which science would make no progress, and would remain petrified as in the middle ages, and with the simultaneous necessity of scientific conservatism, without which the roots of past study could give no fruit, a compromise was not arrived at, nor ought it to have been, but instead of it truth, in the form of the law of Avogadro-Gerhardt, received by means of the Congress a wider development, and soon afterwards conquered all minds. Then the new so-called Gerhardt atomic weights established themselves, and in the seventies they were already in general use.
[19]A bubble of gas, a drop of liquid, or the smallest crystal, presents an agglomeration of a number of molecules, in a state of continual motion (like the stars of the Milky Way), distributing themselves evenly or forming new systems. If the aggregation of all kinds of heterogeneous molecules be possible in a gaseous state, where the molecules are considerably removed from each other, then in a liquid state, where they are already close together, such an aggregation becomes possible only in the sense of the mutual reaction between them which results from their chemical attraction, and especially in the aptitude of heterogeneous molecules for combining together. Solutions and other so-called indefinite chemical compounds should be regarded in this light. According to the principles developed in this work we should regard them as containing both the compounds of the heterogeneous molecules themselves and the products of their decomposition, as in peroxide of nitrogen, N2O4and NO2. And we must consider that those molecules A, which at a given moment are combined with B in AB, will in the following moment become free in order to again enter into a combined form. The laws of chemical equilibrium proper to dissociated systems cannot be regarded in any other light.
[19]A bubble of gas, a drop of liquid, or the smallest crystal, presents an agglomeration of a number of molecules, in a state of continual motion (like the stars of the Milky Way), distributing themselves evenly or forming new systems. If the aggregation of all kinds of heterogeneous molecules be possible in a gaseous state, where the molecules are considerably removed from each other, then in a liquid state, where they are already close together, such an aggregation becomes possible only in the sense of the mutual reaction between them which results from their chemical attraction, and especially in the aptitude of heterogeneous molecules for combining together. Solutions and other so-called indefinite chemical compounds should be regarded in this light. According to the principles developed in this work we should regard them as containing both the compounds of the heterogeneous molecules themselves and the products of their decomposition, as in peroxide of nitrogen, N2O4and NO2. And we must consider that those molecules A, which at a given moment are combined with B in AB, will in the following moment become free in order to again enter into a combined form. The laws of chemical equilibrium proper to dissociated systems cannot be regarded in any other light.
[20]This strengthens the fundamental idea of the unity and harmony of type of all creation and is one of those ideas which impress themselves on man in all ages, and give rise to a hope of arriving in time, by means of a laborious series of discoveries, observations, experiments, laws, hypotheses, and theories, at a comprehension of the internal and invisible structure of concrete substances with that same degree of clearness and exactitude which has been attained in the visible structure of the heavenly bodies. It is not many years ago since the law of Avogadro-Gerhardt took root in science. It is within the memory of many living scientific men, and of mine amongst others. It is not surprising, therefore, that as yet little progress has been made in the province of molecular mechanics; but the theory of gases alone, which is intimately connected with the conception of molecules, shows by its success that the time is approaching when our knowledge of the internal structure of matter will be defined and established.
[20]This strengthens the fundamental idea of the unity and harmony of type of all creation and is one of those ideas which impress themselves on man in all ages, and give rise to a hope of arriving in time, by means of a laborious series of discoveries, observations, experiments, laws, hypotheses, and theories, at a comprehension of the internal and invisible structure of concrete substances with that same degree of clearness and exactitude which has been attained in the visible structure of the heavenly bodies. It is not many years ago since the law of Avogadro-Gerhardt took root in science. It is within the memory of many living scientific men, and of mine amongst others. It is not surprising, therefore, that as yet little progress has been made in the province of molecular mechanics; but the theory of gases alone, which is intimately connected with the conception of molecules, shows by its success that the time is approaching when our knowledge of the internal structure of matter will be defined and established.
[21]If Be = 9, and beryllium chloride be BeCl2, then for every 9 parts of beryllium there are 71 parts of chlorine, and the molecular weight of BeCl2= 80; hence the vapour density should be 40 orn40. If Be = 13·5, and beryllium chloride be BeCl3, then to 13·5 of beryllium there are 106·5 of chlorine; hence the molecular weight would be 120, and the vapour density 60 orn60. The composition is evidently the same in both cases, because 9 : 71 ∷ 13·5 : 106·5. Thus, if the symbol of an element designate different atomic weights, apparently very different formulæ may equally well express both the percentage composition of compounds, and those properties which are required by the laws of multiple proportions and equivalents. The chemists of former days accurately expressed the composition of substances, and accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6, Si = 14, &c. The Gerhardt equivalents are also satisfied by them, because O = 16, C = 12, Si = 28, &c., are multiples of them. The choice of one or the other multiple quantity for the atomic weight is impossible without a firm and concrete conception of the molecule and atom, and this is only obtained as a consequence of the law of Avogadro-Gerhardt, and hence the modern atomic weights are the results of this law (seeNote28).
[21]If Be = 9, and beryllium chloride be BeCl2, then for every 9 parts of beryllium there are 71 parts of chlorine, and the molecular weight of BeCl2= 80; hence the vapour density should be 40 orn40. If Be = 13·5, and beryllium chloride be BeCl3, then to 13·5 of beryllium there are 106·5 of chlorine; hence the molecular weight would be 120, and the vapour density 60 orn60. The composition is evidently the same in both cases, because 9 : 71 ∷ 13·5 : 106·5. Thus, if the symbol of an element designate different atomic weights, apparently very different formulæ may equally well express both the percentage composition of compounds, and those properties which are required by the laws of multiple proportions and equivalents. The chemists of former days accurately expressed the composition of substances, and accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6, Si = 14, &c. The Gerhardt equivalents are also satisfied by them, because O = 16, C = 12, Si = 28, &c., are multiples of them. The choice of one or the other multiple quantity for the atomic weight is impossible without a firm and concrete conception of the molecule and atom, and this is only obtained as a consequence of the law of Avogadro-Gerhardt, and hence the modern atomic weights are the results of this law (seeNote28).
[22]The percentage amounts of the elements contained in a given compound may be calculated from its formula by a simple proportion. Thus, for example, to find the percentage amount of hydrogen in hydrochloric acid we reason as follows:—HCl shows that hydrochloric acid contains 35·5 of chlorine and 1 part of hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1 part by weight of hydrogen, consequently 100 parts by weight of hydrochloric acid will contain as many more units of hydrogen as 100 is greater than 36·5; therefore, the proportion is as follows—x: 1 ∷ 100 : 36·5 orx=100/36·5= 2·739. Therefore 100 parts of hydrochloric acid contain 2·739 parts of hydrogen. In general, when it is required to transfer a formula into its percentage composition, we must replace the symbols by their corresponding atomic weights and find their sum, and knowing the amount by weight of a given element in it, it is easy by proportion to find the amount of this element in 100 or any other quantity of parts by weight. If, on the contrary, it be required to find the formula from a given percentage composition, we must proceed as follows: Divide the percentage amount of each element entering into the composition of a substance by its atomic weight, and compare the figures thus obtained—they should be in simple multiple proportion to each other. Thus, for instance, from the percentage composition of hydrogen peroxide, 5·88 of hydrogen and 94·12 of oxygen, it is easy to find its formula; it is only necessary to divide the amount of hydrogen by unity and the amount of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained, which are in the ratio 1 : 1, which means that in hydrogen peroxide there is one atom of hydrogen to one atom of oxygen.The following is a proof of the practical rule given abovethat to find the ratio of the number of atoms from the percentage composition, it is necessary to divide the percentage amounts by the atomic weights of the corresponding substances, and to find the ratio which these numbers bear to each other. Let us suppose that two radicles (simple or compound), whose symbols and combining weights are A and B, combine together, forming a compound composed ofxatoms of A andyatoms of B. The formula of the substance will be AxBy. From this formula we know that our compound containsxA parts by weight of the first element, andyB of the second. In 100 parts of our compound there will be (by proportion)100.xA/xA +yBof the first element, and100.yB/xA +yBof the second. Let us divide these quantities, expressing the percentage amounts by the corresponding combining weights; we then obtain100x/xA +yBfor the first element and100y/xA +yBfor the second element. And these numbers are in the ratiox:y—that is, in the ratio of the number of atoms of the two substances.It may be further observed that even the very language or nomenclature of chemistry acquires a particular clearness and conciseness by means of the conception of molecules, because then the names of substances may directly indicate their composition. Thus the term ‘carbon dioxide’ tells more about and expresses CO2better than carbonic acid gas, or even carbonic anhydride. Such nomenclature is already employed by many. But expressing the composition without an indication or even hint as to the properties, would be neglecting the advantageous side of the present nomenclature. Sulphur dioxide, SO2, expresses the same as barium dioxide, BaO2, but sulphurous anhydride indicates the acid properties of SO2. Probably in time one harmonious chemical language will succeed in embracing both advantages.
[22]The percentage amounts of the elements contained in a given compound may be calculated from its formula by a simple proportion. Thus, for example, to find the percentage amount of hydrogen in hydrochloric acid we reason as follows:—HCl shows that hydrochloric acid contains 35·5 of chlorine and 1 part of hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1 part by weight of hydrogen, consequently 100 parts by weight of hydrochloric acid will contain as many more units of hydrogen as 100 is greater than 36·5; therefore, the proportion is as follows—x: 1 ∷ 100 : 36·5 orx=100/36·5= 2·739. Therefore 100 parts of hydrochloric acid contain 2·739 parts of hydrogen. In general, when it is required to transfer a formula into its percentage composition, we must replace the symbols by their corresponding atomic weights and find their sum, and knowing the amount by weight of a given element in it, it is easy by proportion to find the amount of this element in 100 or any other quantity of parts by weight. If, on the contrary, it be required to find the formula from a given percentage composition, we must proceed as follows: Divide the percentage amount of each element entering into the composition of a substance by its atomic weight, and compare the figures thus obtained—they should be in simple multiple proportion to each other. Thus, for instance, from the percentage composition of hydrogen peroxide, 5·88 of hydrogen and 94·12 of oxygen, it is easy to find its formula; it is only necessary to divide the amount of hydrogen by unity and the amount of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained, which are in the ratio 1 : 1, which means that in hydrogen peroxide there is one atom of hydrogen to one atom of oxygen.
The following is a proof of the practical rule given abovethat to find the ratio of the number of atoms from the percentage composition, it is necessary to divide the percentage amounts by the atomic weights of the corresponding substances, and to find the ratio which these numbers bear to each other. Let us suppose that two radicles (simple or compound), whose symbols and combining weights are A and B, combine together, forming a compound composed ofxatoms of A andyatoms of B. The formula of the substance will be AxBy. From this formula we know that our compound containsxA parts by weight of the first element, andyB of the second. In 100 parts of our compound there will be (by proportion)100.xA/xA +yBof the first element, and100.yB/xA +yBof the second. Let us divide these quantities, expressing the percentage amounts by the corresponding combining weights; we then obtain100x/xA +yBfor the first element and100y/xA +yBfor the second element. And these numbers are in the ratiox:y—that is, in the ratio of the number of atoms of the two substances.
It may be further observed that even the very language or nomenclature of chemistry acquires a particular clearness and conciseness by means of the conception of molecules, because then the names of substances may directly indicate their composition. Thus the term ‘carbon dioxide’ tells more about and expresses CO2better than carbonic acid gas, or even carbonic anhydride. Such nomenclature is already employed by many. But expressing the composition without an indication or even hint as to the properties, would be neglecting the advantageous side of the present nomenclature. Sulphur dioxide, SO2, expresses the same as barium dioxide, BaO2, but sulphurous anhydride indicates the acid properties of SO2. Probably in time one harmonious chemical language will succeed in embracing both advantages.
[23]This formula (which is given in my work on ‘The Tension of Gases,’ and in a somewhat modified form in the ‘Comptes Rendus,’ Feb. 1876) is deduced in the following manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is the molecular weight and D the density referred to hydrogen. But it is equal to the weights0of a cubic centimetre of a gas in grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the weightsof a cubic centimetre of a gas at a temperaturetand under a pressurep(in centimetres) is equal tos0p/76(1 +at). Therefore,s0=s.76(1 +at)/p; hence D = 76.s(1 +at)/0·0000898p, whence M = 152s(1 +at)/0·0000898p, which gives the above expression, because 1/a= 273, and 152 multiplied by 273 and divided by 0·0000898 is nearly 6200. In place ofs,m/vmay be taken, wheremis the weight andvthe volume of a vapour.
[23]This formula (which is given in my work on ‘The Tension of Gases,’ and in a somewhat modified form in the ‘Comptes Rendus,’ Feb. 1876) is deduced in the following manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is the molecular weight and D the density referred to hydrogen. But it is equal to the weights0of a cubic centimetre of a gas in grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the weightsof a cubic centimetre of a gas at a temperaturetand under a pressurep(in centimetres) is equal tos0p/76(1 +at). Therefore,s0=s.76(1 +at)/p; hence D = 76.s(1 +at)/0·0000898p, whence M = 152s(1 +at)/0·0000898p, which gives the above expression, because 1/a= 273, and 152 multiplied by 273 and divided by 0·0000898 is nearly 6200. In place ofs,m/vmay be taken, wheremis the weight andvthe volume of a vapour.
[24]The above formula may be directly applied in order to ascertain the molecular weight from the data; weight of vapourmgrms., its volumevc.c., pressurepcm., and temperaturet°; fors= the weight of vapourm, divided by the volumev, and consequently M = 6,200m(273 +t)/pv. Therefore, instead of the formula (seeChapter II., Note 34),pv= R(273 +t), where R varies with the mass and nature of a gas, we may apply the formulapv= 6,200(m/M)(273 +t). These formulæ simplify the calculations in many cases. For example, required the volumevoccupied by 5 grms. of aqueous vapour at a temperaturet= 127° and under a pressurep= 76 cm. According to the formula M = 6,200m(273 +t)/pv, we find thatv= 9,064 c.c., as in the case of water M = 18,min this instance = 5 grms. (These formulæ, however, like the laws of gases, are only approximate.)
[24]The above formula may be directly applied in order to ascertain the molecular weight from the data; weight of vapourmgrms., its volumevc.c., pressurepcm., and temperaturet°; fors= the weight of vapourm, divided by the volumev, and consequently M = 6,200m(273 +t)/pv. Therefore, instead of the formula (seeChapter II., Note 34),pv= R(273 +t), where R varies with the mass and nature of a gas, we may apply the formulapv= 6,200(m/M)(273 +t). These formulæ simplify the calculations in many cases. For example, required the volumevoccupied by 5 grms. of aqueous vapour at a temperaturet= 127° and under a pressurep= 76 cm. According to the formula M = 6,200m(273 +t)/pv, we find thatv= 9,064 c.c., as in the case of water M = 18,min this instance = 5 grms. (These formulæ, however, like the laws of gases, are only approximate.)
[25]Chapter I., Note34.
[25]Chapter I., Note34.
[26]The velocity of the transmission of sound through gases and vapoursclosely bears on this. It = √(Kpg)/D(1 +at), whereKis the ratio between the two specific heats (it is approximately 1·4 for gases containing two atoms in a molecule),pthe pressure of the gas expressed by weight (that is, the pressure expressed by the height of a column of mercury multiplied by the density ofa= 0·00367, andtthe temperature. Hence, ifKbe known, and as D can he found from the composition of a gas, we can calculate the velocity of the transmission of sound in that gas. Or if this velocity be known, we can findK. The relative velocities of sound in two gases can he easily determined (Kundt).If a horizontal glass tube (about 1 metre long and closed at both ends) be full of a gas, and be firmly fixed at its middle point, then it is easy to bring the tube and gas into a state of vibration, by rubbing it from centre to end with a damp cloth. The vibration of the gas is easily rendered visible, if the interior of the tube be dusted with lycopodium (the yellow powder-dust or spores of the lycopodium plant is often employed in medicine), before the gas is introduced and the tube fused up. The fine lycopodium powder arranges itself in patches, whose number depends on the velocity of sound in the gas. If there be 10 patches, then the velocity of sound in the gas is ten times slower than in glass. It is evident that this is an easy method of comparing the velocity of sound in gases. It has been demonstrated by experiment that the velocity of sound in oxygen is four times less than in hydrogen, and the square roots of the densities and molecular weights of hydrogen and oxygen stand in this ratio.
[26]The velocity of the transmission of sound through gases and vapoursclosely bears on this. It = √(Kpg)/D(1 +at), whereKis the ratio between the two specific heats (it is approximately 1·4 for gases containing two atoms in a molecule),pthe pressure of the gas expressed by weight (that is, the pressure expressed by the height of a column of mercury multiplied by the density ofa= 0·00367, andtthe temperature. Hence, ifKbe known, and as D can he found from the composition of a gas, we can calculate the velocity of the transmission of sound in that gas. Or if this velocity be known, we can findK. The relative velocities of sound in two gases can he easily determined (Kundt).
If a horizontal glass tube (about 1 metre long and closed at both ends) be full of a gas, and be firmly fixed at its middle point, then it is easy to bring the tube and gas into a state of vibration, by rubbing it from centre to end with a damp cloth. The vibration of the gas is easily rendered visible, if the interior of the tube be dusted with lycopodium (the yellow powder-dust or spores of the lycopodium plant is often employed in medicine), before the gas is introduced and the tube fused up. The fine lycopodium powder arranges itself in patches, whose number depends on the velocity of sound in the gas. If there be 10 patches, then the velocity of sound in the gas is ten times slower than in glass. It is evident that this is an easy method of comparing the velocity of sound in gases. It has been demonstrated by experiment that the velocity of sound in oxygen is four times less than in hydrogen, and the square roots of the densities and molecular weights of hydrogen and oxygen stand in this ratio.
[27]If the conception of the molecular weights of substances does not give an exact law when applied to the latent heat of evaporation, at all events it brings to light a certain uniformity in figures, which otherwise only represent the simple result of observation. Molecular quantities of liquids appear to expend almost equal amounts of heat in their evaporation. It may be said that the latent heat of evaporation of molecular quantities is approximately constant, because thevis vivaof the motion of the molecules is, as we saw above, a constant quantity. According to thermodynamics the latent heat of evaporation is equal tot+ 273/xA +yB(n′ -n)dp/dT× 13·59, wheretis the boiling point,n′ the specific volume (i.e.the volume of a unit of weight) of the vapour, andnthe specific volume of the liquid,dp/dT the variation of the tension with a rise of temperature per 1°, and 13·89 the density of the mercury according to which the pressure is measured. Thus the latent heat of evaporation increases not only with a decrease in the vapour density (i.e.the molecular weight), but also with an increase in the boiling point, and therefore depends on different factors.
[27]If the conception of the molecular weights of substances does not give an exact law when applied to the latent heat of evaporation, at all events it brings to light a certain uniformity in figures, which otherwise only represent the simple result of observation. Molecular quantities of liquids appear to expend almost equal amounts of heat in their evaporation. It may be said that the latent heat of evaporation of molecular quantities is approximately constant, because thevis vivaof the motion of the molecules is, as we saw above, a constant quantity. According to thermodynamics the latent heat of evaporation is equal tot+ 273/xA +yB(n′ -n)dp/dT× 13·59, wheretis the boiling point,n′ the specific volume (i.e.the volume of a unit of weight) of the vapour, andnthe specific volume of the liquid,dp/dT the variation of the tension with a rise of temperature per 1°, and 13·89 the density of the mercury according to which the pressure is measured. Thus the latent heat of evaporation increases not only with a decrease in the vapour density (i.e.the molecular weight), but also with an increase in the boiling point, and therefore depends on different factors.
[27 bis]The osmotic pressure, vapour tension of the solvent, and several other means applied like the cryoscopic method to dilute solutions for determining the molecular weight of a substance in solution, are more difficult to carry out in practice, and only the method ofdetermining the rise of the boiling pointof dilute solutions can from its facility be placed parallel with the cryoscopic method, to which it bears a strong resemblance, as in both the solvent changes its state and is partially separated. In the boiling point method it passes off in the form of a vapour, while in cryoscopic determinations it separates out in the form of a solid body.Van't Hoff, starting from the second law of thermodynamics, showed that the dependence of the rise of pressure (dp) upon a rise of temperature (dT) is determined by the equationdp= (kmp/2T2)dT, wherekis the latent heat of evaporation of the solvent,mits molecular weight,pthe tension of the saturated vapour of the solvent at T, and T the absolute temperature (T = 273 +t), while Raoult found that the quantity (p-p′)/p(Chapter I., Note50) or the measure of the relative fall of tension (pthe tension of the solvent or water, andp′of the solution) is found by the ratio of the number of molecules,nof the substance dissolved, and N of the solvent, so that (p-p′)/p= Cn/(N +n) where C is a constant. With very dilute solutionsp- p′may be taken as equal todp, and the fractionn/(N +n) as equal ton/N (because in that case the value of N is very much greater thann), and then, judging from experiment, C is nearly unity—hence:dp/p=n/N ordp=np/N, and on substituting this in the above equation we have (kmp/2T2)dT =np/N. Taking a weight of the solventm/N = 100, and of the substance dissolved (per 100 of the solvent)q, whereqevidently =nM, if M be the molecular weight of the substance dissolved, we find thatn/N =qm/100M, and hence, according to the preceding equation, we have M =0·02T2/k·q/dT, that is, by taking a solution ofqgrms. of a substance in 100 grms. of a solvent, and determining by experiment the rise of the boiling pointdT, we find the molecular weight M of the substance dissolved, because the fraction 0·02T2/kis (for a given pressure and solvent) a constant; for water at 100° (T = 373°) whenk= 534 (Chapter I., Note11), it is nearly 5·2, for ether nearly 21, for bisulphide of carbon nearly 24, for alcohol nearly 11·5, &c. As an example, we will cite from the determinations made by Professor Sakurai, of Japan (1893), that when water was the solvent and the substance dissolved, corrosive sublimate, HgCl2, was taken in the quantityq= 8·978 and 4·253 grms., the rise in the boiling pointdT was = O°·179 and 0°·084, whence M = 261 and 263, and when alcohol was the solvent,q= 10·873 and 8·765 anddT = 0°·471 and 0°·380, whence M = 266 and 265, whilst the actual molecular weight of corrosive sublimate = 271, which is very near to that given by this method. In the same manner for aqueous solutions of sugar (M = 342), whenqvaried from 14 to 2·4, and the rise of the boiling point from 0°·21 to 0°·035, M was found to vary between 339 and 364. For solutions of iodine I2in ether, the molecular weight was found by this method to be between 255 and 262, and I2= 254. Sakurai obtained similar results (between 247 and 262) for solutions of iodine in bisulphide of carbon.We will here remark that in determining M (the molecular weight of the substance dissolved) at small but increasing concentrations (per 100 grms. of water), the results obtained by Julio Baroni (1893) show that the value of M found by the formula may either increase or decrease. An increase, for instance, takes place in aqueous solutions of HgCl2(from 255 to 334 instead of 271), KNO3(57–66 instead of 101), AgNO3(104–107 instead of 170), K2SO4(55–89 instead of 174), sugar (328–348 instead of 342), &c. On the contrary the calculated value of M decreases as the concentration increases, for solutions of KCl (40–39 instead of 74·5), NaCl (33–28 instead of 58·5), NaBr (60–49 instead of 103), &c. In this case (as also for LiCl, NaI, C2H3NaO2, &c.) the value ofi(Chapter I., Note49), or the ratio between the actual molecular weight and that found by the rise of the boiling point, was found to increase with the concentration,i.e.to be greater than 1, and to differ more and more from unity as the strength of the solution becomes greater. For example, according to Schlamp (1894), for LiCl, with a variation of from 1·1 to 6·7 grm. LiCl per 100 of water,ivaries from 1·63 to 1·89. But for substances of the first series (HgCl2, &c.), although in very dilute solutionsiis greater than 1, it approximates to 1 as the concentration increases, and this is the normal phenomenon for solutions which do not conduct an electric current, as, for instance, of sugar. And with certain electrolytes, such as HgCl2, MgSO4, &c.,iexhibits a similar variation; thus, for HgCl2the value of M is found to vary between 255 and 334; that is,i(as the molecular weight = 271) varies between 1·06 and 0·81. Hence I do not believe that the difference betweeniand unity (for instance, for CaCl2,iis about 3, for KI about 2, and decreases with the concentration) can at present be placed at the basis of any general chemical conclusions, and it requires further experimental research. Among other methods by which the value ofiis now determined for dilute solutions is the study of their electroconductivity, admitting thati= 1 +a(k- 1), wherea= the ratio of the molecular conductivity to the limiting conductivity corresponding to an infinitely large dilution (seePhysical Chemistry), andkis the number of ions into which the substance dissolved can split up. Without entering upon a criticism of this method of determiningi, I will only remark that it frequently gives values ofivery close to those found by the depression of the freezing point and rise of the boiling point; but that this accordance of results is sometimes very doubtful. Thus for a solution containing 5·67 grms. CaCl2per 100 grms. of water,i, according to the vapour tension = 2·52, according to the boiling point = 2·71, according to the electroconductivity = 2·28, while for solutions in propyl alcohol (Schlamp 1894)iis near to 1·33. In a word, although these methods of determining the molecular weight of substances in solution show an undoubted progress in the general chemical principles of the molecular theory, there are still many points which require explanation.We will add certain general relations which apply to these problems. Isotonic (Chapter I., Note19) solutions exhibit not only similar osmotic pressures, but also the same vapour tension, boiling point and freezing temperature. The osmotic pressure bears the same relation to the fall of the vapour tension as the specific gravity of a solution does to the specific gravity of the vapour of the solvent. The general formulæ underlying the whole doctrine of the influence of the molecular weight upon the properties of solutions considered above, are: 1. Raoult in 1886–1890 showed thatp-p′/p·100/a·M/m= a constant Cwherepandp′ are the vapour tensions of the solvent and substance dissolved,athe amount in grms. of the substance dissolved per 100 grms. of solvent, M andmthe molecular weights of the substance dissolved and solvent. 2. Raoult and Recoura in 1890 showed that the constant above C = the ratio of the actual vapour densityd′ of the solvent to the theoretical densitydcalculated according to the molecular weight. This deduction may now be considered proved, because both the fall of tension and the ratio of the vapour densitiesd′/dgive, for water 1·03, for alcohol 1·02, for ether 1·04, for bisulphide of carbon 1·00, for benzene 1·02, for acetic acid 1·63. 3. By applying the principles of thermodynamics and calling L1the latent heat of fusion and T1the absolute (=t+ 273) temperature of fusion of the solvent, and L2and T2the corresponding values for the boiling point, Van't Hoff in 1886–1890 deduced:—Depression of freezing point/Rise of boiling point=L2/L1·T12/T22Depression of freezing point =AT12a/L1M1Rise of boiling point =AT22a/L2M1where A = 0·01988 (or nearly 0·02 as we took it above),ais the weight in grms. of the substance dissolved per 100 grms. of the solvent, M1the molecular weight of the dissolved substance (in the solution), and M the molecular weight of this substance according to its composition and vapour density, theni= M/M1. The experimental data and theoretical considerations upon which these formulæ are based will be found in text-books of physical and theoretical chemistry.
[27 bis]The osmotic pressure, vapour tension of the solvent, and several other means applied like the cryoscopic method to dilute solutions for determining the molecular weight of a substance in solution, are more difficult to carry out in practice, and only the method ofdetermining the rise of the boiling pointof dilute solutions can from its facility be placed parallel with the cryoscopic method, to which it bears a strong resemblance, as in both the solvent changes its state and is partially separated. In the boiling point method it passes off in the form of a vapour, while in cryoscopic determinations it separates out in the form of a solid body.
Van't Hoff, starting from the second law of thermodynamics, showed that the dependence of the rise of pressure (dp) upon a rise of temperature (dT) is determined by the equationdp= (kmp/2T2)dT, wherekis the latent heat of evaporation of the solvent,mits molecular weight,pthe tension of the saturated vapour of the solvent at T, and T the absolute temperature (T = 273 +t), while Raoult found that the quantity (p-p′)/p(Chapter I., Note50) or the measure of the relative fall of tension (pthe tension of the solvent or water, andp′of the solution) is found by the ratio of the number of molecules,nof the substance dissolved, and N of the solvent, so that (p-p′)/p= Cn/(N +n) where C is a constant. With very dilute solutionsp- p′may be taken as equal todp, and the fractionn/(N +n) as equal ton/N (because in that case the value of N is very much greater thann), and then, judging from experiment, C is nearly unity—hence:dp/p=n/N ordp=np/N, and on substituting this in the above equation we have (kmp/2T2)dT =np/N. Taking a weight of the solventm/N = 100, and of the substance dissolved (per 100 of the solvent)q, whereqevidently =nM, if M be the molecular weight of the substance dissolved, we find thatn/N =qm/100M, and hence, according to the preceding equation, we have M =0·02T2/k·q/dT, that is, by taking a solution ofqgrms. of a substance in 100 grms. of a solvent, and determining by experiment the rise of the boiling pointdT, we find the molecular weight M of the substance dissolved, because the fraction 0·02T2/kis (for a given pressure and solvent) a constant; for water at 100° (T = 373°) whenk= 534 (Chapter I., Note11), it is nearly 5·2, for ether nearly 21, for bisulphide of carbon nearly 24, for alcohol nearly 11·5, &c. As an example, we will cite from the determinations made by Professor Sakurai, of Japan (1893), that when water was the solvent and the substance dissolved, corrosive sublimate, HgCl2, was taken in the quantityq= 8·978 and 4·253 grms., the rise in the boiling pointdT was = O°·179 and 0°·084, whence M = 261 and 263, and when alcohol was the solvent,q= 10·873 and 8·765 anddT = 0°·471 and 0°·380, whence M = 266 and 265, whilst the actual molecular weight of corrosive sublimate = 271, which is very near to that given by this method. In the same manner for aqueous solutions of sugar (M = 342), whenqvaried from 14 to 2·4, and the rise of the boiling point from 0°·21 to 0°·035, M was found to vary between 339 and 364. For solutions of iodine I2in ether, the molecular weight was found by this method to be between 255 and 262, and I2= 254. Sakurai obtained similar results (between 247 and 262) for solutions of iodine in bisulphide of carbon.
We will here remark that in determining M (the molecular weight of the substance dissolved) at small but increasing concentrations (per 100 grms. of water), the results obtained by Julio Baroni (1893) show that the value of M found by the formula may either increase or decrease. An increase, for instance, takes place in aqueous solutions of HgCl2(from 255 to 334 instead of 271), KNO3(57–66 instead of 101), AgNO3(104–107 instead of 170), K2SO4(55–89 instead of 174), sugar (328–348 instead of 342), &c. On the contrary the calculated value of M decreases as the concentration increases, for solutions of KCl (40–39 instead of 74·5), NaCl (33–28 instead of 58·5), NaBr (60–49 instead of 103), &c. In this case (as also for LiCl, NaI, C2H3NaO2, &c.) the value ofi(Chapter I., Note49), or the ratio between the actual molecular weight and that found by the rise of the boiling point, was found to increase with the concentration,i.e.to be greater than 1, and to differ more and more from unity as the strength of the solution becomes greater. For example, according to Schlamp (1894), for LiCl, with a variation of from 1·1 to 6·7 grm. LiCl per 100 of water,ivaries from 1·63 to 1·89. But for substances of the first series (HgCl2, &c.), although in very dilute solutionsiis greater than 1, it approximates to 1 as the concentration increases, and this is the normal phenomenon for solutions which do not conduct an electric current, as, for instance, of sugar. And with certain electrolytes, such as HgCl2, MgSO4, &c.,iexhibits a similar variation; thus, for HgCl2the value of M is found to vary between 255 and 334; that is,i(as the molecular weight = 271) varies between 1·06 and 0·81. Hence I do not believe that the difference betweeniand unity (for instance, for CaCl2,iis about 3, for KI about 2, and decreases with the concentration) can at present be placed at the basis of any general chemical conclusions, and it requires further experimental research. Among other methods by which the value ofiis now determined for dilute solutions is the study of their electroconductivity, admitting thati= 1 +a(k- 1), wherea= the ratio of the molecular conductivity to the limiting conductivity corresponding to an infinitely large dilution (seePhysical Chemistry), andkis the number of ions into which the substance dissolved can split up. Without entering upon a criticism of this method of determiningi, I will only remark that it frequently gives values ofivery close to those found by the depression of the freezing point and rise of the boiling point; but that this accordance of results is sometimes very doubtful. Thus for a solution containing 5·67 grms. CaCl2per 100 grms. of water,i, according to the vapour tension = 2·52, according to the boiling point = 2·71, according to the electroconductivity = 2·28, while for solutions in propyl alcohol (Schlamp 1894)iis near to 1·33. In a word, although these methods of determining the molecular weight of substances in solution show an undoubted progress in the general chemical principles of the molecular theory, there are still many points which require explanation.
We will add certain general relations which apply to these problems. Isotonic (Chapter I., Note19) solutions exhibit not only similar osmotic pressures, but also the same vapour tension, boiling point and freezing temperature. The osmotic pressure bears the same relation to the fall of the vapour tension as the specific gravity of a solution does to the specific gravity of the vapour of the solvent. The general formulæ underlying the whole doctrine of the influence of the molecular weight upon the properties of solutions considered above, are: 1. Raoult in 1886–1890 showed that
p-p′/p·100/a·M/m= a constant C
wherepandp′ are the vapour tensions of the solvent and substance dissolved,athe amount in grms. of the substance dissolved per 100 grms. of solvent, M andmthe molecular weights of the substance dissolved and solvent. 2. Raoult and Recoura in 1890 showed that the constant above C = the ratio of the actual vapour densityd′ of the solvent to the theoretical densitydcalculated according to the molecular weight. This deduction may now be considered proved, because both the fall of tension and the ratio of the vapour densitiesd′/dgive, for water 1·03, for alcohol 1·02, for ether 1·04, for bisulphide of carbon 1·00, for benzene 1·02, for acetic acid 1·63. 3. By applying the principles of thermodynamics and calling L1the latent heat of fusion and T1the absolute (=t+ 273) temperature of fusion of the solvent, and L2and T2the corresponding values for the boiling point, Van't Hoff in 1886–1890 deduced:—
Depression of freezing point/Rise of boiling point=L2/L1·T12/T22
Depression of freezing point =AT12a/L1M1
Rise of boiling point =AT22a/L2M1
where A = 0·01988 (or nearly 0·02 as we took it above),ais the weight in grms. of the substance dissolved per 100 grms. of the solvent, M1the molecular weight of the dissolved substance (in the solution), and M the molecular weight of this substance according to its composition and vapour density, theni= M/M1. The experimental data and theoretical considerations upon which these formulæ are based will be found in text-books of physical and theoretical chemistry.
[28]A similar conclusion respecting the molecular weight of liquid water (i.e.that its molecule in a liquid state is more complex than in a gaseous state, or polymerized into H8O4, H6O3or in general intonH2O) is frequently met in chemico-physical literature, but as yet there is no basis for its being fully admitted, although it is possible that a polymerization or aggregation of several molecules into one takes place in the passage of water into a liquid or solid state, and that there is a converse depolymerization in the act of evaporation. Recently, particular attention has been drawn to this subject owing to the researches of Eötvös (1886) and Ramsay and Shields (1893) on the variation of the surface tension N with the temperature (N = the capillary constanta2multiplied by the specific gravity and divided by 2, for example, for water at 0° and 100° the value ofa2= 15·41 and 12·58 sq. mm., and the surface tension 7·92 and 6·04). Starting from the absolute boiling point (Chapter II., Note29) and adding 6°, as was necessary from all the data obtained, and calling this temperature T, it is found that AS =kT, where S is the surface of a gram-molecule of the liquid (if M is its weight in grams,sits sp. gr., then its sp. volume = M/s, and the surface S = ∛(M/s)2), A the surface tension (determined by experiment at T), andka constant which is independent of the composition of the molecule. The equation AS =kT is in complete agreement with the well-known equation for gasesvp= RT (p.140) which serves for deducing the molecular weight from the vapour density. Ramsay's researches led him to the conclusion that the liquid molecules of CS2, ether, benzene, and of many other substances, have the same value as in a state of vapour, whilst with other liquids this is not the case, and that to obtain an accordance, that is, thatkshall be a constant, it is necessary to assume the molecular weight in the liquid state to bentimes as great. For the fatty alcohols and acidsnvaries from 1½ to 3½, for water from 2¼ to 4, according to the temperature (at which the depolymerization takes place). Hence, although this subject offers a great theoretical interest, it cannot be regarded as firmly established, the more so since the fundamental observations are difficult to make and not sufficiently numerous; should, however, further experiments confirm the conclusions arrived at by Professor Ramsay, this will give another method of determining molecular weights.
[28]A similar conclusion respecting the molecular weight of liquid water (i.e.that its molecule in a liquid state is more complex than in a gaseous state, or polymerized into H8O4, H6O3or in general intonH2O) is frequently met in chemico-physical literature, but as yet there is no basis for its being fully admitted, although it is possible that a polymerization or aggregation of several molecules into one takes place in the passage of water into a liquid or solid state, and that there is a converse depolymerization in the act of evaporation. Recently, particular attention has been drawn to this subject owing to the researches of Eötvös (1886) and Ramsay and Shields (1893) on the variation of the surface tension N with the temperature (N = the capillary constanta2multiplied by the specific gravity and divided by 2, for example, for water at 0° and 100° the value ofa2= 15·41 and 12·58 sq. mm., and the surface tension 7·92 and 6·04). Starting from the absolute boiling point (Chapter II., Note29) and adding 6°, as was necessary from all the data obtained, and calling this temperature T, it is found that AS =kT, where S is the surface of a gram-molecule of the liquid (if M is its weight in grams,sits sp. gr., then its sp. volume = M/s, and the surface S = ∛(M/s)2), A the surface tension (determined by experiment at T), andka constant which is independent of the composition of the molecule. The equation AS =kT is in complete agreement with the well-known equation for gasesvp= RT (p.140) which serves for deducing the molecular weight from the vapour density. Ramsay's researches led him to the conclusion that the liquid molecules of CS2, ether, benzene, and of many other substances, have the same value as in a state of vapour, whilst with other liquids this is not the case, and that to obtain an accordance, that is, thatkshall be a constant, it is necessary to assume the molecular weight in the liquid state to bentimes as great. For the fatty alcohols and acidsnvaries from 1½ to 3½, for water from 2¼ to 4, according to the temperature (at which the depolymerization takes place). Hence, although this subject offers a great theoretical interest, it cannot be regarded as firmly established, the more so since the fundamental observations are difficult to make and not sufficiently numerous; should, however, further experiments confirm the conclusions arrived at by Professor Ramsay, this will give another method of determining molecular weights.
[28 bis]Their variance is expressed in the same manner as was done by Van't Hoff (Chapter I., Notes19and49) by the quantityi, taking it as = 1 whenk= 1·05, in that case for KI,iis nearly 2, for borax about 4, &c.
[28 bis]Their variance is expressed in the same manner as was done by Van't Hoff (Chapter I., Notes19and49) by the quantityi, taking it as = 1 whenk= 1·05, in that case for KI,iis nearly 2, for borax about 4, &c.
[29]We will cite one more example, showing the direct dependence of the properties of a substance on the molecular weight. If one molecular part by weight of the various chlorides—for instance, of sodium, calcium, barium, &c.—be dissolved in 200 molecular parts by weight of water (for instance, in 3,600 grams) then it is found that the greater the molecular weight of the salt dissolved, the greater is the specific gravity of the resultant solution.MolecularweightSp. gr. at 15°MolecularweightSp. gr. at 15°HCl36·51·0041CaCl21111·0236NaCl58·51·0106NiCl21301·0328KCl74·51·0121ZnCl21361·0331BeCl2801·0138BaCl22081·0489MgCl2951·0203
[29]We will cite one more example, showing the direct dependence of the properties of a substance on the molecular weight. If one molecular part by weight of the various chlorides—for instance, of sodium, calcium, barium, &c.—be dissolved in 200 molecular parts by weight of water (for instance, in 3,600 grams) then it is found that the greater the molecular weight of the salt dissolved, the greater is the specific gravity of the resultant solution.
[29 bis]With respect to the optical refractive power of substances, it must first be observed that the coefficient of refraction is determined by two methods: (a) either all the data are referred to one definite ray—for instance, to the Fraunhofer (sodium) line D of the solar spectrum—that is, to a ray of definite wave length, and often to that red ray (of the hydrogen spectrum) whose wave length is 656 millionths of a millimetre; (b) or Cauchy's formula is used, showing the relation between the coefficient of refraction and dispersion to the wave lengthn= A +B/λ, where A and B are two constants varying for every substance but constant for all rays of the spectrum, and λ is the wave length of that ray whose coefficient of refraction isn. In the latter method the investigation usually concerns the magnitudes of A, which are independent of dispersion. We shall afterwards cite the data, investigated by the first method, by which Gladstone, Landolt, and others established the conception of the refraction equivalent.It has long been known that thecoefficient of refraction nfor a given substance decreases with the density of a substance D, so that the magnitude (n- 1) ÷ D = C is almost constant for a given ray (having a definite wave length) and for a given substance. This constant is called therefractive energy, and its product with the atomic or molecular weight of a substance therefraction equivalent. The coefficient of refraction of oxygen is 1·00021, of hydrogen 1·00014, their densities (referred to water) are 0·00143 and 0·00009, and their atomic weights, O = 16, H = 1; hence their refraction equivalents are 3 and 1·5. Water contains H2O, consequently the sum of the equivalents of refraction is (2 × 1·5) + 3 = 6. But as the coefficient of refraction of water = 1·331, its refraction equivalent = 5·958, or nearly 6. Comparison shows that, approximately, the sum of the refraction equivalents of the atoms forming compounds (or mixtures) is equal to the refraction equivalent of the compound. According to the researches of Gladstone, Landolt, Hagen, Brühl and others, the refraction equivalents of the elements are—H = 1·3, Li = 3·8, B = 4·0, C = 5·0, N = 4·1 (in its highest state of oxidation, 5·3), O = 2·9, F = 1·4, Na = 4·8, Mg = 7·0, Al = 8·4, Si = 6·8, P = 18·3, S = 16·0, Cl = 9·9, K = 8·1, Ca = 10·4, Mn = 12·2, Fe = 12·0 (in the salts of its higher oxides, 20·1), Co = 10·8, Cu = 11·6, Zn = 10·2, As = 15·4, Bi = 15·3, Ag = 15·7, Cd = 13·6, I = 24·5, Pt = 26·0, Hg = 20·2, Pb = 24·8, &c. The refraction equivalents of many elements could only be calculated from the solutions of their compounds. The composition of a solution being known it is possible to calculate the refraction equivalent of one of its component parts, those for all its other components being known. The results are founded on the acceptance of a law which cannot be strictly applied. Nevertheless the representation of the refraction equivalents gives an easy means for directly, although only approximately, obtaining the coefficient of refraction from the chemical composition of a substance. For instance, the composition of carbon bisulphide is CS2= 76, and from its density, 1·27, we find its coefficient of refraction to be 1·618 (because the refraction equivalent = 5 + 2 × 16 = 37), which is very near the actual figure. It is evident that in the above representation compounds are looked on as simple mixtures of atoms, and the physical properties of a compound as the sum of the properties present in the elementary atoms forming it. If this representation of the presence of simple atoms in compounds had not existed, the idea of combining by a few figures a whole mass of data relating to the coefficient of refraction of different substances could hardly have arisen. For further details on this subject, see works onPhysical Chemistry.
[29 bis]With respect to the optical refractive power of substances, it must first be observed that the coefficient of refraction is determined by two methods: (a) either all the data are referred to one definite ray—for instance, to the Fraunhofer (sodium) line D of the solar spectrum—that is, to a ray of definite wave length, and often to that red ray (of the hydrogen spectrum) whose wave length is 656 millionths of a millimetre; (b) or Cauchy's formula is used, showing the relation between the coefficient of refraction and dispersion to the wave lengthn= A +B/λ, where A and B are two constants varying for every substance but constant for all rays of the spectrum, and λ is the wave length of that ray whose coefficient of refraction isn. In the latter method the investigation usually concerns the magnitudes of A, which are independent of dispersion. We shall afterwards cite the data, investigated by the first method, by which Gladstone, Landolt, and others established the conception of the refraction equivalent.
It has long been known that thecoefficient of refraction nfor a given substance decreases with the density of a substance D, so that the magnitude (n- 1) ÷ D = C is almost constant for a given ray (having a definite wave length) and for a given substance. This constant is called therefractive energy, and its product with the atomic or molecular weight of a substance therefraction equivalent. The coefficient of refraction of oxygen is 1·00021, of hydrogen 1·00014, their densities (referred to water) are 0·00143 and 0·00009, and their atomic weights, O = 16, H = 1; hence their refraction equivalents are 3 and 1·5. Water contains H2O, consequently the sum of the equivalents of refraction is (2 × 1·5) + 3 = 6. But as the coefficient of refraction of water = 1·331, its refraction equivalent = 5·958, or nearly 6. Comparison shows that, approximately, the sum of the refraction equivalents of the atoms forming compounds (or mixtures) is equal to the refraction equivalent of the compound. According to the researches of Gladstone, Landolt, Hagen, Brühl and others, the refraction equivalents of the elements are—H = 1·3, Li = 3·8, B = 4·0, C = 5·0, N = 4·1 (in its highest state of oxidation, 5·3), O = 2·9, F = 1·4, Na = 4·8, Mg = 7·0, Al = 8·4, Si = 6·8, P = 18·3, S = 16·0, Cl = 9·9, K = 8·1, Ca = 10·4, Mn = 12·2, Fe = 12·0 (in the salts of its higher oxides, 20·1), Co = 10·8, Cu = 11·6, Zn = 10·2, As = 15·4, Bi = 15·3, Ag = 15·7, Cd = 13·6, I = 24·5, Pt = 26·0, Hg = 20·2, Pb = 24·8, &c. The refraction equivalents of many elements could only be calculated from the solutions of their compounds. The composition of a solution being known it is possible to calculate the refraction equivalent of one of its component parts, those for all its other components being known. The results are founded on the acceptance of a law which cannot be strictly applied. Nevertheless the representation of the refraction equivalents gives an easy means for directly, although only approximately, obtaining the coefficient of refraction from the chemical composition of a substance. For instance, the composition of carbon bisulphide is CS2= 76, and from its density, 1·27, we find its coefficient of refraction to be 1·618 (because the refraction equivalent = 5 + 2 × 16 = 37), which is very near the actual figure. It is evident that in the above representation compounds are looked on as simple mixtures of atoms, and the physical properties of a compound as the sum of the properties present in the elementary atoms forming it. If this representation of the presence of simple atoms in compounds had not existed, the idea of combining by a few figures a whole mass of data relating to the coefficient of refraction of different substances could hardly have arisen. For further details on this subject, see works onPhysical Chemistry.