CONDENSATION-RATIOS.

205

and temperature, viz. 11-2 litres, as the unit-volume, while others prefer to use the litre itself as the unit.

Three condensation-ratios are exhibited in these tables. In the first the condensation is 0; in the second it is, and in the third it is. The typical character of the three compounds, chlorhydric acid, water, and ammonia, is also clearly brought out; each of these bodies represents a group of compounds which obey the same structural law. The tables also show very clearly the fact that very unequal weights of the compounds tabulated occupy equal spaces, under the same conditions of temperature and pressure. The space occupied by the compound molecule is, in each case, exactly twice the unit-volume.

259. The symbols H, Cl, O, and N represent the relative weights of the same volume of four elements which are gaseous at common temperatures and pressures; the symbols Br, I, S, and Se, represent the relative unit-volume weights of four other elements which are not gases under the ordinary atmospheric conditions, but which can be converted into gases at a higher temperature. At this higher temperature their unit-volume weights have been experimentally determined, and from these observed volume-weights, the unit-volume weights which they would possess at the ordinary pressure and temperature have been deduced. The symbols of these eight elements, therefore, represent at once the combining weights and the relative weights of equal volumes (specific gravities) of these substances in the gaseous state. In the present state of the science, these eight symbols are the only ones of which this can be affirmed; tellurium would undoubtedly make a ninth, if the relative size of its combining weight had been experimentally determined, but until this determination has been made, the symbol Te represents only the combining weight of the element, and not its equal-volume weight as well.

The relative sizes of the combining weights of four other elements in the state of vapor, have been experimentally ascertained. These four elements are arsenic, phosphorus, cadmium, and mercury. When we come to study these elements, we shall find that the symbols of arsenic and phosphorus, namely, As and P, represent only the half-volume weights of these two bodies, while the

206

COMBINING WEIGHT AND VOLUME-WEIGHT.

symbols of cadmium and mercury represent the two-volume weights of these volatile metals. Coincidence of the combining weight and the volume-weight has been established for eight elements; discrepancy between the combining weight and the volume-weight has been proved for four elements; of the remaining elements, constituting more than four-fifths of the whole number, the equal-volume weights are wholly unknown, inasmuch as these elements have never been converted into vapor under conditions which permit the experimental determination of the equal-volume weights of their vapors. For example, the symbols Na and K represent the combining weights of these two metals; but they can be held to represent the weights of the unit-volumes of these metals only by pure assumption, or, at best, on the uncertain evidence of analogies, since the unit-volume weights of these metals, when converted by intense heat into gases, have never yet been determined. As the great majority of the known elements cannot be volatilized, or made gaseous, by the highest temperatures as yet at our command, under conditions which permit the chemist to experiment with the gases produced, it is plain that composition by weight is, in the present state of chemistry, of far greater practical importance than composition by volume. The symbols of all the elements represent their combining weights, as determined by ponderal analysis; the symbols of eight elements represent also the equal-volume weights of the substances they stand for. These eight elements, though few in number, are nevertheless the leading elements in inorganic chemistry.

260. The volume of the molecule of every compound gas in the above tables is twice that occupied by the atom of hydrogen. Two volumes of compound gas invariably result from the chemical combination of one volume of hydrogen with one volume of chlorine, of two volumes of hydrogen with one of oxygen, of three volumes of hydrogen with one of nitrogen, and these instances are but types of large classes of chemical reactions. In organic chemistry the same law holds good for a great multitude of complicated compounds of carbon; the molecule of every organic compound in the state of vapor occupies a volume twice as large as that occupied by an atom of hydrogen, or, in other words,

DOUBLE OR PRODUCT-VOLUME.

207 twice the unit-volume. This doubled volume is often called the normal or product-volume of a compound gas. Since the combining weight of a compound gas or vapor occupies two unitvolumes, it is obvious that the weight of one volume, which is the specific gravity of the gas or vapor, is deduced from the combining weight by dividing the latter by two. The specific gravity of a compound gas or vapor is, therefore, one-half its combining weight.

261. Molecular condition of elementary gases.-Bearing in mind our definitions of atom and molecule (§§ 38, 39), let us inquire what inferences concerning the molecular condition of simple gases in a free state can be legitimately drawn from our knowledge of the molecular condition of compound gases. To give definiteness to our conceptions, let us assume the unit-volume of the elements to be one litre; the product-volume of a compound will then be two litres. Two litres, the product-volume, of chlorhydric acid gas are made up of one litre of hydrogen and one litre of chlorine, united without condensation, and each molecule of chlorhydric acid must contain at least one atom of hydrogen and one of chlorine. In these two litres of chlorhydric acid there must be some definite number of molecules; the number is, of course, indeterminable; but let us assign to it some numerical value, say 1000, in order tc give clearness to our reasoning. One litre of chlorhydric acid will then contain 500 molecules, and since equal volumes of all gases, whether simple or compound, are assumed to contain, under like conditions, the same numbers of molecules (§ 39), one litre of hydrogen or of chlorine will also contain 500 molecules. But the one litre of hydrogen and the one litre of chlorine, which, by uniting, produced 2 litres =1000 molecules of chlorhydric acid, must each have contained 1000 atoms of hydrogen and of chlorine respectively, for each molecule of chlorhydric acid demands an atom of hydrogen and an atom of chlorine. The litre of hydrogen, or of chlorine, then, contains 500 molecules, but 1000 atoms,—each molecule of the simple gas being made up of two atoms of the single element, just as each molecule of the compound gas under review is composed of two atoms, one of hydrogen and one of chlorine. It is clear that this train of reasoning is independent of the particular numerical value assumed as the number of molecules in two litres of chlor

208

MOLECULES OF ELEMENTARY GASES.

hydric acid. If, therefore, the molecule of chlorhydric acid is represented by the formula HCl, and the diagram

there is good reason to assign to free hydrogen and free chlorine the formulæ HH and CIC1, and to represent the constitution of all uncombined gases by such diagrams as

H +

= H

HH

C+ Cl = CICI

Upon these models the molecular formulæ of all the elements with which we have become acquainted might readily be written. It is only in a free state that the elementary gases and vapors are thus conceived to exist as molecules; when they enter into combination, it is by atoms rather than by molecules. An atom of hydrogen unites with an atom of chlorine; three atoms of hydrogen combine with one of nitrogen.

If this view of the molecular structure of free elementary gases and vapors be correct, perfect consistency would require that no equation should ever be written in such a manner as to represent less than two atoms, or one molecule, of an element in a free state as either entering into or issuing from a chemical reaction. Thus instead of H+0=H20, N+3H=NH ̧, HC1+Na=NaCl + H, it would be necessary to write

2HH + 00 = 2H2O,

NN + 3HH = 2NH„,

2HCl + NaNa = 2NaCl + HH.

We have not heretofore conformed to this theoretical rule, and do not propose to do so in the succeeding pages, and this for two reasons: first, because many equations, representing chemical reactions, must be multiplied by two in order to bring them into conformity with this hypothesis concerning molecular structure; the equations are thus rendered unduly complex; secondly, because, in undertaking to make chemical equations express the molecular constitution of elements and compounds, as well as the equality of the atomic weights on each side of the sign of equality, there is imminent danger of taking the student away from the sure

ground of fact and experimental demonstration, into an uncertain region of hypotheses based only on definitions and analogies. The symbol Na represents 23 proportional parts by weight of the metal sodium; of the molecular symbol NaNa, the most that can be said is, that some strong analogies justify us in assuming, for the present, in default of any experimental evidence on the subject, that a molecule of free sodium gas, if we could get at it, would be found to consist of two least combining parts by weight of sodium. We know as much, at least, of the molecular structure of sodium as we do of four-fifths of the recognized chemical elements. For the present, the biatomic structure of the molecule of a simple gas or vapor in the free state must take place, in an elementary manual, as an ingenious and philosophical hypothesis, rather than as a general and indubitable fact.

CHAPTER XVI.

PHOSPHORUS.

262. Phosphorus occurs somewhat abundantly and very widely diffused in nature. It is never found in the free state, but almost always in combination with oxygen and some one of the metals. The most abundant of its compounds is phosphate of calcium; small quantities of this mineral are found in most rocks and soils, and in several localities it occurs in large beds. Phosphate of calcium is the chief mineral constituent of the bones of animals; it contains one-fifth of its own weight of phosphorus. The proportion of phosphorus present in most of the ordinary rocks, and in the soils which have resulted from their disintegration, is usually very small, and phosphorus would be an exceedingly costly substance if we were compelled to collect it directly from this source; but it so happens that the phosphorus-compounds are important articles of food for plants and animals, and it is easy to obtain through their intervention the phosphorus which was before widely diffused, but has been by them concentrated.

P