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Volume 35, 1902
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Art. LVII.—The Exhibition of a Maximum or Minimum in the Properties of certain Series of Organic Compounds.

[Read before the Wellington Philosophical Society, 18th March, 1903.]

The aim of the following paper is to collect the various data in which a maximum or minimum is exhibited in an homologous series, and to show that in many cases the cause is due to the influence of molecular association. For the sake of convenience two main subdivisions are made: A. When the maximum or minimum is clearly seen. B. When it is hidden.

A. (1.) When the Compounds are in the Gaseous State.— The only example of this yet observed is described in the preceding paper. The molecular association of the fatty acids in phenol solution first increases as the series is ascended, and then, having reached a maximum, continues to decrease.

Assuming for the present that the molecular weight of acetic acid is normal when the freezing-point of its solution is depressed 1°, and that the molecular depression is inversely proportional to the amount of association, the following values are obtained for the association factors:—

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Table I.
Acid. No. of Carbon Atoms in Molecule. Association Factor.
Acetic 2 1·00
Propionic 3 1·01
Butyric 4 1·03
Valeric 5 1·05
Hexoic 6 1·06
Heptoic 7 1·07
Lauric 12 1·11
Stearic 18 1·01

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:—

Table II.
Ester. [a]. Association Factor (15°)
Amyl formate + 2·01 1·08
" acetate + 2·53 1·02
" propionate + 2·77 1·00
" butyrate + 2·69 0·94
" valerate + 2·52 0·92
" hexoate + 2·40 0·90

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

[Footnote] * Easterfield and Robertson, Trans. N.Z. Inst., 1901, 499.

[Footnote] † Trans. Chem. Soc., 1899, 347.

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

Table III.
Acid. Melting-point.
Benzoic 121°
Phenylacetic 77
Phenylpropionic 49
Phenylbutyric 47
Phenylvaleric 52

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°:—

Table IV.
Salt. Solubility (0°). Solubility (100°).
Calcium formate 16·15 (increase) 18·40
" acetate 37·40 (decrease) 29·65
" propionate 42·80 (increase) 48·44
" butyrate 20·31 (decrease) 15·85
" valerate 9·82 (decrease) 8·78
" hexoate 2·23 (increase) 2·57
" heptoate 0·95 (increase) 1·26
" octoate 0·33 (increase) 0·50
" nonoate 0·16 (increase) 0·26

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

[Footnote] * Lumsden, Journ. Chem. Soc, 1902, 350.

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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.

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Table V.
Acid. Boiling-point. Differences.
Acetic 118° 23
Propionic 141 22
Butyric 163 23
Valeric 186 19
Hexoic 205 19
Heptoic 224 12
Octoic 236 18
Nonoic 254 15
Capric 269

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.

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Table VI.
Acid. Boiling-point. Differences.
C9 185° 17
C10 202 11
C11 213 13
C12 226 10
C13 236 12
C14 248 9
C15 257 12
C16 269 8
C17 277* 10
C18 287 11
C19 298

This behaviour of the fatty acids is probably due to the

[Footnote] * This boiling-point is interpolated.

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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:—

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Table VII.
Met y Differences. Ethyl. Differences. Propyl. Differences.
Acetate 57·5° 22 77° 23 101° 21·5
Propionate 79·5 23 100 20 122·5 21·5
Butyrate 102·5 25 120 25 143 24·5
Valerate 127·5 22 145 22·5 167·5 18
Hexoate 149·5 23·5 167·5 20 185·5 21
Heptoate 173 20 187·5 20 206·5 18
Ochoate 193 20 207·5 20 224·5 18
Nonoate 213 227·5

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

[Footnote] * Rec. Trav. Chim., 1899, 18, 247.

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

Table VIII.
Boiling-point. Differences.
Acetyl chloride 51–52° 26·5
Propionyl " 78–80 21·5
Butyryl " 100–101 27
Valeryl " 127–128 18·5
Hexoyl " 145–14629
Heptoyl " 174–175 20
Octoyl " 194–195 26
Nonoyl " 220

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.

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Table IX.
Acid. Number of Carbon Atoms in Molecule. Boiling-point (10 mm.). Differences. Boiling-point (100 mm.). Differences.
Adipic 6 205·5° 6·5 265° 7
Pimelic 7 212 7·5 272 7
Suberic 8 219·5 6·0 279 7·5
Azelaic 9 225·5 6·5 286·5 8
Sebacic 10 232 294

[Footnote] *Ber., 22, 816.

[Footnote] † In phenol solution, although sebacic acid associates more rapidly than the corresponding fatty acid, the initial association of the latter is greater.

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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.

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Table X.
Number of Carbons in Radical R. Boiling-point of Aldehydes—R. CHO. Differences Boiling-point of Ketones—R. COCH3. Differences. Boiling-point of Ketones—R. COC2H5 Differences.
1 21° 28 56·5° 24 80·5° 22
2 49 25 80·5 21·5 102·5 21
3 74 29 102 25 123 23
4 103 25 127 24·5 146* 20
5 128 25 151·5 21·5 166 23
6 153 173 190
7 161

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:—

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Table XI.
Boiling-point. Differences.
Aceto nitrile 81·5° 15·5
Propiono " 97 21·5
Butyro " 118·5 22·5
Valero " 141 13·5
Hexöo " 154·5 22
Heptöo " 176 21
Octöo " 197 18
Nonoo " 215 18

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-,

[Footnote] * This boiling-point is interpolated.

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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.

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Table XII.
Boiling-point. Differences.
Nitromethane 101° 13·5
Nitroethane 114·5 16·5
Nitropropane 131 20·5
Nitrobutane 151·5 (8·5)
Nitropentane (150–160)? (16)
Nitrohexane 176 19
Nitroheptane 195

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

[Footnote] * A measure of the association at the boiling-point may be obtained from Teouton's law, MW/T = a constant, where W is the latent heat of vaporisation. For substances known to be normal in the liquid and gaseous states the value of the constant is in the neighbourhood of 21. For the esters and ketones a regular value of about 21 is obtained, but the acids and nitriles give exceedingly low values, indicating that the vapour at their boiling-points is strongly associated. The nitriles give fairly constant values, but still a little too low. Thus we find the order of complexity is nitroparaffin, fatty acid, nitrile, ketone, ester—the same order as indicated from the data for the boiling-points. The alcohols, on the other hand, give a high value, indicating association of the lighter molecules.

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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.

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Table XIII.
Boiling-point. Difference.
Methyl alcohol 66° 12
Ethyl " 78 19
Propyl " 97 20
Butyl " 117 20
Amyl " 137 20
Hexyl " 157 19
Heptyl " 176 19·5
Octyl " 195·5 18
Nonyl " 213·5 17·5
Decyl " 231
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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:—

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Table XIV.
C3 Oxalic acid 212°
C4 Succinic " 180
C6 Adipic " 148
C8 Suberic " 140
C10 Sebacic " 127
C3 Malonic acid 132°
C5 Glutaric " 97
C7 Pimelic " 103
C9 Azelaic " 117-5

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.

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Table XV.
C4 Methyl malonic acid 130°
C5 Ethyl " 111-5°
C6 Propyl " 93-5
C7 Butyl " 98-5
C8 Valeryl " 82
C10 Heptyl " 97

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.

[Footnote] * Bull. Soc. Chim., 1899, 578.

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Table XVI.
C2 Amide 82°
C4 " 115
C6 " 100
C8 " 110
C10 " 98
C12 " 112
C14 " 102
C16 " 101
C18 " 109
C20 " 99
C3 Amide 79°
C5 " 115
C7 " 95
C9 " 92
C11 " 81
C13 " 98
C15 " 108

The odd members behave regularly, showing a maximum at the C5 amide, and then the values fall to a minimum. This is the only example of two changes of this nature that I have been able to find. The melting-points of the amides with an even number of carbon atoms show a more or less irregular nature.

The anilides also show a somewhat similar behaviour, but in this case it is the minimum which is reached in the C5 compound.

(b.) Heats of Formation of the Oxalic Acids: The following data are due to Stohmann, Kleber, and Langbeim:—*

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Table XVII.
Acid. Heat of Formation. Differences.
Oxalic 196-8° 15-9
Malonic 212-7 13-5
Succinic 226-2 2-6
Glutaric 228-8 11-3
Adipic 240-1 2-3
Pimelic 242-4 7-0
Suberic 249-4 7-3
Azelaic 256-7 7-5
Sebacic 264-2

The values for the heat of formation increase with the molecular weight just as the boiling-points do. But on taking differences and separating the values thus obtained alternately into two sections we find that both series reach a minimum in the neighbourhood of pimelic acid. This is the only instance in which the two minima occur in neighbouring members; usually there is a wide difference.

General Conclusions.

As regards the position of the maximum or minimum in the series, we must first consider the results in division A. In only one case does the change occur well up the series;

[Footnote] * J. pr. Chem., 40, 202.

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this is for the fatty acids in phenol, the association of which compounds reaches a maximum at about the twelfth member.

When, as in B, the data are divided into two sets the point under consideration is reached early in the one series, and generally much later in the other. Almost always the position for the first of the changes occurs in the neighbourhood of the compound with a chain containing five carbon atoms. This is in accordance with the stereo-chemical conclusion that a chain of this length returns on itself.

In all the examples enumerated under B, except that of the differences of the boiling-points of the alcohols, the data for the series alternately increase and decrease as the molecular weight increases. Further, in two out of the four examples in A a probable connection is shown. From this we arrive at the general result.

In all cases where we find a maximum or minimum in the physical properties of a series, either by taking each member in turn or by taking alternate members, the data for that series, either for the same or a closely related property, is found to rise and fall alternately.”

Again, whenever the series dealt with referred to the liquid or gaseous state evidence of molecular association has been forthcoming. Consequently we obtain the second conclusion: “A maximum or minimum in a series is due to the molecular complexity of one or more members of that series.”