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for the paraffin series from C2He to C14H30. The data for other series are as follows:
These data for these families and for a few other short series, derivable like the above from table xxv. of the "Laws of Molecular Force," can be represented according to the following scheme, wherein the meaning of the column headed MB will be explained in a little.
COO+2H+(n−1)CH, 4·0+·9(n−1)29 +17·5(n − 1)
CN+ H+nCH 3.5+9n 24 +17n
This scheme embodies the principle of the Dynic Equivalents, for an atom such as I is represented as producing the
same effect on the value of (M2) whatever may be the number of CH2 groups it is associated with. In the "Laws of Molecular Force" it was shown that there is a striking parallelism between the values of the dynic equivalents of the atoms and of their refraction equivalents. I had a strong impression that this must be due to the fact that both quantities were nearly proportional to the volumes of the atoms, but was not then able to test the idea through lack of values of the volumes of the atoms. But by means of the characteristic equation for liquids given in that paper, and an unpublished simplified form of it, I have been able to get approximate values of the limiting volumes of the members of a number of series of compounds. Let B be the limiting volume of a gramme of substance of molecular mass (weight) M; then the differences in Mẞ for a difference CH, in composition are as follows:paraffins 157, alkyl iodides 164, alkyl bromides 17, alkyl chlorides 16, alkyl oxides 17.3, alkyl amines 17-3, esters 17-5, and benzene series 16.8. The values of MB for the lowest available members of these series are CH, 25, CH2I 52, CH,Br 46, CH¿Cl 55·5, (C2H25)2O 83, NH, 20, СН¿О2 64, and CH 75.5; so that for MB we have the scheme given above with (M2)*.
The following are the few data on which the numbers in the scheme for the nitriles, sulphides, nitro-compounds, nitrates, and sulphocyanates are founded, on the assumption that in (M2) CH2 has a value 9 and in MS approximately 17.
In Table IV. there are no values given for the olefine series CnH2n; but the data for the olefines in table xxv. of the "Laws of Molecular Force" show that (M27) for C2Han is practically identical with that for CnH2n+2. On this account the dynic equivalent of the two terminal hydrogens of a paraffin CH2n+2 was, in the "Laws of Molecular Force," said to be negligible; but the better mode of expression in accordance with the usages of physical chemistry would be to say that the double-bonded union of two carbon atoms in an olefine changes the dynic equivalent of the two carbon atoms by an amount equal to that of the two terminal hydrogen atoms of the paraffin. The first point to be noticed about the expressions for (M) in Table IV. is that in the paraffins the
two terminal hydrogen atoms H+H are apparently represented by an initial term 2.2, which is more than twice as large as the value 9 for CH,; while in the MB expression for the paraffins the term 9 which represents the volume of H+H is only about half of the 15.7 for CH2. Associated with this peculiarity of the paraffins, there must be taken another, namely, that methane, CH4, while chemically the first of the paraffins, separates itself absolutely from the series as regards molecular force, but not as regards MB. In respect of molecular force it behaves as an element, as is shown in the "Laws of Molecular Force," and in the "Viscosity of Gases and Molecular Force" (Phil. Mag. Dec. 1893); and its value of (M2), namely 1-5, is only a half of the 3.1 which it would be if it came within the scheme for the paraffins in Table IV. Thus it appears to be necessary for at least two CH, groups to be associated before each takes its characteristic value in (M); and this must be connected with the series-building power of carbon. It should be noticed that the value of CH, in (M27) depends only slightly on the mode of association of the carbon and hydrogen atoms according to the usual structural formulas, because isomeric substances have almost always nearly equal values; thus, according to the equation M=1190 × 10-v1T, as v1 varies very slightly from one isomer to another, we see that amongst isomers (M2) varies nearly as the square root of the boiling-point. Take pentane, CH, as an instance: for normal pentane, CH3(CH2)3CH3, the boiling-point is 38° C., while for tetramethylmethane, C(CH3), it is 90.5 C.; so that (M2) for the latter is (282-5/311), or 953 times that for the former, which, according to the scheme, is 67; and, accordingly, there is only a difference of 3, corresponding to the great difference in structure attributed to these two pentanes. Thus it is not the position of the two terminal H atoms in the paraffins that determines their apparent large value of 2.2; and provisionally we have to recognize two values for H+H, one being 2.2, and the other a fraction of 9, and must leave the hydrogen atom to be returned to after we have considered some others.
In the alkyl haloid compounds we must regard the halogen atom as displacing one of these terminal H atoms, for the value of each CH, group in (M7) still remains the same. Hence if we assume that the one terminal H left has a value 1.1 in (M2/) and 4.5 in Mß, we can calculate at once from the schemes in Table IV. the values of the halogen atoms in
(M2), and also the limiting volumes of the atoms, and similarly with the other atoms and radicals involved in Table IV.: for instance, in that Table Cl+H has a value 3'3, whence that of Cl is 2-2; so in Mẞ the volume of Cl+H is 23.5, so that the volume of Cl is 19. In this way have been derived from Table IV. the values now given in Table VI. for the parts contributed to (M2) and MB by various atoms and radicals, which after this will sometimes be denoted by the symbols F and B: in the third row of numbers are given the values of the ratio B/F.
For the first ten atoms and radicals the approach in the ratio to constancy is close enough to show that F is nearly proportional to B, or that attracting-power in these atoms is nearly proportional to the volume of the atom; the mean value of the ratio for the first ten is 10, of which the value for CH2 is nearly double, and that for the terminal H of paraffins less than half; the value for NH, will be considered presently along with those of some other compounds of hydrogen. It would appear from the values for NO2, NO3, CN, and CNS, that the value for N of F is 17, and of B is about 15.
It will be useful at this stage to consider the values of (M2) and MB in those inorganic compounds for which they are obtainable from table xxv. of the "Laws of Molecular Force."
For the first six compounds the ratio is the same as the average in the last Table; but in H2S, H2O, and NH, it falls to a lower value, the reason for which appears to be the presence of the H atoms operating like the two terminal H atoms in the paraffins. To see whether this is the case, let us suppose S, O, and N carry the values already found for them into (M2) and MB, then we get for
In each case the ratio comes near to the value 4 found for the terminal H in the paraffins; though both in (M2) and MB, H3 in NH3 appears smaller than H2 in H2S, H2O, or the paraffins.
Returning to the values of the ratio in Table VII., the values for the compounds of P and As seem also to come near to the value 10; but this has no particular significance, as we shall see later on that a different principle is at work amongst some of these compounds; even at present we can see that (M2) for PCl, has a value 6.6, which is exactly three times the value adopted for Cl, leaving nothing for P; and when we turn to the value for CCl4, namely 6-8, which is a good deal less than that for 4C1, we must recognize clearly that we are getting into a type of compound in which the pure additive principle ruling in the carbon series no longer applies. Of course, in connexion with CCl, it may be said that it might be expected to be exceptional because CH is so; but then CH3Cl and CHI are not exceptional, a fact well worthy of attention in view of the exceptional nature of CH4. Indeed, if we take the series of ratios 9 for Cl, 12 for CHCl3, and 12 for CCI,, with 13 for SiCl4, and 13 for SnCl4, we see an increasing departure from proportionality between (M2) and volume MB, which will become comprehensible when we have dealt with inorganic compounds as a whole. An attempt to trace the intermediate cases, such as that of CHCl3, would lead us into too much detail, though promising light on the great old controversy in chemistry between the dualistic and unitary theorists and on the transition from electrolyte to non-electrolyte.
But without going into transition cases, there are a few more values which we ought to discuss before leaving the carbon serial compounds, as they bear upon the large value of F which belongs to the H atom when apart from the