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66
[PHYSICAL
CHEMISTRY

application there are many other cases in which actinic rays occasion chemical actions; these are treated in the article Photochemistry. Transformations of electrical into chemical energy are witnessed in the processes of electrolysis (q.v.; see also Electrochemistry and Electrometallurgy). The converse is presented in the common electric cell.

Physical Properties and Composition.

For the complete determination of the chemical structure of any compound, three sets of data are necessary: (1) the empirical chemical composition of the molecule; (2) the constitution, i.e. the manner in which the atoms are linked together; and (3) the configuration of the molecule, i.e. the arrangement of the atoms in space. Identity in composition, but difference in constitution, is generally known as “isomerism” (q.v.), and compounds satisfying this relation differ in many of their physical properties. If, however, two compounds only differ with regard to the spatial arrangement of the atoms, the physical properties may be (1) for the most part identical, differences, however, being apparent with regard to the action of the molecules on polarized light, as is the case when the configuration is due to the presence of an asymmetric atom (optical isomerism); or (2) both chemical and physical properties may be different when the configuration is determined by the disposition of the atoms or groups attached to a pair of doubly-linked atoms, or to two members of a ring system (geometrical isomerism or allo-isomerism). Three sets of physical properties may therefore be looked for: (1) depending on composition, (2) depending on constitution, and (3) depending on configuration. The first set provides evidence as to the molecular weight of a substance: these are termed “colligative properties.” The second and third sets elucidate the actual structure of the molecule: these are known as “constitutional properties.”

In any attempts to gain an insight into the relations between the physical properties and chemical composition of substances, the fact must never be ignored that a comparison can only be made when the particular property under consideration is determined under strictly comparable conditions, in other words, when the molecular states of the substances experimented upon are identical. This is readily illustrated by considering the properties of gases—the simplest state of aggregation. According to the law of Avogadro, equal volumes of different gases under the same conditions of temperature and pressure contain equal numbers of molecules; therefore, since the density depends upon the number of molecules present in unit volume, it follows that for a comparison of the densities of gases, the determinations must be made under coincident conditions, or the observations reduced or re-computed for coincident conditions. When this is done, such densities are measures of the molecular weights of the substances in question.

Volume Relations.[1]—When dealing with colligative properties of liquids it is equally necessary to ensure comparability of conditions. In the article Condensation of Gases (see also Molecule) it is shown that the characteristic equation of gases and liquids is conveniently expressed in the form (p + a/v²)(vb) = RT. This equation, which is mathematically deducible from the kinetic theory of gases, expresses the behaviour of gases, the phenomena of the critical state, and the behaviour of liquids; solids are not accounted for. If we denote the critical volume, pressure and temperature by Vk, Pk and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/dv = 0, d²p/dv² = 0 at the critical point, that Vk = 3b, Pk = a/27b², Tk = 8a/27b. Eliminating a and b between these relations, we derive PkVk/Tk = 3/8R, a relation which should hold between the critical constants of any substance. Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not 3/8R but 1/3.7R; this means that the critical density is, as a general rule, 3.7 times the theoretical density. Deviation from this rule indicates molecular dissociation or association. By actual observations it has been shown that ether, alcohol, many esters of the normal alcohols and fatty acids, benzene, and its halogen substitution products, have critical constants agreeing with this originally empirical law, due to Sydney Young and Thomas; acetic acid behaves abnormally, pointing to associated molecules at the critical point.

The critical volume provides data which may be tested for additive relations. Theoretically the critical volume is three times the volume at absolute zero, i.e. the actual volume of the Volume at critical point and at absolute zero. molecules; this is obvious by considering the result of making T zero in the characteristic equation. Experimentally (by extrapolation from the “law of the rectilinear diameter”) the critical volume is four times the volume at absolute zero (see Condensation of Gases). The most direct manner in which to test any property for additive relations is to determine the property for a number of elements, and then investigate whether these values hold for the elements in combination. Want of data for the elements, however, restricts this method to narrow limits, and hence an indirect method is necessary. It is found that isomers have nearly the same critical volume, and that equal differences in molecular content occasion equal differences in critical volume. For example, the difference due to an increment of CH2 is about 56.6, as is shown in the following table:—

 

Name. Formula. Crit. Vol. Vol. per CH2
Methyl formate H·CO2CH3  171    
Ethyl formate H·CO2C2H5  228 227.5 56.5
Methyl acetate CH3·CO2CH3  227  
Propyl formate H·CO2C3H7  284 283.3 55.8
Ethyl acetate CH3·CO2C2H5  285  
Methyl propionate C2H5·CO2CH3  28l  
Propyl acetate CH3·CO2C3H7  343 340.7 57.4
Ethyl propionate C2H5·CO2C2H5  343  
Methyl n-butyrate C3H7·CO2CH3  339  
Methyl isobutyrate  337  

Since the critical volume of normal pentane C5H12 is 307.2, we have H2 = C5H12 – 5CH2 = 307.2 − 5 × 56.6 = 24.2, and C = CH2 − H2 = 32.4. The critical volume of oxygen can be deduced from the data of the above table, and is found to be 29, whereas the experimental value is 25.

The researches of H. Kopp, begun in 1842, on the molecular volumes, i.e. the volume occupied by one gramme molecular weight of a substance, of liquids measured at their boiling-point under atmospheric pressure, brought to light a series of additive relations which,Volume at boiling-point. in the case of carbon compounds, render it possible to predict, in some measure, the composition of the substance. In practice it is generally more convenient to determine the density, the molecular volume being then obtained by dividing the molecular weight of the substance by the density. By the indirect method Kopp derived the following atomic volumes:

C. O. H. Cl. Br. I. S.
11 12.2 5.5 22.8 27.8 37.5 22.6.

These values hold fairly well when compared with the experimental values determined from other compounds, and also with the molecular volumes of the elements themselves. Thus the actually observed densities of liquid chlorine and bromine at the boiling-points are 1.56 and 2.96, leading to atomic volumes 22.7 and 26.9, which closely correspond to Kopp’s values deduced from organic compounds.

These values, however, require modification in certain cases, for discrepancies occur which can be reconciled in some cases by assuming that the atomic value of a polyvalent element varies according to the distribution of its valencies. Thus a double bond of oxygen, as in the carbonyl group CO, requires a larger volume than a single bond, as in the hydroxyl group –OH, being about 12.2 in the first case and 7.8 in the second. Similarly, an increase of volume is associated with doubly and trebly linked carbon atoms.

Recent researches have shown that the law originally proposed by Kopp—“That the specific volume of a liquid compound (molecular volume) at its boiling-point is equal to the sum of the specific volumes of its constituents (atomic volumes), and that every element has a definite atomic value in its compounds”—is by no means exact, for isomers have different specific volumes, and the volume for an increment of CH2 in different homologous series is by no means constant; for example, the difference among the esters of the fatty acids is about 57, whereas for the aliphatic aldehydes it is 49. We may therefore conclude that the molecular volume depends more upon the internal structure of the molecule than its empirical content. W. Ostwald (Lehr. der allg. Chem.), after an exhaustive review of the material at hand, concluded that simple additive relations did exist but with considerable deviations, which he ascribed to differences in structure. In this connexion we may notice W. Städel’s determinations:

CH3CCl3 . . 108   CHClBr·CH3 . . 96·5
CH2Cl·CHCl2 . . 102.8   CH2Br·CH2Cl . . 88
  1. For the connexion between valency and volume, see Valency.