On the other hand, the rate of association alternately increases and decreases; thus in this case there is an intimate relationship between the attainment of maximum association and the wavy nature of a closely related property.

Generally speaking, association decreases with rise in molecular weight. This was observed by Ramsay and Shields and by Traube in the case of liquids, and is also true for the association of the fatty acids in the gaseous state as measured by their vapour densities.^* An increase of molecular complexity which extends to far up the series, as in the case of the aliphatic acids in phenol, has never been previously observed.

(2.) When the Compounds are in the Liquid State.—Examples of this are exceedingly numerous for the rotary power of optically active compounds. Guye showed that in many cases the explanation may be given from his hypothesis of the product of asymmetry. Frankland,^† on the other hand, explains the maximum or minimum in many cases as due to the association of the initial members of the series. A clear case of this is exhibited by the esters of active amyl alcohol (Guye and Chavanne). The association factor is calculated according to Traube's formula:—

Here it is seen that when there is no association the values of [a] regularly increase.

(3.) When the Compounds are Solids.—(a.) The Melting-points of the Phenyl Fatty Acids:—

Now, molecular complexity raises the boiling-point; and, in general, when the boiling-point of an isomer rises the melting-point is found to fall. Consequently, when the melting-point falls in an homologous series (a rise being expected) it may naturally be concluded that the association of the molecules becomes greater with the fall of melting-point.

(b.) The Solubilities of the Calcium Salts of the Fatty Acids:^* In the case of the normal acids the salts increase in solubility from formate to propionate, and then decrease quickly with the increase of the number of carbon atoms. In the following table the values of the solubilities are given for the temperatures 0° and 100°:—

Near the member where the maximum solubility occurs it is found that there is alternate increase and decrease of solubility between 0° and 100°. This is comparable with the association of the fatty acids (A (1)) where the rate alternates, but the association reaches a maximum.

Lumsden states that one of the causes that determines the solubility is osmotic pressure. Now, osmotic pressure is influenced by association; so we see in this case also that there is a possibility of the cause of the phenomenon being molecular association.

B. (1.) When the Compounds are in the Gaseous State.— Again, the only example of this type is furnished by the fatty

acids in phenol (see above, Article LVI.), whose rates of association alternately increase and decrease. If the even members alone are considered it is found that the rate slowly falls to a minimum, and then rapidly increases.

(2.) When the Compounds are Liquids.—(a.) The Boiling-points of the Fatty Acids and their Derivatives, the Ketones, Nitroparaffins, and Nitriles: If the boiling-points of the fatty acids are considered a continual increase is noticed. On taking successive differences, however, the numbers obtained are of a wavy nature. As is seen in the following table, the second set of differences decreases, reaching a minimum and then increasing again. The other series also decreases, but more slowly, perhaps reaching a minimum higher up the series.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

The same alternate rise and fall is shown if the boiling-points are taken at a pressure of 100 mm. In this case, however, the even to odd differences are smaller, and reach the minimum first, whilst at atmospheric pressure the reverse is the case.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

This behaviour of the fatty acids is probably due to the

association of the vapour at the boiling-point, for the following reasons:—

(1.) It is less noticeable in the case of the esters, which are only slightly associated.

(2.) The minimum is less marked when the boiling-points under reduced pressure are considered, and under reduced pressure the amount of association is reduced.

(3.) It is not exhibited by series of compounds which are associated neither in the liquid nor gaseous state, nor, on the other hand, by the alcohols which form liquid (not gaseous) molecular complexes.

Among the esters the successive differences are much more regular. In the following table the boiling-points of the methyl, ethyl, and propyl esters of the fatty acids are given:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

For each series the first set of differences shows a clear maximum between the esters derived from the C₄ and C₅ acids, the number being in all cases practically the same (25). The acids themselves show a maximum at the same place, although it is much less marked. In the other set of differences there is a general tendency for the numbers to decrease, but the characteristic minimum observed in the acids finds no parallel among their ethereal salts.

In general the methyl esters bear a much closer resemblance to the acids themselves than do the esters with larger alkyl radicals. This is seen, for instance, in their higher melting-point and the greater complexity of the liquid molecules. At the boiling-point such differences disappear. This is only another example showing that the boiling-point is a comparable temperature for physical data.

Much more clearly than with the esters is a similar relation exhibited by the acid chlorides. The following table is given by Henry,^* who pointed out the large variations in successive differences of the boiling-points, but did not appear

to show the regular formation of a maximum at the number 29:—

This maximum occurs in the same series as the maximum shown by the esters and the acids themselves, but one place higher. The acid chlorides also differ from the esters and the acids themselves, by the fact that the average for the set of larger differences (27) is considerably greater than the corresponding number (22) for the acids and their ethereal salts. On the other hand, a resemblance is shown to the esters' slight differences between the numbers of the same set, while this is not the case among the acids. This, then, is the true test for the magnitude of the molecular complexity of the gaseous molecule at the boiling-point.

Acids of the oxalic series tend to decompose when heated, consequently their boiling-points cannot be determined under the ordinary conditions. Krafft,^* however, has determined the boiling-points of some of the higher members under reduced pressure. The results show the usual waviness, but the differences are smaller than for the corresponding fatty acids under the same conditions. Hence it is reasonable to conclude that the association of the dibasic acids in the state of vapour is less than that of the fatty acids from which they are derived.^†

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

From analogy with the fatty acids it is to be expected that the esters of these acids would exhibit similar relations. But the data are too scanty and inconsistent among themselves to draw any conclusions therefrom.

The data for various aldehydes and ketones are presented in the next table, as they show a similarity to the results already obtained.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

The maximum in all cases occurs in the usual place—i.e., the second member of the first set of differences. The ketones of the type R. COCH₃ show practically as much association as the aldehydes, thus differing from the other series of ketones, which is almost normal. The methyl esters, it will be remembered, differed largely from the acids whence they were derived; but here the alkyl radical replaces a hydroxyl hydrogen, while in the case of the aldehydes the hydrogen is joined directly to a carbon atom.

Seeing that when the gaseous molecule is associated at the boiling-point results of this nature are obtained, the nitriles and nitroparaffins ought to behave in a similar manner. That this is the case is seen from the following tables:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Here, again, the maximum is observed in exactly the same place as among the acids and their esters, the aldehydes and ketones. Further, there is an exceedingly pronounced minimum in the other series; this corresponds to a similar mini-,

mum though not so sudden, among the data for the acid chlorides, and to the characteristic minimum, which occurs in the next number of this series for the fatty acids.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

The numbers in brackets are rendered doubtful owing to the result obtained for the boiling-point of nitropentane. The higher limit is taken as the more probable, but this cannot affect the general conclusions. This series is exactly similar to the nitriles. The changes occur in the same positions, and are perhaps a little more marked, indicating a greater molecular complexity of the gaseous molecules.^*

The hydrocarbons, their halogen derivatives, the alcohols, amines, and ethers, exhibit no such behaviour. But-in-none of these series has any considerable association been noticed. In all the instances where the wavy character occurs there is either a carboxyl group > C = 0 in the molecule or a nitrogen atom. In the cases of the acids and ketones the molecular complexes are possibly of the types

For monobasic acids a greater complexity has never been observed either in vapour-density determinations or in benzene

zene or phenol solution. In the case of the esters, which have the general formula

the alkyl group R' appears to hinder the association.

For the nitriles R · C≡N there is the possibility of the formation of an immense number of complexes.

Now, seeing that all the compounds which behave in the manner described possess a double or treble linkage, it is reasonable to suppose that the nitroparaffins also are of this type. The following formulæ, out of the number that have been proposed for these compounds, show an ethylene linkage:—

The latter two, however, are the more probable, for several reasons. The hydroxyls explain the strong association in the liquid state (1-82 Traube); the association of the vapour and the phenomenon of the boiling-points of the series is due to the double linking. This structure also furnishes an explanation of the acid nature of these compounds; (2) makes these compounds exactly similar to the fatty acids, except that the group = NOH replaces the group = O.

(b.) The Boiling-points of the Alcohols: This series behaves in quite a different manner. The necessary data are shown in Table XIII.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

The differences of the boiling-points reach a maximum early in the series, and then very slowly decrease. When the boiling-points are taken at reduced pressure the relative decrease is larger for the same alcohols. Now, at the lower temperature the liquid molecules are to a greater amount associated, and consequently this maximum is caused by the molecular complexity of the liquids. In all the cases mentioned above the results are different, but the explanation for those compounds is that the association of the vapour is the cause of the abnormal behaviour.

(3.) When the Compounds are in the Solid State.—(a.) Melting-points: Among the normal acids of the oxalic series the melting-points rise and fall, each term of the even series melting at a higher temperature than either of its two homologues of the odd series. If, however, the odd and even members are considered separately, a minimum melting-point is observed among the compounds containing an odd number of carbon atoms. This was pointed out by Massol,^* and is shown in the following table:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

From these data it seems probable that the numbers for the melting-points in the even series will also fall to a minimum in the neighbourhood of the C₁₄ acid.

The substituted malonic acids behave in a similar manner.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Here the minimum is reached when the substituent chain contains five carbon atoms; in the previous case the C₅ and in the fatty acids themselves the C₅ compound also shows the minimum melting-point.

In the case of the amides of the fatty acids the results are not so regular. Nevertheless, it is interesting to compare them.