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Originally appearing in Volume V06, Page 68 of the 1911 Encyclopedia Britannica.
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DENSATION OF GASES and MOLECULE) iS (p+a/v2) (v—b) =RT, in which a and b are quantities which depend on the composition of the gas, and vary from one gas to another. It may be surmised that the quantitative measures of most physical properties will be found to be connected with the chemical nature of substances. In the investigation of these relations the physicist and chemist meet on common ground; this union has been attended by fruitful and far-reaching results, and the correlation of physical properties and chemical composition is one of the most important ramifications of physical chemistry. This branch receives treatment below. Of considerable•intportance, also, are the properties of solids, liquids and gases in solution. This subject has occupied a dominant position in physico-chemical research since the investigations of van't Hoff and Arrhenius. This subject is treated in the article SOLUTION; for the properties of liquid mixtures reference should also be made to the article DISTILLATION. Another branch of physical chemistry has for its purpose the quantitative study of chemical action, a subject which has brought out in clear detail the analogies of chemical and physical equilibrium (see CHEMICAL ACTION). Another blanch, related to energetics (q.v.), is concerned with the transformation of chemical energy into other forms of energy—heat, light, electricity. Combustion is a familiar example of the transformation of chemical energy into heat and light; the quantitative measures of heat evolution or absorption (heat of combustion or combination), and the deductions therefrom, are treated in the article THERMOCHEMISTRY. Photography (q.v.) is based on chemical action induced by luminous rays; apart from this practical II 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 con- verse 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: (I) 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 (0 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: (I) 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 deter-mined 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.'—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) (v— b) 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=o, d2p/dv2--o at the critical point, that Vk=3b, Pk=a/27b2, Tk=8al27b. Eliminating a and b between these relations, we derive. PkVk/Tk= sR, 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 I R. but R; 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. ' For the connexion between valency and volume, see VALENCY.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 Vo/umeat molecules; this is obvious by considering the result of Vole / making T zero in the characteristic equation. Experi- poin and mentally (by extrapolation from the" law of the rectilinear at absolutet diameter ") the critical volume is four times the volume zero 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•CO2CHa 171 formate . . H•CO2CzH5 228 l 56.5 !Ethyl Methyl acetate . . CH3.CO2CHa 227.5 227.( Propyl formate . . H•CO2C3H7 284 55.8 Ethyl acetate . CH3•CO2C2H5 285 283.3 Methyl propionate . C2H5•CO2CH3 281 Propyl acetate . . CH3•CO2CaH7 343 57.4 Ethyl propionate . C2H5•CO2C2Hs 343 340.7 Methyl n-butyrate . CaH7•CO2CHa 339 Methyl isobutyrate. 337 Since the critical volume of normal pentane C5H12 is 307.2, we have H2=C5H,2—5CH2=307.2—5X56.6=24.2, and CCH2—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 Volume at under atmospheric pressure, brought to light a series of boi/in additive relations which, in the case of carbon compounds, g- render it possible to predict, in some measure, the corn- p°iat. . position 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. 0. H. Cl. Br. I. S. II 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 I2.2 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 dig. 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 differ- ences in structure. In this connexion we may notice W. Stadel's determinations: CH,CC13 Io8 CHCIl3r•CHa 96.5 CH2C1•CHC12 102.8 CH2Br•CH2CI . 88 These differences do not disappear at the critical point, and hence the critical volumes are not strictly additive. Theoretical considerations as to how far Kopp was justified in choosing the boiling-points under atmospheric pressure as being comparable states for different substances now claim our attention. Van der Waal's equation (p+alv2) (v - b) = RT contains two constants a and b determined by each particular substance. If we express the pressure, volume and temperature as fractions of the critical constants, then, calling these fractions the " reduced " pressure, volume and temperature, and denoting them by r, ¢ and 0 respectively, the characteristic equation becomes (sr +3/0) (3ct - 1) = 8B ; which has the same form for all substances. Obviously, therefore, liquids are comparable when the pressures, volumes and temperatures are equal fractions of the critical constants. In view of the extremely slight compressibility of liquids, atmospheric pressure may be regarded as a coincident condition; also C. M. Guldberg pointed out that .for the most diverse substances the absolute boiling-point is about two-thirds of the critical temperature. Hence within narrow limits Kopp's determinations were carried out under coincident conditions, and therefore any regularities presented by the critical volumes should be revealed in the specific volumes at the boiling-point. The connexion between the density and chemical composition of solids has not been investigated with the same completeness as in the case of gases and liquids. The relation between the atomic volumes and the atomic weights of the 'solid elements exhibits the periodicity which generally characterizes the elements. The molecular volume is additive in certain cases, in particular of analogous compounds of simple constitution. For instance, constant differences are found between the chlorides, bromides and iodides of sodium and potassium: I. Diff. II. Diff. Diff. I. & II. KC1= 37'4 6.9 NaCl = 27.1 6.7 10.3 • KBr=44.3 9.7 NaBr=33.8 9.7 10.5 KI =54.0 NaI =43.5 10.5 According to H. Schroeder the silver salts of the fatty acids exhibit additive relations; an increase in the molecule of CH2 causes an increase in the molecular volume of about 15.3. Thermal Relations. Specific Heat and Composition.-The nature and experimental determination of specific heats are discussed in the article CALORIMETRY; here will be discussed the relations existing between the heat capacities of elements and compounds. In the article THERMODYNAMICS it is shown that the amount of heat required to raise a given weight of a gas through a certain range of temperature is different according as the gas is maintained at constant pressure, the volume in-creasing, or at constant volume, the pressure increasing. A gas, therefore, has two specific heats, generally denoted by C, and C,, when the quantity of gas taken as a unit is one gramme molecular weight, the range of temperature being 1° C. It may be shown that CPC„=R, where R is the gas-constant, i.e. R in the equation PV = RT. From the ratio CS/C,, conclusions may be drawn as to the molecular condition of the gas. By considerations based on the kinetic theory of gases (see MOLECULE) it may be shown that when no energy is utilized in separating the atoms of a molecule, this ratio is 5/3=1'67. If, however, an amount of energy a is taken up in separating atoms, the ratio is expressible as C5/C„=(5--a)/(3+a), which is obviously smaller than 5/3, and decreases with increasing values of a. These relations may be readily tested, for the ratio CD/C„ is capable of easy experimental determination. It is found that mercury vapour, helium, argon and its associates (neon, krypton, &c.) have the value 1.67; hence we conclude that these gases exist as monatomic molecules. Oxygen, nitrogen, hydrogen and carbon monoxide have the value 1.4; these gases have diatomic molecules, a fact capable of demonstration by other means. Hence it may be inferred that this value is typical for diatomic molecules. Similarly, greater atomic complexity. is reflected in a further decrease in the ratio C5/C,,. The following table gives a comparative view of the specific heats and the ratio for molecules of variable atomic content. The abnormal specific heats of the halogen elements may be due to a loosening of the atoms, a preliminary to the dissociation into monatomic molecules which occurs at high temperatures. In the more complex gases the specific heat varies considerably with temperature; only in the case of monatomic gases does it remain Molecular Content. Examples. C5. C,. Cp/C,,. Monatomic . . Hg, Zn, Cd, He, Ar, &c.. 5 3 1.66 H2, 02, N2 (o°-zoo') . 683 483 1.41 Diatomic C12, Br2, I2 (0°-200°) . 8.6 6.6 1.30 HC1, HBr, HI, NO, CO 1.41 Triatomic . H2O, H2S, N20, CO2 . 9.2 7.2 1.28 Tetratomic AS4, P' . . . . 13.4 11'4 175 NH3, C21-12 . 11.6 9.6 1.21 Pentatomic . CHCI3 . . . 14 12 1.17 Hexatomic . C21-14' C2H2Br . . . 16.4 14.4 1.14 constant. Le Chatelier (Zeit. f. phys. Chem. i. 456) has given the formula C,=6.5+aT, where a is a constant depending on the complexity of the molecule. as an expression for the molecular heat at ccnstant pressure at any temperature T (reckoned on the absolute scale). For a further discussion of the ratio of the specific heats see MOLECULE. Specific Heats of Solids.-The development of the atomic theory and the subsequent determination of atomic weights in the opening decades of the loth century inspired A. T. Petit and P. L. Dulong to investigate relations (if any) existing between specific heats and the atomic weight. Their observations on the solid elements led to a remarkable generalization, now known as Dulong and Petit's law. This states that " the atomic heat (the product of the atomic weight and specific heat) of all elements is a constant quantity." The value of this constant when H= 1 is about 6.4; Dulong and Petit, using 0=1, gave the value •38, the specific heat of water being unity in both cases. This law-purely empirical in origin-was strengthened by Berzelius, who redetermined many specific heats, and applied the law to determine the true atomic weight from the equivalent weight. At the same time he perceived that specific heats varied with temperature and also with allotropes, e.g. graphite and diamond. The results of Berzelius were greatly extended by Hermann Kopp, who recognized that carbon, boron and silicon were exceptions to the law. He regarded these anomalies as solely due to the chemical nature of the elements, and ignored or regarded as insignificant such factors as the state of aggregation and change of specific heat with temperature. The specific heats of carbon, boron and silicon subsequently formed the subject of elaborate investigations by H. F. Weber, who showed that with rise of temperature the specific (and atomic) heat increases, finally attaining a fairly constant value; diamond, graphite and the various amorphous forms of carbon having the value about 5.6 at moo'', and silicon 5.68 at 232°; while he concluded that boron attained a constant value of 5.5. Nilson and Pettersson's observations on beryllium and germanium have shown that the atomic heats of these metals increase with rise of temperature, finally becoming constant with a value 5.6. W. A. Tilden (Phil. Trans., 1900, p. 233) investigated nickel and cobalt over a wide range of temperature (from -182.5° to toe); his results are: Cobalt. Nickel. f From -182.5° to -78.4° . . 4.1687 4.1874 - 78.4°to 15° • 5.4978 5'6784 15° to 100° . 6'0324 6'3143 It is evident that the atomic heats of these intimately associated elements approach nearer and nearer as we descend in temperature, approximating to the value 4. Other metals were tested in order to determine if their atomic heats approximated to this value at low temperatures, but with negative results. It is apparent that the law of Dulong and Petit is not rigorously true, and that deviations are observed which invalidate the law as originally framed. Since the atomic heat of the same element varies with its state of aggregation, it must be concluded that some factor taking this into account must be introduced; moreover, the variation of specific heat with temperature introduces another factor. We now proceed to discuss molecular heats of compounds, that is, the product of the molecular weight into the specific heat. The earliest generalization in this direction is associated with F. E. Neumann, who, in 1831, deduced from observations on many carbonates (calcium, magnesium, ferrous, zinc, barium and lead) that stoichiometric quantities (equimolecular weights) of compounds possess the same heat capacity. This is spoken of as " Neumann's law." Regnault confirmed Neumann's observations, and showed that the molecular heat depended on the number of atoms present, equiatomic compounds having the same molecular heat. Kopp systematized the earlier observations, Volume relations of solids. Specific heat of gases. [PHYSICAL Diff. 67° I0° 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 ifs 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 some-what 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 InCI, InC12 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 Pk Vk/Tk=3—1R or Tk/Pk=3.7Vx/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. C1. -0-. =0. N. N=. p Double Triple linkage. linkage. 1.35 0.57 2.66 0.87 1.27 1.6 1.86 3.01 o•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 he 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 C,H1802 Methyl octoate . . 192.9° Amyl butyrate . . 184.8° Ethyl heptoai'e . . 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 too °. 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 Consritu- of the molecule. As a general rule, compounds formed rive with a great evolution of heat have high boiling-points, influences. 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 ease of the chloracetic acids:
PETER DENS (1690-1775)
DENSITY (Lat. densus, thick)

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