EMPIRICAL AND RATIONAL FORMULE. 87 position by weight—which should recall the materials from which the formulated substance was made, and prophesy the products of its decomposition—which should not only name and number the atoms of the substance, but should also suggest such a grouping or arrangement of those atoms as might serve to interpret its known reactions. Such formulæ are called rational formulæ. Thus NaHO is the empirical formula of caustic soda, while Na,O,H,O is a rational formula of the same substance, which recalls the facts that it may be made from anhydrous oxide of sodium and water, and that it enters into many reactions in which the Na,O goes one way and the H2O another. Another rational formula of the same substance is Na } 0, H which suggests many reactions in which caustic soda is involved either as product or ingredient-for example, the decomposition of water by metallic sodium (see Exp. 14), which may be thus written :: We shall hereafter meet with many such reactions, in which an atom of sodium replaces an atom of hydrogen; the formula Na H } 2 2 O suggests this large class of reactions by implying that caustic soda is itself constituted as water in which an atom of sodium has replaced an atom of hydrogen. Such formulæ as H2O,N,O,, PыO,N,O,, Na,O,N,O,, and Na,O,H,O, are called dualistic, because they represent these bodies as of a dual nature -as being made up of two oxides which were distinct before they were brought together to form the compound, and will be distinct when separately extracted from it; in a dualistic formula these two distinct parts are conventionally represented as having some separate existence within the compound itself. The supposition is not unnatural; thus, for example, common plaster of Paris is a substance containing the metal calcium and the elements sulphur and oxygen in the proportions by weight which are correctly expressed by the formula CaSO,; but this substance may be made by methods which suggest another formula. If we put together quicklime CaO, and anhydrous sulphuric acid SO, in due proportions, under suitable conditions, plaster of Paris, or, as its chemical name is, sulphate of calcium, results or if we mix slaked lime CaO,H,O with strong sulphuric acid H,O,SO,, in proper proportions, at a suitable temperature, we shall again obtain sulphate of calcium, and water will be eliminated : CaO,H,O + H,O,SO, = CaO,SO, + 2H,0. Accordingly we find that the great majority of chemists have hitherto written the formula of sulphate of calcium, hydrated oxide of calcium, and hydrated sulphuric acid, in conformity with the suggestion of these reactions, CaO,SO,, CaO,H,O, and H,O,SO, respectively. Of positive knowledge concerning the actual grouping of the imaginary atoms which are supposed to make up the hypothetical molecule of a compound body, we have absolutely none, and it must never be forgotten that a rational formula is merely a suggestion of some of the chemical processes in which the substance formulated is capable of taking part. In some cases the rational formula may point to the majority of all known transformations of the substance; but generally it suggests only a few of the possible changes. Since a rational formula never represents a fact, but only an hypothesis or opinion, it is to be expected that a great diversity of rational formulæ should be in use among chemists; and this is really the case. The dualistic view, above illustrated, has long been, and still is, the prevailing view of the proximate composition of inorganic compounds; but in the chemistry of the very numerous compounds which the element carbon forms with oxygen, hydrogen, and nitrogen, a different view, called the doctrine of types, widely obtains, and has been adopted by not a few chemists as affording the best theoretical representation of all chemical combinations, whether in the inorganic or organic kingdom. According to this doctrine every possible chemical combination may be imagined to be built upon the plan, or framed upon the type or model, of some one of the four substances, chlorhydric acid, water, ammonia, and marsb-gas. These will all shortly be to us well-known substances; but the most important of these types is water, a body with whose composition we are already familiar; we are therefore competent to write upon the type of water the formulæ of several substances with which we have already dealt, and which are classified under this type: Hydrated Oxide of Calcium, slaked lime,= }0,=1 molecule. Ca H 2 Nitrate of Lead=2(NO2)}0,=one molecule. SO 2 Pb Sulphuric acid=' So,}0,=one molecule. H Sulphate of Calcium 80,=one molecule. Ca re In these formulæ it is to be observed that K, Na, and NO, place one atom of hydrogen in one molecule of water, while Ca, Pb, and SO, replace two atoms of hydrogen in two molecules of water. Facts of this class will accumulate as we advance, and will be the subject of future discussion. The typical notation is doubtless capable of expressing, in a logical and consistent system, the greater part of the reactions of inorganic as well as of organic chemistry; but at present it finds its best application in the chemistry of the compounds of carbon, and has gained but little foothold in the great departments of mineral and industrial chemistry. The need of rational formulæ is much more urgently felt in that department of chemistry, called organic, which treats of the chemistry of carbon, than in the wider field of mineral and inorganic chemistry. Among the very numerous compounds of carbon there are many cases in which one empirical formula represents not one compound, but several; hence it becomes of consequence to determine, or to guess, how the atoms of a compound are arranged, as well as to know what and how many the atoms The diversity of opinion concerning this arrangement of are. atoms is so great, and the possible modes of grouping the numerous atoms which often enter into organic compounds are so many, that the number of rational formulæ proposed for any organic substance is commonly large in proportion to the thoroughness with which the substance has been studied. For acetic acid, for example, one of the best-known of the compounds of carbon with oxygen and hydrogen, no less than nineteen different rational formulæ have been proposed. Remembering that a rational formula is never to be regarded as the expression of an absolute truth, but only as a guide in classification, an aid to the memory, and a help in instruction, and holding fast to the empirical formula as containing all the results of actual observation and experiment, we shall endeavor to familiarize the student with both the dualistic and typical guesses at the hidden mysteries of chemical processes and the unknowable structure of chemical compounds, giving the preference rather to the dualistic view, as being that which at the present moment prevails in the great bulk of chemical literature, and has become incorporated into the language of the chemical arts. Lest any doubt should suggest itself to the student's mind as to the value of symbolic formula, let it be observed that they express the elementary composition of a compound much more tersely than words can, that they are written and read more rapidly than the sentences of the same signification would be, and that by their brevity, clearness, and precision they greatly facilitate the comparative study and comprehensive classification of chemical compounds. Again, the chemical equations, of whose construction we have already had several examples, enable us to set forth with precision the changes which accompany complicated, as well as simple, reactions. Thus the somewhat complex decomposition of nitric acid by copper takes definite form in the appropriate equation which has been given above (p. 74), and the very simple reaction by which nitric oxide yields red fumes of hyponitric acid in contact with air or oxygen is concisely stated by the simple equation NO+0=NO,. The chemistry of the analysis of nitric oxide by potassium (§ 70) is all condensed into the equation NO+K ̧=K ̧0+N. When a little ice-cold water is added to liquid hyponitric acid (Exp. 43), the reaction which occurs is very concisely set forth in the equation; Empirical: 2NO2+ H2O = Hyponitric 2 2 ΗΝΟ, + nitrous acid. 2 2 3 HNO, Nitric acid. 3 2 Dualistic: 4NO, 2H,0 = + H2O, N2O, + H2O, NO,. But besides having all the advantages of a short hand, chemical symbols are susceptible of another application of hardly less importance; they often direct the chemist beforehand to the most perfect experiment among many similar, or point out in anticipation the possibility of certain methods of research, and the inevitable fruitlessness of others. Thus the equation actually directs the chemist to the due proportion of copper for the exact decomposition of anhydrous nitric acid (§ 73); neither four, nor six, nor any other number than five, parts of copper, would give a perfect reaction without excess of either ingredient. Practically, an excess of copper does no harm, and is always used to make sure of the decomposition. The student should endeavor, from the beginning, to familiarize himself with the use of chemical symbols and equations, and to this end he should invariably write the formula of every reaction described or actually witnessed in the execution of an experiment. CHAPTER VII. CHLORHYDRIC ACID. 95. Muriatic (sea-salt) acid, called in modern nomenclature chlorhydric acid, is a liquid which has been known for centuries, and is to-day an article of commerce, largely employed in the useful arts. The pure acid is a gas, as ammonia is; the liquid muriatic acid of commerce is only an aqueous solution of this |