that the replacement of a hydrogen atom by a methyl group is attended by a constant increase in the heat of combustion. The same difference attends the introduction of the methyl group into many classes of compounds, for example, the paraffins, olefines, acetylenes, aromatic hydrocarbons, alcohols, aldehydes, ketones and esters, while a slightly lower value (157.1) is found in the case of the halogen compounds, nitriles, amines, acids, ethers, sulphides and nitro compounds. It therefore appears that the difference between the heats of combustion of two adjacent members of a series of homologous compounds is practically a constant, and that this constant has two average values, viz. 158.6 and 157.1.
An important connexion between heats of combustion and constitution is found in the investigation of the effect of single, double and triple carbon linkages on the thermochemical constants. If twelve grammes of amorphous carbon be burnt to carbon dioxide under constant volume, the heat evolved (96.96 cal.) does not measure the entire thermal effect, but the difference between this and the heat required to break down the carbon molecule into atoms. If the number of atoms in the carbon molecule be denoted by n, and the heat required to split off each atom from the molecule by d, then the total heat required to break down a carbon molecule completely into atoms is nd. It follows that the true heat of combustion of carbon, i.e. the heat of combustion of one gramme-atom, is 96.96+d. The value of d can be evaluated by considering the combustion of amorphous carbon to carbon monoxide and carbon dioxide. In the first case the thermal effect of 58.58 calories actually observed must be increased by 2d to allow for the heat absorbed in splitting off two gramme-atoms of carbon; in the second case the thermal effect of 96.96 must be increased by d as above. Now in both cases one gramme-molecule of oxygen is decomposed, and the two oxygen atoms thus formed are combined with two carbon valencies. It follows that the thermal effects stated above must be equal, i.e. 58.58 + 2d = 96.96 + d, and therefore d = 38.38. The absolute heat of combustion of a carbon atom is therefore 135.34 calories, and this is independent of the form of the carbon burned.
Consider now the combustion of a hydrocarbon of the general formula CnH2m. We assume that each carbon atom and each hydrogen atom contributes equally to the thermal effect. If α be the heat evolved by each carbon atom, and β that by each hydrogen atom, the thermal effect may be expressed as H = nα + 2mβ−A, where A is the heat required to break the molecule into its constituent atoms. If the hydrocarbon be saturated, i.e. only contain single carbon linkages, then the number of such linkages is 2n − m, and if the thermal effect of such a linkage be X, then the term A is obviously equal to (2n − m)X. The value of H then becomes H = nα + 2mβ − (2n−m)X or nξ + mη, where ξ and η are constants. Let double bonds be present, in number p, and let the energy due to such a bond be Y. Then the number of single bonds is 2n−m−2p, and the heat of combustion becomes H1 = nξ + mη + p(2X−Y). If triple bonds, q in number, occur also, and the energy of such a bond be Z, the equation for H becomes
H = nξ + mη + p(2X−Y) + q(3X−Z).
This is the general equation for calculating the heat of combustion of a hydrocarbon. It contains four independent constants; two of these may be calculated from the heats of combustion of saturated hydrocarbons, and the other two from the combustion of hydrocarbons containing double and triple linkages. By experiment it is found that the thermal effect of a double bond is much less than the effect of two single bonds, while a triple bond has a much smaller effect than three single bonds. J. Thomsen deduces the actual values of X, Y, Z to be 14.71, 13.27 and zero; the last value he considers to be in agreement with the labile equilibrium of acetylenic compounds. One of the most important applications of these values is found in the case of the constitution of benzene, where Thomsen decides in favour of the Claus formula, involving nine single carbon linkages, and rejects the Kekulé formula, which has three single and three double bonds (see section IV.).
The thermal effects of the common organic substituents have also been investigated. The thermal effect of the “alcohol” group C·OH may be determined by finding the heat of formation of the alcohol and subtracting the thermal effects of the remaining linkages in the molecule. The average value for primary alcohols is 44.67 cal., but many large differences from this value obtain in certain cases. The thermal effects increase as one passes from primary to tertiary alcohols, the values deduced from propyl and isopropyl alcohols and trimethyl carbinol being:—primary = 45.08, secondary = 50.39, tertiary = 60.98. The thermal effect of the aldehyde group has the average value 64.88 calories, i.e. considerably greater than the alcohol group. The ketone group corresponds to a thermal effect of 53.52 calories. It is remarkable that the difference in the heats of formation of ketones and the paraffin containing one carbon atom less is 67.94 calories, which is the heat of formation of carbon monoxide at constant volume. It follows therefore that two hydrocarbon radicals are bound to the carbon monoxide residue with the same strength as they combine to form a paraffin. The average value for the carboxyl group is 119.75 calories, i.e. it is equal to the sum of the thermal effects of the aldehyde and carbonyl groups
The thermal effects of the halogens are: chlorine = 15.13 calories, bromine = 7.68; iodine = −4.25 calories. It is remarkable that the position of the halogen in the molecule has no effect on the heat of formation; for example, chlorpropylene and allylchloride, and also ethylene dichloride and ethylidene dichloride, have equal heats of formation. The thermal effect of the ether group has an average value of 34.31 calories. This value does not hold in the case of methylene oxide if we assign to it the formula H2C·O·CH2, but if the formula H2C·O·CH2 (which assumes the presence of two free valencies) be accepted, the calculated and observed heats of formation are in agreement.
The combination of nitrogen with carbon may result in the formation of nitriles, cyanides, or primary, secondary or tertiary amines. Thomsen deduced that a single bond between a carbon and a nitrogen gramme-atom corresponds to a thermal effect of 2.77 calories, a double bond to 5.44, and a treble bond to 8.31. From this he infers that cyanogen is C:N·N:C and not N⫶C·C⫶N, that hydrocyanic acid is HC·N, and acetonitrile CH3·C⫶N. In the case of the amines he decides in favour of the formulae
| H2C:NH3 | H2C |  NH2 |
H2C | NH·CH3
|
| H3C | H3C | |||
| primary, | secondary, | tertiary. | ||
These involve pentavalent nitrogen. These formulae, however, only apply to aliphatic amines; the results obtained in the aromatic series are in accordance with the usual formulae.
Optical Relations.
Refraction and Composition.—Reference should be made to the article Refraction for the general discussion of the phenomenon known as the refraction of light. It is there shown that every substance, transparent to light, has a definite refractive index, which is the ratio of the velocity of light in vacuo to its velocity in the medium to which the refractive index refers. The refractive index of any substance varies with (1) the wave-length of the light; (2) with temperature; and (3) with the state of aggregation. The first cause of variation may be at present ignored; its significance will become apparent when we consider dispersion (vide infra).The second and third causes, however, are of greater importance, since they are associated with the molecular condition of the substance; hence, it is obvious that it is only from some function of the refractive index which is independent of temperature variations and changes of state (i.e. it must remain constant for the same substance at any temperature and in any form) that quantitative relations between refractivity and chemical composition can be derived.
The pioneer work in this field, now frequently denominated “spectro-chemistry,” was done by Sir Isaac Newton, who, from theoretical considerations based on his corpuscular theory of light, determined the function (n2–1), where n is the refractive index, to be the expression for the refractive power; dividing this expression by the density (d), he obtained (n2–1)/d, which he named the “absolute refractive power.” To P. S. Laplace is due the theoretical proof that this function is independent of temperature and pressure, and apparent experimental confirmation was provided by Biot and Arago’s, and by Dulong’s observations on gases and vapours. The theoretical basis upon which this formula was devised (the corpuscular theory) was shattered early in the 19th century, and in its place there arose the modern wave theory which theoretically invalidates Newton’s formula. The question of the dependence of refractive index on temperature was investigated in 1858 by J. H. Gladstone and the Rev. T. P. Dale; the more simple formula (n–1)/d, which remained constant for gases and vapours, but exhibited slight discrepancies when liquids were examined over a wide range of temperature, being adopted. The subject was next taken up by Hans Landolt, who, from an immense number of observations, supported in a general way the formula of Gladstone and Dale. He introduced the idea of comparing the refractivity of equimolecular quantities of different substances by multiplying the function (n–1)/d by the molecular weight (M) of the substance, and investigated the relations of chemical grouping to refractivity. Although establishing certain general relations between atomic and molecular refractions, the results were somewhat vitiated by the inadequacy of the empirical function which he employed, since it was by no means a constant which depended only on the actual composition of the substance and was independent of its physical condition. A more accurate expression (n2–1)/(n2+2)d was
