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and, having made many others, he was able to show that the molecular heat was an additive property, i.e. each element retains the same heat capacity when in combination as in the free state. This has received confirmation by the researches of W. A. Tilden (Phil. Trans., 1904, 203 A, p.139) for those elements whose atomic heats vary considerably with temperature.

The specific heat of a compound may, in general, be calculated from the specific heats of its constituent elements. Conversely, if the specific heats of a compound and its constituent elements, except one, be known, then the unknown atomic heat is readily deducible. Similarly, by taking the difference of the molecular heats of compounds differing by one constituent, the molecular (or atomic) heat of this constituent is directly obtained. By this method it is shown that water, when present as “water of crystallization,” behaves as if it were ice.

Deductions from Dulong and Petit’s Law.—Denoting the atomic weight by W and the specific heat by s, Dulong and Petit’s law states that 6.4 = Ws. Thus if s be known, an approximate value of W is determinate. In the determination of the atomic weight of an element two factors must be considered: (1) its equivalent weight, i.e. the amount which is equivalent to one part of hydrogen; and (2) a factor which denotes the number of atoms of hydrogen which combines with or is equivalent to one atom of the particular element. This factor is termed the valency. The equivalent weight is capable of fairly ready determination, but the settlement of the second factor is somewhat more complex, and in this direction the law of atomic heats is of service. To take an example: 38 parts of indium combine with 35.4 parts of chlorine; hence, if the formula of the chloride be InCl, InCl2 or InCl3, indium has the atomic weights 38, 76 or 114. The specific heat of indium is 0.057; and the atomic heats corresponding to the atomic weights 38, 76 and 114 are 3.2, 4.3, 6.5. Dulong and Petit’s law thus points to the value 114, which is also supported by the position occupied by this element in the periodic classification. C. Winkler decided the atomic weight of germanium by similar reasoning.

Boiling-Point and Composition.—From the relation between the critical constants PkVk/Tk = 1/3.7R or Tk/Pk = 3.7Vk/R, and since Vk is proportional to the volume at absolute zero, the ratio Tk/Pk should exhibit additive relations. This ratio, termed by Guye the critical coefficient, has the following approximate values:—

C. H. Cl. –O–. =O. N. N=. P. Double
1.35 0.57 2.66 0.87 1.27 1.6 1.86 3.01 0.88 1.03

Since at the boiling-point under atmospheric pressure liquids are in corresponding states, the additive nature of the critical coefficient should also be presented by boiling-points. It may be shown theoretically that the absolute boiling-point is proportional to the molecular volume, and, since this property is additive, the boiling-point should also be additive.

These relations have been more thoroughly tested in the case of organic compounds, and the results obtained agree in some measure with the deductions from molecular volumes. In general, isomers boil at about the same temperature, as is shown by the isomeric esters C9H18O2:—

Methyl octoate 192.9°  Amyl butyrate 184.8°
Ethyl heptoate 187.1°  Heptyl acetate 191.3°
Propyl hexoate 185.5°  Octyl formate 198.1°
Butyl pentoate 185.8  

Equal increments in the molecule are associated with an equal rise in the boiling-point, but this increment varies in different homologous series. Thus in the normal fatty alcohols, acids, esters, nitriles and ketones, the increment per CH2 is 19°–21°; in the aldehydes it is 26°–27°. In the aromatic compounds there is no regularity between the increments due to the introduction of methyl groups into the benzene nucleus or side chains; the normal value of 20°–21° is exhibited, however, by pyridine and its derivatives. The substitution of a hydrogen atom by the hydroxyl group generally occasions a rise in boiling-point at about 100°. The same increase accompanies the introduction of the amino group into aromatic nuclei.

While certain additive relations hold between some homologous series, yet differences occur which must be referred to the constitution of the molecule. As a general rule, compounds formed Constitutive influences. with a great evolution of heat have high boiling-points, and vice versa. The introduction of negative groups into a molecule alters the boiling-point according to the number of negative groups already present. This is shown in the case of the chloracetic acids:

CH3CO2H = 118° Diff.
ClCH2·CO2H = 185° 67°
Cl2CH·CO2H = 195° 10°
Cl3C·CO2H = 195°–200°

According to van ’t Hoff the substitution of chlorine atoms into a methyl group occasions the following increments:—

Cl in CH3 66°
Cl in CH2Cl   39°
Cl in CHCl2 13°.

The introduction of chlorine, however, may involve a fall in the boiling-point, as is recorded by Henry in the case of the chlorinated acetonitriles:—

NC·CH3.   NC·CH2Cl.   NC·CHC12.   NC·CC13.
81°   123°   112°   83°
  42°   –11°   –29°  

The replacement of one negative group by another is accompanied by a change in the boiling-point, which is independent of the compound in which the substitution is effected, and solely conditioned by the nature of the replaced and replacing groups. Thus bromine and iodine replace chlorine with increments of about 22° and 50° respectively.

A factor of considerable importance in determining boiling-points of isomers is the symmetry of the molecule. Referring to the esters C9H18O2 previously mentioned, it is seen that the highest boiling-points belong to methyl octoate and octyl formate, the least symmetrical, while the minimum belongs to amyl butyrate, the most symmetrical. The isomeric pentanes also exhibit a similar relation CH3(CH2)4CH3 = 38°, (CH3)2CHC2H5 = 30°, (CH3)4C = 9.5°. For a similar reason secondary alcohols boil at a lower temperature than the corresponding primary, the difference being about 19°. A. E. Earp (Phil. Mag., 1893 [5], 35, p. 458) has shown that, while an increase in molecular weight is generally associated with a rise in the boiling-point, yet the symmetry of the resulting molecule may exert such a lowering effect that the final result is a diminution in the boiling-point. The series H2S = –61°, CH3SH = 21°, (CH3)2S = 41° is an example; in the first case, the molecular weight is increased and the symmetry diminished, the increase of boiling-point being 82°; in the second case the molecular weight is again increased but the molecule assumes a more symmetrical configuration, hence the comparatively slight increase of 20°. A similar depression is presented by methyl alcohol (67°) and methyl ether (–23°).

Among the aromatic di-substitution derivatives the ortho compounds have the highest boiling-point, and the meta boil at a higher, or about the same temperature as the para compounds. Of the tri-derivatives the symmetrical compounds boil at the lowest temperature, the asymmetric next, and the vicinal at the highest.

An ethylenic or double carbon union in the aliphatic hydrocarbons has, apparently, the same effect on the boiling-point as two hydrogen atoms, since the compounds CnH2n+2 and CnH2n boil at about the same temperature. An acetylenic or triple linkage is associated with a rise in the boiling-point; for example, propargyl compounds boil about 19.5° higher than the corresponding propyl compound.

Certain regularities attend the corresponding property of the melting-point. A rule applicable to organic compounds, due to Adolf v. Baeyer and supported by F. S. Kipping (Jour. Chem. Soc., 1893, 63, p.465) states, that the melting-point of any odd member of a homologous series is lower than the melting-point of the even member containing one carbon atom less. This is true of the fatty acid series, and the corresponding ketones and alcohols, and also of the succinic acid series. Other regularities exist, but generally with many exceptions. It is to be noted that although the correlation of melting-point with constitution has not been developed to such an extent as the chemical significance of other physical properties, the melting-point is the most valuable test of the purity of a substance, a circumstance due in considerable measure to the fact that impurities always tend to lower the melting-point.

Heat of Combustion and Constitution.—In the article Thermochemistry a general account of heats of formation of chemical compounds is given, and it is there shown that this constant measures the stability of the compound. In organic chemistry it is more customary to deal with the “heat of combustion,” i.e. the heat evolved when an organic compound is completely burned in oxygen; the heat of formation is deduced from the fact that it is equal to the heats of formation of the products of combustion less the observed heat of combustion. The researches of Julius Thomsen and others have shown that in many cases definite conclusions regarding constitution can be drawn from quantitative measurements of the heats of combustion; and in this article a summary of the chief results will be given.

The identity of the four valencies of the carbon atom follows from the fact that the heats of combustion of methane, ethane, propane, trimethyl methane, and tetramethyl methane, have a constant difference in the order given, viz. 158.6 calories; this means