GIFT OF MICHAEL REESE LAW AND THEOKY IN CHEMISTRY LAW AND THEOBY IN CHEMISTRY A COMPANION BOOK FOE STUDENTS BY DOUGLAS CARNEGIE, M.A. SOMETIME SCHOLAR AND DEMONSTRATOR IN CHEMISTRY OF GONVILLK AND CAIUS COLLEGE, CAMBRIDGE LONDON LONGMANS, GREEN, AND CO. AND NEW YORK: 15 EAST 16 th STEEET 1894 All rights reserved o PEEFACE THIS book contains the substance of a summer-school course of eight lectures delivered before an audience of school teachers of elementary chemistry at Colorado College, Colorado Springs, U.S.A. It is not therefore adapted to beginners, but it is hoped that it may be found useful by such students as wish to recapitulate and co-ordinate the more im- portant principles of chemistry before proceeding to more detailed and advanced works. The qualification companion book occurring on the title-page is used advisedly, for text-book continuity and completeness cannot be claimed for the matter of the following pages. The seven chapters are in reality short and independent essays on the subjects of which they severally treat. In the choice of subject-matter I was chiefly in- fluenced by the two following considerations. Firstly, I desired to treat of those subjects which in my opinion are essential to a liberal understanding of the science, but which are inadequately treated in, or altogether crowded out of, the current text-books of elementary chemistry. In the second place, I vi PKEFACE wished to restate and emphasise such points as in my experience present especial difficulties to the student. Throughout, the attempt has been made to keep the information up to date, and to indicate, with due appreciation of perspective, the trend of modern research in its relation to the science as a whole. In this connection it is perhaps scarcely necessary to state that the hope was to excite interest rather than to satisfy it. I would here express my sincerest thanks to my friend, Mr. Pattison Muir, for the very valuable help he has given me. DOUGLAS CAENEGIE. BLACKHEATH. CONTENTS CHAP. PAGE I. ALCHEMY AND THE BIRTH OP SCIENTIFIC CHEMISTRY 1 II. THE PHLOGISTIC PERIOD AND THE BEGINNINGS OF CHEMICAL THEORY 24 III. CHEMICAL CLASSIFICATION. MIXTURES, COMPOUNDS, ELEMENTS .40 IV. THE ATOMIC THEORY 69 V. THE CLASSIFICATION OF COMPOUNDS. ACIDS, BASES, SALTS 121 VI. ISOMERISM AND MOLECULAR ARCHITECTURE . . 148 VII. CHEMICAL EQUILIBRIUM 186 vii LIB/ Of TH UNIVERSITY LAW AND THEOKY IN CHEMISTRY CHAPTER I. ALCHEMY AND THE BIRTH OF SCIENTIFIC CHEMISTRY. IN the ancient world the only scientific pursuits which were considered reputable, and which led to fame or distinction, were politics, philosophy, and mathematics. Dyeing, tanning, bronze founding, glass making, soap making are all industries which boast a remote antiquity, but the early practice of these arts was confined to the slaves, and the ignominy of attempting any adaptation of theory to practice never for a moment suggested itself to the noble-born. But while the actual practice of what we now under- stand by the term commercial chemistry was in the hands of the uneducated, and possessed no literature,^ the philosophers theorised on the composition and nature of matter, and to trace these theories and their consequences is, as we shall find, to trace the early history of our science. The early Greek philosophers of the seventh to the A 2 LAW AND THEORY IN CHEMISTRY fifth centuries B.C. belonged to one or other of two schools known as the Ionic and the Eleatic schools respectively. The adherents of the Ionic school believed that in all the apparently diverse things by which they were surrounded there existed a common principle or substratum (ap^rf), and they sought to evolve order and simplicity out of the apparent diversity in terms of this common principle. Accord- ing as the attempt was made to investigate and detect this principle by the observation of natural phenomena, or by the unaided exercise of the mind, we find Thales asserting water to be the substratum of all things, or Pythagoras selecting number as the one real thing in nature. The attitude of the Pythagorean branch of the Ionic school is well illustrated by the following quotation from Plato's seventh book of the " Republic " : " We shall pursue astronomy with the help of problems just as we pursue geometry, but if we wish to become thoroughly acquainted with astronomy we will let the heavenly bodies alone." The disciples of the Eleatic school founded by Xenophanes did not attempt to explain the material universe, but they espoused a philosophy of an essen- tially negative character. Assuming unity and im- mutability in the universe, without attempting to further specify or explain either the one or the other, they maintain that change and the apparent diversity of things are inexplicable delusions of the senses. Reason was made the only criterion of truth, and as reason apparently led to results at variance with the THE BIRTH OF SCIENTIFIC CHEMISTRY 3 information conveyed by the senses, 1 the latter were regarded as fallacious. To summarise the differences between the two schools briefly, we may say that while the Ionic school sought to explain the many in the one, the Eleatic school denied the real existence of the many and assumed the one. The views of Empedocles (440 B.C.) do not, however, strictly conform to either of the two schools just de- scribed. Unlike the Eleatics, he aimed at a rational explanation of the diversity and change in the universe, and unlike the Ionic school this explanation was given in terms, not of one, but of four common principles, viz., earth, fire, air, and water. These substances, to which Empedocles assigned mythological names, were regarded as the constituents or elements out of which everything else was built up. In Empedocles' opinion, their association in different proportions sufficiently accounted for all the diversities presented by the world to the senses. But to account for the continual changes that are ever taking place in these diversities, Empedocles had to assume the existence of two other rival elements, viz., love and strife, 2 the former causing the attraction and combination of unlike elements, the latter causing their disruption. If we substitute the seventy odd elements of to-day's chemistry for the four Empedoclean elements first mentioned, and then the 1 Zeno's well-known paradox of Achilles and the tortoise may here be instanced. 2 We should be inclined to regard the "love" and "strife" of Empedocles rather in the light of powers or influences than as elements. But Burnet (Early Greek Philosophy] states that Empedocles himself regarded them as corporeal elements co-equal with the other four. 4 LAW AND THEORY IN CHEMISTRY term affinity for the remaining " love " and " strife/' we cannot but be struck with the close analogy which the views of this early Greek philosopher bear to those held in the nineteenth century concerning the composition of, and the changes undergone by, the material universe. The views of Empedocles were modified, and in their modified form popularised by Aristotle (385-322 B.C.). The great Stagy rite regarded all substances as portions of one and the same fundamental matter, modified by the greater or less quantities of the four " elementary principles " earth, fire, air, and water which it had impressed on it. This conception of elementary prin- ciples has nothing in common either with our present conceptions of the elements or with the original views of Empedocles. It is one of those abstract ideas ori- ginally borrowed in all probability from India, where Buddha taught that in addition to the four principles already mentioned, other two ether and consciousness existed, and it is very difficult for us to replace our clear-cut notions of definite concrete elements by these unreal products of the Oriental imagination. It must not be supposed that Aristotle intended to convey the idea that water, air, fire, and earth, as we now understand these terms in a purely materialistic sense, constituted the universe by their manifold com- binations. The elementary principle of earth implied to the Aristotelian school merely the possession by the bodies supposed to contain it, of the properties of drvness and coldness. Similarly the principle of water implied coldness and moistness, the principle of fire, THE BIETH OF SCIENTIFIC CHEMISTRY 5 heat and dryness, and the principle of steam or air, heat and moistness. Accordingly it was held that one specific kind of matter could be totally changed into another by merely altering the proportion in which the principles had been impressed on the fundamental matter of the first substance by altering the ratio of its heat, coldness, dryness, and moistness. Thus by imparting more heat to water (fundamental matter especially richly im- pressed with the principle of water) it becomes steam or air. By taking away its moisture and cooling it, it becomes, as was then taught, rock crystal or petri- fied water, fundamental matter especially rich in the principle of earth. , The important point to note is that the Aristotelian doctrine favoured the idea of a possible transmutation of any one substance into any other. Experiments having as their aim the change of one substance into another seem first to have been ex- tensively practised in Egypt, which was once called Klimi (Greek, %?7/ua) on account of the darkness of its soil ; Khmi literally meaning black soil. And it came about that the art which had as its aim and object the transmutation of material things received the name of the country where it first flourished the art was called fflpla, 1 just as a certain form of wool- spinning is called worsted-making from the village of Worsted in Norfolkshire, where the industry had birth. 1 The use of this term to designate the art first appears, so far as we know, in the fourth century. 6 LAW AND THEORY IN CHEMISTRY In the seventh century the great wave of Islamism rolled westward from Arabia towards Europe, and the missionaries of Mahomet overran and conquered Egypt. During their sojourn in Egypt, the Arabians found the dwellers in the land executing what were then regarded as actual transformations of matter. 1 For in- stance, when molten sulphur was poured into mercury, the metallic properties of the latter disappeared and the mercury and sulphur changed into a solid substance black as the raven's wing. When this black substance was heated gently for some time, it changed into the beautiful red substance now used as a paint under the name vermilion. This does not strike us now as a very wonderful change, but owing to the way in which the early naturalists were wont to symbolise things, it was to them a change of the profoundest type. For black was with them emblematic of evil, while red denoted virtue ; and the change from a black substance into a brilliant red one was in their eyes as the miracle of an evil tree bringing forth good fruit. But the change which appealed most to the Arabian conquerors was the, to their minds, less miraculous change or transmutation of the base or common metals into the noble metals, gold and silver. Though the 1 It is probable that prior to their invasion of Egypt, the Arabians had already learnt something of Egyptian arts through the Nestorians. In the fifth century this Christian sect was banished from its home in Constantinople to the desert of Thebais in Egypt, whence its followers gradually migrated eastwards. THE BIRTH OF SCIENTIFIC CHEMISTRY 7 modus operandi of this transmutation was kept very secret, 1 yet the" possibility of the transmutation was regarded as a well-ascertained fact during the first centuries of the Christian era. The Arabians carried away with them in their western trend this idea of the ennobling of the base metals, and introduced it into Europe under the title Alchema ; the prefix Al being the Arabic for the definite article, and chema being the Arabic rendering of yyiiia, but signifying dark in the sense of obscure or secret rather than black. In all probability the prefix Al was added for the purpose of conferring a dignity and distinction on the art as being the highest and most reputable of all arts, just as the Spanish discoverers of the New World called the American crocodile el lagarto the lizard because it was the largest and most formidable lizard-like animal they had ever seen. El lagarto and alcherna persist in the language of to-day as the words alligator and alchemy. The word alchemy gave rise by apherisis to the word chemist, and this in turn to the word chemistry. 2 (Of. poet and poetry.) 1 The earliest chemistry of all is to be found in the ayia r^vv) or holy art, whose secrets were kept sacred under "pain of the peach tree" (i.e., under the penalty of being poisoned by hydrocyanic acid), whose study was confined to the priesthood and the sons of kings, and whose laboratories were the temples. 2 There are some who, rejecting the derivation of the word Alchemy given in the text, would derive X 7 ?/-"' 01 from %iy/.eia (a mingling, or infusion) from "xyfibs (juice), which in turn is related to x^ iv (t pour). Hence the two current methods of spelling the word chemistry = chymistry. Picton in his book The Story of Chemistry rejects both these deriva- 8 LAW AND THEORY IN CHEMISTRY The Arabian alchemists, as we learn from the writings of Geber works dating from the eighth century and constituting the oldest chemical literature extant 1 had a theory of their own respecting the nature of the metals. Aristotle's theory was wide and applied to all kinds of matter, whereas the alchemistic theory was specialised and had reference more particularly to the metals. The latter theory, moreover, did not re- place the former, but only supplemented it. Aristotle's elementary principles were still recognised, but regarded as the more remote factors in determining the properties of matter, while Geber's elements represented the more proximate constituents of matter in general and of the metals in particular. Geber's idea, which met with a general adoption by the alchemists, was that the metals consist of sulphur and mercury in varying proportions. His sulphur and mercury did not, however, mean what these words now connote to us definite chemical individuals with invariable properties. The names had for him an tions, and asserts that Alexander of Aphrodisia (a great exponent of the Aristotelian doctrines in the second century A.D.) invented the word chyniike for the operations of the laboratory ; but surely it is unusual to invent words out of one's inner consciousness without any attempt at appropriateness, historical or otherwise, in the resulting invention. Though Alexander may have thrown the word chymike current on the world, it does not follow that in the selection of the word he was uninfluenced by anything save inventive power. 1 Some philologists would derive the word Gibberish [said to have been originally Geberish] from the alchemist Geber, notwithstanding the fact that Geber's writings, compared with the inflated and unintelligible jargon of other alchemical productions, are models of conciseness and clearness. THE BIRTH OF SCIENTIFIC CHEMISTRY 9 abstract meaning ; his sulphur and mercury varied in kind and in properties. Thus gold and silver were very rich in " pure or perfect kinds " of mercury, but the one contained a red sulphur, and the other a white. In short, Gefcer's elements were rathei of the nature of elementary principles than of the nature of elements as we now understand the latter term. Since the change in purity as well as the change in relative proportion of these two metallic constituents was assumed to be under the control of the experi- menter, it is obvious that the attempt to transmute the base metals into gold was quite legitimate from a theoretical standpoint. Further, it was generally believed that the evolution of the base metals into the noble ones, gold and silver, was a change which was proceeding spontaneously and constantly in nature, and that therefore the alchemists' task virtually consisted in an artificial acceleration of a perfectly natural process. Alchemy scarcely merits the dignity of being classed as a science. For some of its followers it was a transcendental philosophy which amounted almost to a religion ; but for the majority it was nothing more nor less than an empiric trade. Its chief service to science lies in the fact that it stimulated experiment blind and thoroughly haphazard experiment perhaps, but still experiment. Its most fatiguing and laborious study was prosecuted by the majority, not so much out of a desire for scientific triumph or for truth's io LAW AND THEOEY IN CHEMISTRY sake, as out of a thirst for that power which the so- called philosopher's stone with its Midas touch was to confer. The alchemists never dreamed of trying to convert gold into lead. The philosopher's stone was the name given to a mythical theurgic powder 1 which was to have the power of fermenting millions of times its own weight of fused base metal into gold. The strangest and most diverse ingredients were mixed together in the attempts to prepare this much sought for powder; we read of snails' slime, serpents' teeth, gall stones taken from cats, blood, hair, white of egg, &c., in addition to the never failing ingredient, mercury. The philosopher's stone was generally identified with what in more general terms was called the " One Thing" the perfect form of matter which was to combine in itself all the properties of all other kinds of matter in their highest perfection. Hence we can in a measure account for the many and varied in- gredients which were believed to be necessary to its production. Many of the receipts for making the philosopher's stone that have come down to us are perfectly un- intelligible, so allegorical is the language in which they are couched. Sometimes the directions seem fairly explicit, till one comes to the concluding item "add carefully a sufficiency of you know ivliat" 1 It may here be stated that some philologists find in the generally entertained belief that the " stone " would turn out to be a black powder, a derivation of the word alchemy. See article " Chemie " in Ladenburg's Ilandworterbuch der Chemie. THE BIRTH OF SCIENTIFIC CHEMISTRY 11 Several reasons may be assigned for this secrecy and mystery, and sometimes one, sometimes another of these reasons may have been operative. In the first place, the alchemists were undoubtedly desirous of keeping their profession strictly limited as to numbers, a result which would be effected by the adoption of what practically amounted to a private code. Again, there were alchemists whose attitudes towards their profession are sufficiently expressed in the following quotation : " If thou shouldst reveal that in a few words which God hath been forming a long time, thou shouldest be condemned on the great day of judgment as a traytor to the majestie of God." Finally, there may have been some alchemists who out of vanity or for purposes of self -aggrandisement asserted, with intent to deceive, their knowledge of the transmuting } substance. Obviously it would be expedient for such men to express themselves so obscurely as to render it impossible for others to bring their statements to the test of experiment. With the Benedictine monk, Basil Valentine, begins the period of iatro or medical chemistry, a period lasting from the fifteenth to the seventeenth century, during which transmutation was in abeyance. Here- tofore the apothecaries had prescribed purely vegetable preparations only, but now we find mineral specifics contesting the field with them and partially re- placing them. The true goal of alchemy had come to be looked on as the attainment of health, not 12 LAW AND THEORY IN CHEMISTRY wealth " a back tough as Hercules " rather than the riches of Solomon and the philosopher's stone was endued with all the attributes of an elixir of life in addition to its now secondary transmuting powers. 1 It was even customary at this period to ascribe the great ages of the patriarchs to their possession of the health-giving stone. 2 It is probable that the idea of the prophylactic and life - sustaining function of the stone originated in the great propensity of the alchemists for sym- bolism and metaphor. They even went the length of constructing their apparatus symbolically retorts, for instance, being frequently fashioned so as to resemble men, the bulb of the retort being the stomach, the crown of the retort being the head, and the beak being the nose. 3 1 Van Helmont (1577-1644), the originator of the generic term gas and the discoverer of the existence of several distinct kinds of gases, believed that the universal solvent or "alkahest," not the philosopher's stone, would prove to be the true elixir vitse. 2 See Jonson's Alchemist, act ii. sc. i., where reference is also made to the belief that such mythological stories as those of the Golden Fleece, the Hesperian Gardens, the Boon of Midas, &c., were "all abstract riddles of the stone." It may be asked how it came about that the patriarchs died, seeing that they were possessed of the elixir of life. The alchemist would have made answer in this wise. Every person has a predestined maximum lease of life a limit which he cannot possibly pass, but a limit to which by reason of disease he seldom attains. Now it was not claimed for the magic stone that it was more mighty than destiny. All it could do would be, by prevent- ing sickness and consequent premature death at three-score years and ten or thereabouts, to enable men to enjoy the maximum lease of life stretching well up into the hundreds. 3 See Bolton, Trans. Neiv York Acad. Sc., December 1882, March 1883. THE BIRTH OF SCIENTIFIC CHEMISTRY 13 In further conformity with this propensity, the alche- mists also referred to the base metals as the diseased metals, the lepers, &c., and figuratively spoke of their transmutation into gold as a healing of their diseases. Thus in all probability arose the idea of the alchemist's elixir of life. In the blind search for this elixir many valuable drugs were discovered and fairly fully investigated. Valentine busied himself chiefly with the therapeutics of antimony and its compounds, and he very thinly veiled his impatience with and contempt for " the deplorable, putrid, and stinking bag of worms," that failed to see the wonderful virtues of antimony as he himself saw them. In addition to his book, The Triumphal Chariot of Antimony, Valentine left behind him a complication in the views which had been current up to his day respecting the nature of the metals. This complication, which consisted in the assertion of the presence in the metals of a third elementary principle, viz., salt, 1 did not inaugurate any material advance in views respecting the composition of matter. This new idea, however, was soon generally accepted, and in contemporary literature we find all kinds of fanciful analogies in- stituted between such diversities as the Trinity, body, soul, and spirit, and the trio salt 0, sulphur ^, and mercury $ 1 The principle of salt was represented in that portion of the metal which resisted the action of heat, and remained behind as a solid residuum. 14 LAW AND THEORY IN CHEMISTRY Valentine had shown a laudable boldness and inde- pendence in ushering in, against strenuous opposition, the reign of iatro-chemistry, but his immediate successor, Philippus Aureolus Theophrastus Bombastus Paracelsus von Hohenheim that strange character, half scientist, half charlatan carried on the crusade with a vehement intrepidity amounting almost to truculence. After forcibly expressing his contempt for the old school of " medicasters " by a public holocaust of the works of the celebrated physicians Galen (second century) and Avicenna (tenth century), he continued to work in the field first opened up by Valentine, and enriched medicine by the knowledge he contributed thereto of many valuable mineral specifics l (corrosive sublimate, tinc- ture of perchloride of iron, &c.), which still figure in the pharmacopoeias of to-day. He also substituted the more or less pure active principles of plants for the crude electuaries of the apothecary, and it is interesting to note that it was probably through his introduction from the East, and liberal use, not of a mineral, but of a vegetable drug, viz., laudandum, 2 that Paracelsus effected those wonderful cures which gained for him his great and widespread reputation. 3 1 "The medicines are ranged in boxes according to their natures, whether chymical or galenical preparations." Quoted in Johnson's Dictionary. 2 Laudandum (of which the modern word for opium, viz., laudanum, is a contraction) is the Latin gerundive signifying "meet to be praised." 3 In his poem " Paracelsus," Browning, while making use of incidents in the life of the chemist as a mise en scene, sketches the career of an ideal Paracelsus. THE BIRTH OF SCIENTIFIC CHEMISTRY 15 Early in his career, Paracelsus devoted himself to an experimental study of transmutation, but it was not long before he concluded that it was a chimera. Some of the best minds among his contemporaries and im- mediate successors were doubtless influenced by the conclusions of so great a personality, and renouncing alchemy, devoted themselves to medical chemistry. At any rate the decline of alchemy, properly so-called, dates from the time of Paracelsus. Most of the so- called alchemists of the latter portion of the middle ages were in reality frauds of the lowest order, whose stock-in-trade consisted in a little leger de main, and an unlimited amount of the inflated and highly allegorical language in which the alchemists were wont to give their recipes for the elusive stone, and to impress the lay mind. In the memoirs of the Academy of Sciences for 1772, Geoffrey makes an exposd of the ways and means of these pseudo-alchemists. Hollow stirring rods con- taining gold, and temporarily stopped with wax, crucibles with false bottoms previously charged with the precious metals, and composite rods one half gold soldered to the other half iron, and the whole coloured uniformly were among the properties of the craft. Thus equipped, the charlatans practised on the cre- dulity of the public, easily leading it to believe them possessed of clairvoyance, and a supernatural power enabling them to control natural agencies. Telling fortunes by the stars, dispensing "familiars to rifle with at horses and win cups," &c., they pursued a 1 6 LAW AND THEORY IN CHEMISTRY royal road to wealth. Instances of such frauds occur throughout mediaeval literature and history. One of Ben Jonson's best constructed plays The Alchemist is based on the despicable chicanery of a " cunning man," well named Subtle, and his confederate, Face. In the Canterbury Tales, again, Chaucer, apparently moved by some sudden resentment, departs from the order of the poem set forth in the prologue to introduce " The Chanones Yemannes Tale." A yeoman or servant falls in with the body of pilgrims on their way to Canterbury, and, after detailing to them the seductive horrors of alchemy, relates the story of some trickery that his late master, the Chanon, had practised on a priest. In actual history we find these pseudo-alchemists figuring in the retinues of bankrupt kings and spend- thrift potentates along with chaplains, jesters, and so forth. At the instigation of Edward II., we read that John Cremer, Abbot of Westminster, invited the famous Spanish chrysop&iis, 1 Eaymond Lully, to come over to England for the purpose of replenishing the royal exchequer; and Henry VI. for long enter- tained a firm and costly belief in alchemy, in spite of the fact that Henry IV. had passed a law said to be the shortest in the statute-book making the practice of alchemy a felony. Indeed, most of the European courts so fostered and encouraged alchemy during the 1 Chrysopceia (literally, gold making) was a synonym of the term alchemy in use during a long period. See Ben Jonson's Alchemist, act ii. sc. i. THE BIRTH OF SCIENTIFIC CHEMISTRY 17 fourteenth and fifteenth centuries that the markets of the day were glutted with worthless and counterfeit coin. Several coins and medals, which are claimed to be products of the alchemical art, are still preserved in the Eoyal Cabinet of Coins in Munich, and in the Imperial Cabinet in Vienna. 1 As many of these relics un- doubtedly consist of pure gold and silver, one is forced to conclude either that the bullion from which they were made was produced fraudulently by such tricks as Geoffrey has explained (p. 15), or that the noble metals resulted from the application of cupellation processes to base metals which were believed to be pure, but which in reality carried noble metal. In agreement with the first conclusion, we read that in 1709 a certain retainer alchemist, Domenico Manuel by name, being detected in his knavery, experienced the irony of execution on a gilded gallows at Kiistrin. In support of the alternative conclusion, it may be stated that there is in the British Museum a facsimile of a silver medal made by Becher (see post, p. 24), which was in all likelihood obtained by the cupellation of argentiferous lead supposed by Becher to be pure lead. 2 The medal bears on its reverse the following inscription : "Anno 1675 mense Julio Ego J. J. Becher Docter hanc unciarn argenti purissimi ex plumbo arte alchymica transmutavi." 1 See H. C. Bol ton's Contributions of Alchemy to Numismatics ; also Reyher, De numis quibusdem ex chymico metallo factis. 2 The original of this interesting medal is in the Vienna Cabinet of Coins. B i8 LAW AND THEOKY IN CHEMISTRY On the obverse is the usual representation of Saturn with his wooden leg, scythe, &c. For the alchemists believed the metals to be under the influences of the planets ; and sluggish lead had assigned to it as its patron star the planet Saturn the slowest moving planet with which the alchemists were acquainted. 1 Becher, regarding the production of his medal as a bond fide case of transmutation, seems to have valued it simply as a chemical curiosity ; for we are told that he expressed himself more interested in the solution of nature's riddles than in the heaping up of wealth. 2 Even so late as the year 1843 we find one of the pseudo-alchemistic cult, one Francois Cambriel, of 19 Judas Street, advertising in a leading paper his readi- ness to teach in a course of nineteen lessons all the secrets of the Hermetic Art. 3 But that the bond fide alchemists themselves tho- roughly believed in the possibility of transmutation, there can be no doubt. 4 Such facts as the following 1 The personification of Saturn as a lame man with hour-glass and scythe, &c., is due to the fanciful identification of the Roman Saturnus with the Grecian Cronus during the Hellenising period. 2 Becher's offer to the Government of Holland to provide it with six millions of golden thalers per annum if it would provide a certain amount of silver and unlimited sea-sand, does not seem to have been taken up in spite of the fact that an experiment made in 1679 is said to have turned out six times more productive than Becher had anticipated ! 3 So called after the mythical Hermes Trismegistos, the reputed founder of all arts and sciences, and the Grecian representative of the old Egyptian godhead Thoth the deified intellect. 4 Even such reputed early-day chemists as Davy, Dumas, and Bergman, could not bring themselves to utterly reject the idea of the possibility of transmutation. Peter Woulfe, a fellow of the Royal THE BIETH OF SCIENTIFIC CHEMISTRY 19 could not but foster the brightest hopes of men who, satisfied with surface views of things, never questioned what was under the veneer. Iron plunged into a green solution obtained by dissolving certain ores (containing copper) in nitric acid, was itself apparently changed into the more valuable metal copper ; and copper melted with tutty (an impure oxide of zinc) acquired the bright rich yellow colour of gold. And in the metallurgy of the alchemists much importance was ascribed to purely colour changes ; much was supposed to have been achieved in making base metals take the colour of the noble ones. Indeed, many of the early- day alchemists seem to have believed that to give a base metal the colour and sheen of gold was in effect to change the base metal into gold. In accordance with these beliefs, the transmuting substance is often called a tincture (from tingo, I dye). Thus, on a medal of the year 1647 made by one Hofmann, are inscribed the letters T G V L, probably an abbreviation of the sentence tinctures guttce V libram, meaning that five drops of the tincture used had effected the transmuta- tion of a pound of the base metal from which the medal had been prepared. Again, in the process now known as cupellation, lead heated in a vessel made of bone ash, slowly dis- appeared and left behind a button of silver. Pyrites treated in a similar way often left a legacy of gold. Of course the noble metals were ab initio present in Society of this century, whose name lives in connection with certain pieces of chemical apparatus, was a firm believer in transmutation. 20 LAW AND THEOKY IN CHEMISTRY the lead and the pyrites, but the experiments were for the alchemists, who had no notion of what we now understand by chemical homogeneity, cases of indubi- table transmutation. When one recalls the modern work on the marvellous effects of "traces of impurities" in altering the pro- perties of large masses of matter, one can scarcely be surprised at the attitude of the alchemists. Instance in this connection Carey Lea's so-called allotropic forms of silver. Carey Lea has recently prepared, among others, a blue pulverulent form of silver soluble in water, and an insoluble variety of the colour of burnished gold. These interesting bodies are not, it is true, pure silver; yet they contain some 98 per cent, of the precious metal, and would have been startling discoveries in the days when transmutation was regarded as a possibility. Eeference should also be made here to the marvellous effects of great in- dustrial significance produced in the properties of iron by the addition of mere traces of such substances as aluminium, tungsten, &c. The transition from the vague and uncurbed fantasies of alchemy into the true science of chemistry, was marked by the appearance of a work written in the form of a discussion conducted by a symposium of scientific men, and entitled " The sceptical chymist, or chemico-physical doubts and paradoxes touching the experiments whereby vulgar spagyrists 1 are wont to 1 Chemistry was often referred to as the spagyric art, from U JJ L> _U 1) are all constant. A particular case is when A and B, &c., represent elements uniting to form the single compound C, and the law is generally enunciated in terms of this special case as follows : no matter the conditions of formation, or the proportions in which the constituents are taken, a given chemical compound has always exactly the same percentage composition. Most laws (e.g., the gaseous laws of Boyle and Charles) are only true under specified conditions or between certain narrow limits, but the law now under observa- tion is as far as we can tell an absolute and uncon- ditional one. Working with the haloid salts of silver preparing them in many different ways and from different proportions of the ingredients Stas proved the law accurate to 1 part in 10,000 parts, 1 an accuracy 1 An ordinary chemical balance is capable of an accuracy of 1 in 10 6 , and Miller in his elaborate construction of the standard pound attained an accuracy of 1 in 3 x 10 8 , but in Stas' experiments errors considerable in magnitude when compared with those involved in mere weighing, are incidental to the operations of filtering, washing, incinerating, &c. An accuracy of 1 in 10,000 is about that attainable in a simple measure- ment of length. 74 LAW AND THEORY IN CHEMISTRY of high order when we recall the diverse operations involved. Yet the law of definite proportions has had its vicissi- tudes. In the beginning of this century Berthollet denied its truth as above enunciated, asserting that the composition of a body might vary within certain limits, this variation being dependent on the masses in which its constituents were allowed to react l just as recipes with slight quantitative differences will give to all intents and purposes the same culinary product. In this mistaken view he was successfully opposed by Proust, who was led to a warm espousal of the law by the following experiment. Proust analysed native malachite and found that it gave 71 "9 per cent, of cupric oxide. He then dissolved the mineral in acid and repre- cipitated the malachite in an amorphous form. This artificial product gave on analysis 71 '9 per cent, of cupric oxide. Hence Proust concluded that no matter whether malachite is formed in the crystalline condition in the earth's crust, where it is subjected to the influ- ence of mighty secular processes of which we know next to nothing, or whether it is formed artificially and sud- denly in the laboratory, it has in each case identically the same composition. He then showed that the alleged variable nitrate of mercury which Berthollet brought forward to vindicate his attitude, was not a 1 The influence of mass in causing variations in the relative quantities of the products of a change (not of their individual compositions as Berthollet supposed) lies at the foundation of the study of chemical affinity in the modern acceptation of this term. See Pattison Muir, Principles of Chemistry. THE ATOMIC THEORY 75 homogeneous body but a mixture of mercurous and mercuric nitrates, in proportions varying according to the relative masses of mercury and nitric acid brought together. Thus arose the distinction between homo- geneous substances and non-homogeneous substances or mixtures detailed in Chap. III. Passing on now to the law of multiple proportions. Before Dalton's time the fact had been recognised that a given element A will combine with another element B in two or more proportions to form two or more compounds, for each of which the law of definite pro- portions is true. But up to the year 1803, owing to the customary method of stating the results of analysis, no regularity had been detected in the values of the combination masses of A and B as between compound and compound. Dalton analysed the two compounds of carbon and hydrogen, methane and ethylene; as also the two compounds of carbon and oxygen, carbonic oxide and carbonic anhydride, with these results ETHYLENE. 1 METHANE. = 85-71 p.c. H = 14-28p.c. = 75 p.c. H = 25 p.c. or approximately or approximately 6 C! 6 CARBONIC OXIDE. CARBONIC ANHYDRIDE. = 42-86 p.c. O = 57'24p.c. C = 27'27p.c. = 72'72p.c. or approximately or approximately _ 6 ? = J> = 8 16 1 The percentages here given are not the values actually obtained by Dalton. 76 LAW AND THEOEY IN CHEMISTRY No regularity appears between the valves for the two hydrides on the one hand, or the two oxides on the other, until we consider a constant mass of either of the common elements in the two cases, instead of ex- pressing the results in the conventional percentage form. It is then noticed that the amount of hydrogen combined with six unit masses of carbon in marsh gas is exactly 1 double (not 2 J times, nor 1 T Vy times, but exactly double) the amount of hydrogen combined with six unit masses of carbon in ethylene. Similar observations apply to the oxides of carbon, and indeed to all cases where two elements combine in different proportions to form different compounds. In every case the following regularity is observed. If an element A combines with an element B in two or more pro- portions to form two or more compounds, and if in these compounds we consider a fixed mass of either of the elements, say A, then the masses of B combined in the several compounds with this fixed mass of A, are in general so related that the compounds richer in B contain of B masses expressible as whole multiples of the mass of B, contained in the compound poorest in B. This is Dalton's law of multiple pro- portions. 2 1 This exactness is never of course attained in practice, on account of unavoidable errors of observation, but it is more and more nearly realised as we perfect our analytic methods. Hence the assumption is warranted that the relations in question are in reality absolutely exact. The mathematical conception of a limit is here implicated. 2 Some apology for this diffuse enunciation seems called for. In the majority of chemical text-books, the word multiple is never once intro- duced in the enunciation of the law of multiple proportions, its place THE ATOMIC THEORY 77 What explanation 'can be adduced of these laws? 1 Dalton answered, the atomic theory of matter. Admit, he said, that simple matter of every kind consists of little indivisible particles called atoms, that the atoms of one and the same kind of matter have always exactly the same weight and the same properties, but that the weight and other properties of the atoms differ from substance to substance ; that chemical combination consists in the coming together into intimate contact of definite numbers of simple atoms, to form definite compound atoms which in turn are all exactly similar for one and the same compound, bearing, so to speak, the impress of goods stamped by machinery ; then, admitting all this, the fundamental laws of chemistry being taken by the vague, elastic, yet polarised term "simple ratio." In the statement of the law given in the text the attempt has been made to remedy these defects, even at the expense of brevity. 1 In addition to the two laws given in the text, many add a third the law of reciprocal proportions, or the law of combining weights. As a matter of fact, the perception of the numerical relations embraced by this law did not antedate and pave the way for the atomic theory, but this theory established, certain numerical results necessarily fol- lowing from it were grouped together under one or other of the above titles, thus : if AB and AC represent quantitatively two compounds, then any compound of B and C will be represented quantitatively by ?iBmC, where n and m are whole numbers, and A, B, C, the com- bining weights of the elements. Interpreted in terms of the atomic theory, this law may be regarded as stating that the atoms of a given element have a fixed and unalterable mass in all the compounds that element forms. Agl and AglOs might each have fixed composi- tions without the ratio i" being identical in the two cases as theory demands. Stas, in proving to an accuracy of 1 in 10 7 that the ratio --= is the same in both compounds, has placed the atomic theory on a very exceptional experimenta'l basis. 78 LAW AND THEOEY IN CHEMISTEY follow as necessary consequences. 1 It is quite easy to see how the law of definite proportions follows ; let us examine in detail the sequence of the multiple pro- portion law. Suppose matter to be non-atomic, to be infinitely divisible and absolutely continuous. Let the symbol represent a definite mass (expressed numerically by 6) of carbon on this supposition; and the symbol |U represent under the same conditions a mass of hydrogen, numerically expressed by 1. Then ethylene might be represented as 6 m . Now, analysis in- forms us that methane contains relatively more hydrogen than does ethylene. According to the above supposi- tion, the mass of hydrogen combined with 6 unit masses of carbon in methane might quite easily be 1-1-, 1^, llj, or 2yf, &c. times the mass of hydrogen combined with 6 unit masses of carbon in ethylene ; for hydrogen is jelly-like and structureless, and we can imagine a 1 Stallo divides the phenomena of chemical change into three classes. The first "embraces the persistence of weight and the combination in definite proportions ; the second, the changes of volume and the evolu- tion or involution of energy ; and the third the emergence of a wholly new complement of chemical properties." He asserts that the atomic hypothesis is in no sense an explanation of phenomena of the second and third classes, nor does it fully explain those of class i. in the sense of generalising them and reducing many facts to one. It accounts for them by simply iterating the observed fact in the form of an hypo- thesis. He admits, however, " the merits of the atomic hypothesis as a graphic or expository device as an aid to the representative faculty in realising the phases of chemical or physical transformation." See Concepts of Modern Physics, chap. vii. THE ATOMIC THEORY 79 quantity of it of any mass whatever. Given as representing ethylene, the composition e L| would, a priori, be quite as probable for methane as would But now let us take the atomic theory, and for the sake of present argument assume that ethylene con- sists of 1 atom of carbon weighing 6 units, and 1 atom of hydrogen weighing 1 unit. Then, since methane contains more hydrogen relatively than ethylene, it follows that per 1 atom of carbon methane must contain 2, 3, 4 n atoms of hydrogen ; for atoms are the indivisible units of chemistry. Since all atoms of the same simple substance have exactly the same weight, the law of multiple pro- portions necessarily follows ; the amount of hydro- gen per given amount of carbon must necessarily be in methane a whole multiple of its value in ethylene. To sum up the whole matter ; the existence of a multiple law according to the non-atomic theory of matter is a possibility among an infinity of other equally plausible possibilities ; the odds against its existence are infinitely great. But of an atomic theory of matter, a multiple law is an absolutely necessary consequence. That Dalton clearly saw this consti- tutes, perhaps, his greatest claim on the memory of posterity. 8o LAW AND THEORY IN CHEMISTRY We must now follow Dalton in his attempt to find the weights 1 of the atoms of elementary bodies. He did not, of course, hope to determine the absolute weights of the atoms a determination of which even the advanced chemistry of to-day is incapable. All he attempted to do was to find the relative weights of the atoms. He made the hydrogen atom his standard, and arbitrarily called its weight one ; all other atomic weights were stated in terms of this standard. Thus the statement the atomic weight of oxygen is 16 simply means that the atom of oxygen is sixteen times heavier than the atom of hydrogen, whose absolute weight expressed, say in a fraction of a milligram, is unknown. As an aid to the foundation of a system of atomic weights, Dalton framed a series of empirical rules. We cannot dissect out the train of reasoning which culminated in these rules. They are merely the ex- pression of Dalton's own preconceived notions mere guesses, limited only by the condition that compound atoms are of simple rather than of complex structure, being as a rule made up of very small numbers of elementary atoms. Rule 1. If only one compound of two elements can be obtained, the compound must be assumed a binary 2 one, unless there be good cause for 1 In some recent text-books, atomic mass replaces the term atomic weight. In view of the strict proportionality which exists between mass and weight, and in view of the hold the terms weighing and weight have in the speech of everyday life, this innovation seems to me unnecessary. 2 A binary compound, according to Dalton, is one whose "com- THE ATOMIC THEORY 81 some other conclusion. Rule 2. If two compounds of two elements exist, then one is a binary, and the other a ternary, compound. Rule 3. If three compounds of two elements exist, then one is a binary, and the other two are ternary, compounds. Rule 4. If four compounds of two elements are known we should expect two of them to be ternary, one to be binary, and the fourth to be quaternary. Other rules follow, dealing with the specific gravities of binary, ternary, &c. compounds ; but for these, and indeed for Dalton's work on the atomic theory as a whole, the reader is referred to Ostwald's Klassiker der exakten Wissen- schaften, No. 3, or to the Alembic Club Reprints. 1 To illustrate the application of these rules, we may take the case of the atomic weight of oxygen. To Dalton only, one compound of hydrogen and oxygen was known, viz., water. Hence by Rule 1 the com- pound atom of water consisted of one atom of hydrogen in combination with one atom of oxygen. Now it is found by actual experiments that about 8 grams of oxygen combine with 1 gram of hydrogen to form about 9 grams of water ; or, what is the same thing, 8 1 that - milligrams of oxygen combine with mg. of hydrogen to form ^ mg. of water. Let us sup- pound atom" contains only two simple atoms. In the "compound atom " of a ternary body there are three atoms, and so on. 1 These brochures are more generally attainable than the Memoirs of the Literary and Philosophical Society of Manchester, in which Dalton's papers originally appeared. F 82 LAW AND THEORY IN CHEMISTRY pose, simply for the sake of clearness, that a hydrogen atom weighs ^ mg. 1 1 8 3 mg. H combines with 3 mg. 0. or 1 atom H ,, ,, but, by Kule i., 1 atom H ,,1 atom 0. o Therefore 1 atom weighs - mg. So if we agree to call the atomic weight of hydrogen one, the atomic weight of oxygen will equal eight. In a perfectly similar manner Dalton arrived at the result ; atomic weight of nitrogen = 4f. But 16 (=8 X 2) and 14 (= 4f x 3) are at present regarded as the approximately correct values for the atomic weights of oxygen and nitrogen respectively. Why these num- bers are adopted in preference to Dalton's will not be apparent till we have treated of Avogadro's hypothesis. When we attempt to fix by Dalton's rules the atomic weight of such an element as carbon which combines with hydrogen, oxygen, &c., in more than one pro- portion, we find ourselves on the horns of a dilemma. According to Rule 2, either methane or ethylene is a binary body, but the rule does not indicate any means of assuring ourselves which is the binary body. If ethylene be assumed binary, methane will be ternary. Ethylene will be CH, methane CH 2 , and the atomic weight of carbon will be 6. If, however, methane be 1 This very rough approximation is derived from data furnished by the kinetic theory of gases. THE ATOMIC THEOEY 83 assumed binary, ethylene will be ternary. Under this assumption, the formula for methane will be CH, that for ethylene C 2 H, and the atomic weight of carbon will be 3. Which of these two values for carbon are we to select? There is nothing at all in Dalton's rules to guide us in such cases as these. Failing inspired arch- chemists, one is as justified from the premisses in maintaining that the atomic weight of carbon = 3 as another is in championing the value 6. This ambiguity in Dalton's rules led to great diffe- rences of opinion respecting the atomic weights of several of the elements, and ultimately the confusion became so great that many advocated the renunciation of the atomic theory altogether. The light which it indisputably shed on some points did not in the opinion of many compensate for the fundamental uncertainties with which it was hampered, and which it was power- less to resolve. It is, I think, worthy of note that the very cases which in the first instance suggested to Dalton the law of multiple proportions and the atomic theory were exactly those cases in which his elaborated system was found wanting, and which led to its un- popularity and temporary rejection. This indefiniteness, which trammelled the young atomic theory, was finally resolved by the knowledge accruing from a careful study of the physico-chemical properties of gases, to which we now turn. In 1805, Gay-Lussac and Humboldt, investigating the constancy of the amount of oxygen in the atmosphere, 84 LAW AND THEORY IN CHEMISTRY employed an analytic method first proposed by Volta. This method, which has become classical, consists in mixing the air with hydrogen in a eudiometer, ex- ploding the mixture by an electric spark, and then from the contraction which ensues calculating the amount of oxygen present. To apply this method, an accurate knowledge of the contraction which occurs when liquid water is formed from hydrogen and oxygen is obviously essential. After very careful experiments, Gay-Lussac and Humboldt found that one volume of oxygen combines with two volumes of hydrogen to form a drop of water, whose volume in comparison with the volumes of the gases exploded is in general negligible. 2 vols. H + 1 vol. = water with practically negligible vol. Hence it follows that 3 volumes of the properly mixed gases contract to zero volume on explosion. In other words, suppose 2 cubic feet of hydrogen and 1 cubic foot of oxygen (measured at atmospheric pressure), placed in an air-tight vessel 1 and then exploded, the pressure in the vessel would sink from 15 Ibs. per square inch to nearly zero value. I say nearly, for the water formed would vaporise and exert a small pres- sure (or as it is currently but unfittingly called, a tension) dependent as regards magnitude on the tempe- 1 This experiment was actually performed by Cavendish, who was the first to determine the composition of water by volume (see Chap. II. p. 53). Cavendish introduced the gases, hydrogen and oxygen, mixed in the proper proportions into a vacuous globe, exploded the mixture, and found that the vacuum was re-established, so that several successive charges and explosions could be effected with one initial- exhaustion of the globe. THE ATOMIC THEORY 85 rature. From all of this we conclude that the amount of oxygen in a mixed gas is equal in volume to one- third the contraction caused by sparking after an excess of hydrogen has been added. Supposing the water formed from 2 vols. hydrogen and 1 vol. oxygen is changed into the gaseous state by heating it above 100 C. so as to form super- heated steam ; or supposing the whole experiment is conducted throughout at a high temperature, so that the water formed never condenses, what volume-relation would the water gas or steam bear to the volumes of hydrogen and oxygen which formed it ? In answer to this inquiry, Gay-Lussac and Humboldt found that the volume of steam formed is exactly equal to the volume of the hydrogen (or what is the same thing, to twice the volume of the oxygen) exploded. Here Gay-Lussac and Humboldt met with a quan- titative fact which astonished them by reason of the extreme simplicity of the quantities involved. Two cubic feet of hydrogen combine with exactly one cubic foot of oxygen, not with -9 or 1^, but according to Gay- Lussac and Humboldt with exactly 1 cubic foot, of oxygen to form, not 2 T ^Q, but exactly 2 cubic feet of steam at the same temperature. 1 1 Although we assert in the text the exactness of the ratio 2:1, yet it seems well nigh impossible to prove this exactitude experimentally. Scott and E. W. Morley, employing all the refinements of modern methods, have repeated Gay-Lussac and Humboldt's experiment with the following result : 2*00245 vols. of hydrogen combine with 1 vol. of oxygen (Scott). 2-0023 (Morley). However, in all the theoretical deductions which follow, any slight 86 LAW AND THEORY IN CHEMISTRY The question suggests itself, does a similar simple relationship in the reacting volumes manifest itself in other cases of gaseous combination ? It does. 1 vol. of hydrogen combines with exactly 1 vol. of chlorine to give 2 vols. of hydrochloric acid gas. 1 vol. of nitrogen combines with exactly 3 vols. of hydrogen to give 2 vols. of ammonia gas. 2 vols. of nitrogen combines with exactly 1 vol. of oxygen to give 2 vols. of laughing gas. 1 vol. of carbonic oxide combines with exactly 1 vol. of chlorine to give 1 vol. of phosgene gas. Several other instances might be adduced of Gay- Lussac's Law of Volumes, which states that in homo- geneous gaseous reactions (i.e., reactions in which all the factors and products of the change are gaseous) all the volumes involved are in such simple relationship that the ratios can in every case be expressed in terms of the first six digits. 1 Just as the law of multiple proportions called forth an explanation, so it was not long before the why and wherefore of Gay-Lussac's law was under discus- sion. The outcome of this discussion was the conjee- deviations from simplicity which may possibly exist in the ratios of the combining volumes of gases will be disregarded, and the law of volumes will be accepted as strictly true. 1 It should be noticed that when the factors of a homogeneous gaseous reaction are elements, the volume of the resulting compound is, with very few exceptions, always 2, provided the volume equation be throughout reduced to its simplest terms. The formation of phosphine from its elements furnishes an example of the exceptions referred to. P 4 + 6H 2 = 4PH 3 1 vol. + 6 vols. = 4 vols. THE ATOMIC THEORY 87 ture 1 accepted by several chemists, but first definitely enunciated by Berzelius, that equal volumes of gases contain equal numbers of atoms, and hence that the atomic weights of gases are proportional to their specific gravities. 2 In view of the identical behaviour, qualitatively and quantitatively, of different gases when subjected to pressure and temperature changes, this conjecture seemed very plausible. The laws of Boyle and Charles seem absolutely to demand some such iden- tity in mechanism of the various gases as is implied in Berzelius' conjecture. But apart from this considera- tion, it cannot be denied that the human mind has a peculiar and inherent bias for the uncomplicated, and it is probable that the extreme simplicity of the explana- tion was one of the most potent factors in securing for it a general acceptance. Dalton and his school, however, absolutely refused to accept Berzelius' interpretation of the law of volumes, maintaining that the atomic weights could be deter- mined only from " the ponderable relation of elements 1 Berzelius' interpretation of the Law of Volumes seems scarcely to merit the title of an hypothesis, which " is any supposition we make in order to endeavour to deduce from it conclusions in accordance with facts which are known to be real." 2 Since the specific gravities of oxygen and nitrogen, referred to hydrogen as standard, are respectively 16 and 14, it follows that these values were adopted by Berzelius for the relative atomic weights of these elements. It should be remarked that at first Berzelius regarded the data derived from the law of volumes as belonging to what he called " volume atoms " or "elementary volumes." These he conceived of as something fundamentally distinct from Dalton's atoms. After a time, however, he returned to the Daltonian conception of atoms and applied to these the results following from his hypothesis. See Wurtz, The Atomic Theory, pp. 43-48. 88 LAW AND THEORY IN CHEMISTRY in combination," i.e., from purely analytic data. As an argument against this interpretation, those cases of gaseous combination which occur without change of total volume were adduced. 1 vol. hydrogen combines with 1 vol. chlorine, forming 2 vols. hydrochloric acid gas. Assume that the volume of hydrogen considered is so small that it contains only one atom ; then, accepting Berzelius' conjecture, the equal volume of chlorine with which it combines will contain only one atom, and the double volume of hydrochloric acid gas formed will contain two compound atoms. Now each of these compound atoms must contain at least one hydrogen atom and one chlorine atom. Therefore the two com- pound atoms together must contain at least two atoms of hydrogen and two atoms of chlorine. But we only started with one atom of hydrogen and one atom of chlorine. Therefore matter has been created an absurd conclusion in view of all the proofs that exist of the conservation of matter. 1 Berzelius was bound to admit the justness of this reductio ad absurdum, and in order to meet it emphasised the fact that his so-called hypothesis only extended to the elementary gases, and not to compound gases and 1 A neat but indirect proof of the principle of the conservation of matter is furnished by the constancy of the length of the year. This depends on the masses of the earth and sun. If the masses of the earth were continually changing by reason of the chemical changes taking place, then some alteration in the length of the year would have been produced within historic time. THE ATOMIC THEORY 89 vapours. In this form he continued to make a neces- sarily restricted use of it for the determination of atomic weights. Of Berzelius' work in this direction we shall have occasion to speak later. Just about this period in the history of the atomic theory (1813), an Italian chemist, Avogadro, pointed out that the whole of the differences between Dalton's and Berzelius' attitudes towards the law of volumes would disappear if chemistry would but admit into its philo- sophy a new order of particles of a higher grade of organisation than the atoms. These particles he called molecules, and postulated that all the molecules of the same substance are identically similar, and in general consist of an assemblage of atoms, even in the case of simple gases. Heretofore a radical distinction had existed between the constitution of a simple, and that of a compound, gas. A mass of oxygen was pictured as an assemblage of atoms, each with perfect freedom, and completely independent of its neighbours. In a compound gas, such as hydrochloric acid, on the other hand, the particles enjoying this individuality and freedom were not single atoms else the gas had been a mere mixture of hydrogen and chlorine but atom complexes. Each atom of hydrogen kept perpetual company with an atom of chlorine, the combination forming a discrete and independent particle of the gas. Avogadro asserted that this distinction between the simple and compound gases was unwarranted. He regarded both hydrogen and chlorine as, in a sense, 90 LAW AND THEOEY IN CHEMISTRY compounds ; the one was to him hydride of hydrogen, the other chloride of chlorine. The freely moving and independent particle of hydrogen gas was not a single atom, it was an atom complex. The only difference between a simple and a compound gas is that the atom complex of the former is made up of similar, that of the latter of dissimilar, atoms. Having premised so far, Avogadro then concluded that equal volumes of all gases, simple and compound, contain under similar conditions of temperature and pressure the same num- ber of molecules. This conclusion is generally known as Avogadro 's " hypothesis." ] As will be readily noticed, it is nothing else than Gay-Lussac's conjecture with one word changed molecules replaces atom. In 1814, Ampere independently came to precisely the same general conclusion with regard to the struc- ture of gases, simple and compound. It is easy to see that those instances of gaseous combination wherewith Dalton combated Berzelius' interpretation of the law of volumes involve no in- consistencies when interpreted in the light of Avogadro 1 Avogadro's " hypothesis " is sometimes erroneously stated in the form : All gaseous molecules under like conditions have the same size. What is really meant is that all molecules have the same sized spheres of action, which they occupy and dominate to the exclusion of other molecules. A compact square of fifty soldiers armed with rifles would, in a certain sense, dominate the same extent of country as twenty- five soldiers armed with the same rifles, although the size of the actual squares would be different in the two cases. It may here be stated that Avogadro's generalisation is strictly true only for perfect gases. The ratio of the number of molecules in equal volumes of oxygen and hydrogen at ordinary temperatures and pressures is about 100,020: 100,000. THE ATOMIC THEORY 91 and Ampere's views. The volumetric relations of hydrochloric acid gas merely prove that the molecules of hydrogen and chlorine must contain at least two atoms each. 1 Yet the times were not ripe for this great generali- sation which to-day, under the title Avogadro's law, stands the very foundation and framework of theoretical chemistry. It attracted but little attention at the time of its birth, and soon fell into an oblivion from which 1 The general introduction of these conceptions of the structure of elementary gases at a later period in the history of chemistry, threw a new light on the phenomena of substitution which for a time enjoyed a special prominence. In the formation of a halogen derivative of a hydrocarbon, it had up to date been necessary to ascribe different roles to the admittedly perfectly similar atomic units of the halogen. For instance, in the formation of monochlor-methane, it was held that an atom of chlorine first replaced an atom of hydrogen in the hydro- carbon CH 4 + Cl = CH 3 C1 + H, and then a second atom of chlorine combined with the liberated hydro- gen atom H + Cl = HC1. In other words, substitution was regarded as a complex chemical change taking place in two stages, the chlorine atom in each stage playing a different chemical role. But when it was admitted that the smallest portion of chlorine entering into chemical reaction is a molecule con- taining two atoms, then halogen substitution was seen to be a pure case of double decomposition, impossible of resolution into two con- secutive stages, and recalling in its main features exactly the substi- tution brought about by the action of compound bodies such as nitric acid. The two reactions CH 3 H + C1.C1 = CH 3 C1 + HC1. C 6 H 5 H + OH.NOo = C 6 H 5 N0 2 + HOH. were seen to be quite analogous. It was no longer necessary to ascribe different roles to the smallest individual particles of the halogens. 92 LAW AND THEORY IN CHEMISTRY it was rescued some forty years afterwards by Gerhardt and Laurent. In the year 1818, Dulong and Petit, experimenting on the specific heats of the elements in a solid state, discovered a most striking numerical relation between these values and the atomic weights of the respective elements. The numerical value of the atomic weight of an element multiplied by the value of its specific heat gave, in general, a constant product equal to about 6'25. The limitation "in general" is advisedly introduced, because certain of the current atomic weights did not satisfy this relation. On the strength of the comparatively large number of atomic weights which did satisfy their law, Dulong and Petit pro- nounced inaccurate all those which did not, thus virtually asserting the universality of their law, and establishing it as a powerful instrument for atomic weight determinations. They recognised the arbitrari- ness of the methods of determining atomic weight then in vogue ; for these made the choice of one par- ticular value out of a series, bearing a simple multiple relationship to each other, a matter of, we might almost say, individual taste. In a small annex to a certain kitchen in the city of Stockholm, Dulong and Petit's law was warmly wel- comed. In this kitchen (which has been referred to as one of the magnetic poles of the chemical world), assisted by his cook and equipped with culinary utensils rather than with what we now understand by apparatus, worked one whose name, Johann Jacob Berzelius THE ATOMIC THEOEY 93 (1779-1848), is one of .the greatest on the honour rolls of science. From the very beginning of his scientific career, Berzelius interested himself chiefly in atomic weight determinations. To convert his analytic results into values for the atomic weights, he at first made use of (1) certain rules recalling in their arbitrariness those of Dalton, (2) the law of volumes already mentioned, and (3) his so-called oxygen law. 1 Afterwards he employed in addition to these (4) the law of Dulong and Petit, and (5) the generalisation of Mitscherlich, which has of late years proved itself the very reverse of general. At the outset, Mitscherlich believed that the correla- tion between crystalline form and composition was such, that a mere equality in number of the simple atoms in the compound atoms of two substances, necessitated an identity in the crystal forms, or an isomorphism of the two substances ; and vice versa, that isomorphism necessarily existed between substances whose compound atoms were built up by the same number of simple atoms. The discovery of poly- morphism (the crystallisation of one and the same substance in different forms), however, compelled the 1 Berzelius regarded salts as dual compounds of acid oxide or negative constituent, and basic oxide or positive constituent. Sulphate of soda was written * The oxygen law stated that in all the salts of a given acid the amount of oxygen in the negative constituent bore a constant ratio to the amount present in the positive con- stituent. This law had been previously recognised by the German chemist Richter, who, however, had expressed himself rather obscurely on the point. 94 LAW AND THEORY IN CHEMISTRY admission that atomic complexity alone was not the whole explanation of isomorphism, but that the arrange- ment of atoms must be taken into account. Further, the fact had to be admitted that in the majority of cases the forms of crystals of similarly constituted bodies are only approximately the same, not absolutely identical. Indeed, absolutely perfect geometric iso- morphism is only found in the cases of bodies crys- tallising in the cubic system. Hence Mitscherlich's generalisation in its final form was not the clear-cut and unequivocal statement that it was in its original enunciation. The final statement ran as follows : If the compound atoms of two or more chemically analogous bodies be composed of the same number of simple atoms (no matter the nature of the latter), then the crystals of these bodies will have identical or nearly identical forms. 1 1 Recent research has adduced many exceptions to this elastic gene- ralisation, both in its direct and converse forms. The three dinitro- benzenes belong to the same chemical type, and have all the same atomic complexity ; yet they have so little analogy of form that it would be an obvious overstretching of the term to call them iso- morphous. The exceptions to the generalisation in its converse form are grouped together under the titles isogonous or homeomorphous bodies. Such bodies, while differing greatly in chemical behaviour and even in molecular complexity, are nevertheless isomorphous, e.g., PbCl-2 and Sn(CH 3 ) 2 Cl 2 are isomorphous, as are also KHSO4 and KAlSi 3 O 8 . It is clear throughout that the term isomorphous, which was originally a definite and definable term, is now indefinite and ^indefinable. What degree of similarity in the geometrical forms of crystals is necessary in order that the crystals fall in the category, isomorphous, is a question which chemists are undecided about. They prefer to judge of isomorphism by a series of chemico-physical tests rather than by purely crystallographic considerations. Two substances, A and B, crystallise in the same system with nearly the same forms THE ATOMIC THEORY 95 So marvellously did Berzelius balance probabilities, so carefully did he make use of analogy, so skilfully did he manipulate his roughly improvised apparatus, that his final table of atomic weights (1826), when reduced to the hydrogen standard, 1 shows remarkable agree- and angles. Are they isomorphous ? If they show the same cleavages, similar thermal conductivities, similar etched figures, approximately equal specific volumes ; if a crystal of A grows regularly in a solution of B, or vice versa ; if a crystal of A causes crystallisation in a super- saturated solution of B, or vice versd ; and if mixed solutions of A and B give homogeneous mixed crystals, then the answer is most decidedly yes. It is not a sufficient criterion of isomorphism that one only of these conditions is satisfied, just as an element cannot in general be classified as a metal or a non-metal from the investigation of a single property. For a good account of isomorphism, regarded as a branch of morphotropy (the general study of the inter-relation of chemical composition and crystalline form apart from considerations of similarity in the latter), see Hutchinson's article, "Isomorphism," in Watts Dictionary of Chemistry, vol. iii. ; also Mendeleeff, Principles of Chemistry, vol. ii. p. 7. 1 Berzelius regarded oxygen as the most important chemical element the pole of chemistry. He therefore adopted the oxygen atom as the basis of his atomic weight system, giving it the arbitrary value 100. Modern chemistry has rather favoured Dalton's choice of the hydrogen atom as standard atom with the arbitrary value 1. Quite recently, however, the question of making oxygen the standard element again, assigning it the arbitrary atomic weight 16, has been much discussed. There is much to be said in favour of the return. The values of a large majority of the atomic weights involve an accurate knowledge of the atomic weight of oxygen. Unfortunately the determination of the atomic weight of oxygen referred to H = 1 is an extremely difficult chemical task, and new results differing often in the first decimal place are continually demanding recognition. Every adoption of a new value necessitates the alteration of the atomic weights of all those elements whose oxy-compounds have furnished the necessary analytical data. If O = 16 were universally adopted as the standard, the only atomic weight that need be affected by new data for the composition of water would be that of hydrogen ; and for all practical purposes the changes it would undergo might with safety be overlooked and the value 1 steadily adhered to. A small change in the accepted value of the 96 LAW AND THEOKY IN CHEMISTRY ments with the values for the atomic weights current to-day. To this statement we must, however, make three well-defined exceptions, viz., potassium, silver, and sodium. Lacking the data for the application of the law of specific heat in these three cases, values almost exactly twice too great were assigned to the atomic weights of these elements. I would emphasise the fact that Berzelius made use of no one universally applicable guide in constructing his system of atomic weights. He applied to the results of analysis sometimes one, sometimes another, of the five methods above given, and in cases of doubt he selected with something akin to inspiration. One is almost tempted to say that Berzelius was lucky. Despite the great renown of Berzelius as an analytical atomic weight of oxygen may involve quite a large change in the values of other atomic weights, or it may involve none at all. The following approximate values necessary for the determination of the atomic weight of barium by Struve's method are instructive. Struve deduced the atomic weight of barium from the ratio BaClo : BaSO 4 :: 100 : ] 12'1, assuming values for the atomic weights of Cl, O, and S. = 16 = 15-96 (1) Molecular weight of KC1 deduced from } ~,.~ ^.oo reduction of KG 10 3 . . . . ( ' 4 (2) Atomic weight of Ag deduced from ratio ) in^.g 107 '4 Ag : KC1 \ (3) Molecular weight of AgCl from the reduc- ) 149.9 142-5 tion of AgC10 3 . . . 1 (4) Atomic weight of Cl (= mol. wt. AgCl- | o^.^ 35.1 at. wt. Ag) i (5) Atomic weight of S from ratio Ag : Ag 2 S0 4 31 '1 30 '9 (6) Atomic weight of Ba .... 135'6 132-66 An initial error in the atomic weight of oxygen of | per cent, is multiplied up into a percentage error of 2*2 in the atomic weight of barium as determined by Struve. THE ATOMIC THEORY 97 chemist of the highest rank, many refused to accept his estimates of the atomic weights, not only because they differed in many instances from those upheld by the school of Dalton, but also on account of the discovery of inaccuracies and inconsistencies inherent in the system itself. Using Berzelius' value for the atomic weight of carbon, 12 '2, many anomalies had been noticed in the results of organic analysis. The atomic weight of this element was therefore redetermined by Dumas and others, with the result that the Berzelian value was found -2 too high. This discovery not only shook the confidence of some of Berzelius' disciples in their master, but was made by his opponents the occasion of heaping all manner of sarcasm and unjust criticism on the great Swedish chemist. But perhaps Dumas' work on the vapour densities of elements which are solid or liquid at ordinary tem- peratures (1827) did more to bring the Berzelian system of atomic weights into discredit than did the detection of a If per cent, error in the atomic weight of carbon. Berzelius had arrived at the values Hg = 200 and P = 31 for the atomic weights of these elements by a combination of some of the methods above indicated. But Dumas found that the vapour of mercury is only 100 times heavier than that of hydrogen under the same temperature and pressure conditions ; while the vapour of phosphorus is 62 times heavier than that of hydrogen. Therefore if, as Berzelius had maintained, equal volumes of gases contain equal G 98 LAW AND THEORY IN CHEMISTRY numbers of atoms, then the atomic weights of mercury and phosphorus must be respectively 100 and 62. If, on the contrary, Berzelius' values were the true ones, then his interpretation of the law of volumes an inter- pretation lying at the very foundations of his atomic weight system must necessarily lack generality. The atomic weights of mercury and phosphorus being re- spectively 200 and 31, a given volume of mercury vapour can only contain half as many atoms as the same volume of hydrogen ; while a given volume of phosphorus must contain twice as many atoms as the same volume of hydrogen. The atomic theory now enters upon the most troub- lous period of its career. So many different values for the atomic weights of the elements were compet- ing with each other for general acceptance, and so vanishingly small did the chances of any universal agreement on the subject appear, that it was proposed to do away with the atomic theory and its attendant uncertainties altogether, and to return to a system of constants (with suitable notation) for the elements, which constants, being simply the numerical expressions of ascertained facts, could involve no doubt and admit of no uncertainty. This new system, which was to bring peace and prosperity in its wake, was called the equivalent system, and was pioneered by Wollaston. According to Wollas- ton the symbol of an element was to represent that mass thereof which combines with unit mass of hydrogen a pure number expressing the result of an experi- THE ATOMIC THEORY 99 ment, nothing more. 1 The numerical value of this mass he called the equivalent number, or simply, the equivalent of the element. Just as those quantities of acids which neutralise, i.e., combine with, a fixed quantity of base are equivalent, so those quantities of the elements which combine with a fixed mass of hydrogen were also regarded as equivalent. Yet this new system, seemingly so simple and un- equivocal in its inception, soon had to encounter difficulties as great as any that had ever beset the atomic theory. Only a few of the elements could be made to combine with hydrogen directly to form hydrides ; how then were the equivalents of the remaining elements to be determined ? One unit mass of hydrogen combines with 35 J unit masses of chlorine, and chlorine can be made to combine with nearly all the elements that do not form hydrides. Here then seemed a way out of the difficulty; the equivalent of an element was taken to be that mass thereof which combines with unit mass of hydrogen, or 35J unit masses of chlorine. 2 But unfortunately in cases where an element combines 1 As a matter of fact, Wollaston's standard of equivalency was not unit mass of hydrogen, but ten unit masses of oxygen. This, however, does not in any way affect the line of argument in the text (see note 1, p. 95). 2 It is to be observed that the equivalent of any element may be determined as well by investigating the mass of hydrogen which a given mass of the element replaces, as by finding the mass of hydrogen with which a given mass of the element combines. For every combi- nation of an element with chlorine, bromine, &c., may be regarded as a substitution product of hydrochloric acid, hydrobromic acid, &c. ioo LAW AND THEORY IN CHEMISTRY with both chlorine and hydrogen, the equivalent de- duced from the chloride does not always coincide with that deduced from the hydride. Again some elements, notably carbon, form numerous compounds with hydro- gen (methane, ethane, ethylene, &c., in the case of carbon), and each of these compounds would give a different value to the equivalent for carbon. Who was to decide which particular compound was to be selected for fixing the value in question? That an element should be possessed of several equivalents seemed a pure contradiction in terms. Further complications arose when Gmelin and Gay- Lussac attempted to make equivalent the formulas of all compound bodies, including the most important class of salts. 1 As long as the terms equivalent, or equivalent weight, are restricted to acids and bases among compound bodies, they have perfectly clear and definite meanings, and are still employed in this con- nection in modern volumetric analysis. But it is hard to appreciate the application of the terms to salts. However, this application was made in different ways by different chemists, with the result that instead of applying the equivalents of the elements deduced from hydrides, chlorides, &c., to transform the results of analysis of compounds into formulas for these com- 1 Here the idea of equivalency is somewhat changed. " AgO.S0 3 , and NaO, 80s, are equivalent, not because they have equal powers of displacement or combination with regard to any criterion, but because they are the results of the union of bodies in such proportions that the equal powers of combination of the constituent parts were satisfied in the act of combining." THE ATOMIC THEORY 101 pounds, the problem was often reversed, and the equivalents of the elements were deduced from pre- sumed equivalences between salts. 1 The values obtained in this way did not in general agree with those directly obtained from analysis of hydrides, chlorides, &c. Thus both the values 4f and 14 for the equivalent of nitrogen found supporters ; while the equivalent of phosphorus was either 10J, 15 4 5, or 31. It is almost impossible for us now to appreciate fully the reasoning of the chemists of this period. The confusion of ideas which prevailed, 2 the gratuitous 1 See Wurtz, The A tomic Theory, p. 71, et scq. 2 Here it may be well to distinguish between the three terms com- bining weight, equivalent, and atomic weight. The idea of combining weights was associated with, and early recognised as a necessary consequence of, the atomic theory (see note 1, p. 77). The atomic weights were either numerically equal to, or whole multiples of, certain characteristic numbers called combining weights that could be assigned to the elements from analyses of their compounds, quite independently of any assumptions or suppositions. Hence it would seem that the terms combining weight and equivalent mean essentially the same thing ; they do. The only difference between them is a chronological one. The equivalent notation came after the atomic theory, and was in- tended to be independent of it. It was an attempt to replace what up to date had proved itself from a chemical standpoint an unsatisfactory theory. Combining weights had their names changed to equivalents when the atomic theory had been weighed and found wanting. The reason for this change in nomenclature is not far to seek. It is an epitomised history. The atomic weights of the Daltonian school were in many instances numerically equal to the combining weights assigned to the elements, and the two terms, though radically distinct, thus came to be used more or less synonymously. Wollaston, in proposing the name equivalent weights for the constants of his new system, was simply desirous of avoiding a term which had become, quite wrongly, more or less identified with a theory. The term equivalent was to connote fact, and fact alone. The difference between the terms atomic weight on the one hand, 102 LAW AND THEORY IN CHEMISTRY assumptions which flourished, and the reckless use of the analogic method, combine to render its history one of the most unsatisfactory and bewildering pieces of modern scientific literature. Owing to the numerical coincidences in many cases of the atomic weights and the equivalents of the elements, the two terms, though fundamentally so distinct in their connotations, came to be used indifferently and synonymously. 1 It was Gerhardt and Laurent who, resuscitating the long-eclipsed hypothesis of Avogadro, led the way out of this confusion worse confounded. The equivalent system presented to the mind of Gerhardt great in- consistencies, which, in his opinion, could only be and equivalent or combining weight on the other, is more fundamental than the purely chronological one distinguishing equivalent from com- bining weight. The term atomic weight implies a theory of the structure of matter, the other two terms do not. The atomic weight of chlorine is 35'5 ; its equivalent or combining weight is also 35*5. The former statement calls up the following mental picture. Chlorine gas is made up of a number of indivisible ultimate particles called atoms equal among themselves, and each 35^ times as heavy as the similar ultimate particles of which a mass of hydrogen consists. Whereas the latter statement simply implies that a mass of chlorine weighs 35^ times as much as the mass of hydrogen with which it chemically combines. Though all idea of an equivalent notation is now abandoned, the terms equivalent and combining weight are still used, but now synonymously to denote the smallest mass of an element that combines with unit mass of hydrogen, or 35^ unit masses of chlorine, or with (approximately) 8 unit masses of oxygen. Indeed it will be shown further on that the equivalent, as thus defined, really determines the final value adopted for the atomic weight of an element. 1 Even as late as the year 1834 we find a committee of the British Association for the Advancement of Science passing the following reso- lution : "We are of opinion that it would save much confusion if every chemist would always state explicitly the exact quantities which he intends to represent by his symbols. " THE ATOMIC THEORY 103 removed by a partial return to the Berzelian system of atomic weights. The inconsistencies that especially appealed to Gerhardt were something of this nature. The equivalents of carbonic anhydride and water being represented as C0 2 and HO respectively (C = 6, = 8), Gerhardt noticed that when these substances were pro- duced in reactions involving organic bodies, they always appeared in such relative quantities that the accepted equivalents of the organic bodies could never be repre- sented as giving rise to a single equivalent, but always to 2, 4, or more equivalents of the oxides of carbon and hydrogen. Thus the interaction of acetic acid and sodium car- bonate was represented as follows C 8 H 8 8 + 2 NaC0 3 - C 8 H 6 8 Na 2 + 2 C0 2 + 2 HO. It seemed incongruous and unnatural that organic bodies should be so differently constituted from in- organic ones as to be incapable of furnishing single equivalents of water and carbonic anhydride when undergoing chemical transformations. Gerhardt there- fore proposed a return to the Berzelian values C = 12, = 16, S = 32. Adopting these values, the difference noted between organic and inorganic substances dis- appears. The formulae for the equivalents of water, sodium carbonate, and acetic acid become now H 2 0, Na 2 C0 3 , and C 4 H 8 4 respectively. The formula for the equivalent of carbonic anhydride still remains C0 2 , the equivalent weight being, however, doubled. The 104 LAW AND THEORY IN CHEMISTRY equation representing the interaction between acetic acid and sodium carbonate now takes the form C 4 H 8 4 + Na 2 C0 3 = C 4 H 6 Na 2 4 + C0 2 + H 2 involving only single equivalents of carbonic anhydride and water. But there still remained in Gerhardt's opinion a want of uniformity in the equivalent notation. He noticed that the current formulae representing the equivalent weights of compounds were not strictly comparable, in that quantities of bodies correspond- ing to their formulas expressed in grams, 1 say, did not occupy the same volume when converted into the gaseous state under similar conditions. Thus, C0 2 , C 4 H 12 2 , and C 4 H 8 4 were the accepted formulas for the equivalents of carbonic anhydride, alcohol, and acetic acid respectively. Volume in gaseous state (re- TTI i 4. -m \^4- duced to and 760 mm.) of Equivalent Weight. equivalent weight expres ' sed in grams. C0 2 .... 44 22-4 litres C 4 H 12 2 ... 92 44-8 C 4 H 8 4 ... 120 44-8 Now Gerhardt proposed to make such alterations as were necessary to reduce all formulae to a common gaso- 1 Of course the interpretation of formula) in grams is quite arbitrary, but so long as we are ignorant of the absolute weight of the hydrogen atom we cannot fix the absolute weights of compound atoms. What we practically do is to make the conveniently simple and concrete supposition (which we know to be far from true) that the hydrogen atom weighs 1 gram, and the compound atoms of carbonic anhydride, alcohol, and ether, 44 grams, 92 grams, and 120 grams respectively, THE ATOMIC THEORY 105 metric standard. Those masses of substances were to be equivalent which occupy the same volume in the gaseous state, and the formulae representing the com- positions of these masses were to be the equivalent formulas. It is evident that this reform of Gerhardt's is nothing else than a return to Avogadro's " hypo- thesis." Laurent clearly recognised this, and impressed on Gerhardt the advisability of replacing the term equivalent by molecule when it has reference to com- pounds ; and by molecule or atom, as the case may be when it is used in connection with elements. Hence- forth Laurent's nomenclature will be observed. Although Gerhardt returned to the Berzelian atomic weights, yet it is interesting to remark that considera- tions, not of an atomic structure of matter, but of an equivalence, physical rather than chemical in its nature, lay at the foundation of his reform, which ultimately resulted in the complete abandonment of the equivalent system so called. The question as to which formulae he was to alter next presented itself to Gerhardt. Was he to double the formula of carbonic anhydride so as to make the smallest particle, conserving all the properties of the substance in mass, occupy the same volume as did the accepted molecule of alcohol. Or was he to halve the formula of alcohol so as to make its molecule occupy the same volume as the accepted molecule of carbonic anhydride ? To settle this question he had to determine what volume a standard molecule, such as that of hydrogen, occupies. From the volumetric com- io6 LAW AND THEOKY IN CHEMISTRY position of hydrochloric acid gas, it follows that the molecules of hydrogen and chlorine must each contain an even number of atoms ; two at the least. That the hydrogen molecule does not contain more than two atoms is proved by the fact that hydrochloric acid is a monobasic acid, and only under most exceptional con- ditions forms sodium and potassium salts containing hydrogen. 1 Hence the molecular weight of hydrogen is 2, and, availing ourselves of the convenient supposition for theoretical purposes of note 1, p. 104, we may provision- ally say that it weighs 2 grams. But it is a well- established constant that one litre of hydrogen under standard temperature and pressure weighs '0896 grams. Therefore 2 grams of hydrogen will under these conditions occupy 224 litres. Hence it follows that carbonic acid has the right formula, and that the formulae of alcohol, acetic acid, and organic bodies generally must be halved. 2 1 Suppose for an instant that the molecule of hydrogen is tetratomic. Then the formula of hydrochloric acid would be fL 2 C\x, and it would necessarily be either a dibasic acid forming two sodium salts or a mono- basic acid forming under all conditions salts of the type M'HCl^, where M is a monovalent atom or radicle. We have no good proof that the molecule of chlorine is not of higher atomicity than 2. However, chlorine is chemically very analogous to iodine, and it seems almost certain, from specific gravity determinations carried out on the vapour of this body through a wide temperature range, that its molecule does not contain more than 2 atoms. 2 The doubled formulae of organic bodies generally was due (1) to the fact that these formulse were in many cases derived from analyses of silver derivatives, and Berzelius' value for the atomic weight of silver was twice too great ; (2) to the fact that certain views (embraced under the title dualism) held at this period regarding the constitution THE ATOMIC THEORY 107 Gerhardt's proposed reform did not, however, meet with general acceptance till after the brilliant work of Williamson on the ethers. This research incontestably showed by purely chemical reasoning the necessity for halving the formula of alcohol in accordance with Gerhardt's views, i.e., in accordance with the hypo- thesis of Avogadro. Starting with ethyl alcohol, Williamson hoped to pre- pare therefrom an alcohol of higher molecular weight. To this end he first treated ethyl alcohol with potassium and then with ethyl iodide. Contrary to expectation, the product was not an alcohol at all, but ordinary ether C 4 H 10 0. This is inconsistent with the formula C 4 H 12 2 for ethyl alcohol ; for if the latter body contains per molecule twice as much oxygen as ether, then the product of the above reactions ought to have contained twice as much oxygen as ether, because there has simply been replacement of H by C 2 H 5 . The only way out of this difficulty appeared to be the representation of alcohol by the halved formula C 2 H 6 0. Alcohol. Ether. 2 H 5 I o C 2 H 5 I Hj C 2 H 5 j of bodies and the mechanism of chemical changes demanded the double formulse for their expression. For details, see Meyer, History of It follows that Gerhardt's halving of the molecular weights of acetic acid, alcohol, &c., necessitated the halving of the Berzelian values for the atomic weights of silver and the alkali metals. Unfortunately Gerhardt carried his views to an extreme, and, without good warrant, halved the atomic weights of twenty-three other elements, an error which was afterwards pointed out and rectified by Cannizzaro, who applied to the cases in question Dulong and Petit's law of specific heat, io8 LAW AND THEORY IN CHEMISTRY True, a representation of this special formation of ether could be given in terms of the doubled formula, thus 2KI But according to this mode of representation, a mixture of methyl and ethyl ethers ought to result if methyl iodide were used instead of ethyl iodide. C 2 H 6 I 2 = C 4 H 10 + C 2 H 6 4 2 KI, (ethyl ether) (methyl ether) As a matter of fact, however, a single ether a so- called mixed ether and not a mixture of two ethers is the result ; and this can only be adequately repre- sented in terms of the formula C 2 H 6 for alcohol. (ethyl methyl ether) Accordingly the molecular weight of alcohol was halved, and thereupon the Gerhardt-Avogadro hypo- thesis began to grow in general favour, and to acquire that recognition which to-day classes it as the most important instrument for the determination of atomic weights. Before demonstrating the use of the Gerhardt- Avogadro generalisation in the determination of atomic weights, we must first throw it into a more convenient equational form. THE ATOMIC THEORY 109 X Y w grams w' grams n molecules n molecules Let H represent a volume of hydrogen weighing 1 gram. Let X and Y represent equal volumes of other gases x and y, weighing respectively w and w' grams. Let there be n molecules of hydrogen present in the volume H ; then, assuming the truth of Avogadro's generalisation, there will be n molecules of x in the equal volume X and n of y in the equal volume Y. Now the specific gravity 1 of x (referred to hydrogen as standard) is obviously w. And the specific gravity of y is w'. Further, the weight of one molecule of x must be grams, and the weight of one molecule of y must be Hence n Molecular weight of x _ n _ w _ Specific gravity of x. Molecular weight of y w>_ w' Specific gravity of y. In other words, Avogadro's generalisation may be re- 1 In chemistry, the term " vapour-density " is generally used when " specific gravity of vapour " is really meant. Density is simply mass per unit volume ; it is of two dimensions. Specific gravity is the ratio of the density of a body to that of some standard substance. The number expressing its value for any given substance is a pure number and has therefore no dimensions. i io LAW AND THEORY IN CHEMISTRY stated in the form: the molecular weights of gases vary directly as their specific gravities. 1 Since x and y are any two gases whatever, let y represent hydrogen. Then- Molecular weight of x Specific gravity of x. Molecular weight of hydrogen Specific gravity of hydrogen. Molecular weight of x __ Specific gravity of x. ~~2~ 1 or, molecular weight of x = 2 x specific gravity of x. If, as is frequently the case, air be taken as the stan- dard of specific gravity, the above equation becomes Molecular weight of x = 2 x 14-44 x specific gravity of x, = 28 '88 x specific gravity of x, air being, bulk for bulk, approximately 1444 times heavier than hydrogen. Having now thrown Avogadro's generalisation into a numerical and equational form, we proceed to apply it 1 Avogadro's law admits of still another mode of expression. The gaseous laws of Boyle and Charles are succinctly summed up in the equation pv = RT. Where p is the pressure, v the volume, and T the absolute temperature of a given mass of any gas, R is a constant depending (1) on the mass of the gas taken, and (2) on the nature of the gas. However, if we agree to apply the equation in all cases to masses of gases equal to their Avogadrean molecular weights interpreted in grams, then R no longer varies from gas to gas, but has the constant approximate value, 84,700 (the pressure being expressed in gravitation units grams per square centimetre). THE ATOMIC THEORY in to the determination of an atomic weight, say, to the determination of the atomic weight of oxygen. I. II. III. IV. V. Carbon monoxide . 42-86C : 57 '140 14 28 12 C : 16 Carbon dioxide . ' 27 '27 C : 72730 22 44 12 C : 32 Osmic oxide . . 74 '93 Os : 25 '07 127-6 255-2 191-3 Os : 64 Water . . . 1111 H : 88'890 9 18 2 H : 16 ! Arsenious anhydride 75. 78 As: 24 '220 198 396 300-4 As : 96 Nitric oxide 46-67N : 53 -330 15 30 14 N : 16 Sulphuric anhydride 40'OOZ : 60-000 40 80 32 S : 48 &c. &c. &c. &c. &c. Having selected several the larger the number the better gaseous or gasifiable compounds of oxygen (column i.), whose percentage compositions (column ii.) are known to a fair degree of accuracy, we find their approximate specific gravities in the gaseous state 1 (column iii.). From these values we deduce the approxi- mate molecular weights 2 (column iv.) by means of one 1 For practical details see Muir and Carnegie, Practical Chemistry, p. 121. 2 The definitions of molecular weight given in many of the text- books are exceedingly vague, e.g. : "The molecularweights are the weights of two volumes, for mole- cules occupy two volumes if an atom of hydrogen occupies one." "The molecular weight of a gaseous element or compound is a number which tells the weight of two volumes of the gas, that is, the weight of that volume of the gas which is equal to the volume occupied by two parts by weight of hydrogen." In the following definition, the attempt is made to avoid the indefinite terms " volumes " and " parts by weight." The molecular weight of any substance is that weight thereof (expressed in terms of any unit whatever) which in the gaseous state occupies the same volume as do two unit weights of hydrogen, the same conditions of temperature and pressure and the same weight unit being observed in both cases. ii2 LAW AND THEORY IN CHEMISTRY or the other of the equations just developed. Then we re-state the percentage compositions in such a way as to give the molecular compositions (column v.). The ratio 12 : 16 (column v.) is just the same thing as the ratio 42'86 : 57-14 (column ii.), but 12 + 16 = 28 the molecular weight of carbon monoxide. And so on for all the other bodies mentioned. Now these molecular magnitudes have been deduced from equations which are based on the supposition that the smallest mass of hydrogen ever found in any molecule (i.e., the atom of hydrogen), is numerically represented by unity ; and a glance at column v. con- vinces us that the smallest mass of oxygen found in the molecule of any compound considered is, in terms of the same mass unit, represented numerically and approximately by 16. But the least amount of oxygen that can by theory exist in a molecule is an atom. Therefore the approximate atomic weight of oxygen is 16. 1 The method of procedure in the case of any other element is exactly similar. It still remains to show how the approximate atomic weight assists us to a knowledge of the true atomic weight, which now follows upon a very accurate deter- mination of the equivalent of the element, i.e., the 1 We cannot positively and finally assert that the atomic weight of oxygen is 16. We can only say that the probability of the approximate value O 16 is almost infinitely great. A new substance might be discovered whose molecule contained only 8i unit masses of oxygen (H atom = 1 unit mass) ; and there are chemists who, desirous of emphasising this vanishing possibility, speak of the maximum atomic weight of oxygen being approximately equal to 16. THE ATOMIC THEORY 113 smallest mass of the element which combines with unit mass of hydrogen, or with that mass of oxygen which itself combines with unit mass of hydrogen. In the case of oxygen the equivalent is not yet definitely agreed upon (see note 1, p. 95). As a probable result from all the recent elaborate deter- minations of this most important constant, Ostwald (LehrbucJi der Allgemeinen Chemie, p. 48) gives the value 7'974 [H = 1]. Suppose W 7t grams of hydrogen combine with W;,. grams of an element X, atomic weight Z, to form a hydride whose molecular formula W is H m X n< Then is the equivalent of the element X, and the ratio Z x n W, m W or Z = equivalent number x necessarily holds. In other words, the atomic weight of any element is numerically equal to its equivalent number multiplied by a fraction involving, as a rule, only the lower digits. In general, m is a whole multiple of n, so that the value of the atomic weight becomes a whole multiple of the equivalent number, or Z = r x equivalent number, where r = 1, 2, 3, &c. ii4 LAW AND THEOKY IN CHEMISTEY In the case of oxygen, then, it follows that the atomic weight may be either 7-974 or 15-948 = (7'974 x 2) or 23-922 = (7'974 x 3) &c. The approximate value 16, already arrived at by the application of Avogadro's generalisation, enables us to select without any hesitation from these possi- bilities the value 15*948 as the interim atomic weight of oxygen. Until Kaoult's recent work, the constancy in the volumes occupied by gaseous molecules (Avogadro's generalisation) was the only known example of a colligative property. 1 Kaoult established the fact that 1 Following Ostwald, we may divide all chemico-physical properties into three classes ; additive, constitutive, and colligative. Weight is the one and only true example of an additive property, for the weight of a compound is exactly equal to the weights of the elements which have reacted to form the compound. The majority of chemico-physical properties which have been quantitatively investigated, belong to the class of constitutive properties. Let A B D and ABC represent two compounds of distinct types, and X', X" the respective values for these bodies of some constitutive property, such as molecular volume / _ molecular weighty Let ^ e and d repregent the atomic vo l u mes \ specific gravity / / atomic weight \ of ^ ^ Q and ^ respectively> in the free state> \ specific gravity/ Then X' and X" are not necessarily equal to a + b + d and a + b + c, respectively ; for A B and D in compounds of the type A B D may have volumes a' b' and d', while in compounds of the type ABC, A and B may have still other values a" and b". Hence X' = a' + b' + d' X" = a" + b" + c". It will be seen, however, that constitutive properties involve an additive THE ATOMIC THEORY 115 dilute solutions of indifferent bodies also exhibit well- marked colligative properties. A given quantity of solvent has its freezing point, or, if volatile, its vapour pressure for a given temperature, lowered a constant amount in each case, by the solution therein of different substances, in quantities propor- tional to their molecular weight. Just as the colligative property expressed in Avogadro's generalisation gave rise to a method for molecular weight determination (and thence for atomic weight valuation), so Raoult's results have in the hands of Beckman and others led to new practical methods of great utility for the determina- tion of molecular weights. These new methods are all the more valuable in that they can be applied to bodies which cannot be conveniently gasified, or cannot be gasified without decomposition, i.e., to bodies which, owing either to refractoriness or instability, fall outside the pale of Avogadro's generalisation. Since Van't Hoff showed that Raoult's empirical laws can be derived by thermodynamical reasoning one from the other, and both from a certain theory of solution suggested by the phenomena of osmotic pressure, they have been very widely and generally applied to the determinations of molecular weights in cases unsuited to the gaseous specific gravity method. element ; and indeed, as soon as we know the values of any property peculiar to the atoms in a given class of compounds, the evaluation of constitutive properties for bodies of that class is a matter of pure addi- tion. Avogadro's generalisation is the expression of a colligative pro- perty. No matter what the composition or complexity of a gaseous molecule may be, it will occupy under given conditions a given deter- mined space. ii6 LAW AND THEOEY IN CHEMISTRY Of the two methods due to Baoult, that founded on the lowering of freezing point seems the most practical and popular ; it has therefore received a special name, being known as the cryoscopic method. For the details of the practice and theory of these methods the reader is referred to Ostwald's Solutions, translated from the Lehrbuch der Allgemeinen Chemie. It cannot be too strongly emphasised that chemists, in applying to bodies in the solid and liquid states the constants determined for the molecules of these bodies in the gaseous state, do not thereby intentionally commit themselves to any theory of the molecular structure of solids and liquids. Chemical changes find adequate interpretation in terms of the formulae derived from a study of gases ; indeed, it seems as if the complex mole- cules of solids and liquids, under the necessary condi- tions for chemical change, and prior to such change, break down into simpler molecules, comparable, if not identical in magnitude, with the gaseous molecules. 1 In other words, it happens that the gaseous molecule remains the chemically reacting unit in the solid or liquid state, although the physical molecules (i.e., the smallest masses of solids and liquids which exhibit all the properties, physical and chemical, of the substances 1 Seeing that the unit of chemical activity of a solid or liquid is not necessarily the physico-chemical molecule of that substance, but may be only a dissociation product thereof, comparable in magnitude with the true gaseous molecule, there are those who advocate the restriction of the terms molecule and molecular weight to purely gaseous pheno- mena, using the non-committal terms, reacting unit and reacting weight, in describing the interactions of solids and liquids. THE ATOMIC THEORY 117 peculiar to their solid or liquid states), are almost certainly polymers of the gaseous molecules. If MN be the formula of the gaseous molecule, then (M^Na;) and (M^N^) represent the physical molecules of the same substance in the liquid and solid states re- spectively ; x and y being whole numbers, and y in all probability greater than x. It may be that the time is coming when we shall ex- press more in our equations than we do at present, this increased information involving the true molecular magnitudes of the solids and liquids (or dissolved substances) interacting, i.e., the absolute values of x and y. That this polymerisation, or condensation of the simpler into more complex molecules, does often take place as a substance passes from the gaseous into the liquid state is certain, if we are justified in the universal application to vapours of Avogadro's generalisation. With many substances it makes itself evident even before the liquid state is reached. At high tempera- tures and low pressures gaseous nitric peroxide has the triatomic molecule N0 2 ; at lower temperatures and higher pressures these simpler molecules combine in pairs to form hexatomic molecules N 2 4 . Again, acetic acid vapour at high temperatures is made up of molecules C 2 H 4 2 , while at temperatures near its con- densing point the molecules have the more complex formula C 4 H 8 O 4 . Indeed in many cases the specific gravities of the vapours of substances gradually increase as the temperature of the boiling-point is approached, u8 LAW AND THEORY IN CHEMISTRY indicating a gradual increase in complexity of the molecules. 1 Now the gaseous and liquid states are really continu- ous, despite the apparent discontinuity which appears in the majority of cases under ordinary conditions of temperature and pressure. Hence we are led to the conclusion that the molecular condensation which ap- pears in some cases as the liquid state is approached (but in other cases is so delayed as not to manifest itself until the upper limiting temperature of the liquid state has been actually passed) will continue to take place in increasing degree as the temperature is lowered after the liquid state is reached. That this conclusion is just has been verified in 1 The variability in the values of specific gravity determinations of vapours at different temperatures is well manifested in the case of the chlorides of aluminium and iron, and in this connection has caused much discussion. Griinewald and Meyer hold that the specific gravity of ferric chloride does not become approximately constant for any con- siderable temperature interval until a temperature of over 700 has been reached, when the vapour consists of molecules having the composi- tion FeCla. On the other hand, Nilson and Pettersson maintain that the specific gravity of the vapour is constant for quite a large temperature interval, with 321 as its lower limit. Their experiments led to the molecular formula Fe 2 Cl6. Again, while Friedel and Crafts upheld the formula A1 2 C1 6 for aluminic chloride, Nilson and Pettersson are led by their experiments to support the formula A1C1 3 . It seems necessary to admit that in both cases molecules of the types M 2 C1 6 and MCl;j exist ; an admission which surrounds the expression' "molecular weight of a gas " with indefiniteness. For all purely equational purposes it matters little which formula we use ; but the true molecular formula, if indeed we can speak of a true molecular formula in these cases, is a point of great moment regarded from the standpoint of the valency theory (see Chapter VI.). Obviously the whole discussion turns on the difficulty of proving the existence and nature of the decompositions and dissociations taking place in a gas at high temperatures. THE ATOMIC THEORY 119 several cases by the application of Raoult's cryoscopic method of molecular weight determination. 1 Yet it must be remembered that the cryoscopic method can only be applied to fairly dilute solutions, and it is almost cer- tain that in such solutions the molecule of a dissolved solid or liquid is smaller than it would be in the homo- geneous solid or liquid state. The mere act of solution often dissociates the molecules of the solid or liquid, to such an extent that the dissociated molecules are of the same magnitude as the gaseous molecules ; some- times, however, the dissociation does not proceed so far, the extent of the dissociation being dependent on the nature of the indifferent solvent used. Acetic acid, used as a solvent, seems to have a great dissociating tendency ; hydrocarbon solvents, on the other hand, manifest this property in a much less pronounced degree. 2 In short the cryoscopic method can only 1 Measurements of other physical quantities also point to the exist- ence of complex liquid molecules. Eb'tvos finds it impossible to explain certain observations of his on surface tension, unless it be admitted that molecules of liquids are from case to case more complex in vary- ing degree than the molecules of the same substances in the gaseous state. Recently Ramsay and Shields have come to similar general conclusions. See Chemical Society's Journal, Ixiii. p. 1089. 2 Because certain liquids (e.g., acetic ether) possess in all solvents the same molecular weight as they do in the gaseous state, it has been suggested that the gaseous molecules of such bodies do not polymerise when liquefaction takes place. This seems quite a misleading sug- gestion. It is not probable that the dissociation tendency is a function only of the solvent ; the greater or less stability of the molecular complex of the dissolved substance itself must also be a factor. And surely it is not improbable that in some bodies the molecular com- plexes peculiar to the liquid state may be held together so loosely that they break down even under the influence of comparatively inert hydrocarbon solvents. 120 LAW AND THEORY IN CHEMISTRY furnish us with a minimum value for the molecular weight of a solid or liquid body. Of the true molecular weight of solids nothing is known. It is supposed that the polymerisation of the molecules in the solid state is greater than it is in the liquid state that the molecule of ice is heavier than the molecule of water. Perhaps one and the same solid substance can have different weighted molecules accord- ing to the conditions of its formation and existence, and with this difference may, perhaps, be associated the phenomena of allotropism (or physical isomerism) and polymorphism (see p. 93, and Chap. VI.). CHAPTER V. THE CLASSIFICATION OF COMPOUNDS. ACIDS, BASES, SALTS. BEFORE dealing with the more important classes of compounds, it is advisable to preface a few remarks on a classification of the elements which, in spite of indefiniteness and artificiality, still enjoys a greater or less degree of popularity. At one time it was believed that chemical action is essentially electrical in its nature, and that every chemical change is the result of the play of the stronger or weaker attractions of oppositely electrified atoms or groups of atoms. Berzelius especially developed this view of the electrical nature of chemical affinity. He believed each atom to be electrically bipolar each atom to have a definite charge of positive, and a definite charge of negative, electricity. 1 Since these charges were in general supposed to be unequal in amount, the charge present in greater amount gave a more or less positive or negative character to the atom as a whole. In accordance with the results of experi- ments on the behaviour of several compounds when 1 If Berzelius had expressed himself in terms of electric potential, the necessity for assuming a bipolar electrical distribution in the atom would have been obviated. 122 LAW AND THEORY IN CHEMISTRY electrolysed (i.e., when decomposed by the electric current), Berzelius arranged the elements in an electro- chemical series such that the element with the most negative atoms stood at the head, and the element with the most positive atoms at the bottom, of the series, any intermediate element being more negative than those below it in the series, and more positive than those above it. It was soon recognised that the elements towards the electro-negative end of the series thus constructed had properties in common which were different from those common to the elements towards the electro- positive end of the series. The electro-negative ele- ments are, as a rule, of comparatively low specific gravity, bad conductors of heat and electricity, and more or less transparent. Their oxides are for the most part readily soluble in water, and produce solu- tions with a sour taste and great solvent and corrosive powers. The elements themselves show an aptitude for combining with hydrogen to produce hydrides and decompose water, combining with its hydrogen and setting free its oxygen. The electro-positive elements, on the other hand, have as a class relatively high specific gravities, and possess a peculiar lustre. They are good conductors of heat and electricity, and are translucent only when reduced to very thin layers. Their oxides are for the most part insoluble in water, but they have the power of reacting with the solutions of the oxides of the electro-negative elements so as to destroy all the char- THE CLASSIFICATION OF COMPOUNDS 123 acteristic properties of the latter. Further, the electro- positive elements do not readily form compounds with hydrogen, and decompose water, combining with its oxygen and liberating the hydrogen. It seemed good therefore to divide the elements into two classes. (1) The electro-negative elements or the non-metals. 1 (2) The electro-positive elements or the metals. If this classification enabled us to make anything approaching to a satisfactory definition of acids, bases, and salts, it might despite its indefiniteness 2 be re- tained. But we shall show further on that it does not possess this much to be desired merit, and may also remark here that the only satisfactory classification of the elements that afforded by the periodic law does not favour any such simple and fundamental division as is embraced in the terms metal and non-metal. Before passing on to acids, bases, and salts, it is also 1 By some the word " metalloid " is used in preference to " non- metal." In view of the significance of the termination oid as generally used, this preference is scarcely justified. 2 This indefiniteness is a necessary accompaniment of all classi- fications which are not based on one definite criterion. A number of properties are currently regarded as metallic, a number of other properties as non-metallic. These properties in each case are not con- sidered of equal value inter se in deciding as to the metallic or non- metallic character of the element possessing them, but yet there exists no authoritative conventional scale of values. An element as a rule possesses properties falling under each category, and the non-metallic properties have to be weighed against the metallic ones in the un- adjusted balances of private opinion. In the absence of all convention it is impossible to give a final and indisputable answer to the question, " Is tellurium a metal or a non-metal ? " 124 LAW AND THEORY IN CHEMISTRY necessary to say a few words on a thoroughly arbitrary classification of compounds which is in vogue. All compounds, by convention, fall under one or other of the two headings organic and inorganic; and hand in hand with this classification goes a division of the science at large into two branches organic and in- organic chemistry. But "carbon compounds" and " the chemistry of carbon compounds " are undoubtedly much more appropriate titles than "organic compounds" and "organic chemistry" respectively. For compara- tively very few of the bodies treated in this main subdivision of compounds are, as the latter titles seem to imply, products of organisms, i.e., of life ; while, on the other hand, some substances included among in- organic compounds are products of vital metabolism. Since Lemery's time (1645-1715) up till the be- ginning of this century, chemists were possessed of the idea that the products of organisms most of which are compounds of carbon could not be made artifi- cially, but that their production absolutely demanded the intermediacy of life the operation of the so-called vital force. "Operations of chymistry fall short of vital force; no chymist can make milk or blood of grass." Further, it was the custom to ascribe the variable results obtained in analyses of animal and vegetable products to the fact that such bodies did not conform to the fundamental law of chemistry (law of fixity of composition), and not to the difficulties attendant on the analytical methods and the purifica- tion of complex carbon compounds. Hence a very THE CLASSIFICATION OF COMPOUNDS 125 sharp distinction was made between organic and in- organic or mineral compounds. But the distinction is now recognised as existing for convenience only. 1 Exactly the same laws hold in the case of carbon compounds as in the realm of mineral or inorganic chemistry, and many of those carbon compounds which are products of the life of organisms have been synthesised independently of the living laboratory, i.e., of vital force so called. Thus there exists no better reason than convenience to be adduced for this primary division of compounds, and no valid excuse exists for retaining the effete and mis- leading term "organic compounds" in preference to the more fitting title " carbon compounds." The com- pounds of nitrogen are increasing so rapidly, that before long it may be advisable to study them as a class apart, just as has been the case with carbon compounds. In discussing acids, bases, and salts, it will be only too apparent that we are unable to give satisfactory definitions of these classes of compounds, and farther, that any of the attempts at definition that may be advanced are not independent one of another. In other words, we cannot attempt to define one of these classes of compounds without implying or assuming the definitions of the other classes. In physics all definitions can be expressed quite independently of one 1 A sign of the extremely arbitrary nature of this classification is seen in the fact that the oxides of carbon, together with the bodies they form by direct combination, are included in inorganic chemistry. 126 LAW AND THEORY IN CHEMISTRY another in terms of powers of three fundamental units, but in chemistry we have no approach to such definition. Acids. Probably the first acid known to the ancients, certainly the one best known to them, was vinegar. Regarding the solvent powers of this comparatively feeble acid, most exaggerated notions were entertained ; witness the belief that Hannibal therewith etched a passage over the Alps for his army. The alchemists, however, knew most of the mineral acids. Geber (eighth century) describes the preparation of aquafortis (nitric acid) and also of aqua regia, which he obtained by dissolving sal ammoniac in aqua fortis. Geber also knew of oil of vitriol. The iatro-chemist Valentine (beginning of the sixteenth century) first made spiritus salis (hydrochloric acid), and showed that aqua regia can be made by mixing this new spiritus with aqua fortis. Later iatro-chemists, Libavius and Glauber, contributed much to an increased knowledge and more extended use of the acids by introducing improved methods of preparation. But as yet no attempt at the classification of bodies by their properties had been made, and the generic term acid had not arisen. Boyle was the first to group together into one class all substances which have the following properties : (1) a sour taste, (2) a great solvent action, (3) the power of precipitating sulphur from alkaline solutions of this substance, (4) a reddening action on many vegetable blues such as litmus, (5) the power of acting on wood ashes to produce substances without either THE CLASSIFICATION OF COMPOUNDS 127 the astringent solvent properties of acids or the soapy cleansing properties of solutions of wood ashes. Bodies possessing these properties were called collectively acids. Even down to the beginning of the eighteenth century most chemists were satisfied with the explanation that all substances possessing these properties did so in virtue of a greater or less amount of a common con- stituent which was called the "primordial acid." Such a vague explanation did not however satisfy Lavoisier, who renounced all alchemistic fancies of "primordial acids" and "principles of acidity." He thought, as we have seen, that oxygen was the acid producer, and that therefore every acid owes its acidity in some way to the oxygen which it necessarily contains. It must be here emphasised that Lavoisier did not regard the elements of water, and therefore hydrogen, as necessary constituents of acids. His acids were mere dissemi- nations in water of our acid anhydrides (or acidic oxides) binary compounds of some non-metal with oxygen. Thus to Lavoisier sulphuric acid was S0 3 , and not H 2 0, S0 3 , or H 2 S(V Up to the year 1787 all the substances known to 1 It is now believed that after their solution in water, the acid anhydrides as such lose their identity ; a new class of bodies called hydroxides being formed. These bodies contain as proximate parts of their molecules one or more hydroxyl (OH) radicles. Thus when S0 3 reacts with H 2 O, a rearrangement of atoms is believed to accom- pany combination, so that the resulting compound is represented as S0 2 (OH) 2 (sulphuryl di-hydroxide), and not as SO 3 , H 2 O (hydrated sulphuric oxide). Similar remarks apply to the solutions of the oxides of certain metals known as the alkaline oxides, and the alkaline -earth oxides. Thus potassium oxide K 2 O reacts with water in the process of dissolving in it to form potassium hydroxide K(OH). 128 LAW AND THEORY IN CHEMISTRY have the properties of acids as laid down by Boyle were products of the interaction of water with the oxides of non-metals ; hence the oxides of the non-metals were called acid (acidic) oxides. In the year just mentioned Berthollet took up the in- vestigation of prussic acid (discovered some three or four years previously by Scheele), and came to the conclusion that it had true acid properties but yet was entirely free from oxygen. In 1796 he came to the same conclusion for sulphuretted hydrogen, or sul- phydric acid, as it may be called. Lavoisier's reputa- tion was, however, more mighty than Berthollet's facts, and as regards acids, matters remained in statu quo until Davy in 1810 clearly proved that hydrochloric acid does not contain any oxygen, but is a compound of hydrogen with an element chlorine. Further, in 1813, hydriodic acid was shown to be altogether free from oxygen, and it was remarked that iodic anhy- dride shows no acid properties until it is dissolved in water, i.e., until the element hydrogen is introduced. Davy then began to recognise that there is no one particular acid-forming element. He noticed that hydrogen is a universal constituent of acids, but he did not rush over to the converse and say that all hydrogenised bodies are necessarily acids. On the contrary, he regarded the existence of acid properties as depending chiefly on the other elements combined with the hydrogen, and not on the hydrogen itself. The result of Davy's work was that acids came to be classed as hydracids (acids free from oxygen) and THE CLASSIFICATION OF COMPOUNDS 129 oxyacids (acids formed from acidic oxides). Shortly afterwards Liebig came to the same conclusions as Davy, and defined acids as particular compounds of hydrogen in which the latter can be replaced by metals. The growth of our knowledge since Davy's time has not brought us a satisfactory expression of any generalisation as to the particular compounds of hydrogen enjoying this property. We are in fact bound to admit that an acid belongs to that category of things which are perfectly conceivable but indefin- able. With Boyle and Liebig we can enumerate the properties which we agree shall be connoted by the term acid we can agree as to what are to be regarded as acidic functions, but that is all. The difficulty remains that several bodies possessing some, or may be all, of these properties are, for other reasons, not regarded as acids. We have no one property which we can use as an absolute criterion of acidity. Thus the salt copper sulphate turns blue litmus red, and causes an effervescence of carbon dioxide when mixed with a soluble carbonate. Bisulphate of sodium turns blue litmus red, causes effervescence with soluble carbonate, and contains hydrogen which is replaceable by metals ; yet on account of the method of its formation it is not regarded as an acid. It seems hopeless then to attempt any definition of the term acid in terms of chemical properties. If we attempt a definition from the point of view of composition rather than properties, we meet with I 130 LAW AND THEORY IN CHEMISTRY equally great difficulties. As Davy and Liebig saw, all bodies regarded as acids contain hydrogen, but all hydrogenised bodies are not acids. Evidently the hydrogen must be combined with certain elements, and in a definite manner, to produce an acid. Let us try to generalise in this direction. The oxides of the non-metals react with water to produce hydroxides which are called acids (see note, p. 127). Therefore we might attempt to define acids as the hydroxides of the non-metals [Cl(OH)] or of non-met- allic groups [S0 2 (OH)J. iBut the bodies HC1, HBr, HI, &c., are called acids. Hence we must enlarge our definition to include these hydracids. Acids are the hydrides and hydroxides of non-metallic elements. But this is not a successful definition ; for nitrogen and phosphorus are generally regarded as non-metals by those who employ the latter term, yet their hydrides are not acidic. 1 Again, the bodies H 2 PtCl 6 and H 4 FeC 6 N 6 are acids, but neither PtCl 6 nor FeC 6 N 6 can be called groups of non- metallic elements. It seems hopeless then, even had the title non-metal a strict connotation, to attempt to satisfactorily define an acid in terms of its qualitative composition. We cannot define an inorganic acid in terms of its pro- perties alone, nor in terms of its composition alone, nor in terms of both together; composition, properties, and synthetical history must all be taken into account in deciding a body's claim to rank as an acid. 1 Ammonia nevertheless contains hydrogen directly replaceable by the metals K, Na. THE CLASSIFICATION OF COMPOUNDS 131 Acids are classified according to their strengths or affinities, and also according to their basicities. The former classification will be taken up in the chapter on chemical equilibrium. The latter classification is due to Liebig, who distinguished acids as mono-, di-, tri-, tetra- basic, &c., according as they possessed one, two, three, four, or more atoms of hydrogen per molecule replace- able by metals. It is not always true that the replace- able hydrogen atoms are coequal in number with the total hydrogen atoms present in the molecule. In cases where this equality exists the basicity of the acids can at once be determined from their formulae ; but the equality must have been proved by experiment to exist. The experimental investigation of basicity takes the form of a determination of the maximum number of stable potassium or sodium salts the acids can form. 1 Bases. From early times it had been noticed that the extracts of the ashes of burnt plants possessed certain characteristic properties. For example, these extracts have great cleansing power, apparently dissolving grease and fat ; they are soapy to the touch, and have the property of restoring to their normal colours vege- table blues which have been reddened by acids. The active principle of these extracts was called an alkali, this title first appearing in Geber's writings, and liter- ally meaning the ash. 2 Soon it was discovered that a 1 For practical details see Muir and Carnegie, Practical Chemistry, p. 38 et seq. 2 The active principle of wood ashes is in reality potassium carbonate. This is no longer classed as an alkali ; it is a salt with alkaline pro- perties. 132 LAW AND THEOKY IN CHEMISTRY solution of the highly volatile ammonia or hartshorn also possessed the above properties. Hence a distinc- tion was made between fixed and volatile alkalis. It was Stahl who first noticed that, in addition to the above enumerated properties, alkalis have the power of reacting with acids to produce indifferent substances. It was as if the properties of acids and alkalis were diametrically opposed, and in combination mutual neutralisation took place, just as would be the case with two equal and opposite magnetic poles a sort of cancelling out of positive and negative. So far the substances which had the power of thus neutralising acids were all soluble in water. Sometime later it was found that certain almost insoluble sub- stances which are very fixed in the fire, i.e., do not melt nor change in any way, have the same property. These were called the earths, and Rouelle in 1744 combined alkalis and earths into the one class base, defining a base as any substance which combines with and neutralises an acid. It is almost impossible to give a concise and exact definition of base as that term is now applied. Speaking loosely, the oxides of the metals, and the hydroxides they form when they are made to combine directly or indirectly with water, are regarded as bases ; hence metallic oxides are often spoken of as basic oxides. May we not then define a base as the oxide or hydroxide of a metal ? Such a definition does not include hydrides of certain non-metals (ammonia NH 3 , phosphine PH 3 , &c.), which are established as bases ; THE CLASSIFICATION OF COMPOUNDS 133 and, further, it does not indicate that the higher oxides of some metals have acidic functions. We are equally unsuccessful when we try to frame a definition in terms of properties. All bases do not react with acids so as to neutralise the latter, i.e., completely destroy their characteristic properties, as Rouelle, to whom only the strongest bases were known, believed. The solution obtained when sulphuric acid is treated with an excess of the base copper oxide still possesses acid characters. Again, while some bases act on vegetable colouring matters, others do not. Nor can bases be said to be bodies which in reacting with acids cause a replacement of the hydrogen of the acids by metals, for the bases N 2 H 4 , NH 3 , PH 3 , &c., do not contain metals, and the products of their interaction with acids are of the nature of additive, not substituted, compounds. True, the definition, " A base is a substance which reacts with acids to produce a salt and water at most," holds good, but it is a definition in terms of acids which cannot be defined, and involving a new class of bodies, salts which themselves require definition. Hence we must conclude that while it is possible to lay down what we mean by basic characters or functions, it is impossible to define bases ; for many bodies which are not regarded as bases exhibit basic characters, and many bases exhibit only a few of what are all admittedly basic functions. A rough classification of the more important inor- ganic bases follows. The table clearly "shows the true relation of the terms alkali and base. In some elemen- 134 LAW AND THEORY IN CHEMISTRY tary text-books the terms are used as if they were synonymous. This is not the case. An alkali is a particular kind of hydroxide which is a particular kind of base. Every alkali is a base, but every base is not an alkali. Alkaline oxides (K,0, Na 2 0, Eb 2 O, Cs 2 0, KbaO, Li 2 0) form very" soluble hydroxi- des with marked basic char- acters called alkalis. Alkaline earth oxides (CaO, SrO, BaO) form slightly soluble hydroxides with less pronounced bisic char- acters than the alkalis. The lower oxides of the re- maining metals fall under this heading. The hy- droxides of these oxides are formed by adding an alkali, or alkaline earth hydroxide, to solutions of . the oxides in acids. Oxides and hy- droxides of the metals. Oxides which directly react with water to produce hy- droxides. Oxides which do not directly react with water. Hydrides of certain non- metals, and their deriva- tives. > Ammonia NET 3 , amidogen NoH 4 , hydroxylamine NH 2 OH, phosphine PH 3 , &c." However convenient classifications of oxides into acidic, basic, intermediate, and indifferent varieties may be for an elementary presentment of chemistry, a glance from the vantage-ground of. facts which are not usually referred to in elementary courses, but which are none the less facts on that account, shows such classifications to be imperfect and arbitrary to a degree. New reactions and new substances are continually being discovered, which testify to the fact that oxides generally are capable of exhibiting under one set of conditions what are currently accepted as acid char- acters ; under another set of conditions, what are THE CLASSIFICATION OF COMPOUNDS 135 currently accepted as basic characters. For instance, chromium trioxide is usually classed as an acidic oxide, because it reacts readily with the alkalis, partially destroying the characteristic properties of the latter. But it also reacts with sulphuric acid, destroying its characteristic properties, and surely this is a basic function. True, the salt formed in this latter case does not correspond to Cr0 3 , but it has not yet been authoritatively laid down that such correspondence is an essential feature of acids, or bases as the case may be. It seems, however, to be tacitly assumed that an oxide has no claim to rank as acidic or basic until it can be proved to produce corresponding salts. Thus, true basic rank was denied to Pb0 2 until the recent preparation of the corresponding salts PbCl 4 , Pb(C 2 H 3 2 ) 4 , &c. In spite of its reaction with hydro- chloric acid, it was regarded as a feeble acidic oxide destitute of true basic properties. Now in virtue of these new salts it ranks as an intermediate oxide. 1 1 When an acid and base interact to produce a salt only, or a mix- ture of salt and water only, the salt is said to correspond to both the acidic oxide of the acid and the basic oxide of the base. BaO + H 2 S0 4 = BaS0 4 + H 2 O 2 BaO 2 + 2 H 2 SO 4 = 2 BaS0 4 + 2 H 2 O + O 2 . According to definition, BaS0 4 corresponds to the oxides S0 3 and BaO, but it does not correspond to the oxide BaOo. If other factors (e.g., oxygen from the air) than the acid and base be involved, the resulting salt is not regarded as corresponding to one or other of the oxides involved. Thus potassium manganate K 2 MnO 4 (regarded as K 2 O MnO 3 ) does not correspond to the oxide MnO 3 from which it is prepared. i 3 6 LAW AND THEOKY IN CHEMISTRY Even if the restriction of correspondence (as denned in the note) were imposed, the difficulties attendant on the classification of oxides would not be greatly lessened. Barium peroxide, for example, though it reacts readily with H 2 S0 4 (S0 3 ) does not form a corresponding salt therewith. Hence it ought not to rank as a basic oxide. But barium peroxide reacts readily with the acidic oxide S0 2 , giving as sole product the salt BaS0 4 ; therefore, from this point of view, the peroxide is a basic oxide. When manganese dioxide' is heated with potash in the presence of air, a salt K 2 Mn0 4 is formed. This is said not to correspond to the dioxide Mn0 2 , but to the trioxide MnO 3 , and its formation under these conditions is not regarded as any proof of acidic properties in Mn0 2 . This seems to imply that the Mn0 2 is first oxidised to Mn0 3 by the oxygen of the air, and this acidic oxide then reacts with the potash to form the corresponding salt potassium manganate. But we have no proof that the Mn0 2 does not itself first combine with the potash to form a corresponding manganite, which as soon as it is formed oxidises to manganate. Or, since K 9 is known to be peroxidised when heated in the air, it may be that the exceedingly un- stable salt K 2 Mn0 4 results from the interaction of the acidic oxide Mn0 2 and the basic oxide K 2 2 . But enough has been said to indicate some of the difficulties attendant on the attempt to rigidly classify the oxides. Before treating of salts, the subject of neutralisation THE CLASSIFICATION OF COMPOUNDS 137 merits a passing notice. When an alkali in aqueous solution is added to an aqueous solution of a strong acid in just the right quantity to destroy completely both the characteristic properties of the acid and the alkali for the two sets of properties disappear simul- taneously the acid is said to be neutralised by the alkali, and vice versd. We might employ the disappearance of any one of the characteristic properties of acids or alkalis as an index of the realisation of complete neutralisation, but the property hitherto almost universally selected for this purpose is the reddening action of acids, and the blueing action of alkalis on the vegetable colour litmus the tinctorial matter of a certain species of lichen. The normal hue of this substance is purple, but it turns red when treated with acids, and blue when treated with alkalis. Suppose then we have an acid solution which we wish to exactly neutralise with a solution of alkali, we add a few drops of litmus solution to the acid, and then add the alkali solution cautiously till the red solution containing the acid becomes purple. The neutralisation is then considered to be exact, whereas, if too much alkali had been added, the solu- tion would be blue, if too little, red. Processes of this kind are known generally as processes of titration, for they are usually carried out with, or rather involve somehow, solutions whose strength or titre is known beforehand ; and colouring matters like litmus used as aids to exact titration are called indicators. But the introduction of numerous coal-tar products which give I 3 8 LAW AND THEORY IN CHEMISTRY colour changes with acids and alkalis 1 leads us to ask if the neutral tint of litmus is an index of exact neutralisation, i.e., the presence of acid and alkali in precisely the quantities theoretically necessary for com- plete combination. These new artificially prepared indicators are so sensitive that they do not show intermediate neutral tints as is the case with litmus. They not only differ among themselves in sensitiveness to, but also in their qualitative attitudes towards, one and the same solu- tion. Thus, potassium sulphite solution is neutral to phenolphthalein, but changes violet litmus to blue just as an alkali does. Copper sulphate solution is acid as tested by litmus, but neutral in its behaviour to lacmoid. Saliva, which is normally neutral to litmus, is strongly alkaline to lacmoid and acid to turmeric ; and 1 Among these new indicators may be mentioned Phenolphthalein : with acids, colourless ; with alkalis, purple red. Methyl orange : with acids, pink ; with alkalis, pale yellow. Lacmoid : with acids, red ; with alkalis, blue. , Rosolic acid : with acids, pale yellow ; with alkalis, violet red. The behaviour of a substance in the rfile of indicator, seems to be determined by the balance of acidic and basic characters in its mole- cule. If the acidic properties are relatively strong, the indicator is especially sensitive to bases, and can be successfully used in the titration of salts formed from weak acids, such as carbonates, sul- phides, borates, &c. For carbonic, sulphydric, and boric acids, which are liberated during the process of such titrations, are unable to affect the colour of the indicator. If, on the other hand, basic characters have the predominance in the molecule, then the indicator, being very sensitive to acids, is useless for titrations wherein even such feeble acids as carbonic, sulphydric, &c., are produced. The differences in sensitiveness of these indicators have been applied to the simplification and shortening of many processes of volumetric analysis. THE CLASSIFICATION OF COMPOUNDS 139 so on. Indicators, then, differ among themselves in their testifications as to acidity, alkalinity, and neutrality, and there is no reason why the indications of litmus should be accepted in preference to those of other colouring matters. Salts. The term salt did not always have its present connotation. It was at one time loosely applied to all substances which tasted like sea-salt, were easily soluble in water and recoverable from their solutions by evaporation. Of these characteristics solubility was regarded as the most important; hence among the alchemists we find an acid referred to as sal acidum, an alkali as sal alkali, while a salt proper was distinguished as sal salsum. It was Eouelle who, totally disregarding solubility relations, appropriated the term salt for the product of the interaction of an acid with a base or metal. The essential feature of an interaction of this kind is the replacement, total or partial, of the replaceable hydrogen of the acid by equivalent quantities of metals. If the whole of the replaceable hydrogen of an acid is displaced by a metal, the resulting salt is in general called a normal salt. Thus Na 2 C0 3 (from the acid H 2 C0 3 Aq) CuS0 4 (from H 2 S0 4 ) and Na 3 P0 4 (from H 3 P0 4 ) are all normal salts. The normal salts formed by the interaction of the strong acids (HC1, H 2 S0 4 , HN0 3 , &c.) and the strong bases (KOH, NaOH) were the first to be investigated. As such salts (e.g., K 2 S0 4 , NaCl, KN0 3 , &c.) were all neutral to litmus, it was once customary to regard as synonymous the terms neutral salt and 140 LAW AND THEORY -IN CHEMISTRY normal salt. But it is now known that many normal salts are not neutral. When the metal of a weak base, e.g., Fe(OH) 3 replaces all the hydrogen of a strong acid, e.g., HC1, a normal salt with acidic properties results, e.g., FeCl 3 . On the other hand the interaction of a strong base, e.g., KOH and a weak acid, e.g., H 2 C0 3 gives a normal salt with alkaline properties, e.g., K 2 C0 3 . It' only a. portion of the replaceable hydrogen of the acid is replaced by metal, as in the compounds NaHS0 4 , NaHC0 3 , Na 2 HP0 4 , the resulting salts are called acid salts. This title does not necessarily imply the posses- sion of any other acidic property than the presence of one or more hydrogen atoms replaceable by metals ; as we shall see presently, it does not always imply even this characteristic. It denotes a particular composition rather than a definite set of properties. Thus the slightly alkaline body Na 9 HP0 4 is in terms of our definition an acid phosphate of sodium, while acid sodium carbonate NaHC0 3 possesses very pronounced alkaline properties. 1 But it is necessary to enlarge our ideas of acid salts. If acid salts were nothing else than acids in which part of the replaceable hydrogen is substituted by an equivalent quantity of metal, then it follows that a dibasic acid like carbonic acid (H 2 C0 3 Aq) should be capable of forming only one acid sodium salt NaHC0 3 . 1 Acid salts containing replaceable hydrogen and formed from dibasic acids are often distinguished from the normal salts formed from the same acid and base by the prefix bi-. Thus NaHSC>4 is bisulphate of sodium ; NaHCOs bicarbonate of sodium, and so on. THE CLASSIFICATION OF COMPOUNDS 141 But there is another way of looking at, and defining, acid salts. In the normal sodium salt of carbonic acid Na 2 C0 3 or Na 2 O.C0 2 the acid oxide : the basic oxide : : one reacting weight : one reacting weight. In the acid salt 2NaHC0 3 or Na 2 0.2C0 2 .H 2 the acid oxide : the basic oxide : : two reacting weights : one reacting weight. In other words an acid carbonate of sodium is a i , . , . reacting weights of acidic oxide salt 111 which the ratio - reacting weights of basic oxide exceeds the value unity. This is a wider definition than the one previously given, in that it does not point to any limit for the number of possible acid salts. It prepares us for the statement that a second acid carbonate of sodium exists. This is the so-called sesquicarbonate of sodium which has the composition 2Na 2 0.3C0 2 .3H 2 0. Every oxy-salt can be conventionally regarded as a compound of basic with acidic oxide. Let us suppose that in the normal salt of a given metal the ratio reacting weights of acidic oxide _ reacting weights of basic oxide then if other salts formed from the same acid and base or metal exist in which the above ratio has a greater value than n, they must be regarded as acid salts. 142 LAW AND THEOKY IN CHEMISTRY We see then that it is not necessary that every acid salt should contain replaceable hydrogen. Thus, in addition to the normal sulphate of antimony Sb 2 (S0 4 ) 3 [Sb 2 3 .3S0 3 ], a sulphate having the composition Sb 2 S 4 15 [Sb 2 3 .4S0 3 ] is known. It is therefore in terms of our latest definition an acid salt, and as such it is commonly regarded, though it does not contain replaceable hydrogen. Why then, it may be asked, should it not be called a normal salt, seeing that all the hydrogen of the acid from which it has been formed (H 2 S0 4 ) has been re- placed? The answer is, that by tacit consent only those salts are called normal which, in addition to the absence of replaceable hydrogen, can be represented as containing whole multiples of the radicles of the acid forming them. 1 Thus all normal sulphates can be represented as containing electro-positive element united with %(S0 4 ) ; all normal carbonates will contain %(C0 3 ) ; all normal phosphates n (P0 4 ) ; and so on. T- ,, ,. reacting weights of acidic oxide If the ratio ^ for a reacting weights of basic oxide particular salt fall below the value n peculiar to the normal salt, then the salt is called a basic salt. In normal mercuric sulphate HgS0 4 [HgO.S0 3 ] n = 1 ; in the sulphate Hg 3 S0 6 [SHgO.SOJ n equals only J. This latter compound is therefore a basic sulphate of mercury. These basic salts constitute quite a large 1 The molecular formula of acids may be conceived as made up of two parts ; one part consisting of the whole of the replaceable hydrogen, the residue constituting the other part being called the acid radicle. THE CLASSIFICATION OF COMPOUNDS 143 and important class of bodies. They are for the most part insoluble substances formed when excess of water acts on the normal salts formed from weak bases, or when excess of weak base is allowed to interact with acid and a strong acid. From the fact that there are several acids which do not contain oxygen and have therefore no corre- sponding acidic oxides, it follows that our definitions of acid and basic salts in terms of the ratio reacting weights of acidic oxide reacting weights of basic oxide lacks generality. We can, however, regard all acid and basic salts from one common standpoint, provided we apply a vaguely extended meaning to the word neutra- lisation. When a weak base interacts with a strong acid, the resulting normal salt as we have seen has in general distinctly acid properties. In virtue of these properties it can interact with more basic oxide, producing what we may conceive of as a nearer approach to absolute neutralisation in the form of a basic salt. According to this view, the weaker bases should show themselves particularly prone to form basic salts with strong acids ; and this is known to be actually the case. Again, when a strong base interacts with a weak acid, basic properties predominate in the normal salt, in virtue of which it is capable of further interaction with more acid or acidic oxide, with the realisation of more perfect neutralisation in the form of an acid salt. 144 I AW AND THEORY IN CHEMISTRY Thus it follows that acid salts are formed chiefly from the strong bases. It has been customary to regard the excess of acid in an acid salt over and above that necessary for the production of a normal salt, as less intimately com- bined or associated with the base than that portion of the acid which just suffices for conditions of normality. Similar remarks apply to excess of base in basic salts. In conformity with these unsubstantiated views, acid and basic salts are often represented as molecular com- pounds of normal salt and acid on the one hand, and of normal salt and base on the other. Thus basic bismuth chloride is sometimes written Bi 2 3 .BiCl 3 [3 BiOCl] ; sesquicarbonate of sodium, according to this method of representation, becomes 2Na 2 C0 3 .H 2 C0 3 .2H 2 0, and acid sulphate of potassium, KgSO^E^SO^ 1 But if normal salts still retain acid and basic func- tions, enabling them now to combine with more base, now with more acid, the question naturally arises, why should not normal salts with residual acidic functions combine with normal salts possessed of residual basic functions? This question introduces us to the class 1 According to this view of the matter, the so-called hyperacid salts formed by monobasic acids, e.g., KC1.HC1 or KHC1 2 , KF.HF or KHF 2 &c., ought not to be distinguished from the ordinary acid salt such as Na 2 SO4. HgSO^ The term " hyperacid salts " for these com- pounds is an outgrowth of the primitive views on acid salts, which represented them as acids in which only part of the replaceable hydro- gen is replaced by metals. According to these views it is, of course, impossible for a monobasic acid to form acid salts ; and hence the introduction of the term " hyperacid salts " to meet the necessities of THE CLASSIFICATION OF COMPOUNDS 145 of double salts which is at present receiving a good deal of attention. Normal sulphate of sodium, Na 2 S0 4 , exhibits re- sidual basic properties in its interaction with sul- phuric acid to produce the acid sulphate of sodium Na 2 S0 4 .H 2 S0 4 (2 NaHS0 4 ). To zinc sulphate, by reason of the existence of such basic salts as S0 3 .2 ZnO, S0 3 .4 ZnO,.2 H 2 0, S0 3 .6 Zn0.10H 2 0, and SOo.8 ZnO. 2 H must be ascribed residual acidic o ^ properties. What wonder then that basic Na 2 S0 4 combines with acidic ZnS0 4 , forming the double sul- phate Na 2 S0 4 .ZnS0 4 .4H 2 ? The double halides are an especially important class of bodies, and much is to be hoped from their further investigation. Their formation and existence admit of a provisional explanation similar to that just employed in connection with the double sulphates. By reason of the existence of the unstable hyperacid salts having the general formula MX.HX, where X is a halogen and M the metal of an alkali, slight basic properties must be allowed to the alkaline halides. But the normal salts formed by the interaction with the haloid acids of the weaker bases (i.e., the oxides and hydroxides of the heavy metals) have a surplus of acidic characters. Hence we have a large series of com- pounds, called double halides, of the general formula n (MX) m (M'Xa.) where MX represents alkaline halide and M'Xa- the halide of some element other than the metal of an alkali. The following are a few examples, picked at random, of such double halides BeCl 2 .2KCl ; K 1 4 6 LAW AND THEORY IN CHEMISTRY MgF 2 .NaF, PbI 2 .3NH 4 Cl. In accordance with the manner of regarding double salts here developed, it is found that these are most readily formed by halides corresponding to those oxides which in turn most readily form basic salts. Attempts have been made from time to time to remove the so-called double halides from the ill- defined and artificial class of molecular compounds by assigning to them normal unitary atomic structures. 1 These attempts necessi- tated certain extensions of our ideas of valency (see next chapter) which have not met with general acceptance ; and until some more satisfactory theory of the structure of the double halides is framed, these bodies will, in all probability, continue to be empiri- cally regarded as molecular compounds of the simple metallic halides from which they are prepared. Inorganic compounds are not all included under the titles acids, bases, and salts. There is in addition a large and rapidly growing number of little-investigated binary bodies, such as the phosphides, the borides, the nitrides, the silicides, the carbides, the selenides, the tellurides, the arsenides, and the antimonides. Most of these substances (which may for the present be classed together under the heading indifferent bodies 2 ) are formed by direct union of the elements at high tem- 1 For the distinction between molecular and atomic compounds see p. 155. 2 The oxide NO together with several hydrides, e.g., SiH 4 , PoH 4 , would also fall under this category of indifferent bodies. For an exhaustive list of these indifferent bodies, the reader is referred to Ramsay, System of Inorganic Chemistry, p. 497 ct seq. THE CLASSIFICATION OF COMPOUNDS 147 peratures and are decomposed by water. Though in several cases the phosphides, &c., of an element M are of the same type as the phosphides, &c., of the element hydrogen (e.g., P 2 H 6 an( ^ ^V^'s)? J 6 ^ they cann t be regarded as salts of the latter. For the hydrogen compounds do not exhibit the most universal of acid properties the possession of hydrogen atoms directly replaceable by equivalent quantities of other elements. CHAPTER VI. ISOMERISM AND MOLECULAR ARCHITECTURE. WITH respect to the arrangement of the simple atoms in the compound atom (molecule) the earlier chemists did not concern themselves. The determination of the mere composition and formula of the compound atom was a problem more than sufficient for their day. But during the years 1820-25 the discovery and investi- gation of cyanic, fulminic, and cyanuric acids forced chemists to face the question of the mutual relations of the atoms in the molecule. These three acids were found to have identically the same percentage composi- tion, and yet the properties of the three bodies differed most pronouncedly. So foreign did the possibility of the existence of two or more different bodies of the same percentage com- position appear to the early chemical philosophy, that Berzelius for long refused to admit it. Finally, how- ever, the accumulation of well-authenticated instances of the phenomenon, among which the different tartaric acids may especially be mentioned, not only forced Berzelius to an admission, but led him to introduce the general term "isomerism" 1 for the class of facts under observation. 1 Much confusion exists in regard to the precise use of the terms isomerism, metamerism, &c. Some, regarding identity of percentage 148 MOLECULAR ARCHITECTURE 149 What explanation of isomerism could there possibly be other than a difference in atomic arrangements in the molecules of isomeric bodies ? Henceforth it was acknowledged that the properties of a substance depend not only on its composition but also on the atomic architecture of its molecules. Now the architecture of two molecules having identical atomic compositions can differ in two ways. The relative positions of the atoms remaining the same, their distances apart may differ ; or the atomic distances being constant or without in- fluence, the relative positions may differ. It is be- lieved, not without strong evidence, that differences in the relative positions of the atoms constitute the sole determining cause of isomerism ; differences in atomic distances, if indeed such exist, being without influence. composition as the sole condition of isomerism, divide isomers into the two classes polymers and metamers ; polymers having different mole- cular weights, metamers the same molecular weight. Others again give two meanings a wide and a restricted one to the term isomer. As before, all bodies having the same percentage composition are isomers in the wide sense. Such isomers are then classified into (a) bodies of different molecular weights, (j3) bodies of the same molecular weight. Bodies of the former class are polymers. The latter class is further subdivided into (a') bodies of the same type or isomers in the restricted sense, and (/3') bodies of different types or metamers. Throughout this chapter the terms will be used in accordance with Berzelius' first suggestion, viz. : Polymers bodies of the same percentage composition and different molecular weights. Isomers bodies of the same percentage composition and the same molecular weight. Metamers closely related isomers which are capable of very readily changing one into another. (See article "Isomerism" in Watts' Dictionary of Chemistry.) i5o LAW AND THEOEY IN CHEMISTRY At any rate, all known cases of isomerism can be ex- plained in terms of differences in atomic arrangement alone. 1 Two, and only two isomers of the formula C 2 H 6 are known ; all attempts to produce a greater number have been futile. But it is obviously possible to arrange the nine atoms in a multitude of different ways. Why then does not a multitude of isomers exist ? There must be a something limiting the possible groupings of a num- ber of atoms in a molecule, whose cause must surely be sought for in the nature of the atoms themselves. To take an analogy. Imagine a number of athletes of widely varying strength or holding power. So long as we pay no regard to their holding powers it is evident that we can arrange these athletes in a large number of different groups in each group the relative positions of the athletes being different. But the number of possible arrangements is very much diminished as soon as we make the stipulation that the groups are to be conditioned by, and exist in virtue of, the holding powers of the individual athletes groups such as the "human trees" which so fre- quently form one of the items in a circus programme. So it is with the atoms in a molecule ; they are not thrown together " higgledy-piggledy " and without any dependence on the intrinsic peculiarities of the atoms, 1 The distances between those atoms of a molecule which have " strong affinities " for each other may be a determining cause in isomeric change. ButJ the isomcric change from one body A to another body B is a very different thing from the isomerism of A and B. (See p. 183). MOLECULAK ARCHITECTURE 151 but the molecule owes its continued existence to the definite holding or linking power of its constituent atoms. To this property or power of atoms the general term valence or valency has been applied. As at the birth-time of the recognition of valency, no molecules were known containing per one atom of hydrogen more than one atom of any other element X (i.e., as there were no bodies of the type HX n ), and as the hydrogen atom had already been chosen as the standard for atomic weights, it seemed well to make it also the standard for valencies. Any atom X which held in combination one atom of hydrogen, and formed a molecule HX, was called a monovalent atom. The existence of the molecule H 2 Y established the diva- lency of Y, and so on. It will readily be seen that valency is nothing else than a special name given to equivalency when this is applied to atoms, and it is not therefore surprising that the same difficulties as beset the attempt to establish an equivalent system appear again in the later attempts to fix the valencies of the elementary atoms. Only a few elements combine with hydrogen to form gasifiable molecules, and had we to rely only on hydrides, our knowledge of the valencies of the atoms of the elements would be very incomplete. Fluorine, chlorine, bromine, and iodine, however, combine atom for atom with hydrogen, hence they are univalent atoms, and may be used as middlemen to fix the valencies of elements which do not form hydrides. Unfortunately 152 LAW AND THEORY IN CHEMISTRY the valency of an atom as derived from a study of the halides of the element does not always agree with the valency as fixed by the hydride, e.g., PH 3 , PF 5 . More- over, many elements form at least two gasifiable halides with the same halogen, e.g., HgCl, HgCl 2 . Which particular halide is to determine the valency of the atom in question ? Can we, indeed, correctly speak of the valency of an atom ? l This question has given rise to two opposing schools. One school, vaguely referring the phenomena of valency back to some objective attribute of the atom, asserts the necessary constancy of valency. The valency of an atom is, according to this school, as constant as its 1 From a study of the periodic law, Mendeleeff arrived at the follow- ing generalisation : The sum of the " equivalents " of oxygen and hydrogen with which a single non-metallic atom is combined in its highest salt forming oxide on the one hand, and in its maximum hydride on the other, is constant for all non-metallic atoms, and is equal to 8. Thus, the highest salt-forming oxide of carbon is CO* ; the maximum hydride of carbon is CH 4 . In each case the carbon atom is combined with four "equivalents," and 4 + 4 = 8. The pairs of com- pounds PH 3 , PoO 5 ; AsH 3 , As 2 O 5 ; TeO 3 , TeHo, illustrate the same principle. It is obvious that by " equivalents," Mendeleeff here means something very much akin to valencies ; and in this connection he asks why the valency of an atom should be gauged by its hydrides rather than by its oxides. It should be noted that Mendeleeff' s generalisa- tion is founded on the assumption that peroxides (i.e., oxides of higher types than the so-called group oxides) are not strictly salt-forming do not form corresponding salts. The recent isolation of salts M 2 S 2 O 8 (where M monovalent atom) corresponding to sulphur peroxide S-jO? is at variance with this assumption. The sum of the " equivalents " of sulphur in S a O 7 , and SH 2 is 9, and not 8. Some other criterion than the power of forming corresponding salts must lie at the basis of a classification of oxides adapted to Mendeleeff 's generalisation. Further, the partiality of the generalisation, including as it virtually does only the non-metals, is against it. See Mendeleeff 's Principles of Chemistry, vol. ii., appendix 1. MOLECULAR ARCHITECTURE 153 weight, although under certain conditions it is not wholly in evidence. Among modern chemists, van't Hoff may be cited as an adherent of this school. He assumes that the attractions in virtue of which the atoms of a molecule hold together, are of the same order as the gravitative attractions of ponderable masses. This being the case, he shows that the intensity of the attraction over the surface of an atom would be constant only if the atom were truly spherical. If, on the contrary, the atom had any other figure than the sphere, then at certain points on its surface the attrac- tive forces would have maximal values these values being unequal inter se. According to van't Hoff's view, then, the valency of an atom expresses the total number of points of maximal attraction this number being dependent on the form of the atom. As the form of the atom is presumably constant, the valency is also constant. If, however, under certain conditions the movements of the atoms conditioning the temperature of the gas become so energetic that only the higher maxima of attraction are powerful enough to come into effective operation, the atom will apparently pos- sess a valency lower than its actual valency. 1 1 In view of the fact that Faraday's law of electrolysis can be stated in terms of valency data, it may seem somewhat surprising that no satisfactory electrical theory of the cause of valency has appeared. Yet it should be remembered that valency had its origin, and finds its chief application, in organic chemistry, and the great majority of organic compounds, i.e., all organic compounds which are not salts nor acids, are non-electrolytic. In electrolysis the positive electricity may be regarded as conveyed through the electrolyte from anode to kathode by the metallic atoms, the negative electricity from kathode to anode UBRAf?y 154 LAW AND THEORY IN CHEMISTRY The opposing school, most non-committal and un- imaginative, does not attempt to theorise on, or explain in any way, the phenomena of valency. It does not speak of the absolute valency of any atom, but only of the maximum known valency of an atom or, less general still, of the valency of an atom in a particular compound. 1 The history of the school of constant valency is an instructive one. Its attempts to vindicate its tenets gave rise not only to such familiar distinctions as those involved in the terms saturated and unsaturated bodies, atomic and molecular compounds, but also to the cele- brated so-called theory of bonds. by the non-metallic atoms or acid radicles. Atoms and radicles in their capacity as carriers of electricity during electrolysis are called ions. Faraday's law can be stated in the following form : The elec- trical carrying power of an ion is directly proportional to its valency. In other words, a quantity of electricity, positive or negative, which is conveyed through a salt solution by an ?z-valent atom or radicle, would require for its convection n monovalent atoms or radicles. If a current of electricity be passed through two electrolytic cells in suc- cession, the amount of electricity passing through each cell in a unit of time is the same. If in the first cell we have a salt of a divalent metallic atom, in the second a salt of a monovalent metallic atom, then for every atom (or what is the same thing, for every atomic weight expressed in any mass unit) of the divalent metal deposited in the first cell we shall have two atoms (two atomic weights in the same mass unit) of the monovalent metal deposited in the second cell. See Lodge, Modern Views of Electricity, p. 72 et seq. The table given in note 1, p. 159, could quite well be constructed from quantitative electrolytic determinations alone. 1 Apropos of the attitudes of these rival schools, Ostwald writes : " Fragt man nach dem Wege, auf welchem eine Entscheidung zu treffen wore, so kann eine solche nur auf Grundlage einer bestimmten, wohl begriindeten Hypothese iiber die Natur dessen, was wir Valenz nennen, erlaugt werden." MOLECULAR ARCHITECTURE 155 The nitrogen atom combines with three atoms of hydrogen to form NH 3 ; therefore nitrogen is trivaleht. In order to express this fact clearly and succinctly, the notation -/^V was employed. At first the lines proceed- ing from the circle enclosing the symbol for nitrogen were regarded in their true light simply as a species of chemical shorthand ; but soon they came to be regarded as symbolising some objective characteristics of the atoms called bonds or units of affinity. The nitrogen atom was trivalent, because it was possessed of three bonds or units of affinity. It did not hamper the advance of the school, that for long no satis- factory answer could be given to the question, what is the nature of a bond or affinity unit ? But chemists are not the only people who have at times deceived themselves into the belief that to name the unknown is to explain and progress. 1 But if nitrogen is trivalent, and hydrogen and iodine both monovalent, how, it was asked by the opponents of the school, could the existence of the molecule NH 4 I be explained ? In terms of the difference between atomic and molecular compounds, was the answer. Only in the former class of bodies, it was said, is valency operative. Ammonium iodide is a loose molecular compound of the two atomic compounds NH 3 and HI, in the former of which the nitrogen atom displays its customary 1 Thanks to van't HofF s theory of valency, we may now, without being accused of a mere glossing of our ignorance, employ the term "bond." Some such term, properly understood, is not only generally useful, but it is absolutely indispensable in describing the results of the new stereo-chemistry (vide infra). The word bond is much to be pre- ferred to its once synonymous term " unit of affinity." 156 LAW AND THEORY IN CHEMISTRY trivalency. The attraction (or energy degradation), in virtue of which the atomic compounds HI and NH 3 mutually hold each other in combination, is not only independent of, but of a quite different order from, the attractions associated with the valencies of the atoms, and instrumental in holding together the parts of atomic compounds. The former attractions are attributes of the molecules as wholes, and are of a physical rather than a chemical nature. However, experiments on the substituted ammonium iodides (NH 4 I in which the H atoms are replaced by different monovalent organic radicles) showed in this special case the artificiality of the distinction between atomic and molecular compounds, and the necessity of regarding ammonium iodide as a true atomic com- pound in which the nitrogen atom, holding in direct combination the four atoms of hydrogen and the one atom of iodine, must be pentavalent. 1 The school of constant valency was bound to recog- nise the justness of these conclusions, to which it immediately adapted itself by instituting a distinction between saturated and unsaturated compounds, main- taining the while that the nitrogen atom was constantly pentavalent instead of trivalent, as hitherto upheld. Here will be observed a slight departure from the original signification of valency ; the valency of an atom is now measured by the number of bonds it possesses. 1 The behaviours of such presumed inorganic molecular compounds as KT1I 4 [KI.T1I 3 ], K 3 SbBr 3 Cl 3 [SbBr 3 .3K01], &c., are also not in harmony with the deductions which necessarily flow from the admission of molecular combination as distinguished from true atom linking. MOLECULAR ARCHITECTURE 157 It at first sight seems more definite than the original signification in that a cause for the phenomena is assigned. But phenomena which are not understood are not cleared up by the mere assigning of causes whose natures are themselves darkly obscure. It is worthy of remark that till van't Hoff's time no satis- factory explanation was advanced of the reason why an atom forms sometimes a saturated, sometimes an unsaturated molecule. Conceptions of valency had their origin in the study of carbon compounds, and it is in the field of carbon compounds that the developed theory to-day finds its most successful applications. 1 The reasons for this are not far to seek. The carbon atom is peculiar in that its valency determined from all its highest forms of com- bination containing only a single carbon atom in the molecule, is constant. The molecules CH 4 , CHC1 3 , CHBr 4 , CC1 4 , CS 2 , and C0 2 all point to the tetravalency of carbon. 2 Again, carbon compounds are for the most part easily vaporised, and hence the molecular 1 It should be particularly noted that organic chemistry, though largely indebted to, is nevertheless quite independent of, the theory of valency. Mendeleeff has shown that the application of Newton's third law of motion in the form in which it appears when regarded as a corollary of the first law, combined with the principle of substitution, is capable of effecting all that the doctrine of valency really effects, viz., the limitation of the number of isomers possible for a given atomic com- plex, and the provision for each isomer of an appropriate molecular ground plan. (See Mendeleeff, Nature, t vol. xl. No. 1032, and Carnegie, American Chemical Journal, vol. xv. No. 1.) 2 It may be that some day this series will be rendered complete by the discovery of a substance having the molecular composition CN 2 ; the group N 2 being tetravalent, as in the molecule of hydrazine 158 LAW AND THEORY IN CHEMISTRY weights of the majority of carbon compounds are known. On the other hand, of only some sixty inorganic compounds of the type MX 7l are the true molecular weights known, and it is impossible to draw unequivocal conclusions regarding the valency of an element M which does not from gasifiable compounds of the type MX n , where X represents some monovalent atom or group. No compound of sodium has been vaporised. Sodium chloride may have the molecular composition NaCl, in which case sodium is a monovalent atom ; but there is no di priori reason why the molecular composi- tion of salt should not be Na 2 01 2 . . . Na ?l Cl n , in which cases the sodium atom may be respectively di- tri- . . . n . . . (2n 1)- valent. Further, of the elements with gasifiable compounds of the type MX TO none except silicon, which is very closely related to carbon, shows a constant valency as X is varied. Thus, the phosphorus atom is trivalent in phosphine PH 3 , and pentavalent in phosphorus pen- tafluoride PF 5 . Nor, by reason of the comparative simplicities of the molecules of inorganic bodies, the thorough and so to speak annihilatory nature of the changes they undergo, and the absence of marked cases of isomerism among them, 1 are questions rela- 1 The only well-marked cases of isomerism (it may, however, be polymerism) in inorganic chemistry are afforded by the so-called inorganic amines the numerous and complex bodies which are formed by the action of ammonia, under varied conditions, on the salts of such metals as platinum, cobalt, chromium, and rhodium. See Ramsay, System of Inorganic Chemistry, p. 524, et seq. The structural formulae which have in some cases been assigned, to these inorganic isomers are open to great doubt and uncertainty. MOLECULAE ARCHITECTURE 159 ting to structure of so much importance in inorganic chemistry as they are in the domain of carbon com- pounds. For all these reasons the theory of valency admits of much more definite and productive application to carbon compounds than to inorganic bodies; indeed it may seriously be questioned whether the necessarily loose and gratuitous applications of considerations of valency to inorganic compounds have not impeded the progress of the science at large. 1 That such applications brought discredit on the theory itself will be admitted by most. 1 The valency data of greatest practical importance in inorganic chemistry are here tabulated I. Metals and basic radicles (a) monovalent, K, Na, Li, Rb, Cs, NH 4 , Ag, Hg ous , Cu ous , Au ous , Tl ous , BiO. (j8) divalent, Ca, Sr, Ba, Pb, Mg, Zn, Cd, Hg ic , Cu ic , Sn, Fe U8 , Cr ous , Mn ous , Co, Ni, Be, Pt ous , UO 2 . (7) trivalent, Au ic , Al, Bi, Fe ic , Cr ic , Tl ic . (5) tetravalent, Sn ic , U ous , Pt ic . II. Non-metals and acidic radicles (a) monovalent - Cl, - Br, - 1, - F, nitrites - NO 2 , nitrates - NO 3 , hypochlorites-CIO, chlorates- C1O 3 , cyanides - ON, cyanates - CNO, thiocyanates - CNS, metaphosphates - PO 3 , perchlorates-C!O 4 . (|8) divalent - O, - S, sulphites - S0 3 , sulphates - SO 4 , thiosul- phates- S 2 O 3 , carbonates - CO 3 , silicofluorides-SiF 6 , chro- mates - CrO4, dichromates - Cr 2 07, orthomolybdates - Mo0 4 , tungstates- WO 4 , metaborates - B 2 O 4 , pyroborates - B 4 O 7 , metasilicates - Si0 3 . (7) trivalent, phosphites - PO 3 , phosphates - P0 4 , ferricyanides -Fe(CN) 6 , arsenites - AsO 3 , arseniates - AsO 4 , ortho- borates - BO 3 . (5) tetravalent, ferrocyanides - Fe(CN) 6 , pyrophosphates - P 2 O 7 , orthosilicates - SiO 4 . By means of this table, the formula of any common inorganic salt can be found. Place the symbols for the metal and acid radicle of the 160 LAW AND THEORY IN CHEMISTRY The chief services that the theory of valency has ren- dered the chemistry of carbon compounds have been in the domain of isomerism. The theory enables us to pre- dict with absolute certainty the number of isomers con- sistent with a given molecular composition. The general idea one is apt to glean from much of the literature on the subject is that valency lies at the basis of the so-called constitutional or structural formulae. This is not the case. What does lie at the basis of structural formulas is merely the conception of definite atomic linkage a conception of lower order than that of valency. It is quite possible to symbolise succinctly the chemical relations of a body to give it a structural salt in juxtaposition ; then multiply one or other of these symbols, or it may be both, so that the metallic atoms and acid radicles become equivalent. Express these multiples in small subscripts placed after the respective symbols, and the result is the formula required. Thus calcium phosphate is Ca 3 (PO^o ; for we must take three divalent atoms and two trivalent radicles in order to get a balance of the valencies of the two constituent parts of the salt. The table is necessarily incomplete. Elements which form halides of several types, but no stable oxysalts, e.g., W and Mo, have been omitted. As regards the formulae of oxides, the table is only available for those markedly basic oxides which form corresponding salts ; it correctly gives the formulae for such oxides as ferrous oxide, baric oxide, &c., but it does not help us in the cases of the magnetic oxide of iron, baric peroxide, &c. Further, it only gives the formulae for normal salts ; the complex poly-salts formed by weak acids such as boric, molybdic, tungstic, silicic, &c., are most simply represented, not as made up of metal and acid radicle, but of acidic and basic oxide, thus n BO m AO, where BO is the oxide of a metal, AO the oxide of a non-metal, and m n are whole numbers. However, these complex salts can also be represented as derived from the normal salts. Thus the mineral serpentine usually written 2SiO.>3MgO, may also be regarded as a dehydrated acid magnesium ortho-silicate, Mg 3 H 2 (SiO4) 2 -H. 2 O = Mg 3 Si:>07. Obviously, the table does not inform us as to the possible number or the limit forms of such complex salts. ' MOLECULAR ARCHITECTURE 161 formula recalling its mode of formation, suggesting its decompositions, &c., by means of certain conventions respecting the written arrangements and groupings of the constituent atoms, and without in any way having recourse to the teachings of valency. Thus, the symbol HO . S . OH conveys much information concerning sul- phuric acid, and yet is framed without any regard to the doctrine of valency. This symbol pictures the fact of the symmetry of the sulphuric acid molecule, and therefore the impossibility of the existence of isomeric forms of the derivatives HBS0 4 and RR'S0 4 . Further, knowing the equal value, substitutionally, of Cl and (OH), of H and K, &c., and also the readiness with which hydroxyl groups linked to the same atom interact, the following transformations are at once suggested by the symbol given 00 00 C1.S.C1 Cl.S.OH Cl.S.OK KO.S.OK S.O 0000 To argue whether the sulphur atom is tetra- or hexa- valent in sulphuric acid is profitless. The formulas HO .0 HO S OH S HO do not convey any more information about the pro- perties of sulphuric acid than does the simple representation HO . S . OH. O 1 62 LAW AND THEORY IN CHEMISTRY Before proceeding to illustrate the applications of considerations of valency to organic bodies, it is first necessary to speak of the valencies of compound radicles. A compound radicle is a group of atoms which, like a single elementary atom (simple radicle) appears as an undecomposed whole throughout a large series of compounds or transformations. Like an atom, too, a compound radicle has a definite valency. These compound radicles, or stable atom complexesj play so conspicuous and important a role in the field of carbon compounds that they were once regarded as the true atoms of organic chemistry, which itself was supposed to be adequately defined as the chemistry of compound radicles. As random examples of these compound radicles we may cite ethyl C 2 H 5 , ethyoxyl 2 H 5 0, hydroxyl OH, carboxyl COOH, and amidogen NH 2 all monovalent radicles, for each combines with a single atom of hydrogen to form a gaseous mole- cule ; the divalent radicles ethenyl C 2 H 4 , carbonyl CO, and the trivalent radicles, glyceryl C 3 H 5 and methenyl CH. Now, if the carbon atom can hold in combination four hydrogen atoms, it will also hold in combination four monovalent compound radicles, and therefore such molecules as OC 2 H 5 H NH 2 I I I C 2 H 5 - C - OCoH 5 HOOC - C - COOH H - C - COOH, &c. I I I OC 2 H 5 H H ought to, and do, exist. MOLECULAR ARCHITECTURE 163 Hence we are bound to give an extended significance to the statement the carbon atom is tetravalent. Not only does it imply that the carbon atom combines with four atoms of hydrogen to form a gaseous molecule, but further that in any molecule a carbon atom is capable of directly interacting with four, but no more than four, other atoms, the particular valencies of these atoms being a matter of indifference. Thus in the ethyl ether of ortho-carbonic acid, C(OC 2 H 5 ) 4 , the heavily printed carbon atom directly interacts with four divalent oxygen atoms, each of which again directly interacts with a monovalent ethyl group. In glycocine CH 2 .KH 2 .COOH the heavily printed carbon atom acts on two mono- valent hydrogen atoms, one trivalent nitrogen atom, and one tetravalent carbon atom four atoms in all. Let us now proceed to apply these considerations to isomerism. A body is discovered having the molecular composition C 2 H 6 0. Can it have isomers, and if so, how many? The answer returned by the valency theory is this. If the constituent atoms can be arranged in n different ways so that each of the carbon atoms never interacts directly with more than four other atoms, and each of the oxygen atoms with more than two other atoms, then n isomers, all told, are possible. As a matter of fact, it is found on trial that the atoms C 2 H 6 can be arranged in only 164 LAW AND THEOKY IN CHEMISTRY two ways, subject to the restrictive conditions just stated H H H H I I II H C C H H C C H II II H H H H In strict accordance with this result, all attempts to prepare more than two isomers of the composition C 2 H 6 have failed. The two known substances having this formula are methyl ether and ordinary alcohol. The problem next rises, which of these formulse are we to ascribe to methyl ether ; which to alcohol ? This is solved by the knowledge of the fact that one atom of hydrogen in the alcohol molecule differs from the remaining five in that it alone can be replaced by alkali metals. Now, in the left-hand formula all the atoms of hydrogen are similarly related to the molecule, but in the right-hand formula five atoms of hydrogen directly interact with carbon atoms (i.e., are directly linked to carbon atoms), while the sixth hydrogen atom acts only indirectly on a carbon atom through the oxygen atom. Therefore the right-hand formula belongs to the molecule of alcohol, and therefore by exclusion the left-hand one represents methyl ether. Further, the syntheses and all the known transformations of methyl ether, and ethyl alcohol, are in strict conformity with, and indeed are deducible from, their appropriate symbols thus arrived at. Although in many cases more isomers ought to exist MOLECULAR ARCHITECTURE 165 according to the teachings of valency than are at present known, 1 yet in no case is a greater number of isomers known than is provided for, and anticipated by, the valency theory. Till within quite recent years this statement could not have been made. It would seem to follow from the simple case already considered, that isomerism ought always to be accom- panied by differences in chemical properties, these differences finding expression in, and being due to, the differing molecular architectures of the isomers. Yet bodies are known which, having the same molecular weight and the same composition, undergo precisely the same chemical transformations, and are yet quite different in such physical properties as crystalline form, solubility, action on polarised light, &c. Such bodies, on account of the identity of their chemical transfor- mations, must be assigned identical formulae identical molecular architectures ; and for this reason they were for long regarded as forming exceptions to, or at least falling outside the pale of the province of the "theory" of valency. Hence they were relegated to a kind of suspense class, bearing the title physical isomers. We now know, thanks to the researches of van't Hoff and Le Bel, that these are not exceptional pheno- mena, but are fully provided for by the theory of valency, if we do not limit the possible different 1 For instance, nine heptanes having the composition CrHie, ought to exist according to the teachings of valency ; as yet, however, only four bodies having this composition have been isolated. 1 66 LAW AND THEORY IN CHEMISTRY arrangements of atoms in space by the different arrange- ments possible in a plane. It is not irrational to assert that two isomers t of the formula CH 2 C1 2 should exist. For the formulae H H I I Cl C Cl Cl C H I I H Cl while both in accordance with the dictates of valency, obviously differ. In the right-hand formula the two chlorine atoms are not related to the rest of the mole- cule in the same way as they are in the left-hand formula. Why should not this difference entail a difference in properties a possible isomerism of the molecule CH 2 C1 2 ? It evidently does not, for all attempts to prepare two different bodies of the formula CH 2 C1 2 (and Henry has made many such) have failed. We are therefore compelled to still further enlarge our conceptions of valency by the conclusion that there is really no difference between the above formulas that the order of cyclical arrangement of the atoms round the central carbon atom is, in effect, immaterial. Con- sequently, no isomeric molecules of the types CHR r 3 , CHR T R n 2 , CHR'^'R 111 , CR^R'V CR^R 11 , CR 1 R ir R III R IV , should exist. In partial accordance with this con- clusion, no isomers of the first five types are known, but, contrary to the conclusion, all the simplest of the so-called physical isomers conform to the sixth type, MOLECULAR ARCHITECTURE 167 " 1 !^ possess what is called an asymmetric carbon atom. Van't Hoff and Le Bel showed the way out of this difficulty by reminding us that molecules are tri- and not di-dimensional entities. We get a spatial conception of molecules in accord- ance with the limitations of valency, if we conceive the carbon atom placed at the centre of a tetrahedron, its four "valencies" or "bonds" being directed towards the four solid angles a, b, c, d, of the tetrahedron. So long as the monovalent atoms or radicles on which the carbon atom directly in- teracts are not all different, then it is impossible to place them at the angles a, I, c, d, so as to occupy in dif- ferent dispositions different spatial relations to the central carbon atom. Let A stand for one of the dispositions, and B for another, and suppose the two tetrahedra interpenetrative, then it will always be possible, no matter the dispositions, so to place A inside B, or vice versd, that the similar atoms or radicles attached to the central carbon atoms will fall together and occupy the same region of space. In short, the two dispositions will always be super- posable. But when the atoms or groups at the angles a, b, c, d, are all different from one another, then it is possible F IG . 3. 1 68 LAW AND THEORY IN CHEMISTRY to get two dispositions which are non-superposable the one disposition bearing to the other the same rela- tion as does an object to its image in a plane mirror ; the same relation as a left-hand glove bears to a right- hand one. In crystallography this would be called an enantiomorphous relationship. In other words, if in one molecule the atoms or radicles are regarded as disposed around the central carbon atom in a right- handed spiral, then in the other molecule the disposition is a left-handed spiral. Let us illustrate this last case by the lactic acids which indeed first suggested to Wislecenus the neces- sity of introducing stereometric conceptions into the domain of molecular architecture. Three lactic acids are known ; they have all practi- cally identical chemical properties, but differ from each other in their action on polarised light, and in the solubilities of their salts. Dextrolactic acid turns the plane of polarisation to the right; sarcolactic acid to the left; while fermentation lactic acid is optically inactive. The molecules of these lactic acids must, from their chemical relationships, have the structure CH 3 HOOC C H I OH Th,e heavily printed carbon atom in the above symbol is obviously asymmetric. Therefore there are possible MOLECULAR ARCHITECTURE 169 two different dispositions around it of the radicles it holds in combination, viz. : OH COOH COOH OH FIG. 4. FIG. 5. One of these dispositions must characterise dextrolactic acid ; the other, sarcolactic acid. Yet in the present state of our knowledge it is impossible to definitely allocate them. But what of the third lactic acid the inactive modification ? The theory at first sight does not seem to provide for it. It has now been definitely proved that inactive or ordinary lactic acid is not a true chemical unit, but a mixture in compensating quantities of the dextro and laevo modifications. Its formula would be given by placing a plus sign between the above two figures. 1 Attempts have recently been made to find some con- 1 For the further development of stereometric ideas we would refer the reader to Marsh, Chemistry in Space, and Auwers, Die Entivickelung der Stereochemie. Suffice it here to say that there are no known instances of physical isomersion of carbon compounds which do not receive full and adequate interpretation in terms of the attributes of the asymmetric carbon atom. i;o LAW AND THEOKY IN CHEMISTRY nection between the masses of the radicles, R 1 , E/ 1 , R m , and R IV , held in combination by an asymmetric carbon atom, and the nature and amount of the optical activity which, unless compensatory influences come into play, is invariably associated with asymmetric carbon atoms. A regular tetrahedron has six planes of symmetry ; a plane of symmetry bisecting each of the six inter- facial angles of the figure. 1 Let us suppose that the centre of such a tetrahedron is occupied by a carbon atom, and that four atoms or radicles are disposed round the carbon atom so that their masses are concentrated at the apices of the four solid angles of the tetrahedron. So long as these four radicles are not all dissimilar, the centre of gravity of the whole system will be in one or other of the six planes of symmetry of the tetra- hedron, and there will be no optical activity. But when all the radicles or atoms differ among themselves, the centre of gravity of the system no longer falls within any of the planes of symmetry, and optical activity makes its appearance. Let the perpendicular distances of the centre of gravity of the system in this latter case from the six planes of symmetry be d v d 2 , d 3 , dy d & and d 6 . Then the product P = d l X d 2 X d 3 x d X d 5 x d 6 is, according to Guye, a measure of 1 " A plane of symmetry may be defined as a plane which is capable of dividing a body into two halves which are related to each other in the same way that an object is to its reflection in a mirror. More exactly we may say : two objects or two halves of the same object are symmetrical with reference to a plane placed between them, when from any point of one object a normal to this plane, prolonged by its own length on the opposite side of the plane, will meet the corresponding point of the other object." Williams, Elements of Crystallography. MOLECULAR ARCHITECTURE 171 the asymmetry of the molecule, and should therefore be proportional to the optical activity of the substance. If plus and minus signs be conventionally applied to the distances d v d 2 , d 3 , &c., according as they are measured from one side or the other of each plane of symmetry, P may be either positive or negative according to circumstances. Guye has shown how P may be calculated before- hand for any meditated derivative of a given optically active substance. If the passage from an optically active body A to an optically active substitution derivative A' would involve an increase in the value of P, then, according to Guye, we may predict that A' will be more active optically than the parent substance ; if the transformation would involve a diminution in the value of P, then the new body will be less active than the original one from which it was derived. Finally, if the passage from A to A' is accompanied by a change of sign of P, then the parent substance and its derivatives* will produce opposite rotations; one will be a dextro-rotatory sub- stance, the other a laevo-rotatory substance. In the following symbol for active amyl chloride, it can readily be shown that CH CH the centre of gravity of the system falls on the CH 2 C1 \\ 7 c / a cl side of the dotted plane of symmetry C 2 H 5 mH. If there- fore the chlorine atom in the CH 2 C1 group be replaced by a heavier atom, the 172 LAW AND THEORY IN CHEMISTRY HO centre of gravity of the system must still remain on the same side of the plane C 2 H 5 mH, but will be further removed from it. Accordingly it is found that amyl bromide has higher optical activity than the chloride ; and amyl iodide in turn higher activity than the bromide. 1 Let us take another illustrative application of Guye's theory. In the accompanying symbol for dextro-tartaric acid, the centre of gravity would lie on the C0 2 H side of the dotted plane Hmm'H. Let us now replace the H atoms of the hydroxyl groups by acetyl radicles (acetyl = CH 3 CO). This substitution carries the centre of gravity over to the other side of the plane Hmm'H ; and it is found as a matter of fact that diacetyl tartaric acid is laevo-rotatory. Now let us form etherial salts of diacetyl tartaric 1 The values are as follows : [o] D = 1 6' for the chloride. = 4 24' for the bromide. = 8 20' for the iodide. In these equations [ct] D may be taken to represent the angle through which the plane of a polarised ray of sodium light would be turned if it were made to pass through a tube of y^ square centimetre cross section, and of just sufficient length to hold exactly one gram of the substance under examination. FIG. MOLECULAR ARCHITECTURE 173 acid by replacing the H atoms of the carboxyl groups with alkyl monovalent radicles E (e.g., C 2 H 5 , C 3 H 7 , &c.). This brings the centre of gravity of the system back towards the C0 2 E side of the plane Hmw'H, and consequently we find that the Isevo-rotatory power of the etherial salt diminishes as the weight of R increases, until finally the rotation changes sign and the higher etherial salts of diacetyl tartaric acid are dextro-rotatory. Diacetyltartaric acid [a] D = - 23'14 Methyl-diacetyl-tartarate - 14-29 Ethyl + 1-02 Propyl + 6-52 Although many facts are in harmony with pre- dictions founded on Guye's views of the relations between optical activity and molecular asymmetry, CH CH OH HO COOC iP, OH FIG. 8. FIG. 9. yet isolated instances of exceptions to his generalisa- tions are not wanting. Thus from the accompanying diagrams it is easy to see that ethyl gly cerate (Fig. 9) 174 LAW AND THEORY IN CHEMISTRY should have higher optical activity than ethyl lactate (Fig. 8) ; but as a matter of fact the optical constants for these two bodies are as follows : Ethyl lactate [a] D = - 14-19 Ethyl glycerate [a] D = - 9-18 Again, such a body as ethylic diacetyl glycerate CH 2 O.C 2 H 3 H.C.O.C 2 H 3 C OOC 2 H 5 should be optically inactive if mass were the only factor determining optical asymmetry ; for the two isomeric radicles CH 2 . . C 2 H 3 and COOC 2 H 5 have equal masses, and when this is the case P must be zero. For if a, I, c, d represent the masses of the radicles held in combination by an asymmetrical carbon atom in such a way that these masses are concentrated at the apices of a regular tetrahedron, then one of the factors in determining the value of P is (a - b)(a - c) (a - d) (b - c) (b - d) (c - d) (a + b + c + d)* It is clear that if any two of the masses a, b, c, d become equal in value, then P the product of asymmetry must also become zero. When this is the case, the optical activity which is supposed to accom- pany asymmetry in Guye's sense, should disappear. Hence it would appear that in addition to mere mass MOLECULAR ARCHITECTURE 175 relationships, considerations of structure must also find a place in future attempts to quantitatively link to- gether optical activity and molecular asymmetry. So far we have only dealt with what were once regarded as exceptional isomerisms among saturated carbon compounds. We now turn to peculiar cases of isomerism presented by unsaturated carbon compounds of ethylenic and acetylenic types, i.e., compounds in whose molecules one or more of the carbon atoms directly acts on less than four other atoms or radicles. 1 Many of the isomeric bodies of this class, while on the whole resembling each other chemically, yet in addi- tion to purely physical differences manifest also minor chemical contrasts. It is of especial significance that the physical differences alluded to do not, as in the case of saturated bodies, involve optical activity. ' 1 The carbon atoms in ethylene and acetylene are often said to be doubly and trebly linked respectively, and the two substances are represented as follows H-C-H C-H II ' 111 H-C-H C-H C If | symbolises a certain interaction between a pair of carbon C C C atoms, i| and ||| certainly suggest interactions of double and treble C C intensity ; but Thomsen's thermochemical studies in this direction, as well as the salient chemical characteristics of ethylene and acetylene, are at variance with such a state of things. That all the four points of maximal attraction ("bonds") of the carbon atom must always be in active operation is an unwarranted assumption passed down from the early school of constant valency. The intra-molecular movements of ethylene may be of such a nature that only the three greatest maxima of attraction are able to effectually assert themselves. 1 76 LAW AND THEORY IN CHEMISTRY Moreover, these cases of isomerism, unlike the optical isomerism just discussed, are not inconsistent with the two-dimensional expression of the doctrine of valency. As illustrative, let us take the case of the isomerism of maleic and fumaric acids. These two acids differ in their physical properties as follows. While fumaric acid sublimes on being heated, maleic acid has a definite melting point, 130 ; and the latter acid is much more soluble than the former. While the chief reactions 1 of the two acids demand in each case the same rational formula, viz. fC.H.COOH I C.H.COOH yet the following minor differences between the two acids may be cited. Fumaric acid is more stable than maleic, so that reactions which take place with maleic acid, under ordinary conditions, require high tempera- tures and high pressures in the case of fumaric acid. Some reactions, e.g., etherification, proceed in the case of both acids under the same conditions, but at a slower rate with fumaric than with maleic acid, Maleic acid readily yields an anhydride, fumaric acid does not. The action of bromine on the two acids gives rise to different products; from fumaric acid dibromosuccinic acid re- sults ; from maleic, iso-dibromosuccinic acid. Another peculiarity of these isomers is the readiness with which fumaric acid can be changed into maleic acid derivatives, 1 Both acids are dibasic, and are formed from malic acid by dehydra- tion. Reducing agents convert both acids into succinic acid. MOLECULAR ARCHITECTURE 177 and maleic acid into fumaric acid derivatives. Thus, if maleic acid is treated with bromine, and then the elements of hydrobromic acid are subsequently removed by the action of water, the result is bromofumaric acid. Conversely, bromomaleic acid can be obtained by a similar series of operations from fumaric acid. Enough has been said to indicate that we have here a much more pronounced kind of isomerism than that which the lactic acids presented. Moreover, in this case different di-dimensional arrangements of the atoms in the complex C 2 H 2 (COOH) 2 are consistent with the tetravalency of the carbon atom. Hence numerous attempts have been made to assign to the two acids di-dimensional structural formulae. Such structural formulae necessarily involve different radicles in the two cases, despite the great chemical similarity of the acids. Thus, Anschiitz, while retaining the formulae COOH C H II COOH C H for fumaric acid, advocates as best representing the molecular, structure of maleic acid. But these di-dimensional representations met M iy8 LAW AND THEORY IN CHEMISTRY with so little favour generally that the term allo isomerism was provisionally introduced to group to- gether such apparently inexplicable cases of isomerism among unsaturated bodies as are typified by the acids under discussion. 1 When recourse is had to spatial considerations we find that all difficulty disappears, and that the reten- tion of the term allo-isomerism is needless. For there are two, and only two, tri-diniensional arrangements COOH HOOC COOH FIG. 10. FIG. 11. of the atom complex C 2 H 2 (COOH) 2 , in each of which essentially the same structural units obtain, i.e., the same radicles are involved in each case. These two arrangements will be sufficiently obvious from the accompanying plane projections. So far our conceptions of valency have been purely 1 There are, however, many who still maintain that the di-dimen- sional formulae represent the properties and peculiarities of the two acids better than do the accepted tri-dimensional ones. MOLECULAR ARCHITECTURE 179 statical, but Wislicenus, by introducing dynamical ideas, has much extended the original theory of van't Hoff and Le Bel. According to Wislicenus, the atoms in a molecule exert influences on each other even when, according to the teachings of valency, they do not directly interact, i.e., link each other. The negative or chlorous atoms have a great attraction or affinity for the positive or basylous atoms, and this attrac- tion is either partially satisfied in the molecule by the chlorous atoms swinging themselves as near as possible to the basylous atoms ; or it may be that the attraction only sets up an intra-molecular stress which, under favourable conditions of tempera- ture, &c., asserts itself, and causes such a rotational movement in the molecule that the mean distance between the mutually attracting atoms is made as small as possible. In terms of these views, not only is it possible in many cases to assign the appropriate formula to a given isomer, but obscure chemical transformations, such as the before-mentioned mutual convertibility of fumaric and maleic acid derivatives, find a full explanation. Indeed Wislicenus' views have raised the van't Hoff-Le Bell hypothesis from the level of mere co-ordination and explanation of known facts, to the higher level of prophecy; it now not only explains, but anticipates facts. For a complete exposi- tion of Wislicenus' views we would refer the reader to the pamphlet Uber die rdumliche Anordnung der Atome in organischen Molekulen (Hirzel, Leipzig). - UNIVEBSITl i8o LAW AND THEORY IN CHEMISTRY All we can do here is to exemplify these new views very briefly as they bear on the isomerism of maleic and fumaric acids. The first question to be settled is Of the two formulae, which is to be assigned to fumaric, which f -cooj HO O C to maleic acid ? The left-hand formula figures a more stable system than does the right-hand one, for in the former the chlorous carboxyl groups are as near as is possible to the basylous hydrogen atoms. But fumaric acid is, as we have said, a more stable acid than maleic; hence the left-hand formula sym- bolises fumaric acid, and, by exclusion, the right-hand formula maleic acid. The constitution of maleic acid explains its ready dehydration. The water which splits off during the formation of an anhydride from an acid is known to result from the hydroxyl portions of carboxyl groups, and it is but natural to assume MOLECULAR ARCHITECTURE 181 that the proximity in the molecule of these groups would favour a reaction in which both are simul- taneously implicated. Let us now explain by a typical example the rationale of the formation of maleic acid derivatives from f umaric acid. When bromine and fumaric acid are heated to- gether, each molecule of the acid takes up two atoms of halogen. This, in terms of stereometric formulae, can only take place in one way : HOOC HOOC COOH COOH BJ? FIG. 14. But the resulting molecule pictured is in a state of internal stress by reason of the attractions of the strongly positive hydrogen atoms for the strongly negative bromine atoms. As a result of this stress, an intra-molecular rotation around the axis joining the two asymmetric carbon atoms ensues, so as to bring the hydrogen atoms into as close proximity as possible 1 82 LAW AND THEORY IN CHEMISTRY to the bromine atoms. 1 Hence, when by the subse- quent action of water a molecule of hydrobromic acid COOII HBi* COOH Br FIG. 15. COOI COOH is removed, the only possible result is bromo-maleic acid. 1 From the phenomena presented by the isomerism of the three HON.C.C 6 H 5 benzil dioximes, all of which have the formula Meyer HON.C.C 6 Hg and Auwers concluded that carbon atoms may be linked in two ways ; one way admitting of free rotation of the parts of the molecule round the joining axis, and another way inconsistent with any rotational movement. It has, however, been pointed out, that the exceptional isomerisms exhibited by the benzil dioximes might be explained without having recourse to the idea of non-rotational, singly linked, carbon atoms, by applying stereometric considerations to the nitrogen atom e.g., regarding it as occupying one angle of a tetrahedron, its three " valencies " or "bonds" being directed towards the other three angles. But as yet nothing very definite can be said concerning the stereochemistry of the nitrogen atom ; the whole subject has not yet emerged from the purely tentative stage. It may here be stated that an attempt has quite recently been made to account for the isomerism exhibited by amido-platinum compounds of the type MOLECULAR ARCHITECTURE 183 Many substances are known, to each of which it seems necessary to assign more than one formula. Such substances therefore exhibit a peculiar kind of isomerism which has been called tautomerism. Some of the reactions of such a tautomeric body suggest one structure for it, while other of its reactions seem to demand quite another structure. It has been pro- posed to call the alternative structures of a tautomeric body its desmotropic forms or states. Laar, who first drew attention to this form of isomerism, is inclined to think that the molecular architecture of a tautomeric body is changing from moment to moment that the structure of hydrocyanic acid is at one instant HNC and at the next instant NCH. Others, however, are of the opinion that one of the structures, being a more stable configuration than the other, really represents the body in the free state, but that this stable form is under certain conditions, and by the action of certain reagents, primarily trans- formed into the less stable, pseudo, or labile form which then undergoes further change. Thus phloro- glucone behaves sometimes as a phenol giving metallic derivatives and methyl ethers, at other times as a note, p. 158), by applying spatial considerations to the platinum atom. The latter is regarded as occupying the centre of a regular octahedron, at the six solid angles of which are placed the atoms and radicles constituting the molecule. 1 84 LAW AND THEORY IN CHEMISTRY ketone or carboxyl compound giving oximes. The formula appertaining to its stable phenolic form, i.e., to phloroglucone properly so-called, is C.OH HC / \ CH HO.C C.OH CH while its ephemeral labile ketonic form demands the structure CO H 2 C OC CH 2 CO CH, In some instances, both desmotropic forms are capable of continued and. well differentiated existence in the free state and even in solution. Thus succino- succinic ether exists in both a colourless and a yellow modification. It should be remarked that, so far as is known, all cases of tautomerism depend on the mobility in the molecule of hydrogen atoms ; the passage from one desmotropic form to another being effected by the wandering of one or more hydrogen atoms. These new views may perhaps be adduced to account MOLECULAR ARCHITECTURE 185 for the curious transformations exhibited by cyanogen compounds. Potassium cyanate NOOK prepared from cyanic acid NCOS, when treated with ethyl iodide C 2 H 5 I gives ethyl isocyanate OCNC 2 H 5 , and not ethyl cyanate as would naturally be expected. Yet isocyanic acid OCNH, the desmotropic form of cyanic acid NCOH, is not known in the free state ; the ethyl radicle is required to confer stability on the apparently extremely labile configuration OCNH. Similar considerations may be applied in explanation of the behaviour of cyanuric and thiocyanic acids. CHAPTER VII CHEMICAL EQUILIBRIUMS ALTHOUGH the occurrence of chemical interaction between solutions of sodium sulphate and hydrochloric acid is not manifest to the unaided senses by reason of the fact that all the factors and products of the inter- action are soluble colourless bodies, yet we have con- vincing indirect proofs that such an interaction does actually take place. 2 Moreover, the evidence in favour of the occurrence of chemical change between solutions of sodium sulphate and hydrochloric acid is of such a nature that we are forced to conclude that the interac- tion is not correctly represented by the equation q + 2HClAq = 2NaCl Aq + H 2 S0 4 Aq. For, by convention, this equation when interpreted into words would run : Dilute solutions of sodium 1 As dissociation phenomena are generally fully treated in elementary text-books, this chapter has been almost wholly devoted to a study of those equilibria which are established in solutions of chemically interacting substances at ordinary temperatures. 2 See note, p. 193. It is very easy to prove the occurrence of chemical change in the particular system MgSC^Aq + 2NaClAq. although the interaction is not accompanied by visible changes under ordinary conditions. It is only necessary to cool a mixture of the solu- tions of the two salts, when the very slightly soluble sodium sulphate will partially crystallise out in a hydrated form. 186 CHEMICAL EQUILIBKIUM 187 sulphate and hydrochloric acid when brought together in equivalent quantities 1 completely decompose each other with the formation of equivalent quantities of sodium chloride and sulphuric acid which both remain in solution. Now, as a matter of fact, such a complete decomposi- tion of the sodium sulphate and hydrochloric acid does not take place under the specified conditions (dilute solution, and equivalent quantities of the reagents). Only a portion of the system Na 2 S0 4 + 2HC1 + Aq is changed into the system 2NaCl + H 2 S0 4 + Aq. This fact might be adequately represented in the following manner (m + n) Na 2 S0 4 Aq + (ra + n) H 2 Cl 2 Aq = m Na 2 Cl 2 Aq + m H 2 S0 4 Aq + n Na 2 S0 4 Aq + n H 2 Cl 2 Aq From this representation we learn that when (m -f n) 1 Those quantities of acids which neutralise a fixed quantity of any base are equivalent. Conversely those quantities of bases which neutralise a fixed quantity of any acid are equivalent. This was the original and most obvious meaning of equivalency, but the original meaning of the term has been widened so that it now applies to salts as well as to acids and bases. A quantity, x grs., of a salt (MA) is said to be equivalent to a quantity y grs. of an acid A', if the quantity of acid A necessary to produce x grs. of the salt MA is equivalent in the original acceptation of the word to y grs. of the acid A'. Thus the molecular weight of sodium sulphate interpreted in grams [142 grs.] is formed from the molecular weight in grams [98 grs.] of sulphuric acid. But 98 grs. of sulphuric acid is equivalent to, i.e., will neutralise the same quantity of any base as, 73 grs. of hydrochloric acid or two molecu- lar weights of hydrochloric acid expressed in grams. Therefore in accordance with the widened significance of the term equivalence now in vogue, 2HC1, HoSC>4, Na 2 S04 represent equivalent quantities of the substances formulated no matter what mass units be used. i88 LAW AND THEORY IN CHEMISTRY - . equivalents of sodium sulphate are brought together with an equal number of equivalents of hydrochloric acid in dilute aqueous solution, only m equivalents of the two substances undergo chemical change, the residual n equivalents of each substance remaining unchanged. But this is not a perfectly satisfactory method of repre- sentation, for this reason. It suggests that the mole- cules of each of the reacting substances must differ in some way or other among themselves, seeing that some enter into chemical reaction under the conditions, while others apparently do not. And this is not in con- formity with the fundamental principle of the atomic- molecular theory, which principle asserts that the molecules of a substance are all precise replicas one of another, both in structure and attributes. If one molecule of sodium sulphate reacts under certain con- ditions, then we should expect all the molecules of sodium sulphate to react under these conditions. The difficulty disappears at once if we regard re- actions like the one under consideration as the result of two independent and antagonistic chemical changes proceeding simultaneously within the system. 1 When hydrochloric acid is added to an equivalent quantity of sodium sulphate in dilute aqueous solution, 1 That two or more reactions can proceed within a system simul- taneously and independently one of another is the enunciation of the principle of the coexistence of reactions a principle which bears much the same relation to chemistry as does Newton's second law of motion to dynamics. This principle has never been directly proved ; but reasoning founded on the assumption of such mutual independence of reactions has led to results in harmony with experimental fact, and thus the truth of the principle is established. CHEMICAL EQUILIBK1UM 189 molecules of sodium chloride and sulphuric acid are formed at a gradually diminishing velocity as time goes on. 1 The new molecules thus formed do not, however, remain inert, but interact to reproduce molecules of the original substances at a gradually increasing velocity. Let us call the passage from Na 2 S0 4 Aq + H 2 Cl 2 Aq to Na 2 Cl 2 Aq + H 2 S0 4 Aq the direct partial change, and the passage in the opposite direction the reverse partial change. What causes the velocities of the two changes thus defined to vary from moment to moment ? Guldberg and Waage first definitely answered this question, by as- serting that the velocity of every change at any moment varies directly as the product of the number of the equivalents of the factors of the change present in unit volume of the medium of change. As this number is continually varying, owing to the occurrence of change, it follows that the velocity must also continually vary. 1 No chemical change is instantaneous, but every change requires for its occurrence a period of time varying from a fraction of a second too small to measure, to several years. The reactions between various acids and alkalis (i.e., neutralisation) take place in so short a time that it has not been possible to measure their absolute durations. Estimates of their relative durations have, however, been indirectly obtained. On the other hand, many of the reactions between organic bodies proceed very slowly indeed. Witness in this connection the slowness of the chemical changes occurring in the so-called ageing of wine. The use of the word velocity in connection with chemical reactions as introduced by Wenzel in 1777 demands explanation. The original dynamical meaning of the term is space passed over per unit time. But the idea of space does not enter into the definition of the term in its chemical acceptation. The velocity of a chemical reaction at any moment simply denotes the quantity of substance (expressed in equivalents) that undergoes change per unit of time at that moment. IQO LAW AND THEORY IN CHEMISTRY Suppose the two substances A and B combine com- pletely to form a third body C. Let us bring together solutions of A and B, such that 2p equivalents of A and 2q equivalents of B are contained in unit volume of the resulting solution. Then the velocity, V, of the reaction (i.e., the rate at which C is formed) will vary as 2p x 2q. Or stated algebraically Voo pq V = Where K is a constant called the velocity constant for the change. 1 After a certain time there will be left only p equivalents of A, and q equivalents of B in unit volume of the medium of change. The velocity of formation of C at this epoch, according to Guldberg and Waage, would be ~Kpq only Jth its original value. The principle here illustrated is often referred to as Guldberg and Waage's law of mass action. 2 To return now to the interaction of hydrochloric acid and sodium sulphate. The number of equivalents 1 The velocity constant K must be carefully distinguished from the velocity V. Under given conditions K is constant for any given change, but V of course varies from moment to moment. 2 The first to prove the influence of mass in chemical changes was Wenzel, 1777. Wenzel, however, confined his investigations to a single class of changes, viz., the interaction of metals with acids of various strengths. In the beginning of this century, Berthollet asserted the influence of mass in chemical changes in general terms. "Every chemical change is essentially of the nature of a combination, and the power of any substance to enter into combination is proportional to its affinity and to its mass." This is practically the text of Berthollet's famous work, Essai de Statique Chimique. According to Berthollet, a small affinity can be compensated by a large mass, and hence complete reactions are the exception and not the rule in chemistry. Suppose CHEMICAL EQUILIBRIUM 191 expressed in grams or otherwise (i.e., the masses) of NaCl and H 2 S0 4 resulting from the direct change depends not only on the velocity constant peculiar to the change, but also on the numbers of the equiva- lents (i.e., the masses) of HC1 and Na 2 S0 4 in unit volume of the solution. As these latter numbers are continually decreasing, the velocity of the direct partial change must continually decrease from a maximum value downwards. But as the numbers of the equivalents per unit volume of the factors of the direct partial change decrease, the numbers of the equivalents of the factors of the inverse partial change pari passu increase, consequently the velocity of this change is continually increasing from zero upwards. Hence it necessarily follows that a state of what has been called mobile equilibrium between the direct and re- verse partial changes must finally be reached, whereat the velocities of the two changes being exactly equal, the body C has a stronger affinity for A than has B. Then if C be added to AB in equivalent quantity, the reaction AB + C = AC + B will proceed, but not to completion, for the gradually increasing mass of B will eventually compensate its smaller affinity, and make it for- midable enough to contest successfully the diminishing quantities of C. Before Berthollet's time it had been held that reactions are determined entirely by the stronger affinities ; to which view the fdea of incomplete reactions was quite foreign. From his fundamental premiss, however, Berthollet made deductions which Proust proved to be incorrect (see p. 74), and this overthrow of the incorrect deductions unfortunately brought the correct premiss from which they were derived into dis- repute and temporary oblivion. Guldberg and Waage's law of mass action is nothing else than Berthollet's views reinstated and thrown into mathematically exact form. 192 LAW AND THEORY IN CHEMISTRY effective chemical change one way or the other ceases. When this permanent equilibrium point is arrived at, as many equivalents of HC1 and Na 2 S0 4 are de- composed by the direct partial change per unit time as are formed by the reverse partial change in the same time unit ; but the molecules of Na 2 S0 4 , HC1, -IIN0 3 , and NaCl existing at one epoch are not necessarily the same ones which will be present at another subsequent epoch. If they do chance to be identically the same molecules at the two epochs, we can assert that they have not had a continued exist- ence in the interim. In the representation of these so-called incomplete reactions, wherein a state of equilibrium is finally reached, van't Hoff has proposed to replace the sign of equality in the ordinary equations by a pair of oppositely directed arrows, thus H 2 Cl 2 Aq + Na 2 S0 4 Aq ^ Na 2 Cl 2 Aq + H 2 S0 4 Aq. Now, thoroughly appreciating the nature of the dynamical equilibrium which marks the cessation, not of chemical change, but of effective chemical change, in these incomplete reactions, we will return to that method of their representation which we first gave, and which for the immediate purpose in hand is more convenient than the one proposed by van't Hoff. Let us suppose that in the general equation (m + ra)Na 2 S0 4 Aq + (m raH 2 S0 4 Aq m + n equals 100. The question arises, what are the CHEMICAL EQUILIBRIUM 193 individual values of m and n ? This question has been submitted to experiment, and it has been ascertained that m and n in the above reaction have the approxi- mate values 66f and 33J respectively. 1 Moreover, exactly the same state of final equilibrium is arrived at if, instead of setting out with hydrochloric acid and sodium sulphate, we start with hydrochloric acid and the proximate constituents of sodium sulphate, viz., caustic soda and sulphuric acid, in accordance with the following equation (m + n) Na 2 2 H 2 Aq + (m + n) H 2 S0 4 Aq + (m + n) H 2 Cl 2 Aq = mNa 2 C! 2 Aq + mH 2 S0 4 Aq + This latter method of regarding the reacting system emphasises the fact that the reaction virtually consists in a strife between two equivalent quantities of acids to appropriate a quantity of base only just sufficient to neutralise either acid separately. As a result of this competition the base divides itself between the two acids, twice as much base (i.e., 66f equivalents) combining with the hydrochloric acid as combines with the sulphuric acid (33J- equivalents). In accordance with the results of such investigations as the one just described, acids are classed as weak or strong. When two acids in equivalent quantities and 1 For the actual carrying out of methods suited to the investigation of equilibria see Muir and Carnegie's Practical Chemistry, pp. 141-146, 176-184. 194 LAW AND THEORY IN CHEMISTRY in dilute aqueous solution are presented to a dilute aqueous solution of a quantity of base just sufficient to neutralise either acid separately (or what amounts to the same thing, when an acid is allowed to react with an equivalent quantity of the salt of another acid in dilute aqueous solution) the base is in general divided between the two acids, and the strengths (or affinities, or avidities) of the two acids are proportionate to the quantities of base each appropriates. Thus it follows that sulphuric acid is a weaker acid than hydrochloric, the latter acid being approximately twice as strong as the former. By conducting numerous quantitative ex- periments, involving different pairs of acids, we can obtain a table of the relative affinities or strengths of the acids, such as the following one, in which, however, the values assigned the various acids are admittedly only approximate : Nitric acid . . . . . TOO Hydrochloric acid . . . . 1 -00 Hydrobromic acid .... '89 Hydriodic acid ..... -70 Sulphuric acid ..... '49 Selenic acid . . . . . '45 Trichloracetic acid . . . '36 Orthophosphoric acid . . '25 Oxalic acid . . . . '24 Hydrofluoric acid . . . . '05 Citric acid . . . . . '05 Acetic acid ..... '03 Boric acid -01 Silicic acid '00 CHEMICAL EQUILIBRIUM 195 As will be seen nitric and hydrochloric acids are the two strongest acids, being approximately equal in strength. Compared with either of these, acetic acid is seen to be a very feeble one. If equivalent quan- tities of hydrochloric acid and acetic acid were added to a dilute aqueous solution of caustic soda, contain- ing just enough caustic soda to neutralise either acid separately, the caustic soda would divide itself between the hydrochloric and acetic acids in the ratio of 1 : 03, i.e., about 2'91 per cent, of the soda would combine with the acetic acid and 97'09 per cent, with the hydrochloric acid. In a precisely similar way bases have been classed as weak or strong. Of a pair of bases presented in dilute aqueous solution to an acid only just sufficient to neutralise either base separately, that base which appropriates, or combines with, the greater part of the acid is the stronger base. The following table gives the relative strengths of a few of the better investi- gated bases in terms of the arbitrary value unity assigned to the strongest base, lithium hydroxide : Lithium hydroxide .... 1*00 Sodium hydroxide .... *98 Potassium hydroxide . . . . '97 Thallium hydroxide .... '90 Piperidin . . . . . '16 Ammonia ...... *02 We have seen that hydrochloric acid is approximately twice as strong as sulphuric acid if the criterion be a tug-of-war for a quantity of soda insufficient to meet 196 LAW AND THEORY IN CHEMISTRY the conjoint demands of the two acids. It has been found that approximately the same relation holds between the strengths of the two acids whatever base be made the object of competition, whether potash, or soda, or lime, &c. Moreover, as is well known, acids have the power of inverting cane sugar, that is, of transforming it in the presence of water into a mixture of dextrose and laevulose ; and also in this transforma- tion hydrochloric acid is found to act twice as ener- getically as sulphuric acid. Numerous other reactions might be adduced which are either brought about or accelerated by acids, and in all of them hydrochloric acid is approximately twice as effective as sulphuric acid. Similar remarks apply to changes induced or acceler- ated by bases. If lithium hydroxide is fifty times as strong as ammonia when the struggle for a particular acid is the criterion, then it is found to be approxi- mately fifty times as effective as ammonia in bringing about any other change demanding the intervention of a basic substance. On the basis of the approximately concordant results for the strengths of acids and bases derived from the investigation of such diverse changes as we have hinted, it was at one time claimed that the values thus assigned to the acids and bases as representing their strengths, could they be freed from all experimental error, would be perfectly characteristic numbers for the respective acids and bases, quantitatively conditioning all the reactions brought about by them. In pursuance of CHEMICAL EQUILIBRIUM 197 these views, it was proposed to give the generic name of specific affinity constants to the numbers represent- ing the strengths of the acids and bases. On fuller investigation, however, it appeared that neither the claim nor the proposal could be admitted; for the partition of a base between two acids depends not only on the nature of the contending acids, but also on the quantity of water present. A table of strengths or affinities constructed from the results of experiments on the partition of a base between acids in normal solution, 1 does not present the acids in the same order as a table founded on the results of investigations of deci-normal acid solutions. In other words, water cannot be regarded as a merely passive medium when the power of acids is in question; "the power of an acid to do " is a function of the state of dilution of the acid. For instance, in the system acid A, acid A', "base, water, we have not merely a tug-of- war of the two acids A and A' for the base, but the final equilibrium is the expression of the resultant of (1) the "affinity" of A for water, (2) the "affinity" of A' for water, (3) the "affinity" of the base for water, (4) the "affinity" of A for the base, and (5) the "affinity" of A' for the base; and in con- 1 Let the numerical value of the quotient molecular weight of acid number of replaceable H atoms in molecule be called n. Then a normal solution of an acid contains n grams of the pure acid per litre of solution at a specified temperature. A deci- normal solution has T \th the concentration of a normal one. 198 LAW AND THEORY IN CHEMISTRY formity with the law of mass action, every alteration in the quantity of water present necessarily alters the final distribution of matter marking the state of equilibrium from which the strengths of the acids are judged. Quite recently, however, it has been found possible to obtain for the acids characteristic numbers which are independent of their greater or less dilution, and of the particular reactions in which the acids may be implicated. These numbers are now regarded as the true affinity constants of the acids, but they necessarily have quite a different significance from the old system of supposed constants derived from the study of the partition of acids between bases, &c., seeing that they are independent of dilution. When an acid is dissolved in a large quantity of water, it behaves in many respects as if it were (and is accordingly by some believed to be) partially decom- posed into its ions (see note, p. 153). Thus a dilute solution of hydrochloric acid behaves as if it contained, in addition to molecules of HC1, ions of hydrogen and chlorine. If at a certain dilution K the number of undecomposed molecules is just equal to the number decomposed into ions, then K is taken as a measure of the true specific affinity constant of the acid. The investigation of affinity in accordance with these conceptions has as yet been chiefly confined to organic acids, and it is found that the order of the acids in a table of affinities, according to the new definition of affinity, is practically the same as the average order in CHEMICAL EQUILIBRIUM 199 the old tables of supposed affinity constants which were derived from the results of different reactions brought about by acids of varying concentration. 1 We have seen (page 57) that certain phenomena exhibited by fairly strong aqueous solutions point to definite combinations between water molecules and molecules of dissolved substance, i.e., to the existence in solutions of definite liquid hydrates. It is supposed that these liquid hydrates are very unstable bodies which at ordinary temperatures are partially dis- sociated, 2 the original hydrates forming with the products of their dissociations mobile equilibria as represented in the following equations : m (An H 2 0) ^ mn H 2 + ra A m' (An' H 2 0) ; m'ri H 2 + m r A &c., where (m + m + &c.) A represents the salt dissolved in mn = m'ri = &c. molecules of water. The inter- pretation of the above symbolism is that in a solution of A of determined concentration, the hydrates AnHf), A%'H 2 &c. are present, but that these hydrates 1 In the algebraical expression through which the desired affinity constants are obtained from the results of experiment, there is an inherent weakness which makes itself especially felt in the case of the stronger inorganic acids. For further details on the subject of affinity constants the reader is referred to the Lehrbuch der Attge- meincn Chemie of Ostwald, to whom we owe much of the best work that has been done in the direction of raising affinity to a quantitative dignity. 2 A dissociation is a reversible decomposition. When KClOs is heated it decomposes into KC1 and 30, for these two substances do not recombine on cooling to reform potassium chlorate. When PCls is heated, it dissociates into PC1 3 and Cla, because these two gases as they cool in contact combine together completely to reform PC1 5 . 200 LAW AND THEOKY IN CHEMISTKY partially dissociate into anhydrous salt, 1 (mA, m'A &c.) and water (m?iH 2 0, mVH 2 &c.) till mobile equilibria are established for each system, i.e., until in each system as many molecules of the hydrate are dissociated as are reformed per unit of time. As the concentration of the solution is varied, the ratios in which the various dissociating hydrates are present also varies, and at certain stages in the concentration new dissociating hydrate systems would make their appearance, while pre-existing systems would disappear. According to the views here illustrated, solutions have been defined as " fluid and unstable, but definite chemical compounds in a state of dissociation." All the incomplete reactions we have already con- sidered have been homogeneous, 2 but homogeneity in 1 Or it may be, into a hydrate of lower hydration in accordance with the equation m(AnH 2 0)l;m(A^H 2 o) + (mn- ?\H Z 0, where TO, n, and x are integers. 2 When all the products arid factors of a reaction are in the same physical state (same state of aggregation), the reaction is said to be homogeneous. The following are examples of homogeneous reactions : C1 2 + H 2 = 2HC1. NaCl Aq + KN0 3 Aq - KC1 Aq + NaNO 3 Aq. gases. solutions. Fe + S = FeS. solids. The combination of gaseous S0 2 with solid Pb0 2 to form solid PbSO4 is illustrative of non-homogeneous reactions. The significance of the terms homogeneous and non-homogeneous used in connection with reactions or systems must be carefully distinguished from the significance of the same terms when used, as in Chap. III., in con- nection with substances. CHEMICAL EQUILIBRIUM 201 this sense is not an essential condition of incomplete reaction. The very familiar reaction between solutions of common salt and silver nitrate is not correctly repre- sented in the equation AgNOgAq + NaCl Aq = AgCl + NaN0 8 Aq, for when effective chemical change between strictly equivalent quantities of AgN0 3 and NaCl has ceased, it is easy to prove the presence in the non-homogeneous system of traces of undecomposed AgN0 3 and NaCl. In other words, a condition of equilibrium finally supervenes, the equilibrium in this case, however, being so much in favour of the direct partial change, that unless for very accurate work, the decomposition of AgN0 3 by an equivalent quantity of NaCl may be regarded as practically complete. The interaction of steam and heated iron is another familiar instance of an incomplete reaction taking place in a non-homogeneous system. 3Fe + 4H 2 ^ Fe 3 4 + 4H 2 (solid) (gas) (solid) (gas) The sole condition for incompleteness of reaction between equivalent quantities of interacting substances resulting in mobile equilibria is that the products of the change must be of such a nature that they are all retained within the sphere of action of the system considered. 1 If by any means removal from the sphere 1 It follows that the salts in solution in mineral waters, &c., must constitute very complicated dynamic equilibria. The schemes in which analysts are wont to express the results of their analyses are mislead- 202 LAW AND THEORY IN CHEMISTRY of action of one or more of the products of the change is effected, the reaction proceeds to completion. Thus, if in the interaction of steam and heated iron it were possible to allow the hydrogen to escape as soon as formed, without at the same time permitting any steam to escape, then three atoms of iron would completely decompose four molecules of steam. One of the factors necessary to the reverse partial change being removed, that change cannot take place, and the direct partial change meeting with no opposition proceeds to comple- tion. To take another instance actually realised by Berthelot and St. Gilles. When benzoic acid and alcohol are brought together they slowly interact with the production of benzoic ether (ethyl benzoate) and water, which in turn simultaneously interact, reforming the original factors of the change. C r) H 5 COOH + C 2 H 5 OH ^ C 6 H 5 COOC 2 H 5 + H 2 0. Under ordinary conditions effective chemical change ceases when about 66 per cent, of the benzoic acid and alcohol have been transformed into benzoic ether. But when the water resulting from the change is removed from the sphere of action, the whole of the benzoic acid and alcohol is forthwith etherified. This removal of the water from the sphere of action is effected by the addition of barium oxide to the system. As soon as ing. The bases in a homogeneous system can be accurately determined and also the acids, but it is impossible from the results of the quanti- tative analysis only to apportion the acids to the bases so as to represent the actually existing constitution of the system. CHEMICAL EQUILIBRIUM 203 any water is formed it combines with the oxide forming inert barium hydroxide. It is to be noted that the same state of equili- brium is reached whether we set out with the system C 6 H 5 COOH + C 2 H 5 OH or with the systemC 6 H 5 COOC 2 H 5 -f- H 2 0. In the former case effective change proceeds till 66 per cent, of the benzoic acid and alcohol have been transformed into benzoic ether and water ; in the latter case effective change proceeds until 66 per cent, of the ether and water remain undecomposed. This is a perfectly general characteristic of these mobile equilibria. Eepresenting incomplete reactions by the general equation AB + A'B' : A'B + AB' (1) (2) we may say that in all cases the distribution of matter which obtains when equilibrium is established is independent of whether the point of departure be made the system (1) or (2). In a few particular cases this statement admits of very simple proof. For instance, a mixture of equivalent quantities of KClAq and NaN0 3 Aq gives exactly the diffusate as a mixture of equivalent quantities of KN0 3 Aq and NaClAq, showing that in both cases the same equilibriated system zNaClAq + asKNOgAq + (1 - z)KC!Aq + .(1 - is undergoing dialysis. 204 LAW AND THEORY IN CHEMISTRY Another method of rendering an incomplete reaction practically complete as regards some one or more of the members constituting the system will at once be evident on referring to Guldberg and Waage's law of mass action. This method consists in largely increas- ing the mass of one of the factors of the change rela- tively to the other. Thus, if in the etherification of alcohol by benzoic acid we largely increase the number of equivalents of alcohol relatively to the number of equivalents of benzoic acid, or vice versd, then, in either case, we approach indefinitely close to a state of com- plete etherification of the acid on the one hand, or the alcohol on the other. It is in virtue of the action of mass that we are able to completely convert NaCl into NaN0 3 by means of HN0 3 Aq, or conversely to change NaN0 3 into NaCl by means of HClAq. When NaCl, for instance, is treated with HN0 3 Aq a partial change takes place, and NaCl, HC1, NaN0 3 , and HN0 3 are all present. If the system be now heated, the free acids owing to their volatilities pass away, leaving non-volatile NaCl mixed with a little non-volatile NaN0 3 . If more HN0 3 Aq is added to this residue, and the system again heated, a second residue richer in NaN0 3 will result ; and so by repeating the operations of adding HN0 3 Aq and evaporating often enough (i.e., by using a large enough relative mass of HN0 3 ), the NaCl can be completely changed into NaN0 3 . The case of the converse trans- formation of NaN0 3 into NaCl by means of a large excess of HC1 is quite similar. CHEMICAL EQUILIBRIUM 205 In the light of the facts just treated, a reference to the remarks made on solution both in this chapter and in Chapter III. leads us into difficulties. If a substance in solution be largely diluted, i.e., if the relative mass of water be largely increased, we should expect, in accordance with what precedes, that the excess of water would lead to a great increase in the amounts and stabilities of the higher hydrates of the dissolved substance. But those who have experi- mented most with very dilute solutions, find that their results are best summarised in terms of the hypothesis that hydrates do not exist at all in dilute solutions. It appears as if the increased dilution not only breaks up the molecular complexes of water molecules and salt molecules constituting the hydrates, but actually destroys the integrity of the salt molecules themselves, resolving these into their ions. 1 For the present, until more light is shed on the vexed question of solution, we must be content to remember that this difficulty exists without attempting to decide it one way or the other. The question now arises for discussion, are all re- actions between equivalent quantities of mutually interacting bodies incomplete ? May not one or more of the products of certain changes be of such a nature 1 See note, p. 153. An ion may consist of a group of atoms, e.g., SO.*, or of a single atom, e.g., Na. In the latter case the ion and the atom are supposed not to be identical. For the present it is customary to attribute the assumed difference between them to the possession by the ion of a certain charge of electricity proportional to the valency of the atom. 206 LAW AND THEORY IN CHEMISTRY that they are removed from the system's sphere of action as quickly as they are formed, in virtue of their own peculiar properties ? Changes giving rise to bodies with such properties, would proceed to comple- tion even although their factors were brought together in strictly equivalent quantities. Stas has shown that AgBr is not acted on at all by a solution of NaN0 3 , or that if there be any action it is too slight to be detected by the analytic means at our disposal. Hence it follows that the reaction between AgN0 3 Aq and NaBrAq is, so far as we can tell, a complete one, and that the equation AgN0 3 Aq + NaBrAq = AgBr + NaN0 3 Aq is experimentally realised. There are many well-known reactions, such as that between H 2 S0 4 Aq and BaCl 9 Aq, viz., H 2 S0 4 Aq + BaCl 2 Aq = BaS0 4 + 2HClAq, which are for practical purposes regarded as complete, but which, as a matter of fact, are incomplete reactions in which the distribution of matter marking the attain- ment of equilibrium is overwhelmingly in favour of the direct partial change. The BaS0 4 , formed in the above reaction, is slightly soluble in (i.e., interacts with) dilute solutions of HC1, and, in virtue of this slight solubility, there is a reverse partial change, which is the condition for incompleteness of reaction and the establishment of an equilibrium. But the reverse partial change in this case is of very small moment. CHEMICAL EQUILIBRIUM 207 The subject of neutralisation calls for a word or two here. Those particular and important branches of volumetric analysis known as alkalimetry and acidi- metry are founded on the assumption of the absolute truth of such equations as H 2 S0 4 Aq + 2NH 4 OHAq = (NH 4 ) 2 S0 4 Aq + 2H 2 HClAq f NaOHAq = NaClAq + H 2 0. That is to say, these reactions are regarded as complete although there is evidently no removal from the sphere of action, artificial or otherwise, of the products of the neutralisations of equivalent quantities of acids and bases. Here, again, it is probable that we have in- stances of incomplete reactions in which the reverse partial change is so insignificant as to be negligible. That ammonium sulphate is slightly decomposed by water with the formation of free acid and ammonia is probable from the fact that air when passed through solutions of (NH 4 ) 2 S0 4 acquires alkaline properties the solutions themselves meanwhile developing acid characters. This behaviour of ammonium sulphate solution has been adduced to explain the completeness of the interaction of equivalent quantities of ammo- nium sulphate (NH 4 ) 2 S0 4 Aq and potassium carbonate K 2 C0 3 Aq. Seeing that both the factors of this inter- action, and all the possible products formed by double decomposition, are soluble in water and therefore remain within the sphere of action, one would be inclined, off-hand, to class this particular change with the in- complete reactions. 2o8 LAW AND THEORY IN CHEMISTRY According to Berthelot the completeness of the inter- action finds an explanation in terms of the partial decomposition of one of the interacting factors. The ammonium sulphate and water may be regarded as giving rise to some such equilibrium as is represented in the following equation (NH 4 ) 2 S0 4 Aq + 2H 2 OAq ^ 2NH 4 OHAq + H 2 S0 4 Aq. The potassium carbonate destroys this equilibrium by neutralising (and so removing from the sphere of action) the free sulphuric acid present at any moment ; more ammonium salt reacts with water in the tendency to again establish the primitive equilibrium, and so the cycle repeats itself until practically the whole of the ammonium sulphate is decomposed. The experimental investigation of the possibility of the establishment of equilibria in the cases of reactions evolving gases (which under ordinary circumstances escape from the sphere of action) is a very difficult matter. A definite answer has as yet not been furnished to the question, is the equation Zn + E 2 S0 4 Aq 1; ZnS0 4 Aq + H 2 , a correct representation of facts, provided the hydrogen evolved is prevented from leaving the system would the reaction under such conditions be found to be actually incomplete? In the meantime one has little hesitation in giving a theoretical answer in the affirma- tive to such a question. The existence of such equilibria as we have been CHEMICAL EQUILIBEIUM 209 discussing disproves a principle which was enunciated by Thomsen in 1854*, and again in 1864 by Berthelot. The latter naturalist has done so much work in the attempt to establish the principle on an experimental basis that it is now generally referred to as Berthelot's law of maximum work, although priority in the matter undoubtedly belongs to Thomsen. 1 Berthelot enunci- ated his " law " in the following terms : Every chemical change realised without the intervention of external energy tends to the formation of that body or system of bodies, the production of which is accompanied by the development of the greatest quantity of heat. This statement, which simply asserts that every chemical reaction tends to make the system assume that state, in the attainment of which it liberates most heat, further implied to Berthelot the necessity for the occurrence of every transformation that would involve an evolution of heat, and the impossibility of the spontaneous occurrence of every transformation that would involve an absorption of heat. 2 And it is this 1 Berthelot called his principle the "Law of maximum work," from its analogy to a well-established principle in mechanical energetics. If a raised stone be allowed to fall, it falls vertically to the earth's surface, and never in a direction inclined to the plumb line. The vertical direction is the one in which occurs a maximum change of potential into kinetic energy per unit time. This is an instance illustrating the so-called maximum principle which asserts that of all possible changes that one will take place which involves the greatest transformation of energy per unit time. (Throughout the remainder of this chapter it is assumed that the reader has an elementary know- ledge of general energetics.) 2 As a corollary to this "law," Berthelot stated his theorem of the necessity for reactions as follows : " Every chemical change which 210 LAW AND THEORY IN CHEMISTRY practical aspect of the " law " that has chiefly appealed to, and engaged the attention of, chemists generally. Suppose we have a substance quantitatively repre- sented by AB, and we wish to know whether it will interact with a third body quantitatively represented by to form either the bodies AC + B or the bodies BC + A. We may provisionally regard such an inter- action as taking place in two consecutive stages ; in the first stage AB is decomposed into A and B. and then in the second stage A combines with B or C, as the case may be. If A and B combine together to form AB with the evolution of a quantity of heat energy h, we know that exactly the same quantity of energy h must be added in order to reverse the change and resolve AB into A and B. 1 Suppose that the combination of A and gives rise to an evolution of heat energy represented by H, and that the combina- tion of B and C is attended by an evolution of heat H'. can be accomplished without the aid of a preliminary action or the addition of energy from without the system, necessarily occurs if it is accompanied by disengagement of heat." This theorem seems to have been generally applied without regard to the significance of the some- what indefinite qualifications " which can be accomplished . . . from without the system." 1 The principle, that the quantity of heat energy absorbed in de- composing a given mass of a compound into its elements is exactly equal to the heat energy evolved when the elements combine to form the given mass of the compound, was first given by Lavoisier and Laplace. This principle, which is a necessary consequence of the more general principle of the conservation of energy, is also true for chemical changes other than mere synthesis and analysis. If the passage of a complex system from any state A to any other state B, by any path whatsoever, absorbs a quantity of heat energy H, then the reverse passage from B to A by any path will be attended with the evolution of H heat units. CHEMICAL EQUILIBEIUM 211 The following cases must be considered : (1.) H and H' may both be less than h, in which event the "law," or rather its popularised implication, pronounces against the spontaneous occurrence of either change, seeing that both changes under these conditions would be endothermic. 1 (2.) H and H / may both be greater than h, in which case both reactions are exo- thermic, and therefore possible under the conditions. The relative magnitudes of H and H/ according to the " law " decide as to which of the two possible changes will actually occur. If H > H', then AC + B will be formed exclusively ; if H' > H, then BC + A will be the sole products of the reaction. When steam is passed over hot iron, chemical change ensues, resulting in the production of magnetic oxide of iron and hydrogen 3Fe + 4H 2 = Fe 3 4 + 4H 2 , but if retaining the same conditions copper be substituted for iron, the steam is not decomposed with the production of copper oxide and hydrogen in accordance with the equation Cu + H 2 = CuO + H 2 . These facts and many others of a similar nature might be adduced as confirmations of Berthelot's "law." 1 It is to be regretted that the application of so many different significations to the terms exothermic and endothermic has led many chemists to avoid their use altogether. Rigidly defined they are exceedingly convenient terms for the description of thermo-chemical phenomena. In the text an endothermic reaction is taken to mean any reaction which is accompanied by an absorption of heat ; an exo- thermic reaction, any reaction which is accompanied by an evolution of heat. The terms as thus used have no quantitative significance. 212 LAW AND THEORY IN CHEMISTRY For since the formation of a gram molecule (232 grs.) of Fe 3 4 from its elements is accompanied by an evolution of 264,700 heat units, while the resolution of four gram molecules (72 grs.) of steam into its elements is attended by the absorption of only 232,000 heat units, it follows that the realisation of the first change will be attended by the evolution of heat energy to the extent of 32,700 units. On the other hand, the 37,200 units of heat evolved when a gram molecule (80 grs.) of copper oxide is formed from its elements is less than that required, 58,000 units, to resolve a gram molecule (18 grs.) of gaseous water into its elements, and so the realisation of the second reaction would involve an absorption of heat. 1 Further, the generalisation that the readiness and intensity with which reactions take place increase with the thermal values of the reactions, is also in accordance with Berthelot's "law." But on the other hand there are very many facts which are at variance with the "law." Suppose we wish to know, without actually trying the experiment, whether hydrochloric acid gas acts on silver in accor- dance with the empirical equation HC1 + Ag - AgCl + H. Looking up the heat of formation of HC1 (i.e., the 1 The possibility that reactions could take place in such way that the hydrogen of the water combines with the metals and the oxygen is set free, is presumed to be precluded by the fact that such changes would be strongly endothermic, though through lack of data the exact values of the heat absorption in each case cannot be given. CHEMICAL EQUILIBEIUM 213 heat evolved when a gram molecule of hydrochloric acid gas is formed from its elements), we find it to be 220,000. The heat of formation of AgCl is 294,000. Now, applying Berthelot's " law " to these data, we are led to the conclusion that silver will be attacked by hydrochloric acid. But this conclusion is false, for silver is quite unaffected by hydrochloric acid. Again, when electric sparks are sent through a mixture of 2 volumes of hydrogen, with 2 volumes of chlorine and 1 volume of oxygen, hydrochloric acid is exclusively formed, although the formation of water from the hydrogen and oxygen would be attended by a far greater production of heat. But the existence of chemical equilibria is, as we have already hinted, the most generalised argument that can be brought forward in opposition to the "law" of Berthelot. Let us suppose that the direct partial change of a particular case of equilibrium is attended by a heat evolution, then it follows from the well-established principle of the conservation of energy that the reverse partial change must involve a heat absorption. For the same reason, if the direct partial change is endothermic instead of exothermic, then the reverse partial change must be exothermic instead of endothermic. That is to say, an equilibrium demands the occurrence of two simultaneous chemical changes, one of which is associated with an evolution of heat, the other with an absorption of heat ; and when equili- brium is attained, these two changes are proceeding at exactly the same rates. If Berthelot's " law " were true, 2i 4 LAW AND THEOKY IN CHEMISTRY all reactions would belong to the complete type, and incomplete reactions, i.e., equilibria, would be impossible. If we interpret Thomsen and Berthelot's principle as merely asserting that every purely chemical change of a complete type that takes place spontaneously must be accompanied by a loss of chemical energy which will finally appear as heat the lowest form of energy then we are bound to admit the truth of the prin- ciple at the same time as we deprive it of all practical import. For all the so-called chemical changes with which we have to do are not purely chemical changes, in this sense, that other forms of energy besides chemical energy undergo increase and decrease as the distribution of matter changes, and the heat evolved or absorbed by the reaction is a complex quantity, re- presenting not merely the changes of chemical energy, but the resultant of the sum total of energy changes of all kinds. A. purely chemical change is a fiction of much the same order as an absolutely rigid bar, or a perfectly frictionless constraint. Further, it can be shown that in incomplete re- actions (i.e., in cases of equilibrium) the chemical energy of the system suffers no decrease during the course of the reaction ; hence, if purely chemical energy were the only form of energy to be considered, it follows that all reactions leading to the establishment of an equilibrium ought to proceed without any heat absorption or evolution. But this is by no means the case, and so we are forced to the conclusion that in the so-called chemical changes other forms of CHEMICAL EQUILIBRIUM 215 energy besides chemical energy (e.g., volume energy, heat energy, surface energy, &c.) must undergo trans- formations in order that the actually observed thermal disturbances may be accounted for. But recognising the multiplicity of the specific energy changes which give rise to the thermal phenomena attendant on chemical change, the question may still be put, is there absolutely no connection under any conditions between the value and sign of the thermal changes and the necessity for the occurrence of chemical change ? Cannot we predict under any cir- cumstances which of two or more possible changes will occur ? It was a great advance that Horstmann made when he showed that the formulae of thermodynamics can be applied to problems in the domain of chemistry. The leading features of the dissociation of such a substance as chalk, in accordance with the symbolism CaC0 8 ; CaO + C0 2 , are very similar to those of the evaporation of a homo- geneous liquid such as water. But the application of the second law of thermodynamics to the process of evaporation leads to the establishment of very im- portant relationships expressible in a simple formula, and Horstmann, on the strength of the strong analogy between the processes of evaporation and dissociation, applied this particular formula to certain cases of dis- sociation. The results to which the formula led were found to be in harmony with the facts ; and it was not 216 LAW AND THEORY IN CHEMISTRY long before Horstmann showed that the principles and formula of thermodynamics generally are applicable to all cases of chemical equilibrium. In other words, the relations of thermodynamics and chemistry are not limited to the application of one special thermodyna- mical formula to a certain circumscribed class of equi- libria distinguished as dissociations (see note 2, p. 199). The verdict passed on Berthelot's " law " by thermo- dynamics, is that only at absolute zero would such a law obtain that only at the unattainably low tempera- ture of 273 C. could prophecies founded on such a law be relied on. For, presupposing the possibility of chemical change at this temperature, it appears that at absolute zero all reactions would be com- plete ; all reactions would take place with an evolution of heat, and of two or more possible reactions that one would occur which is attended with the greatest heat evolution. The higher the temperature rises above the absolute zero, however, the more does Berthelot's law "deviate from the truth inclining towards it." With the rise of temperature above zero enters, according to thermodynamic deduction, the possibility of incomplete reactions of mobile equilibria, and, moreover, the higher the temperature the more does a given equilibrium shift in favour of the endothermic partial change. Thus, the displacement of HN0 3 from !JaN0 3 Aq by H 2 S0 4 Aq is endothermic; the displacement of H 2 S0 4 from Na 2 S0 4 Aq by HN0 3 Aq is exothermic. Hence it follows that a rise in temperature shifts CHEMICAL EQUILIBRIUM 217 the equilibrium of the system NaN0 3 Aq, H 2 S0 4 Aq, HN0 3 Aq, Na 9 S0 4 Aq in favour of the darker arrow as shown in the following symbolism. 6 Aq + H 2 S0 4 Aq Or, writing the reaction in equational form, Na 2 N 2 6 Aq + H 2 S0 4 Aq = (1 - x) Na 2 N 2 6 Aq + (1 - aj) H 2 S0 4 Aq, we may state the same relation in another way by saying that x decreases in value as the temperature rises. In cases where equilibrium is attained without thermal change, temperature is without influence thereon. Thus, nitric acid displaces hydrochloric acid from salt solution without evolution or absorp- tion of heat; the same is true for the displacement of nitric acid from sodium nitrate solution by hydro- chloric acid, hence in the equation NaN0 3 Aq + HClAq = zNaClAq + a;HN0 8 Aq + (1 - a) NaNOgAq + (1 - x) HClAq the value of x is independent of the temperature. The equilibria resulting from the etherification of alcohols by acids (see p. 202) are also attained with- out thermal disturbance, and are accordingly found to be independent of temperature changes. Having once and for all laid low the spectre of the " Law of maximum work," thermodynamics replaced 2i8 LAW AND THEORY IN CHEMISTRY it with a general law which, though of somewhat the same form as Berthelot's, differs from it in being universally true at all temperatures. This law, called the law of entropy, may be looked on as a particular form of statement of the Protean second law of thermodynamics. It states that a system is in stable equilibrium only when its entropy is a maxi- mum, and therefore that any change which entails an increase in the entropy of the system is not only capable of spontaneous occurrence, but will in fact actually proceed until the entropy of the system reaches the maximum value attainable under the conditions. Unfortunately this quantity or function entropy is a very difficult one to conceive, let alone measure, and the law concerning it is to chemists of more theo- retical interest than practical use. We can, however, arrive at some kind of a conception of entropy by the following considerations. The electrical energy of an isolated charged body is equal to the product JQV, where Q stands for the quantity of electricity with which the body is charged, and V is its potential. Suppose that for one body the electric energy is JQ'V, and for another body JQ"V". What are the conditions that electric energy shall pass from one body to the other? Simply electric connection and the inequality of V and V". If V > V, then electric energy will pass from the first body to the second until the potentials of both bodies is the same, and this will happen even if the electric energy of the first body is greater in amount CHEMICAL EQUILIBRIUM 219 than that of the second body. The passage of electric energy from one system to another is independent of the quantities of energy possessed by the two systems, and depends solely on their potentials. Electric energy always flows from places of high, to places of low potential. On this account V is regarded as the "intensity factor " of electrical energy, and Q as the " capacity factor." Energy of other forms can similarly be re- solved into capacity and intensity factors. For instance, the intensity factor of kinetic energy is velocity, 1 the capacity factor is mass, and so on. What then are the factors of thermal energy ? The intensity factor is very familiar to us and easily capable of evaluation it is temperature. The capacity factor does not appeal directly to our senses, nor can we easily form a clear conception of it. Yet this factor, which we are content to define rather than conceive, has received the name entropy. Hence we can restate the law of entropy in the following way : Any change which can increase the value of the capacity factor of the heat energy of a system takes place with readiness, and the system only then attains a position of stability (of disinclination to undergo any further change) when the value of this capacity factor is at a maximum. In some forms of energy it is not possible to alter the capacity factor by adding energy to the system. 1 Strictly speaking (velocity) 2 , the kinetic energy of a mass m moving with velocity v being | wv 2 . 220 LAW AND THEORY IN CHEMISTRY The addition of kinetic energy to a moving bullet, for instance, cannot alter the mass of the bullet, which here represents the capacity factor. But in the case of heat energy it is otherwise ; here it is possible, by adding thermal energy to a system, to alter thereby the thermal capacity factor of that system. Suppose we have a mass of a solid substance S at the absolute temperature T. Let us impart to S an additional quantity of heat energy q under conditions such that the intensity factor of the heat energy of the system is not thereby altered, i.e., such that T remains constant. This may be simply realised by supposing T to denote the melting point of S, and q to be the latent heat of fusion of S. Let us call the first state of the system A and the final state B. To bring the system to the state A from absolute zero requires an amount of heat energy, say Q ; to bring the system from zero to the state B requires Q + q units of heat energy. There- fore in the passage from A to B the capacity of the system for heat energy has evidently increased, and the increase of heat capacity under the conditions named is called an increase of entropy, and is measured by the quotient ? . But thermodynamics has furnished us with tests of stability involving functions other than entropy ; and some of these tests possess the advantage of being more easily applied to actual cases than the entropy test. 1 1 For details the reader is referred to Parker's Elementary Thermo- dynamics, also to Ostwald's LehrbucJi der aUgemeinen Chemie, to which the author is indebted for the treatment of the subject of entropy given in the text. CHEMICAL EQUILIBRIUM 221 A momentary glance at the expression defining the function known as the free energy, or the thermo- dynamic potential at constant volume, throws clear light on the question of Berthelot's "law." In the equation PA = UA - T A S A F A denotes the free energy and U A the total energy of a system in the state A. Its temperature in this state is T A and its entropy S A . Let us consider another state, B, of this system, for which the values are F B , U B , T A , and S B , the volume and temperature of the systems remaining the same in both states. From the two equations FA = U A - T A S A and F B = U B - T A S B we get by subtraction (F A - F B ) - (U A - U B ) - [T A (S A - SB)]. Now, it results from thermodynamic reasoning that the change from the state A to the state B can only proceed of itself when the free energy of the system is decreased by the passage, i.e., (F A F B ) must be a positive quantity. Rearranging the equation we obtain (U A - U B ) = positive quantity + T A (S A - S B ). The value of S B being greater than that of S A , the whole term T A (S A S B ) must be negative. Of THE UNIVERSITY 222 LAW AND THEORY IN CHEMISTEY Suppose the absolute magnitude of this term to be less than the " positive quantity " term, then (U A U B ) must obviously have a positive value ; that is to say, the change of the system from the state A to the state B has been attended by a loss of energy to the system has been an exothermic change. But this is not the only possible case. If the absolute magnitude of the term T A (S A S B ) be greater than that of the positive quantity term, then (U A U B ) must necessarily have a negative value ; that is to say, the total energy of the system has been increased by its spontaneous passage from the state A to the state B the change has been an endothermic one. It is clear that the importance of the term T A (S A S B ) rises pari passu with the temperature at which the change proceeds. In other words, the higher the temperature the more likely are endothermic reactions to occur. THE END. PRINTED BY BALLANTYNE, HANSON AND CO. EDINBURGH AND LONDON. tfttl 14 DAY USE RETURN TO DESK FROM WHICH BORROWED LOAN DEPT. This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. Iflan'WM BEG'3 LD jAiJG 1300 " ^* R VW RFC'D LD J/lN 1 n 'Cji -t nu 1 A O D*t * r M FEB 16 198866! REC'P 1 H 2'66-PAftL 1AY1419721? MAY (A1724slO)476B Berkeley UNIVERSITY OF CALIFORNIA LIBRARY