Having determined the bases, it remains to determine the acid radicals. There is no general procedure for these operations, and it is customary to test for the acids separately by special tests; these are given in the articles on the various acids. A knowledge of the solubility of salts considerably reduces the number of acids likely to be present, and affords evidence of great value to the analyst (see A.M. Comey, Dictionary of Chemical Solubilities.) In the above account we have indicated the procedure adopted in the analysis of a complex mixture of salts. It is unnecessary here to dwell on the precautions which can only be conveniently acquired by experience; a sound appreciation of analytical methods is only possible after the reactions and characters of individual substances have been studied, and we therefore refer the reader to the articles on the particular elements and compounds for more information on this subject.

Quantitative Inorganic Analysis.

Quantitative methods are divided into four groups, which we now pass on to consider in the following sequence: ([alpha]) gravimetric, ([beta]) volumetric, ([gamma]) electrolytic, ([delta]) colorimetric.

([alpha]) Gravimetric.—This method is made up of four operations: (1) a weighed quantity of the substance is dissolved in a suitable solvent; (2) a particular reagent is added which precipitates the substance it is desired to estimate; (3) the precipitate is filtered, washed and dried; (4) the filter paper containing the precipitate is weighed either as a tared filter, or incinerated and ignited either in air or in any other gas, and then weighed.

(1) Accurate weighing is all-important: for details of the various appliances and methods see WEIGHING MACHINES. (2) No general directions can be given as to the method of precipitation. Sometimes it is necessary to allow the solution to stand for a considerable time either in the warm or cold or in the light or dark; to work with cold solutions and then boil; or to use boiling solutions of both the substance and reagent. Details will be found in the articles on particular metals. (3) The operation of filtration and washing is very important. If the substance to be weighed changes in composition on strong heating, it is necessary to employ a tared filter, i.e. a filter paper which has been previously heated to the temperature at which the substance is to be dried until its weight is constant. If the precipitate settles readily, the supernatant liquor may be decanted through the filter paper, more water added to the precipitate and again decanted. By this means most of the washing, i.e.freeing from the other substances in the solution, can be accomplished in the precipitating vessel. If, however, the precipitate refuses to settle, it is directly transferred to the filter paper, the last traces being removed by washing and rubbing the sides of the vessel with a piece of rubber, and the liquid is allowed to drain through. It is washed by ejecting a jet of water, ammonia or other prescribed liquid on to the side of the filter paper until the paper is nearly full. It can be shown that a more efficient washing results from alternately filling and emptying the funnel than by endeavouring to keep the funnel full. The washing is continued until the filtrate is free from salts or acids. (4) After washing, the funnel containing the filter paper is transferred to a drying oven. In the case of a tared filter it is weighed repeatedly until the weight suffers no change; then knowing the weight of the filter paper, the weight of the precipitate is obtained by subtraction. If the precipitate may be ignited, it is transferred to a clean, weighed and recently ignited crucible, and the filter paper is burned separately on the lid, the ash transferred to the crucible, and the whole ignited. After ignition, it is allowed to cool in a desiccator and then weighed. Knowing the weight of the crucible and of the ash of the filter paper, the weight of the precipitate is determined. The calculation of the percentage of the particular constituent is simple. We know the amount present in the precipitate, and since the same amount is present in the quantity of substance experimented with, we have only to work out a sum in proportion.

([beta]) Volumetric.—This method is made up of three operations:—(1) preparation of a standard solution; (2) preparation of a solution of the substance; (3) titration, or the determination of what volume of the standard solution will occasion a known and definite reaction with a known volume of the test solution.

(1) In general analytical work the standard solution contains the equivalent weight of the substance in grammes dissolved in a litre of water. Such a solution is known as normal. Thus a normal solution of sodium carbonate contains 53 grammes per litre, of sodium hydrate 40 grammes, of hydrochloric acid 36.5 grammes, and so on. By taking 1/10th or 1/100th of these quantities, decinormal or centinormal solutions are obtained. We see therefore that 1 cubic centimetre of a normal sodium carbonate solution will exactly neutralize 0.049 gramme of sulphuric acid, 0.0365 gramme of hydrochloric acid (i.e. the equivalent quantities), and similarly for decinormal and centinormal solutions. Unfortunately, the term normal is sometimes given to solutions which are strictly decinormal; for example, iodine, sodium thiosulphate, &c. In technical analysis, where a solution is used for one process only, it may be prepared so that 1 cc. is equal to .01 gramme of the substance to be estimated. This saves a certain amount of arithmetic, but when the solution is applied in another determination additional calculations are necessary. Standard solutions are prepared by weighing out the exact amount of the pure substance and dissolving it in water, or by forming a solution of approximate normality, determining its exact strength by gravimetric or other means, and then correcting it for any divergence. This may be exemplified in the case of alkalimetry. Pure sodium carbonate is prepared by igniting the bicarbonate, and exactly 53 grammes are dissolved in water, forming a strictly normal solution. An approximate normal sulphuric acid is prepared from 30 ccs. of the pure acid (1.84 specific gravity) diluted to 1 litre. The solutions are titrated (see below) and the acid solution diluted until equal volumes are exactly equivalent. A standard sodium hydrate solution can be prepared by dissolving 42 grammes of sodium hydrate, making up to a litre, and diluting until one cubic centimetre is exactly equivalent to one cubic centimetre of the sulphuric acid. Similarly, normal solutions of hydrochloric and nitric acids can be prepared. Where a solution is likely to change in composition on keeping, such as potassium permanganate, iodine, sodium hydrate, &c., it is necessary to check or re-standardize it periodically.

(2) The preparation of the solution of the substance consists in dissolving an accurately determined weight, and making up the volume in a graduated cylinder or flask to a known volume.

(3) The titration is conducted by running the standard solution from a burette into a known volume of the test solution, which is usually transferred from the stock-bottle to a beaker or basin by means of a pipette. Various artifices are employed to denote the end of the reaction. These may be divided into two groups: (1) those in which a change in appearance of the reacting mixture occurs; (2) those in which it is necessary to use an indicator which, by its change in appearance, shows that an excess of one reagent is present. In the first group, we have to notice the titration of a cyanide with silver nitrate, when a milkiness shows how far the reaction has gone; the titration of iron with permanganate, when the faint pink colour shows that all the iron is oxidized. In the second group, we may notice the application of litmus, methyl orange or phenolphthalein in alkalimetry, when the acid or alkaline character of the solution commands the colour which it exhibits; starch paste, which forms a blue compound with free iodine in iodometry; potassium chromate, which forms red silver chromate after all the hydrochloric acid is precipitated in solutions of chlorides; and in the estimation of ferric compounds by potassium bichromate, the indicator, potassium ferricyanide, is placed in drops on a porcelain plate, and the end of the reaction is shown by the absence of a blue coloration when a drop of the test solution is brought into contact with it.

([gamma]) Electrolytic.—This method consists in decomposing a solution of a salt of the metal by the electric current and weighing the metal deposited at the cathode.

It is only by paying great attention to the current density that good results are obtained, since metals other than that sought for may be deposited. In acid copper solutions, mercury is deposited before the copper with which it subsequently amalgamates; silver is thrown down simultaneously; bismuth appears towards the end; and after all the copper has been precipitated, arsenic and antimony may be deposited. Lead and manganese are partially separated as peroxides, but the remaining metals are not deposited from acid solutions. It is therefore necessary that the solution should be free from metals which may vitiate the results, or special precautions taken by which the impurities are rendered harmless. In such cases the simplicity of manipulation and the high degree of accuracy of the method have made it especially valuable. The electrolysis is generally conducted with platinum electrodes, of which the cathode takes the form of a piece of foil bent into a cylindrical form, the necessary current being generated by one or more Daniell cells.

([delta]) Colorimetric.—This method is adopted when it is necessary to determine minute traces (as in the liquid obtained in the electrolytic separation of copper) of substances which afford well-defined colour reactions.

The general procedure is to make a series of standard solutions containing definite quantities of the substance which it is desired to estimate; such a series will exhibit tints which deepen as the quantity of the substance is increased. A known weight of the test substance is dissolved and a portion of the solution is placed in a tube similar to those containing the standard solutions. The colour-producing reagent is added and the tints compared. In the case of copper, the colour reactions with potassium ferrocyanide or ammonia are usually employed; traces of ammonia are estimated with Nessler's reagent; sulphur in iron and steel is determined by the tint assumed by a silver-copper plate suspended in the gases liberated when the metal is dissolved in sulphuric acid (Eggertz's test) (see W. Crookes, Select Methods in Analytical Chemistry).

Organic Analysis.

The elements which play important parts in organic compounds are carbon, hydrogen, nitrogen, chlorine, bromine, iodine, sulphur, phosphorus and oxygen. We shall here consider the qualitative and quantitative determination of these elements.

Qualitative.—Carbon is detected by the formation of carbon dioxide, which turns lime-water milky, and hydrogen by the formation of water, which condenses on the tube, when the substance is heated with copper oxide. Nitrogen may be detected by the evolution of ammonia when the substance is heated with soda-lime. A more delicate method is that due to J. L. Lassaigne and improved by O. Jacobsen and C. Graebe. The substance is heated with metallic sodium or potassium (in excess if sulphur be present) to redness, the residue treated with water, filtered, and ferrous sulphate, ferric chloride and hydrochloric acid added. A blue coloration indicates nitrogen, and is due to the formation of potassium (or sodium) cyanide during the fusion, and subsequent interaction with the iron salts. The halogens may be sometimes detected by fusing with lime, and testing the solution for a bromide, chloride and iodide in the usual way. F. Beilstein determines their presence by heating the substance with pure copper oxide on a platinum wire in the Bunsen flame; a green coloration is observed if halogens be present. Sulphur is detected by heating the substance with sodium, dissolving the product in water, and adding sodium nitroprusside; a bluish-violet coloration indicates sulphur (H. Vohl). Or we may use J. Horbaczewski's method, which consists in boiling the substance with strong potash, saturating the cold solution with chlorine, adding hydrochloric acid, and boiling till no more chlorine is liberated, and then testing for sulphuric acid with barium chloride. Phosphorus is obtained as a soluble phosphate (which can be examined in the usual way) by lixiviating the product obtained when the substance is ignited with potassium nitrate and carbonate.

Carbon and hydrogen.

Quantitative.—Carbon and hydrogen are generally estimated by the combustion process, which consists in oxidizing the substance and absorbing the products of combustion in suitable apparatus. The oxidizing agent in commonest use is copper oxide, which must be freshly ignited before use on account of its hygroscopic nature. Lead chromate is sometimes used, and many other substances, such as platinum, manganese dioxide, &c., have been suggested. The procedure for a combustion is as follows:—









A hard glass tube slightly longer than the furnace and 12 to 15 mm. in diameter is thoroughly cleansed and packed as shown in fig. 1. The space a must allow for the inclusion of a copper spiral if the substance contains nitrogen, and a silver spiral if halogens be present, for otherwise nitrogen oxides and the halogens may be condensed in the absorption apparatus; b contains copper oxide; c is a space for the insertion of a porcelain or platinum boat containing a weighed quantity of the substance; d is a copper spiral. The end d is connected to an air or oxygen supply with an intermediate drying apparatus. The other end is connected with the absorption vessels, which consist of a tube (e) containing calcium chloride, and a set of bulbs (f) containing potash solution. Various forms of potash bulbs are employed; fig. 2 is Liebig's, fig. 3 Mohr's or Geissler's, fig. 4 is a more recent form, of which special variations have been made by Anderson, Gomberg, Delisle and others. After having previously roasted the tube and copper oxide, and reduced the copper spiral a, the weighed calcium chloride tube and potash bulbs are put in position, the boat containing the substance is inserted (in the case of a difficultly combustible substance it is desirable to mix it with cupric oxide or lead chromate), the copper spiral (d) replaced, and the air and oxygen supply connected up. The apparatus is then tested for leaks. If all the connexions are sound, the copper oxide is gradually heated from the end a, the gas-jets under the spiral d are lighted, and a slow current of oxygen is passed through the tube. The success of the operation depends upon the slow burning of the substance. Towards the end the heat and the oxygen supply are increased. When there is no more absorption in the potash bulbs, the oxygen supply is cut off and air passed through. Having replaced the oxygen in the absorption vessels by air, they are disconnected and weighed, after having cooled down to the temperature of the room. The increase in weight of the calcium chloride tube gives the weight of water formed, and of the potash bulbs the carbon dioxide.

Liquids are amenable to the same treatment, but especial care must be taken so that they volatilize slowly. Difficultly volatile liquids may be weighed directly into the boat; volatile liquids are weighed in thin hermetically sealed bulbs, the necks of which are broken just before they are placed in the combustion tube.

The length of time and other disadvantages attending the combustion method have caused investigators to devise other processes. In 1855 C. Brunner described a method for oxidizing the carbon to carbon dioxide, which could be estimated by the usual methods, by heating the substance with potassium bichromate and sulphuric acid. This process has been considerably developed by J. Messinger, and we may hope that with subsequent improvements it may be adapted to all classes of organic compounds. The oxidation, which is effected by chromic acid and sulphuric acid, is conducted in a flask provided with a funnel and escape tube, and the carbon dioxide formed is swept by a current of dry air, previously freed from carbon dioxide, through a drying tube to a set of potash bulbs and a tube containing soda-lime; if halogens are present, a small wash bottle containing potassium iodide, and a U tube containing glass wool moistened with silver nitrate on one side and strong sulphuric acid on the other, must be inserted between the flask and the drying tube. The increase in weight of the potash bulbs and soda-lime tube gives the weight of carbon dioxide evolved. C.F. Cross and E.J. Bevan collected the carbon dioxide obtained in this way over mercury. They also showed that carbon monoxide was given off towards the end of the reaction, and oxygen was not evolved unless the temperature exceeded 100 deg.

Methods depending upon oxidation in the presence of a contact substance have come into favour during recent years. In that of M. Dennstedt, which was first proposed in 1902, the substance is vaporized in a tube containing at one end platinum foil, platinized quartz, or platinized asbestos. The platinum is maintained at a bright red heat, either by a gas flame or by an electric furnace, and the vapour is passed over it by leading in a current of oxygen. If nitrogen be present, a boat containing dry lead peroxide and heated to 320 deg. is inserted, the oxide decomposing any nitrogen peroxide which may be formed. The same absorbent quantitatively takes up any halogen and sulphur which may be present. The process is therefore adapted to the simultaneous estimation of carbon, hydrogen, the halogens and sulphur.

Nitrogen.

Nitrogen is estimated by (1) Dumas' method, which consists in heating the substance with copper oxide and measuring the volume of nitrogen liberated; (2) by Will and Varrentrapp's method, in which the substance is heated with soda-lime, and the ammonia evolved is absorbed in hydrochloric acid, and thence precipitated as ammonium chlorplatinate or estimated volumetrically; or (3) by Kjeldahl's method, in which the substance is dissolved in concentrated sulphuric acid, potassium permanganate added, the liquid diluted and boiled with caustic soda, and the evolved ammonia absorbed in hydrochloric acid and estimated as in Will and Varrentrapp's method.



Dumas' Method.—In this method the operation is carried out in a hard glass tube sealed at one end and packed as shown in fig. 5. The magnesite (a) serves for the generation of carbon dioxide which clears the tube of air before the compound (mixed with fine copper oxide (b)) is burned, and afterwards sweeps the liberated nitrogen into the receiving vessel (e), which contains a strong potash solution; c is coarse copper oxide; and d a reduced copper gauze spiral, heated in order to decompose any nitrogen oxides. Ulrich Kreusler generates the carbon dioxide in a separate apparatus, and in this case the tube is drawn out to a capillary at the end (a). This artifice is specially valuable when the substance decomposes or volatilizes in a warm current of carbon dioxide. Various forms of the absorbing apparatus (e) have been discussed by M. Ilinski (Ber. 17, p. 1347), who has also suggested the use of manganese carbonate instead of magnesite, since the change of colour enables one to follow the decomposition. Substances which burn with difficulty may be mixed with mercuric oxide in addition to copper oxide.

Will and Varrentrapp's Method.—This method, as originally proposed, is not in common use, but has been superseded by Kjeldahl's method, since the nitrogen generally comes out too low. It is susceptible of wider application by mixing reducing agents with the soda-lime: thus Goldberg (Ber. 16, p. 2546) uses a mixture of soda-lime, stannous chloride and sulphur for nitro- and azo-compounds, and C. Arnold (Ber. 18, p. 806) a mixture containing sodium hyposulphite and sodium formate for nitrates.

Kjeldahl's Method.—This method rapidly came into favour on account of its simplicity, both of operation and apparatus. Various substances other than potassium permanganate have been suggested for facilitating the operation; J.W. Gunning (Z. anal. Chem., 1889, p. 189) uses potassium sulphate; Lassar-Cohn uses mercuric oxide. The applicability of the process has been examined by F.W. Dafert (Z. anal. Chem., 1888, p. 224), who has divided nitrogenous bodies into two classes with respect to it. The first class includes those substances which require no preliminary treatment, and comprises the amides and ammonium compounds, pyridines, quinolines, alkaloids, albumens and related bodies; the second class requires preliminary treatment and comprises, with few exceptions, the nitro-, nitroso-, azo-, diazo- and amidoazo-compounds, hydrazines, derivatives of nitric and nitrous acids, and probably cyanogen compounds. Other improvements have been suggested by Dyer (J.C.S. Trans. 67, p. 811). For an experimental comparison of the accuracy of the Dumas, Will-Varrentrapp and Kjeldahl processes see L. L'Hote, C.R. 1889, p. 817. Debordeaux (C.R. 1904, p. 905) has obtained good results by distilling the substance with a mixture of potassium thiosulphate and sulphide.

Halogens, sulphur, phosphorus.

The halogens may be estimated by ignition with quicklime, or by heating with nitric acid and silver nitrate in a sealed tube. In the first method the substance, mixed with quicklime free from chlorine, is heated in a tube closed at one end in a combustion furnace. The product is dissolved in water, and the calcium haloid estimated in the usual way. The same decomposition may be effected by igniting with iron, ferric oxide and sodium carbonate (E. Kopp, Ber. 10, p. 290); the operation is easier if the lime be mixed with sodium carbonate, or a mixture of sodium carbonate and potassium nitrate be used. With iodine compounds, iodic acid is likely to be formed, and hence the solution must be reduced with sulphurous acid before precipitation with silver nitrate. C. Zulkowsky (Ber. 18, R. 648) burns the substance in oxygen, conducts the gases over platinized sand, and collects the products in suitable receivers. The oxidation with nitric acid in sealed tubes at a temperature of 150 deg. to 200 deg. for aliphatic compounds, and 250 deg. to 260 deg. for aromatic compounds, is in common use, for both the sulphur and phosphorus can be estimated, the former being oxidized to sulphuric acid and the latter to phosphoric acid. This method was due to L. Carius (Ann. 136, p. 129). R. Klason (Ber. 19, p. 1910) determines sulphur and the halogens by oxidizing the substance in a current of oxygen and nitrous fumes, conducting the vapours over platinum foil, and absorbing the vapours in suitable receivers. Sulphur and phosphorus can sometimes be estimated by Messinger's method, in which the oxidation is effected by potassium permanganate and caustic alkali, or by potassium bichromate and hydrochloric acid. A comparison of the various methods for estimating sulphur has been given by O. Hammarsten (Zeit. physiolog. Chem. 9, p. 273), and by Holand (Chemiker Zeitung, 1893, p. 991). H.H. Pringsheim (Ber. 38, p. 1434) has devised a method in which the oxidation is effected by sodium peroxide; the halogens, phosphorus and sulphur can be determined by one operation.

VI. PHYSICAL CHEMISTRY

We have seen how chemistry may be regarded as having for its province the investigation of the composition of matter, and the changes in composition which matter or energy may effect on matter, while physics is concerned with the general properties of matter. A physicist, however, does more than merely quantitatively determine specific properties of matter; he endeavours to establish mathematical laws which co-ordinate his observations, and in many cases the equations expressing such laws contain functions or terms which pertain solely to the chemical composition of matter. One example will suffice here. The limiting law expressing the behaviour of gases under varying temperature and pressure assumes the form pv = RT; so stated, this law is independent of chemical composition and may be regarded as a true physical law, just as much as the law of universal gravitation is a true law of physics. But this relation is not rigorously true; in fact, it does not accurately express the behaviour of any gas. A more accurate expression (see CONDENSATION OF GASES and MOLECULE) is (p + a/v^2)(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 importance, 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 branch, 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 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.[17]—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/v^2)(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 = 0, d^2p/dv^2 = 0 at the critical point, that Vk = 3b, Pk = a/27b^2, T^k = 8a/27b. Eliminating a and b between these relations, we derive PkVk/Tk = (3/8)R, 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 (3/8)R but (1/3.7)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. 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.

Volume at critical point and at absolute zero.

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 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 or 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.C02C2H5 228 56.5 Methyl acetate CH3.CO2CH3 227 / 227.5 Propyl formate H.CO2C3H7 284 55.8 Ethyl acetate CH3.C02C2H5 285 } 283.3 Methyl propionate C2H5.CO2CH3 28l / Propyl acetate CH3.CO2C3H7 343 57.4 Ethyl propionate C2H5.CO2C2H5 343 } 340.7 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 X 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.

Volume at boiling-point.

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, 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. Stadel's determinations:

CH3CCl3 108 CHClBr.CH3 96.5 CH2Cl.CHCl2 102.8 CH2Br.CH2Cl 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+a/v^2)(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 [pi], [phi] and [theta] respectively, the characteristic equation becomes ([pi]+3/[phi]^2)(3[phi]-1) = 8[theta]; 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.

Volume relations of solids.

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. - KCl = 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.

Specific heat of gases.

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 increasing, or at constant volume, the pressure increasing. A gas, therefore, has two specific heats, generally denoted by Cp and Cv, when the quantity of gas taken as a unit is one gramme molecular weight, the range of temperature being 1 deg. C. It may be shown that Cp - Cv = R, where R is the gas-constant, i.e. R in the equation PV = RT. From the ratio Cp/Cv 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 Cp/Cv = (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 Cp/Cv 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 Cp/Cv. 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 constant. Le Chatelier (_Zeit. f. phys. Chem._ i. 456) has given the formula C_p = 6.5 + aT, where a is a constant depending on the complexity of the molecule, as an expression for the molecular heat at constant pressure at any temperature T (reckoned on the absolute scale). For a further discussion of the ratio of the specific heats see MOLECULE.

- - - - - Molecular Examples. Cp Cv Cp/Cv Content. - - - - - Monatomic Hg, Zn, Cd, He, Ar, &c. 5 3 1.66 - - - - - H2, 02, N2 (0 deg.-200 deg.) 6.83 4.83 1.41 Diatomic Br2, I2 (0 deg.-200 deg.) 8.6 6.6 1.30 Cl2,HCl, HBr, HI, NO, CO 1.41 - - - - - Triatomic H2O, H2S, N2O, CO2 9.2 7.2 1.28 - - - - - Tetratomic As4, P4 13.4 11.4 1.175 NH3, C2H2 11.6 9.6 1.21 - - - - - Pentatomic CHCl3 14 12 1.17 - - - - - Hexatomic C2H4, C2H3Br 16.4 14.4 1.14 - - - - -

Specific Heats of Solids.—The development of the atomic theory and the subsequent determination of atomic weights in the opening decades of the 19th 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 O = 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 1000 deg., and silicon 5.68 at 232 deg.; while he concluded that boron attained a constant value of 5.5. Niison 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 deg. to 100 deg.); his results are:—

- - Cobalt. Nickel. - - From -182.5 deg. to -78.4 deg. 4.1687 4.1874 -78.4 deg. to 15 deg. 5.4978 5.6784 15 deg. to 100 deg. 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, 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 P_kV_k/T_k = (1/3.7)R or T_k/P_k = 3.7V_k/R, and since V_k is proportional to the volume at absolute zero, the ratio T_k/P_k should exhibit additive relations. This ratio, termed by Guye the critical coefficient, has the following approximate values:—

Double Triple C. H. Cl. -O-. O. N. N. P. linkage. linkage. 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 deg. Amyl butyrate 184.8 deg. Ethyl heptoate 187.1 deg. Heptyl acetate 191.3 deg. Propyl hexoate 185.5 deg. Octyl formate 198.1 deg. 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 deg.-21 deg.; in the aldehydes it is 26 deg.-27 deg.. 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 deg.-21 deg. 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 deg.. The same increase accompanies the introduction of the amino group into aromatic nuclei.

Constitutive influences.

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 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:

Diff. CH3CO2H = 118 deg. 67 deg. ClCH2.CO2H = 185 deg. 10 deg. Cl2CH.CO2H = 195 deg. 3 deg. Cl3C.CO2H = 195 deg.-200 deg.

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

Cl in CH3 66 deg. Cl " CH2Cl 39 deg. Cl " CHCl2 13 deg.

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 deg. 123 deg. 112 deg. 83 deg. 42 deg. -11 deg. -29 deg.

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 deg. and 50 deg. 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 deg., (CH3)2CHC2H5 = 30 deg., (CH3)4C = 9.5 deg.. For a similar reason secondary alcohols boil at a lower temperature than the corresponding primary, the difference being about 19 deg.. 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 deg., CH3SH = 21 deg., (CH3)2S = 41 deg. is an example; in the first case, the molecular weight is increased and the symmetry diminished, the increase of boiling-point being 82 deg.; 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 deg.. A similar depression is presented by methyl alcohol (67 deg.) and methyl ether (-23 deg.).

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 C{n}H{2n+2} and C{n}H{2n} 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 deg. 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 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 C{n}H{2m}. We assume that each carbon atom and each hydrogen atom contributes equally to the thermal effect. If [alpha] be the heat evolved by each carbon atom, and [beta] that by each hydrogen atom, the thermal effect may be expressed as H = n[alpha] + 2m[beta] - 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 = n[alpha] + 2m[beta] - (2n - m)X or n[xi] + m[nu], where [xi] and [nu] 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 = n[xi] + m[nu] + 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 = n[xi] + m[nu] + 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 Kekule 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 = l5.13 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 H2C NH2 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 (n^2-1), where n is the refractive index, to be the expression for the refractive power; dividing this expression by the density (d), he obtained (n^2-1)/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 (n^2-1)/(n^2+2)d was suggested in 1880 independently and almost simultaneously by L.V. Lorenz of Copenhagen and H.A. Lorentz of Leiden, from considerations based on the Clausius-Mossotti theory of dielectrics.

Assuming that the molecules are spherical, R.J.E. Clausius and O.F. Mossotti found a relation between the dielectric constant and the space actually occupied by the molecules, viz. K = (1 + 2a)/(1 - a), or a = (K - 1)/(K + 2), where K is the dielectric constant and a the fraction of the total volume actually occupied by matter. According to the electromagnetic theory of light K = N^2, where N is the refractive index for rays of infinite wave-length. Making this substitution, and dividing by d, the density of the substance, we obtain a/d = (N^2 - 1)/(N^2 + 2 )d. Since a/d is the real specific volume of the molecule, it is therefore a constant; hence (N^2 - 1)/(N^2 + 2)d is also a constant and is independent of all changes of temperature, pressure, and of the state of aggregation. To determine N recourse must be made to Cauchy's formula of dispersion (q.v.), n = A + B/[lambda]^2 + C/[lambda]^4 + ... from which, by extrapolation, [lambda] becoming infinite, we obtain N = A. In the case of substances possessing anomalous dispersion, the direct measurement of the refractive index for Hertzian waves of very long wave-length may be employed.

It is found experimentally that the Lorenz and Lorentz function holds fairly well, and better than the Gladstone and Dale formula. This is shown by the following observations of Ruhlmann on water, the light used being the D line of the spectrum:—

- t. (n - 1)/d. (n^2 - 1)/(n^2 + 2)d. - 0 0.3338 0.2061 10 0.3338 0.2061 20 0.3336 0.2061 90 0.3321 0.2059 100 0.3323 0.2061 -

Eykmann's observations also support the approximate constancy of the Lorenz-Lorentz formula over wide temperature differences, but in some cases the deviation exceeds the errors of observation. The values are for the H[alpha] line:—

- Substance. Temp. (n^2 - 1)/(n^2 + 2)d. - Isosafrol, C10H10O2 / 17.6 deg. 0.2925 141.2 deg. 0.2962 Diphenyl ethylene, C14H12 / 22 deg. 0.3339 143.4 deg. 0.3382 Quinoline, C9H7N / 16.2 deg. 0.3187 141 deg. 0.3225 -

The empirical formula (n^2 - 1)/(n^2 + 0.4)d apparently gives more constant values with change of temperature than the Lorenz-Lorentz form. The superiority of the Lorenz-Lorentz formula over the Gladstone and Dale formula for changes of state is shown by the following observations of Bruhl (Zeit. f. phys. Chem., 1891, 71, p. 4). The values are for the D line:—

- - - -+ Gladstone and Dale. Lorenz and Lorentz. Substance. Temp. + - - Vapour. Liquid. Vapour. Liquid. - - - -+ Water 10 deg. 0.3101 0.3338 0.2068 0.2061 Carbon disulphide 10 deg. 0.4347 0.4977 0.2898 0.2805 Chloroform 10 deg. 0.2694 0.3000 0.1796 0.1790 + - - - -

[Sidenote: Additive relations.]

Landolt and Gladstone, and at a later date J.W. Bruhl, have investigated the relations existing between the refractive power and composition. To Landolt is due the proof that, in general, isomers, i.e. compounds having the same composition, have equal molecular refractions, and that equal differences in composition are associated with equal differences in refractive power. This is shown in the following table (the values are for H[alpha]):

- - Substance. Mol. Substance. Mol. Diff. for Refract. Refract. CH2. - - Ethylene chloride C2H4Cl2 20.96 Acetic acid 12.93 / 4.49 Ethylidene chloride/ 21.08 Propionic acid 17.42 Fumaric acid C4H4O4 70.89 Butyric acid 22.01 / 4.59 Maleic acid / 70.29 o-Cresol 32.52 Acetaldehyde 11.50 / 4.43 m-Cresol } C7H8O 32.56 Propionaldehyde 15.93 p-Cresol / 32.57 Butylaldehyde 20.52 / 4.59 - -

Additive relations undoubtedly exist, but many discrepancies occur which may be assigned, as in the case of molecular volumes, to differences in constitution. Atomic refractions may be obtained either directly, by investigating the various elements, or indirectly, by considering differences in the molecular refractions of related compounds. The first method needs no explanation. The second method proceeds on the same lines as adopted for atomic volumes. By subtracting the value for CH2, which may be derived from two substances belonging to the same homologous series, from the molecular refraction of methane, CH4, the value of hydrogen is obtained; subtracting this from CH2, the value of carbon is determined. Hydroxylic oxygen is obtained by subtracting the molecular refractions of acetic acid and acetaldehyde. Similarly, by this method of differences, the atomic refraction of any element may be determined. It is found, however, that the same element has not always the same atomic refraction, the difference being due to the nature of the elements which saturate its valencies. Thus oxygen varies according as whether it is linked to hydrogen (hydroxylic oxygen), to two atoms of carbon (ether oxygen), or to one carbon atom (carbonyl oxygen); similarly, carbon varies according as whether it is singly, doubly, or trebly bound to carbon atoms.

A table of the atomic refractions and dispersions of the principal elements is here given:—

- - Dispersion Element. H[alpha] D. H[gamma] H[gamma]- H[alpha] - - Hydrogen 1.103 1.051 1.139 0.036 Oxygen, hydroxyl 1.506 1.521 1.525 0.019 Oxygen, ether 1.655 1.683 1.667 0.012 Oxygen, carbonyl 2.328 2.287 2.414 0.086 Chlorine 6.014 5.998 6.190 0.176 Bromine 8.863 8.927 9.211 0.348 Iodine 13.808 14.12 14.582 0.774 Carbon (singly bound) 2.365 2.501 2.404 0.039 Double linkage of carbon 1.836 1.707 1.859 0.23 Triple 2.22 2.41 0.19 Nitrogen, singly bound and only to carbon 2.76 2.95 0.19 - -

Dispersion and Composition.—-In the preceding section we have seen that substances possess a definite molecular (or atomic) refraction for light of particular wave-length; the difference between the refractions for any two rays is known as the molecular (or atomic) dispersion. Since molecular refractions are independent of temperature and of the state of aggregation, it follows that molecular dispersions must be also independent of these conditions; and hence quantitative measurements should give an indication as to the chemical composition of substances. This subject has been principally investigated by Bruhl; he found that molecular dispersions of liquids and gases were independent of temperature, and fairly independent of the state of aggregation, but that no simple connexion exists between atomic refractions and dispersions (see preceding table). He also showed how changes in constitution effected dispersions to a far greater extent than they did refractions; thus, while the atomic dispersion of carbon is 0.039, the dispersions due to a double and treble linkage is 0.23 and 0.19 respectively.

Colour and Constitution.—In this article a summary of the theories which have been promoted in order to connect the colour of organic compounds with their constitution will be given, and the reader is referred to the article COLOUR for the physical explanation of this property, and to VISION for the physiological and psychological bearings. A clear distinction must be drawn between colour and the property of dyeing; all coloured substances are not dyes, and it is shown in the article DYEING that the property of entering into chemical or physical combination with fibres involves properties other than those essential to colour. At the same time, however, all dyestuffs are coloured substances.

A survey of coloured substances led O.N. Witt in 1876 to formulate his "chromophore-auxochrome" theory. On this theory colour is regarded as due to the presence of a "chromophore," and dyeing power to an "auxochrome"; the latter by itself cannot produce colour or dyeing power, but it is only active in the presence of a chromophore, when it intensifies the colour and confers the property of dyeing. The principal chromophores are the azo, -N=N-, azoxy, =N2O, nitro, -NO2, nitroso, -NO, and carbonyl, =CO, groups. The azo-group is particularly active, both the aliphatic and aromatic compounds being coloured. The simplest aliphatic compounds, such as diazo-methane, diazo-ethane, and azo-formic acid, are yellow; the diamide of the latter acid is orange-red. Of the aromatic compounds azo-benzene is bright orange-red, and [alpha]-azo-naphthalene forms red needles or small steel-blue prisms. The azo-group, however, has little or no colouring effect when present in a ring system, such as in cinnolene, phthalazine and tolazone. The nitro group has a very important action mainly on account of the readiness with which it can be introduced into the molecule, but its effect is much less than that of the azo group. The colour produced is generally yellow, which, in accordance with a general rule, is intensified with an increase in the number of groups; compare, for example, mono-, di-and tri-nitrobenzene. The nitroso group is less important. The colour produced is generally of a greenish shade; for example, nitrosobenzene is green when fused or in solution (when crystalline, it is colourless), and dinitrosoresorcin has been employed as a dyestuff under the names "solid green" and "chlorine." The carbonyl group by itself does not produce colour, but when two adjacent groups occur in the molecule, as for example in the a-diketones (such as di-acetyl and benzil), a yellow colour is produced. It also acts as a chromogenic centre when double bonds or ethylenic linkages are present, as in fluorene ketone or fluorenone. A more complex chromophoric group is the triple ethylenic grouping

=C >C=, =C/

the introduction of which was rendered necessary by the discovery of certain coloured hydrocarbons. As a general rule, hydrocarbons are colourless; the exceptions include the golden yellow acenaphthylene, the red bidiphenylene-ethylene, and the derivatives of fulvene

CH:CH >CH2, CH:CH /

which have been discussed by J. Thiele (Ber., 1900, 33, p. 666). This grouping is not always colour-producing, since diphenyl is colourless.

The most important auxochromes are the hydroxyl (-OH) and amino (-NH2) groups. According to the modern theory of auxochromic action, the introduction of a group into the molecule is accompanied by some strain, and the alteration in colour produced is connected with the magnitude of the strain. The amino group is more powerful than the hydroxyl, and the substituted amino group more powerful still; the repeated substitution of hydroxyl groups sometimes causes an intensification and sometimes a diminution of colour.

We may here notice an empirical rule formulated by Nietzski in 1879:—the simplest colouring substances are in the greenish-yellow and yellow, and with increasing molecular weight the colour passes into orange, red, violet, blue and green. This rule, however, is by no means perfect. Examination of the absorption spectra of coloured compounds shows that certain groupings displace the absorption bands in one direction, and other groupings in the other. If the bands be displaced towards the violet, involving a regression through the colours mentioned above, the group is said to be "hypsochromic"; if the reverse occurs the group is "bathochromic." It may be generally inferred that an increase in molecular weight is accompanied by a change in colour in the direction of the violet.

Auxochromic groups generally aid one another, i.e. the tint deepens as the number of auxochromes increases. Also the relative position of the auxochrome to the chromophore influences colour, the ortho-position being generally the most powerful. Kauffmann (Ber., 1906, 39, p. 1959) attempted an evaluation of the effects of auxochromic groups by means of the magnetic optical constants. The method is based on the supposition that the magnetic rotation measures the strain produced in the molecule by an auxochrome, and he arranges the groups in the following order:—

.OCOCH3 .OCH3 .NHCOCH3 .NH2 .N(CH3)2 .N(C2H5)2 -0.260 1.459 1.949 3.821 8.587 8.816

The phenomena attending the salt formation of coloured and colouring substances are important. The chromophoric groups are rarely strongly acid or basic; on the other hand, the auxochromes are strongly acid or basic and form salts very readily. Notable differences attend the neutralization of the chromophoric and auxochromic groups. With basic substances, the chromophoric combination with a colourless acid is generally attended by a deepening in colour; auxochromic combination, on the other hand, with a lessening. Examples of the first case are found among the colourless acridines and quinoxalines which give coloured salts; of the second case we may notice the colourless hydrochloride and sulphate of the deep yellow o-aminobenzophenone. With acid substances, the combination with "colourless" metals, i.e. metals producing colourless salts with acids, is attended by colour changes contrary to those given above, auxochromic combination being accompanied by a deepening, and chromophoric by a lessening of the tint.

Mention may be made of the phenomenon of halochromism, the name given to the power of colourless or faintly-coloured substances of combining with acids to form highly-coloured substances without the necessary production of a chromophoric group. The researches of Adolf von Baeyer and Villiger, Kehrmann, Kauffmann and others, show that this property is possessed by very many and varied substances. In many cases it may be connected with basic oxygen, and the salt formation is assumed to involve the passage of divalent into tetravalent oxygen. It seems that intermolecular change also occurs, but further research is necessary before a sound theory can be stated.

Quinone Theory of Colour.—A theory of colour in opposition to the Witt theory was proposed by Henry Armstrong in 1888 and 1892. This assumed that all coloured substances were derivatives of ortho- or para-quinone (see QUINONES), and although at the time of its promotion little practical proof was given, yet the theory found wide acceptance on account of the researches of many other chemists. It follows on this theory that all coloured substances contain either of the groupings

_ _ /—— /—— / / ==== or == , \_/ / \_/ \_/

the former being a para-quinonoid, the latter an ortho-quinonoid. While very many coloured substances must obviously contain this grouping, yet in many cases it is necessary to assume a simple intermolecular change, while in others a more complex rearrangement of bonds is necessary. Quinone, which is light yellow in colour, is the simplest coloured substance on this theory. Hydrocarbons of similar structure have been prepared by Thiele, for example, the orange-yellow tetraphenyl-para-xylylene, which is obtained by boiling the bromide C6H4[CBr(C6H5)2]2 with benzene and molecular silver. The quinonoid structure of many coloured compounds has been proved experimentally, as, for example, by Hewitt for the benzene-azo-phenols, and Hantzsch for triaminotriphenyl methane and acridine derivatives; but, at the same time, many substances cannot be so explained. A notable example is provided by the phthaleins, which result by the condensation of phthalic anhydride with phenols. In the free state these substances are colourless, and were assumed to have the formula shown in 1. Solution in dilute alkali was supposed to be accompanied by the rupture of the lactone ring with the formation of the quinonoid salt shown in 2.

/ / O / / HO / / OH / / OH / / / / / / / C / / C / / / C6HO C6H4< / CO COON3 (1) (2)

Baeyer (Ber., 1905, 38, p. 569) and Silberrad (Journ. Chem. Soc., 1906, 89, p. 1787) have disputed the correctness of this explanation, and the latter has prepared melliteins and pyromelliteins, which are highly-coloured compounds produced from mellitic and pyromellitic acids, and which cannot be formulated as quinones. Baeyer has suggested that the nine carbon atom system of xanthone may act as a chromophore. An alternative view, due to Green, is that the oxygen atom of the xanthone ring is tetravalent, a supposition which permits the formulation of these substances as ortho-quinonoids.

The theories of colour have also been investigated by Hantzsch, who first considered the nitro-phenols. On the chromophore-auxochrome theory (the nitro group being the chromophore, and the hydroxyl the auxochrome) it is necessary in order to explain the high colour of the metallic salts and the colourless alkyl and aryl derivatives to assume that the auxochromic action of the hydroxyl group is only brought strongly into evidence by salt formation. Armstrong, on the other hand, assumed an intermolecular change, thus:—

/ / HO / OH / == O ===> / NO2 / == NO2Na. / /

The proof of this was left for Hantzsch, who traced a connexion with the nitrolic acids of V. Meyer, which are formed when nitrous acid acts on primary aliphatic nitro compounds. Meyer formulated these compounds as nitroximes or nitro-isnitroso derivatives, viz. R.C(NO2)(NOH). Hantzsch explains the transformation of the colourless acid into red salts, which on standing yield more stable, colourless salts, by the following scheme:—

N NOH // NO2Na // R.C O // R.C ===> / ===> R.C N NO2 // NO O ONa

Colourless, stable. Coloured, labile. Colourless, stable

He has also shown that the nitrophenols yield, in addition to the colourless true nitrophenol ethers, an isomeric series of coloured unstable quinonoid aci-ethers, which have practically the same colour and yield the same absorption spectra as the coloured metallic salts. He suggests that the term "quinone" theory be abandoned, and replaced by the Umlagerungs theory, since this term implies some intermolecular rearrangement, and does not connote simply benzenoid compounds as does "quinonoid." H. von Liebig (Ann., 1908, 360, p. 128), from a very complete discussion of triphenyl-methane derivatives, concluded that the grouping

R R R .. .. .. A - A - A

was the only true organic chromophore, colour production, however, requiring another condition, usually the closing of a ring.

The views as to the question of colour and constitution may be summarized as follows:—(1) The quinone theory (Armstrong, Gomberg, R. Meyer) regards all coloured substances as having a quinonoid structure. (2) The chromophore-auxochrome theory (Kauffmann) regards colour as due to the entry of an "auxochrome" into a "chromophoric" molecule. (3) If a colourless compound gives a coloured one on solution or by salt-formation, the production of colour may be explained as a particular form of ionization (Baeyer), or by a molecular rearrangement (Hantzsch). A dynamical theory due to E.C.C. Baly regards colour as due to "isorropesis" or an oscillation between the residual affinities of adjacent atoms composing the molecule.

Fluorescence and Constitution.—The physical investigation of the phenomenon named fluorescence—the property of transforming incident light into light of different refrangibility—is treated in the article FLUORESCENCE. Researches in synthetical organic chemistry have shown that this property of fluorescence is common to an immense number of substances, and theories have been proposed whose purpose is to connect the property with constitution.

In 1897 Richard Meyer (Zeit. physik. Chemie, 24, p. 468) submitted the view that fluorescence was due to the presence of certain "fluorophore" groups; such groupings are the pyrone ring and its congeners, the central rings in anthracene and acridine derivatives, and the paradiazine ring in safranines. A novel theory, proposed by J.T. Hewitt in 1900 (Zeit. f. physik. Chemie, 34, p. 1; B.A. Report, 1903, p. 628, and later papers in the Journ. Chem. Soc.), regards the property as occasioned by internal vibrations within the molecule conditioned by a symmetrical double tautomerism, light of one wave-length being absorbed by one form, and emitted with a different wave-length by the other. This oscillation may be represented in the case of acridine and fluorescein as

CH CH CH // // / // / / // / / ==> ==> <== <== , / / // / / // / // // N N N