MOLECULE CHEMICAL ASPECT, The word Molecule is used by chemists to express the unit of a pure substance, that quantity of it which its formula ought to represent. What this quantity is, in any particular case, must be ascertained by studying the chemical actions by which the substance is produced and the chemical changes which it undergoes. We may give one or two illustrations to show how this can be done, as well as to indicate the limits within which these methods can be applied.

The formula usually assigned to acetic acid is C2I402. This agrees with almost all the chemical actions in which it takes part. Thus, one quarter of the hydrogen is replaceable by other metals, as in Coll3K02, &c.; and one, two, or three quarters of the hydrogen can be replaced by chlorine. There must, therefore, be four (or a multiple of four) atoms of hydrogen in the molecule. Similarly, half of the oxygen can be replaced by sulphur, and one-half of the oxygen along with one-quarter of the hydrogen can be replaced by chlorine. There must, therefore, be two (or a multiple of two) atoms of oxygen in the molecule. Again, the formation of marsh gas and carbonate of soda, when acetate of soda is heated with caustic soda, and the formation of aceto-nitrile from cyanide of potassium and iodide of methyl, show that the carbon in acetic acid is divisible by two, or that the molecule contains two (or a multiple of two) atoms of carbon. C211402 is the simplest formula which fulfils these conditions, but the existence of an acid acetate of potash and an acid acetate of ammonia, the formulae of which are usually written C2113K02, C21=1402 and C2I-I3(N114)02, C211402, as if these were compounds derived from two molecules of acetic acid, mizlit lead us to C4-1,04, as this shows that the hydrogen is divisible by eight. In the same way, we can easily satisfy ourselves that Coilto 05, or some multiple of it, is the formula of starch ; that CsII,NO, or some multiple of it, is the formula of indigo blue, and so on. But it is not easy to determine by purely chemical methods whether these formulae themselves, or multiples of them, really represent the molecule. A simple formula. may suffice for a great many of the reactions of a substance, and may enable us to represent a great many of its derivatives, and yet reactions and derivatives may be discovered which require a multiple of that simple formula. This has already been indicated in reference to acetic acid, and a very striking illustration is supplied by mellitic acid. For a long time the formula 04II204 was used for this acid, and by means of it all the then known derivatives were represented. But later investigations by Baeyer proved that this formula must be multiplied by three, the new derivatives obtained by him not being capable of representation with any formula simpler than C42I1,012. Very many examples of the same kind might be adduced, but those given may serve to show the nature of the difficulty of settling the formula and with it the molecular weight of a substance. It need scarcely be said that the multiple formula represents everything which the simple formula represents and something more, and that chemists as a rule take the simplest formula which will answer the purpose. These chemical methods of determining the formula and molecular weight apply equally to all pure substances, but they do not give us absolute values, only numbers to which the molecular weights are proportional. And for purely chemical purposes these are all that we require. Thus, when a chemist speaks of acting on a molecule of succinic acid with two molecules of pentachloride of phosphorus, he means that he mixes them in the proportion of 118 parts of the former to 2 x 177.5 of the latter. For the sake of precision we sometimes speak of a molecule of water (or other substance) in grammes, or even of a gramize-molecule, a grain-molecule, &c. Thus, in the case just mentioned a gramme-molecule of succinic acid means 118 grammes of succinic acid, &c.

But while for practical purposes these proportional numbers are quite sufficient, we cannot leave out of view their relation to the actual constitution of matter. There is good reason to believe that matter consists of discrete particles, and that every pure substance is made up of small portions of matter, all alike, so that one of them, if we could examine it, would give us a complete idea of the chemical composition, constitution, and character of the substance. These small portions, of which the smallest quantity of the substance which we can examine contains many millions, we may call molecules. From the character which we have supposed this molecule to possess - viz., that it fully represents all the chemical properties of the substance - it will be seen that these real, ultimate molecules must be proportional to the molecular weights ascertained by chemical means ; so that, while for practical laboratory or manufacturing purposes we use the gramme, the pound, or the ton as our unit, and speak of 18 grammes, pounds, or tons, as the case may be, of water, as a molecule (or gramme-molecule, ton-molecule, &c,), in dealing with the actual constitution of matter we should use as our unit the mass of a single atom of hydrogen, and our gramme-molecule would then be a definite, very large, but not yet accurately ascertained, number of real molecules.

It has been already shown above that, on the kinetic theory of gas, a gas consists of a number of particles moving about in straight lines in all directions, and that in a homogeneous gas which follows Boyle's and Charles's laws these particles are all alike. The masses of the particles of different gases are therefore to one another in the same proportion as the densities of the gases, temperature and pressure being the same. Thus, in gases, the independently moving particles of the kinetic theory are the molecules of which the chemist is in search, and it becomes important that we should compare our chemically found molecular weights with the densities. Theoretically accurate results could be obtained only in the case of a perfect gas ; but small deviations from Boyle's and Charles's laws do not interfere with the application of this method. Chemical methods, as we have already seen, lead us to a particular number, or a multiple of it, so that our choice is as a rule limited to two or three numbers widely differing from one another. We find that if we do not exceed the limits of chemical stability a gas approaches the state of a perfect gas as the temperature increases, or as the pressure diminishes. Now if one of the numbers rendered probable by chemical evidence nearly coincides with that given by comparison of gas densities, under conditions where the substance sensibly deviates from Boyle's and Charles's laws, we find that by diminishing the pressure or increasing the temperature within the limits of chemical stability, and thus bringing the substance nearer the state of a perfect gas, the correspondence between these two numbers becomes closer. This has already been pointed out and illustrated in the article CHEMISTRY, vol. v. p. 469.

We can now compare the results, in the case of gases, of the chemical and of the physical determination of molecular weight, by giving some examples, placing side by side the formula and molecular weight adopted by chemists, and the mass, in grammes, of the gas occupying the volume of 22.33 x 760/p x (273 + 0/273 litres. This volume is that which one gramme of an ideal gas having the molecular weight 1, and perfectly following Boyle's and Charles's laws, would occupy at pressure p millimetres of mercury and temperature t° C. If, then, w be the molecular weight of any gas, w grammes of it should occupy this volume, and slight deviation from this would indicate slight deviation from Boyle's and Charles's laws. In the annexed table w is the molecular weight and ma the mass contained in 22.33 x 760/p x (273 + 0/273 litres. Where the temperature is not specially stated, the determinations were made under the usual atmospheric conditions.

We shall therefore reserve the term " anomalous vapour density" for those substances the molecular weight of which as given by their vapour density is not reconcilable with any formula which is chemically admissible. In the case of some substances, such as the oxides of chlorine, it has been shown that the discrepancy was due to errors of observation, impure specimens having been used in the experiments ; but there still remain many substances having, in the sense above indicated, an anomalous vapour density. These substances have therefore been examined with special care, with the result of completely vindicating the kinetic theory, and of disclosing a very interesting and theoretically important kind of chemical change. We shall take, as instances of such anomalous vapour densities, the substances in the last division of the table, and show how the anomaly has in these cases been explained.

Sal-ammoniac has the composition represented by the formula NH4C1. This formula agrees with all the chemical actions of the substance and of all the substances in any way related to it, but it does not agree with the results of vapour density determinations. When sal-ammoniac is heated it is converted into vapour or gas, and this vapour or gas is reconverted into solid sal-ammoniac when it is cooled. This looks exactly like the process of sublimation, and it was universally supposed that the vapour given off when sal-ammoniac is heated was really sal-ammoniac vapour. But its vapour density corresponds, not to the formula NII4C1 and the molecular weight 53-5, but to the half of this. Now this formula does not admit of division, and the explanation at once suggests itself, that the vapour examined was not really the vapour of sal-ammoniac, but of hydrochloric acid and ammonia gases, the products of the decomposition of sal-ammoniac.

This would of course completely explain the apparent anomaly ; each molecule NH4C1 dividing into two molecules NH3 and HC1, the gas from a given weight of sal-ammoniac would of course contain twice as many molecules and occupy twice the space which it would do if no such decomposition had occurred. On this supposition the mixed gases would remain uncombincd as long as the temperature was above the decomposing point of sal-ammoniac; if the temperature fell below this point they would unite and reproduce sal-ammoniac. It was necessary, however, to prove that this decomposition occurs.

As has been shown above (p. 618), the rate of diffusion of a gas depends upon its density. In this case the two gases into which the substance may be supposed to break up at the moment of volatilization differ considerably in density ; we ought, therefore, to be able to effect partial separation by means of diffusion, and it has been shown that such partial separation actually does occur. Thus, if we have hydrogen gas on one side of a porous diaphragm and volatilized sal-ammoniac on the other side, we find after a time that, mixed with the hydrogen on the one side, we have what we may for shortness call sal-ammoniac vapour - that is, a vapour which when cooled forms solid sal-ammoniac - with an excess of ammonia, which, being less dense than hydrochloric acid gas, has diffused faster ; while on the other side, also mixed with hydrogen which has diffused through the diaphragm, we have sal-ammoniac vapour with excess of hydrochloric acid, the denser and more slowly diffusing gas. This of course proves that the decomposition has occurred, but it does not prove that the vapour of sal-ammoniac consists entirely of hydrochloric acid and ammonia mixed with one another. That this in fact is not the case has been shown by an ingenious experiment. The two gases were separately raised to a temperature higher than that at which sal-ammoniac volatilizes, and were then allowed to mix in a vessel kept at the same temperature as the two gases. In this vessel a delicate thermometer was placed, and it was found that the mixing of the two gases was accompanied by a small but very decided evolution of heat. This proves that some chemical combination takes place, and that the mixed gases must contain some vapour of NII4C1. Moreover, careful determinations of the vapour density of sal-ammoniac prove that it is a little more than the mean of the densities of ammonia and hydrochloric acid (as compared with air at the same temperature and pressure, 1-01 instead of 0-9255 at 350°C.); and this increase of density on mixing the hot gases is easily explained by supposing that a small proportion is in the condition of NII4C1, while the most of the gas consists of separate NH3 and HC1 molecules.

In a similar way it has been shown that the vapour of oil of vitriol is a mixture of two vapours, - that of water, 1120, and that of sulphuric anhydride, SO3; and that sulphide of ammonium when volatilized breaks up into two volumes of ammonia and one of sulphuretted hydrogen, (NH4)2S = 2NH3 + H2S. We find, therefore, that in the former case, as in that of sal-ammoniac, eu = 2m, and in the latter, w= 3m.

This peculiar kind of decomposition is now known by the name " dissociation." (See vol. v. pp. 475, 476.) In the cases we have mentioned the substances undergo nearly complete dissociation at the temperature at which they volatilize, and recombination takes place when they are cooled and again assume the solid, or, as in the case of oil of vitriol, the liquid state. These substances are therefore not suited for the illustration of the whole course of dissociation. This has been carefully studied in the case of some compounds, in which the dissociation is far from complete, at the boiling point of the substance, with the result that, if AB be the compound dissociating into the separate molecules A and B, we may represent the amount of dissociation as the ratio of the number of pairs of separate A and B molecules to the total number of pairs of A and B, both separate and combined. This ratio we may call B, so that when dissociation is complete B=1.

(1) R increases as the temperature rises. (2) dRldt (where l is temperature) is a maximum when R= (3) The presence of excess of either A or B diminishes the value of R. For instance, PC13 is nearly completely dissociated into PC13 and Ch at 300° C. ; but if a large excess of PCI3 is mixed with the vapour it is found to contain scarcely any CI, so that dissociation is greatly diminished by the presence of excess of PC13. These experimental results are capable of explanation on the kinetic theory of gas, if we adopt Pfaundler's hypothesis. This is, that for each case of dissociation there is a limiting value for the internal kinetic energy 1 of a molecule of AB. If a molecule of AB, by encounters with other molecules or with the wall of the vessel containing the gas, acquires a greater amount of internal kinetic energy than this limit, it at once breaks up into A and B, so that in the gaseous mixture there are no molecules of AB having more internal kinetic energy than the limit. Further, if two molecules, one of A and one of B, meet one another with such a velocity and with such an amount of internal kinetic energy that together the internal kinetic energy is less than the limit, they will unite to form a molecule of AB. Thus the molecules with great internal kinetic energy will be separate molecules of A and ; those with small internal kinetic energy will mostly be united as AB. This hypothesis has been to a considerable extent worked out and applied by Pfaundler and by Naumann, and the deductions from it agree fairly well with the results of experiment ; but in some points the theory has pot been fully developed, and in some it does not seem altogether to accord with observed Lets. Some of these difficulties have been mentioned above. We know enough of the nature of dissociation to see that it belongs to the class of balanced chemical actions, in which a chemical change is reversible, and equilibrium is kept up, with constant external conditions, by the two opposite chemical changes taking place to an equal extent in a given time. We can see that all such eases are explicable by the statistical method, but we cannot apply this method mathematically until we know more of the intimate nature of the molecules and of the way in which they act upon one another. In this discussion of dissociation we have looked specially at the cases in which A, B, and AB are all gaseous, because it was the question of anomalous vapour densities which led us to treat of the subject. Dissociation also occurs where one or two of the substances are solid or liquid.

We now see with what restrictions the method of vapour density is applicable to the determination of molecular weight, and we can understand more fully the example given in the article CREMISTRY, vol. v. p. 469. It is there shown that acetic acid vapour does not conform to the laws of Boyle and Charles until the temperature is raised to about 250°, at the ordinary barometric pressure. At and above that temperature the vapour density corresponds to the formula C211400. At lower temperatures the density corresponds to a higher molecular weight. Now Mayfair and Wanklyn determined the vapour density at much lower temperatures than the ordinary boiling point of acetic acid, by greatly diminishing the pressure of the